That proof, along with a series of additional conjectures that Weil made—the Weil conjectures—established finite fields as a rich landscape for mathematical discovery.
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Although complexity theory has plenty of conjectures as to why various quantum algorithms are beyond the reach of classical computers, these conjectures haven't been proved—until now.
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All of these conjectures are, of course, without any basis.
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Worse yet, are conjectures about what he could possibly do.
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What conjectures do you have about why this is happening?
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I have my theories, but they're only that — imperfect conjectures.
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She said my conjectures about what information Amazon was getting were inaccurate.
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There are several conjectures over the causation of Puerto Rico's unsustainable indebtedness.
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Traffic jams are the work of the "deep state", conjectures Ms Sawy.
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They are closing in on proofs of the central conjectures in the field.
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Despite the conspiratorial conjectures of Clinton's opponents, her politics hide in plain sight.
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So we reached out to Google to see if Phandroid's conjectures here are right.
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Effective policy cannot be built from idealized conjectures; it demands realism, and actual facts.
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This arrangement has led to many conjectures about how each side is wildly different.
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The stories make cumulative lies—or, give us a break, conjectures—of our lives.
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Among conjectures about the cause of the decline in bear sightings, that one seems prominent.
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There seems little reason to favor later conjectures over the details of the primary source.
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For that reason, they are the subject of many of the most famous conjectures in mathematics.
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She even conjectures, persuasively, that they don't really want the baby — she's a crafty one, Mary.
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With these factoids and what you have noticed in the graphs, what additional conjectures do you have?
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In "The Weil Conjectures," Karen Olsson combines their fascinating story with her own renewed interest in math.
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As Reich sees it, the study of ancient DNA has disproved our conjectures about what happened next.
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More time just gives the inflationists more time to chase their mathematical conjectures onto thinner and thinner limbs.
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Some experts say the mutually supportive relationship between the two conjectures increases the chances that both are correct.
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Her mixed-media imagery is not as concrete as visual conjectures can be, but that's not the point.
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Even though the conjectures have not been proven in general, Dr. Sarnak was sure they would be eventually.
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Season 21 of The Bachelor doesn't even premiere until January, so all of these conjectures are a bit premature.
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He put these conjectures into practice in Iraq, where villages that rebelled against colonial rule were bombed by RAF aircraft.
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But by the end, I was interrupting, speaking authoritatively and hilariously, making clever conjectures about the mysteries of the plot.
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The earliest conjectures about CrowdStrike apparently first surfaced on the message board 4chan in March 2017, according to BuzzFeed News.
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Góes dismissed much of Piketty's work on the relationship between wealth accumulation and poverty as "conjectures" with little empirical basis.
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That the attempts have failed may speak more to the quality of the science than the validity of the conjectures.
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"Being thrown five feet into the air by your partner when you are dancing the volta is exhilarating," she conjectures.
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Jorge Santos (left) and Toby Crisford of the University of Cambridge have found an unexpected link between two conjectures about gravity.
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Through a series of interviews, conjectures, and almost break-ins, Taberski attempts to answer the question: What happened to Richard Simmons?
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Becker conjectures that pollution is being preferentially ejected by impacts, regardless of whether the ice is reattaching itself in this manner.
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The White House did not respond to request for comment about the therapists' conjectures, though Trump's doctor has previously hailed his health.
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I'm ready to leave my critical conjectures and artistic concerns behind, when a thought strikes me: what on earth happened to Betty?
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O.J. Simpson could stick close to the facts, The Assassination of Gianni Versace was, like Orth's book, necessarily fleshed out with conjectures.
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To fully understand the dangers of consuming sugar, we need experiments, in humans, that can unambiguously test these 100-year-old conjectures.
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The action, livestreamed on Booker's Facebook page, added further fodder to conjectures about his role as an emerging leader in the Democratic party.
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When Hillary Clinton was running, the American political scene was rife with conjectures about women politicians, based on a data set of one.
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"As the world is roasting," said this reporter, thinking back to a startling new set of conjectures about climate change published this week.
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In some ways this is characteristic of pure number theory problems: It's easy to find examples and formulate conjectures but hard to prove them.
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The many chroniclers of the Parisian expressionist speak in a variety of voices, some dramatic or poetic, and reveal stunning conjectures, sometimes even blatant contradictions.
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He also conjectures that it was a small rock, possibly a meter in length, and the separate flashes of light were the object breaking up.
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In the long national nightmare that has been the crash of Valeant Pharmaceuticals, we've seen Wall Street make some conjectures that were wrong — dead wrong.
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Whether or not that happens is in the realm of conjectures, given the inevitable human tendency to misuse just about anything that makes our lives easier.
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This link is a core part of the "Langlands program," a collection of interconnected conjectures and theorems about the relationship between number theory, geometry and analysis.
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In the wake of insensitive conjectures about West's own mental health, "I Feel Like That" is an act of blowing opinion open and wearing it candidly.
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As Karl Popper noted in Conjectures and Refutations (1963), some people tend to attribute anything they dislike to the intentional design of a few influential 'others'.
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The book "while rich in data…provides no formal empirical testing for these conjectures," Goes wrote, citing his own econometric models that sought to verify Piketty's claims.
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Aside from rough sketches and conjectures, nobody had yet made the effort to "do the math" behind these star-moving technologies, Caplan said in a phone call.
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Seeing works by Congo the chimp takes us from wild aesthetic conjectures to sobering ethical dilemmas around animal agency, art ownership, and basic rights of living creatures.
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Dr Aklin conjectures that the explanation may lie with the relatively paltry nature of what was offered, which amounted to an hour or two's extra lighting per day.
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Goyal did not directly respond to requests for comment but a Jet spokeswoman said the "conjectures being implied with regards to the organization's ways of working" were misleading.
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A new study published in the journal Arctic affirms these earlier conjectures, while adding a new and unexpected cause of death: tuberculosis resulting in adrenal insufficiency, or Addison's disease.
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Lucas thrives on such potty humor; it's her capricious stage for the dismantling of our phallus-obsessed culture that still subconsciously runs on the Oedipal conjectures of Freudian psychoanalysis.
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He completed a doctorate at the University of Nottingham, and developed theories that have solved longstanding conjectures, according to the University of Cambridge, where he now holds a professorship.
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Looking back, Swenson conjectures that one reason he took Ajamu's claims as seriously as he did was that Ajamu was so committed to press his case despite having already gotten out.
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The conjectures of Dr. Langlands, now 81 and an emeritus professor at the Institute for Advanced Study in Princeton, N.J., have proven fertile ground for mathematical advances in the past half-century.
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There had been informal conjectures about reprogramming Microsoft's web browser, the popular Internet Explorer, so that anytime people typed in "Google," they would be redirected to MSN Search, according to company insiders.
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When these conjectures can be proved, they are often enormously powerful: For instance, the proof of Fermat's Last Theorem boiled down to solving one small (but highly nontrivial) section of the Langlands program.
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"To perform it is to court disaster," the pioneering Monteverdi scholar Denis Arnold once wrote of the many interpretive decisions and conjectures that have to be made before a sound is even produced.
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To account for this discrepancy, physicists rely on two related, but logically distinct conjectures, both originally developed by the physicist Roger Penrose nearly 50 years ago: the strong and weak cosmic censorship hypotheses.
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The lines between subjective and objective blur into that spiked vagueness that descends when you're so unhappy that you know you shouldn't trust your own mind, but still believe in its most irrational conjectures.
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Rather, they engaged in glorified guesswork: You typed a few keywords into the Google search bar, and the company's PageRank system returned a long list of statistically backed conjectures about what you wanted to know.
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From the outside, it looked like nonsense, but once those conjectures hit Twitter or Facebook, tens of thousands of people shared them, reaffirming to each other that they had found proof of a sex-trafficking ring.
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"The Manhattan retail environment is too dynamic and should not be included with the pessimistic conjectures about e-commerce's effect on the future of brick and mortar retailing and struggling suburban shopping centers," the group wrote.
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Only after the discovery of the human immunodeficiency virus helped lay such conjectures to rest did it become possible to use specific blood tests for diagnosis and, eventually, to provide antiviral drugs to improve immune defenses.
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These renewed conjectures are bolstered by the circumstance that some years after Neruda's death, former President Eduardo Frei Montalva died under suspicious circumstances in the same room at the very clinic where the great poet had expired.
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Cohen is a drive-by intellectual who moves too fast to question his conjectures — if it occurs to him, it must be true — a verbal prestidigitator who's inclined to let his language do the thinking for him.
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"It's pleasing that there's a connection" between the two conjectures, said John Preskill of the California Institute of Technology, who in 22006 bet Stephen Hawking that the cosmic censorship conjecture would fail (though he actually thinks it's probably true).
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Referred to under the label "4/26"—tomorrow's date—contributors have assembled a number of supposed facts and conjectures that they believe amount to evidence that the US is in imminent danger of a nuclear strike from North Korea.
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South Korean news media offered differing conjectures, including whether Kim Hyok-chol, the North's special nuclear envoy to the United States, had been executed by firing squad in March, as the Chosun Ilbo reported, or was still under interrogation.
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"Our result shows that quantum information processing really does provide benefits — without having to rely on unproven complexity-theoretic conjectures," said Robert König, a co-author of the paper, in a statement from the Technical University of Munich, where he teaches.
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The simple fact of having a Republican in office, Federico conjectures, might allow Republicans to worry a little less about border security — in the same way that partisans assume the economy is better when the president is a member of their party.
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Andrew makes this case in a Cold War context: the moment of greatest risk in the Cold War occurred in the early fifties, when the United States didn't have sufficient intelligence, and filled the shortfall with wild conjectures about nonexistent missile gaps.
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Few government agencies could boast that their mandate was enshrined in the constitution, as the Census Bureau can, thanks to the impassioned arguments of James Madison, who thought that future legislators should "rest their arguments on facts, instead of assertions and conjectures".
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The study's author, Jay D. Teachman, a professor of sociology at Western Washington University, conjectures that married people get into routines, but also that the nonpartnered may have more of an incentive to stay fit and trim because they are in the dating market.
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Steve reasonably conjectures that if the next iPhone has a software home button, it might make the perfect drop target: If Apple's gonna have an onscreen homebutton on the iPhone 8, it would make a lot of sense to spring-load it for drag & drop.
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Here are the books discussed by The Times's critics this week: "American Carnage" by Tim Alberta "The Weil Conjectures" by Karen Olsson "Turbulence" by David Szalay We would love to hear your thoughts about this episode, and about the Book Review's podcast in general.
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But the shift has been slow on that continent and virtually nonexistent in the United States, where defense attorneys have argued that forensic scientists—in many communities employed by the prosecutor's office or police department—should be careful to stick to the facts rather than make conjectures.
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Conspiracy theories and wild conjectures about Clinton's health are so common it's entirely possible that she didn't want to make an issue about it or was concerned that this illness that affects 6900 million Americans each year would somehow be used to make her appear uniquely weak.
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And even though Tormund's talk of getting back to Winterfell to woo Brienne and Beric's musings on how he and his fire sword(!) are ready to die a seventh and final time are the kind of conjectures that usually mark a one-way ticket to death, both manage to scrape by.
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The media, which seems to be repenting for having misread or misrepresented polls that showed a sure Hillary Clinton win, now atones by constantly hedging — offering us a tree of all possible outcomes and a range of fairly noncommittal speculations that can be backed away from if their conjectures prove false.
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Synthesizing these conjectures, Taubes sees insulin resistance as the bedrock disturbance in the body which unleashes a cascade of other hormonal and inflammatory molecules that attack the brain (causing dementia), degrade the heart and the blood vessels (causing heart attack and stroke), disturb the metabolism of uric acid (causing gout), and so on.
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Given how little information is out there about Dee Dee's mother (she died in 1997), Martindale had to make conjectures about what kind of woman Emma was, by trying to understand what kind of person might have raised a daughter like Dee Dee and combining that with what she saw in old photos of Emma.
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Thomas has an English accent that makes any statement sound incredibly convincing; once, as I went to fish my golf ball out of whatever gutter it had landed in, I had to stop and remind myself that I was listening to theoretical conjectures on UFOs and alien light beams, and not an Ivy League law lecture.
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There are similarly some big questions around the larger plot, involving the history between H and London branch head High T (Liam Neeson), the suggestion that their department has a mole, and the tensions between Agent C (Rafe Spall) and H. Most people who know basic cinematic conventions will see all of MIB:I's twists coming, then spin out a series of "But if that's true, this makes no sense any more" conjectures.
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The mathematician Irving Kaplansky is notable for proposing numerous conjectures in several branches of mathematics, including a list of ten conjectures on Hopf algebras. They are usually known as Kaplansky's conjectures.
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The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture.
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In mathematics, the Arthur conjectures are some conjectures about automorphic representations of reductive groups over the adeles and unitary representations of reductive groups over local fields made by , motivated by the Arthur–Selberg trace formula. Arthur's conjectures imply the generalized Ramanujan conjectures for cusp forms on general linear groups.
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The Tait conjectures are three conjectures made by Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture, proved by Morwen Thistlethwaite and William Menasco in 1991.
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The standard conjectures were first formulated in terms of the interplay of algebraic cycles and Weil cohomology theories. The category of pure motives provides a categorical framework for these conjectures. The standard conjectures are commonly considered to be very hard and are open in the general case. Grothendieck, with Bombieri, showed the depth of the motivic approach by producing a conditional (very short and elegant) proof of the Weil conjectures (which are proven by different means by Deligne), assuming the standard conjectures to hold.
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Since 1900, mathematicians and mathematical organizations have announced problem lists, but, with few exceptions, these collections have not had nearly as much influence nor generated as much work as Hilbert's problems. One of the exceptions is furnished by three conjectures made by André Weil during the late 1940s (the Weil conjectures). In the fields of algebraic geometry, number theory and the links between the two, the Weil conjectures were very important . The first of the Weil conjectures was proved by Bernard Dwork, and a completely different proof of the first two conjectures via ℓ-adic cohomology was given by Alexander Grothendieck.
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Avec des remarques qui appuient ou qui éclaircissent ces conjectures ("Conjectures on the original documents that Moses appears to have used in composing the Book of Genesis. With remarks that support or throw light upon these conjectures"). The title cautiously gives the place of publication as Brussels, safely beyond the reach of French authorities.
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In 1974, at the age of twenty, Drinfeld announced a proof of the Langlands conjectures for GL2 over a global field of positive characteristic. In the course of proving the conjectures, Drinfeld introduced a new class of objects that he called "elliptic modules" (now known as Drinfeld modules). Later, in 1983, Drinfeld published a short article that expanded the scope of the Langlands conjectures. The Langlands conjectures, when published in 1967, could be seen as a sort of non-abelian class field theory.
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In mathematics, the Hardy–Littlewood zeta-function conjectures, named after Godfrey Harold Hardy and John Edensor Littlewood, are two conjectures concerning the distances between zeros and the density of zeros of the Riemann zeta function.
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The conjectures 1, 2, and 3 are related to the perfect cuboid problem. Though they are not equivalent to the perfect cuboid problem, if all of these three conjectures are valid, then no perfect cuboids exist.
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The Morita conjectures on normal topological spaces are also named after him.
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The philosopher of science Karl Popper suggested that all scientific theories are by nature conjectures and inherently fallible, and that refutation to old theory is the paramount process of scientific discovery. According to Popper’s Philosophy the Growth of Scientific Knowledge is based upon Conjectures and Refutations. Prof. Shapiro’s doctoral studies with Prof. Dana Angluin attempted to provide an algorithmic interpretation to Karl Popper's approach to scientific discovery in particular for automating the "Conjectures and Refutations" method making bold conjectures and then performing experiments that seek to refute them. Prof.
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All of these conjectures are known to be true only in special cases.
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It would be instantiated by conjectures, assumptions, and perhaps also by forceless utterances.
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Baker's theorem, while the lower two rows are detailed at the six exponentials theorem article. The strongest result that has been conjectured in this circle of problems is the strong four exponentials conjecture.Waldschmidt, (2000), conjecture 11.17. This result would imply both aforementioned conjectures concerning four exponentials as well as all the five and six exponentials conjectures and theorems, as illustrated to the right, and all the three exponentials conjectures detailed below.
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Deligne cohomology is used to formulate Beilinson conjectures on special values of L-functions.
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In 1978, Beilinson published a paper on coherent sheaves and several problems in linear algebra. His two-page note in the journal Functional Analysis and Its Applications was one of the papers on the study of derived categories of coherent sheaves. In 1981 Beilinson announced a proof of the Kazhdan–Lusztig conjectures and Jantzen conjectures with Joseph Bernstein. Independent of Beilinson and Bernstein, Brylinski and Kashiwara obtained a proof of the Kazhdan–Lusztig conjectures.
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Isaac La Peyrère,Astruc, Conjectures sur les memoires..., Isaac (de) la Peyrère, p. 454, and "Table des Matieres" (Table of Matters) p. 520. and Baruch SpinozaAstruc, Conjectures sur les memoires..., p. 439, pp. 452–454, and "Table des Matieres" (Table of Matters), p. 524.
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Equivariant assembly maps are used to formulate the Farrell–Jones conjectures in K- and L-theory.
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In 1949, André Weil posed the landmark Weil conjectures about the local zeta-functions of algebraic varieties over finite fields. Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil These conjectures offered a framework between algebraic geometry and number theory that propelled Alexander Grothendieck to recast the foundations making use of sheaf theory (together with Jean-Pierre Serre), and later scheme theory, in the 1950s and 1960s. Bernard Dwork proved one of the four Weil conjectures (rationality of the local zeta function) in 1960. Grothendieck developed étale cohomology theory to prove two of the Weil conjectures (together with Michael Artin and Jean-Louis Verdier) by 1965.
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A conjectural example in the theory of motives is the so-called motivic t-structure. Its (conjectural) existence is closely related to certain standard conjectures on algebraic cycles and vanishing conjectures, such as the Beilinson-Soulé conjecture.Hanamura, Masaki. Mixed motives and algebraic cycles. III. Math. Res. Lett.
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The Langlands conjectures for function fields state (very roughly) that there is a bijection between cuspidal automorphic representations of GLn and certain representations of a Galois group. Drinfeld used Drinfeld modules to prove some special cases of the Langlands conjectures, and later proved the full Langlands conjectures for GL2 by generalizing Drinfeld modules to shtukas. The "hard" part of proving these conjectures is to construct Galois representations with certain properties, and Drinfeld constructed the necessary Galois representations by finding them inside the l-adic cohomology of certain moduli spaces of rank 2 shtukas. Drinfeld suggested that moduli spaces of shtukas of rank r could be used in a similar way to prove the Langlands conjectures for GLr; the formidable technical problems involved in carrying out this program were solved by Lafforgue after many years of effort.
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The apparent fragility of the various conjectures illustrates the degree of cognitive fog covering these prehistoric landscapes.
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In mathematics, the Fontaine–Mazur conjectures are some conjectures introduced by about when p-adic representations of Galois groups of number fields can be constructed from representations on étale cohomology groups of a varieties. arXiv preprint Some cases of this conjecture in dimension 2 were already proved by .
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There are several different ways of stating the Langlands conjectures, which are closely related but not obviously equivalent.
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Many and various were the conjectures of the guests, concerning a distemperature which seemed rather mental than corporeal.
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These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being. These "proofs", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.
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Graffiti is a computer program which makes conjectures in various subfields of mathematics (particularly graph theory). and chemistry, but can be adapted to other fields. It was written by Siemion Fajtlowicz at the University of Houston. Research on conjectures produced by Graffiti has led to over 60 publications by other mathematicians..
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These conjectures have important implications for the Brumer-Stark conjecture and Gross' conjecture on special values of L-functions.
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The conjecture was proposed by , and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture..
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Wilhelm Schneemelcher states: > In short it must be said that all conjectures concerning the Gospel of > Basilides remain uncertain.
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Karl Popper argued that Adler's individual psychology like psychoanalysis is a pseudoscience because its claims are not testable and cannot be refuted; that is, they are not falsifiable.Popper KR, "Science: Conjectures and Refutations", reprinted in Grim P (1990) Philosophy of Science and the Occult, Albany, 104–110. See also Conjectures and Refutations.
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In the Tait conjectures, a knot diagram is called "reduced" if all the "isthmi", or "nugatory crossings" have been removed.
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Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf. the Pólya conjecture and Euler's sum of powers conjecture). In the case of the latter, the first counterexample found for the n=4 case involved numbers in the millions, although it has been subsequently found that the minimal counterexample is actually smaller.
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The work on the Burnside problem increased interest in Lie algebras in exponent p, and the methods of Michel Lazard began to see a wider impact, especially in the study of p-groups. Continuous groups broadened considerably, with p-adic analytic questions becoming important. Many conjectures were made during this time, including the coclass conjectures.
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The answers were believed to be affirmative. Here a normal P-space Y is characterised by the property that the product with every metrizable X is normal; thus the conjecture was that the converse holds. Keiko Chiba, Teodor C. Przymusiński, and Mary Ellen Rudin proved conjecture (1) and showed that conjectures (2) and (3) cannot be proven false under the standard ZFC axioms for mathematics (specifically, that the conjectures hold under the axiom of constructibility V=L). Fifteen years later, Zoltán Tibor Balogh succeeded in showing that conjectures (2) and (3) are true.
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The last of the Weil conjectures (an analogue of the Riemann hypothesis) would be finally proven in 1974 by Pierre Deligne.
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1798, and "Observations and conjectures on the antiquities of America," Mass. Hist. Soc., Coll. (Boston), 1st ser., 4 (1795): 100–5.
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In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers can then avoid going down blind alleys and learn to modify conjectures to produce provable theorems. It is sometimes said that mathematical development consists primarily in finding (and proving) theorems and counterexamples.
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He formulated what are now known as the Tait conjectures on alternating knots. (The conjectures were proved in the 1990s.) Tait's knot tables were subsequently improved upon by C. N. Little and Thomas Kirkman. James Clerk Maxwell, a colleague and friend of Thomson's and Tait's, also developed a strong interest in knots. Maxwell studied Listing's work on knots.
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Astruc, Conjectures sur les memoires..., p. 454 refers to "...la maladie du dernier siecle". Using methods already well established in the study of the Classics for sifting and assessing differing manuscripts,One of the textual studies he mentions as a basis of his own method is that of Richard Simon; cf. Astruc, Conjectures sur les mémoires..., p.
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On 17 November 1917, while on convalescent leave from service in World War I, Bloch killed his brother Georges, and his aunt and uncle. Several conjectures about the motives for Bloch's crime exist among mathematicians.See the article by Campbell for several anecdotal examples. Henri Cartan and Jacqueline Ferrand note that "certain of these conjectures are outrageously eccentric".
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Given a matrix and a matrix whose components are all integers, Green and Tao give conditions on when there exist infinitely many matrices such that all components of are prime numbers. The proof of Green and Tao was incomplete, as it was conditioned upon unproven conjectures. Those conjectures were proved in later work of Green, Tao, and Tamar Ziegler.
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The first order zero conjectures are used in recent versions of the PARI/GP computer algebra system to compute Hilbert class fields of totally real number fields, and the conjectures provide one solution to Hilbert's twelfth problem, which challenged mathematicians to show how class fields may be constructed over any number field by the methods of complex analysis.
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All of his conjectures were disproved by academic Shakespeareans,Greg, W.W. "A Hundreth Sundrie Flowres", The Library, Vol. 7 (1926), 269-82; ---.
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Greenberg's conjecture is either of two conjectures in algebraic number theory proposed by Ralph Greenberg. Both are still unsolved as of 2020.
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2014 [1963]. Conjectures and Refutations: The Growth of Scientific Knowledge. London: Routledge. p. 55. > I approached the problem of induction through Hume.
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She is known for formulating the umbral moonshine conjectures and for her work on the connections between K3 surfaces and string theory..
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Tilouine has worked on the anticyclotomic main conjecture of Iwasawa theory, special values of L-functions, and Serre-type conjectures for symplectic groups.
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This is one of the steps used in the proof of the Weil conjectures. Behrend's trace formula generalizes the formula to algebraic stacks.
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He formulated and proved function-field versions of the Gras conjectures and Rubin's integral refinement of the abelian Stark conjectures. He has also made important contributions to the Stark conjectures over number fields, formulating an alternative to Rubin's refinement, known as Popescu's conjecture. Although slightly weaker than Rubin's conjecture, it has the advantage that it can presently be shown to remain true under raising the base field or lowering the top field of the extension. Recently, Popescu and Cornelius Greither have formulated equivariant versions of Iwasawa's main conjecture over function fields and global fields, proving most the version for function fields.
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Stark's principal conjecture has been proven in various special cases, including the case where the character defining the L-function takes on only rational values. Except when the base field is the field of rational numbers or an imaginary quadratic field, the abelian Stark conjectures are still unproved in number fields, and more progress has been made in function fields of an algebraic variety. related Stark's conjectures to the noncommutative geometry of Alain Connes. This provides a conceptual framework for studying the conjectures, although at the moment it is unclear whether Manin's techniques will yield the actual proof.
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If you want to believe that the methodology will work, it must be postulated as an axiom. In Popper's case, the axiom is that the methodology of conjectures and refutations is going to work. The conjectures are the searchlight, because they lead to observational results. But this axiom will not help any objective rule in the justification of scientific knowledge.
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In some cases Graves conjectures a process of "iconotropy", or image-turning, by which a hypothetical cult image of the matriarchal or matrilineal period has been misread by later Greeks in their own terms. Thus, for example, he conjectures an image of divine twins struggling in the womb of the Horse-Goddess, which later gave rise to the myth of the Trojan Horse.
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His major contributions are in the field of practical numbers. This prime-like sequence of numbers is known for having an asymptotic behavior and other distribution properties similar to the sequence of primes. Melfi proved two conjectures both raised in 1984Margenstern, M., Résultats et conjectures sur les nombres pratiques, C, R. Acad. Sci. Sér. 1 299, No. 18 (1984), 895-898.
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Every function of S can be written as a product of primitive functions. Selberg's conjectures, described below, imply that the factorization into primitive functions is unique. Examples of primitive functions include the Riemann zeta function and Dirichlet L-functions of primitive Dirichlet characters. Assuming conjectures 1 and 2 below, L-functions of irreducible cuspidal automorphic representations that satisfy the Ramanujan conjecture are primitive.
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A more concrete example would be that of conjectures in mathematics – propositions which appear to be true but which are formally unproven. Very often, conjectures will be provisionally accepted as working hypotheses in order to investigate its consequences and formulate conditional proofs. Materials scientists Hosono et al. (1996) developed a working hypothesis about the nature of optically transparent and electrically conducting amorphous oxides.
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Iasus or Iasos () was a town in ancient Laconia, which Pausanias describes as belonging to the Achaeans.Suda s. v. Ἴασος. William Smith conjectures that Iasus may be the same as Oeum; the editors of the Barrington Atlas of the Greek and Roman World conjecture that it may be the same as Caryae. Its site is dependent on which, if either, of the conjectures is correct.
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Conjectures with wide scope on making this into formal statements were enunciated by Jean-Marc Fontaine, the resolution of which is called p-adic Hodge theory.
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There are two families of conjectures, formulated for general classes of L-functions (the very general setting being for L-functions L(s) associated to Chow motives over number fields), the division into two reflecting the questions of: :(a) how to replace π in the Leibniz formula by some other "transcendental" number (whether or not it is yet possible for transcendental number theory to provide a proof of the transcendence); and :(b) how to generalise the rational factor in the formula (class number divided by number of roots of unity) by some algebraic construction of a rational number that will represent the ratio of the L-function value to the "transcendental" factor. Subsidiary explanations are given for the integer values of n for which such formulae L(n) can be expected to hold. The conjectures for (a) are called Beilinson's conjectures, for Alexander Beilinson.Peter Schneider, Introduction to the Beilinson Conjectures (PDF)Jan Nekovář, Beilinson's Conjectures (PDF) The idea is to abstract from the regulator of a number field to some "higher regulator" (the Beilinson regulator), a determinant constructed on a real vector space that comes from algebraic K-theory.
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As with many famous conjectures in mathematics, there are a number of purported proofs of the Goldbach conjecture, none of which are accepted by the mathematical community.
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Congruences between Hecke rings ::503 3. The main conjectures :Chapter 3 ::517 Estimates for the Selmer group :Chapter 4 ::525 1. The ordinary CM case ::533 2.
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Three cuboid conjectures are three mathematical propositions claiming irreducibility of three univariate polynomials with integer coefficients depending on several integer parameters. They are neither proved nor disproved.
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The remaining 4 are too loosely formulated to be stated as solved or not. A map illustrating the Four Color Theorem Notable historical conjectures were finally proven.
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In mathematics, specifically the field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee the transcendence of at least one of four exponentials. The conjecture, along with two related, stronger conjectures, is at the top of a hierarchy of conjectures and theorems concerning the arithmetic nature of a certain number of values of the exponential function.
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Note that # Alice, using her private key, computes v and then the quotient, Thus, vv = 1, unless z ≠ m. # Alice then tests vv for equality against the values: which are calculated by repeated multiplication of mz (rather than exponentiating for each i). If the test succeeds, Alice conjectures the relevant i to be s; otherwise, she conjectures random value. Where z = m, (mz) = vxv = 1 for all i, s is unrecoverable.
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This passage has provoked various conjectures by historians since.Yule, Henry (1866) Cathay and the Way Thither, being a collection of Medieval notices of China.London: Hakluyt vol. 1, p.
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Olbia () was a town of ancient Cilicia, mentioned by Stephanus of Byzantium. William Smith conjectures that Stephanus may have been confused with the town of Olbasa or Olbe.
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In mathematics, the Mersenne conjectures concern the characterization of prime numbers of a form called Mersenne primes, meaning prime numbers that are a power of two minus one.
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More recently the mapping class group has been by itself a central topic in geometric group theory, where it provides a testing ground for various conjectures and techniques.
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2, Elsevier, 1996, 1447-1540. but both conjectures remain widely open. It is not even known if a single counterexample would necessarily lead to a series of counterexamples.
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This result also implies the following conjecture: > Alternating amphicheiral knots have even crossing number.Alexander > Stoimenow, "Tait's conjectures and odd amphicheiral knots", Bull. Amer. > Math. Soc. (N.S.) 45 (2008), no.
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Connelly has authored or co-authored several articles on mathematics, including Conjectures and open questions in rigidity; A flexible sphere; and A counterexample to the rigidity conjecture for polyhedra.
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This analogy, and the work of Jens Carsten Jantzen and Anthony Joseph relating primitive ideals of enveloping algebras to representations of Weyl groups, led to the Kazhdan–Lusztig conjectures.
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In mathematics, the monster Lie algebra is an infinite-dimensional generalized Kac–Moody algebra acted on by the monster group, which was used to prove the monstrous moonshine conjectures.
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The modularity theorem is a special case of more general conjectures due to Robert Langlands. The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field. Most cases of these extended conjectures have not yet been proved. However, proved that elliptic curves defined over real quadratic fields are modular.
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Little is known about Sirineki history, besides some conjectures based on linguistical consideration. Sirenik Eskimo culture has been influenced by that of Chukchi (witnessed also by folktale motifsМеновщиков 1964: 132).
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Hau JL, Bakshi BR. 2004. Promise and problems of emergy analysis. Ecological Modelling 178:215–225.Mansson, B.A., McGlade, J.M., 1993. Ecology, thermodynamics and H.T. Odum’s conjectures. Oecologia 93, 582–596.
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Cao, Huai- Dong; Zhu, Xi-Ping. A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006), no.
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The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered monetary rewards for solving them.
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Majidzadeh suggests they may be the remains of the lost Aratta Kingdom. Other conjectures (e.g. Daniel T. Potts, Piotr Steinkeller) have connected the site with the obscure city-state of Marhashi.
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One tree at Hartington Road, Brighton, one in Valley Gardens, Brighton, one at Trinity Church, Eastbourne (conjectures). The tree is not known to have been introduced to North America or Australasia.
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A reduced diagram is one in which all the isthmi are removed. Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots.
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This (along with much else) led to quantitative progress on Waring's problem, as part of the Hardy–Littlewood circle method, as it became known. In prime number theory, they proved results and some notable conditional results. This was a major factor in the development of number theory as a system of conjectures; examples are the first and second Hardy–Littlewood conjectures. Hardy's collaboration with Littlewood is among the most successful and famous collaborations in mathematical history.
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There are general conjectures due to Shouwu Zhang and others concerning subvarieties that contain infinitely many periodic points or that intersect an orbit in infinitely many points. These are dynamical analogues of, respectively, the Manin-Mumford conjecture, proven by Raynaud, and the Mordell–Lang conjecture, proven by Faltings. The following conjectures illustrate the general theory in the case that the subvariety is a curve. :Conjecture. Let be a morphism and let be an irreducible algebraic curve.
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In mathematics, the local Langlands conjectures, introduced by , are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
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In 1914, Godfrey Harold Hardy proved that has infinitely many real zeros. Hardy and John Edensor Littlewood formulated two conjectures on the density and distance between the zeros of on intervals of large positive real numbers. In the following, is the total number of real zeros and the total number of zeros of odd order of the function lying in the interval . These two conjectures opened up new directions in the investigation of the Riemann zeta function.
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In: G. Modelski, (ed.), Exploring Long Cycles. Lynne Rienner Publishers, Boulder, CO 1987. Iberall's conjectures on life and mind have been used as a springboard to develop theories of mental activity and action.
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The first result of this kind may have been the theorem of Hilbert and Hurwitz dealing with the case g = 0. The theory consists both of theorems and many conjectures and open questions.
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Dasgupta's research is focused on special values of L-functions, algebraic points on abelian varieties, and units in number fields. In particular, Dasgupta's research has focused on the Stark conjectures and Heegner points.
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Serre (1992) p.29 In fact Colliot-Thélène conjectures WWA holds for any unirational variety, which is therefore a stronger statement. This conjecture would imply a positive answer to the inverse Galois problem.
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In: G. Modelski, (ed.), Exploring Long Cycles. Lynne Rienner Publishers, Boulder, CO 1987. Iberall's conjectures on life and mind have been used as a springboard to develop theories of mental activity and action.
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Conversely, the relation between Kazhdan–Lusztig polynomials and the Ext groups theoretically can be used to prove the conjectures, although this approach to proving them turned out to be more difficult to carry out. 4\. Some special cases of the Kazhdan–Lusztig conjectures are easy to verify. For example, M1 is the antidominant Verma module, which is known to be simple. This means that M1 = L1, establishing the second conjecture for w = 1, since the sum reduces to a single term.
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Critical rationalism is an epistemological philosophy advanced by Karl Popper. Popper wrote about critical rationalism in his works, such as: The Logic of Scientific Discovery (1934/1959), The Open Society and its Enemies (1945),Popper, K., The Open Society and Its Enemies, Princeton University Press, 2013, p.435. Conjectures and Refutations (1963),Popper, K., Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge, 2014, p. 34. Unended Quest (1976),Popper, K., Unended Quest: An Intellectual Autobiography, Routledge, 2005, p. 132.
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In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry. This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type.
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This can be seen as a generalization of Karl Popper's philosophy of science, which conceives the development of new theories as a process of proposing conjectures (blind variation) followed by the refutation (selective elimination) of those conjectures that are empirically falsified. Campbell added that the same logic of blind variation and selective elimination/retention underlies all knowledge processes, not only scientific ones. Thus, the BVSR mechanism explains creativity, but also the evolution of instinctive knowledge, and of our cognitive abilities in general.
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Both the reconstruction and set reconstruction conjectures have been verified for all graphs with at most 11 vertices by Brendan McKay.McKay, B. D., Small graphs are reconstructible, Australas. J. Combin. 15 (1997), 123-126.
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William Courtenay conjectures that this was because of a case that was assigned to Fr. Pasteur by the Pope in April 1334,C. Eubel (ed.), Bullarium Franciscanum Vol. V, no. 1060, pp. 568-569.
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William Joseph Haboush is an American mathematician at the University of Illinois at Urbana-Champaign who is best known for his 1975 proof of one of David Mumford's conjectures, known as the Haboush's theorem.
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The formulation of Stark's conjectures led Harold Stark to define what is now called the Stark regulator, similar to the classical regulator as a determinant of logarithms of units, attached to any Artin representation.
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Albrecht Fröhlich FRS (22 May 1916 – 8 November 2001) was a German-born British mathematician, famous for his major results and conjectures on Galois module theory in the Galois structure of rings of integers.
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The Romans only rarely raced with a team of three.Palmer, Studies of the Northern Campus Martius, p. 28 online; Richardson, Topographical Dictionary, p. 401, conjectures that the site was used for three kinds of races.
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In the mathematical field of algebraic geometry, purity is a theme covering a number of results and conjectures, which collectively address the question of proving that "when something happens, it happens in a particular codimension".
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2, 4, or 6) (mod 8). The first case of this is one of Euler's conjectures: :2 is a biquadratic residue of a prime p ≡ 1 (mod 4) if and only if p = a2 \+ 64b2.
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See Grayling, "Memorial". A few visitors cheered these days, but, toward the end, he was frequently too sickGrayling conjectures that his ailment was either stomach cancer or ulcers. Grayling, "Memorial". to see any of them.
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Pp. 238–246 Carneiro, R. L. "What Happened at Flashpoint? Conjectures on Chiefdom Formation at the Very Moment of Conception." In Chiefdoms and Chieftaincy in the Americas. Ed. by Elsa M. Redman, pp. 18–42.
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The play was inspired by conjectures in P. D. Ouspensky's book A New Model of the Universe (1931). Ouspensky had already expressed these ideas in fiction with Strange Life of Ivan Osokin (1915, translated 1947).
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His work includes numerical analysis—particularly iterative methods in numerical linear algebra, matrix theory, and differential equations—complex approximation theory, particularly Padé approximation (often with Edward B. Saff, Jr.)—and analytic number theory, including high-precision calculations related to the Riemann hypothesis. He is also known for advocating experimentation in mathematics, and for writing a monograph surveying his contributions on scientific computing to resolve open problems and conjectures. Scientific Computation on Mathematical Problems and Conjectures, CBMS-NSF Regional Conference Series in Applied Math., #60, Soc.
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The Ravenel conjectures very roughly say: complex cobordism (and its variants) see more in the stable homotopy category than you might think. For example, the nilpotence conjecture states that some suspension of some iteration of a map between finite CW- complexes is null-homotopic iff it is zero in complex cobordism. This was proven by Ethan Devinatz, Hopkins and Jeff Smith (published in 1988). The rest of the Ravenel conjectures (except for the telescope conjecture) were proven by Hopkins and Smith soon after (published in 1998).
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In mathematics, class field theory is the branch of algebraic number theory concerned with the abelian extensions of number fields, global fields of positive characteristic, and local fields. The theory had its origins in the proof of quadratic reciprocity by Gauss at the end of the 18th century. These ideas were developed over the next century, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin. These conjectures and their proofs constitute the main body of class field theory.
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A similar equality for the cartesian product of graphs was proven by and rediscovered several times afterwards. An exact formula is also known for the lexicographic product of graphs. introduced two stronger conjectures involving unique colorability.
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In 1879, Alfred Kempe published a proof of the four color theorem, one of the big conjectures in graph theory.Kempe, A. B. "On the Geographical Problem of Four-Colors." Amer. J. Math. 2, 193–200, 1879.
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Ungoliant is mentioned in the 2012 film The Hobbit: An Unexpected Journey, the first film of Peter Jackson's film trilogy of The Hobbit, when the wizard Radagast the Brown conjectures on the origin of malevolent giant spiders.
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The site of Cragus has not been determined. William Martin Leake (Geog. Journal, vol. xii. p. 164) conjectures that Cragus may be the same city as Sidyma, a place that is first mentioned by Pliny the Elder.
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In mathematics, Schinzel's hypothesis H is one of the most famous open problems in the topic of number theory. It is a very broad generalisation of conjectures such as the twin prime conjecture named after Andrzej Schinzel.
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Conjectures of Ian G. Macdonald helped to open up large and active new fields with the typical special function flavour. Difference equations have begun to take their place besides differential equations as a source for special functions.
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In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties of a commutative ring to its internal ring structure, particularly its Krull dimension and depth. The following list given by Melvin Hochster is considered definitive for this area. In the sequel, A, R, and S refer to Noetherian commutative rings; R will be a local ring with maximal ideal m_R, and M and N are finitely generated R-modules.
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André Weil's famous Weil conjectures proposed that certain properties of equations with integral coefficients should be understood as geometric properties of the algebraic variety that they define. His conjectures postulated that there should be a cohomology theory of algebraic varieties that gives number-theoretic information about their defining equations. This cohomology theory was known as the "Weil cohomology", but using the tools he had available, Weil was unable to construct it. In the early 1960s, Alexander Grothendieck introduced étale maps into algebraic geometry as algebraic analogues of local analytic isomorphisms in analytic geometry.
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Records survive of several works Clarke attempted after the Conjectures. Announced in the Conjectures, apparently to be his principal work, a volume entitled The Hebrew, Samaritan, Greek, and Roman Medallist was never published. Clarke claimed, in his 1815 genealogy, that he had attempted to read two dissertations to the Society of Antiquaries, but was refused "through the persuasion of two drones, P. C. Webb and C. D.". After this incident, Clarke refused to pay his dues to the Society, and was removed in 1765, owing eleven years worth of dues.
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1\. The two conjectures are known to be equivalent. Moreover, Borho–Jantzen's translation principle implies that can be replaced by for any dominant integral weight . Thus, the Kazhdan–Lusztig conjectures describe the Jordan–Hölder multiplicities of Verma modules in any regular integral block of Bernstein–Gelfand–Gelfand category O. 2\. A similar interpretation of all coefficients of Kazhdan–Lusztig polynomials follows from the Jantzen conjecture, which roughly says that individual coefficients of are multiplicities of in certain subquotient of the Verma module determined by a canonical filtration, the Jantzen filtration.
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The Maison d'Ailleurs originates from the work of the French encyclopedian Pierre Versins, who dedicated his life to writing and the study of what he named "rational romanesque conjectures" ("conjectures romanesques rationnelles" in French). For more than twenty years, he gathered a very important collection of science fiction works. Based on this corpus, he wrote one of the major books in this domain, the Encyclopédie de l'utopie, des voyages extraordinaires et de la science-fiction. In 1976, he donated his assets to the city of Yverdon-les-Bains and the Maison d'Ailleurs was created.
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The next question in fast mapping theory is how exactly is the meaning of the novel word learned? An experiment performed in October 2012 by the Department of Psychology by University of Pennsylvania, researchers attempted to determine if fast mapping occurs via cross- situational learning or by another method, "Propose but verify". In cross- situational learning, listeners hear a novel word and store multiple conjectures of what the word could mean based on its situational context. Then after multiple exposures the listener is able to target the meaning of the word by ruling out conjectures.
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Although there are numerous statements that could have borne the name Ramanujan conjecture, one was highly influential on later work. In particular, the connection of this conjecture with conjectures of André Weil in algebraic geometry opened up new areas of research. That Ramanujan conjecture is an assertion on the size of the tau- function, which has as generating function the discriminant modular form Δ(q), a typical cusp form in the theory of modular forms. It was finally proven in 1973, as a consequence of Pierre Deligne's proof of the Weil conjectures.
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In his book, La Naissance du Christianisme (1933), transl. The Birth of the Christian Religion, (1948), Loisy had expressed doubts about "the noisy conjectures...[which] seem to me somewhat fragile. These conjectures arise generally from persons who have arrived late at the problem of Jesus, and who have not previously made any profound study of the history of Israel and of Christianity...With us P.L Couchoud... postulating a pre-Christian myth of the Suffering Jahve, which a vision of Simon Peter suddenly transformed into a living religion." (p. 6).
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The so-called coclass conjectures described the set of all finite p-groups of fixed coclass as perturbations of finitely many pro-p groups. The coclass conjectures were proven in the 1980s using techniques related to Lie algebras and powerful p-groups. The final proofs of the coclass theorems are due to A. Shalev and independently to C. R. Leedham-Green, both in 1994. They admit a classification of finite p-groups in directed coclass graphs consisting of only finitely many coclass trees whose (infinitely many) members are characterized by finitely many parametrized presentations.
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In mathematics, the Ravenel conjectures are a set of mathematical conjectures in the field of stable homotopy theory posed by Douglas Ravenel at the end of a paper published in 1984. It was earlier circulated in preprint. The problems involved have largely been resolved, with all but the "telescope conjecture" being proved in later papers by others. The telescope conjecture is now generally believed not to be true, though there are some conflicting claims concerning it in the published literature, and is taken to be an open problem.
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Ravenel's conjectures exerted influence on the field through the founding of the approach of chromatic homotopy theory. The first of the seven conjectures, then the nilpotence conjecture, is now the nilpotence theorem. The telescope conjecture, which was #4 on the original list, remains of substantial interest because of its connection with the convergence of an Adams–Novikov spectral sequence. While opinion is against the truth of the original statement, investigations of associated phenomena (for a triangulated category in general) have become a research area in its own right.
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The last and deepest of the Weil conjectures (an analogue of the Riemann hypothesis) was proven by Pierre Deligne. Both Grothendieck and Deligne were awarded the Fields medal. However, the Weil conjectures in their scope are more like a single Hilbert problem, and Weil never intended them as a programme for all mathematics. This is somewhat ironic, since arguably Weil was the mathematician of the 1940s and 1950s who best played the Hilbert role, being conversant with nearly all areas of (theoretical) mathematics and having figured importantly in the development of many of them.
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Larch Prover, or LP for short, is an interactive theorem proving system for multisorted first-order logic. It was used at MIT and elsewhere during the 1990s to reason about designs for circuits, concurrent algorithms, hardware, and software. Unlike most theorem provers, which attempt to find proofs automatically for correctly stated conjectures, LP is intended to assist users in finding and correcting flaws in conjectures — the predominant activity in the early stages of the design process. LP works efficiently on large problems, has many important user amenities, and can be used by relatively naïve users.
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The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine module in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized Kac–Moody algebras.
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Since inspecting the dukedom's organs belonged to the court organist's duties, the museum conjectures that Bach must have known and played this instrument, even though there is no record of it.Geburtstag mit Filmpremiere und Orgelweihe. News service www.eisenachonline.
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See also The Stones of Oxford, Conjectures on a Cockleshell. John Melvin. Papadakis 2011 The design of the Penton Street flats attempted to link modern functionalism with the 19th century terraced houses of the two adjoining Conservation Areas.
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Furthermore, the most exciting application of the new compound could be in fighting prostate cancer since Cohen conjectures that an agent can be attached to the tracer compound, one that can seek out and destroy prostate cancer cells.
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George Palmer (ca. 1746 – March 3, 1826), also known as George Giros de Gentilly, named Palmer) was an English dye chemist, colour theorist, inventor, and soldier. He is best known for his conjectures about colour vision and colour blindness.
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Her elusive nature is indicated by the wildly divergent scholarly conjectures she has prompted: "she was considered a chthonic divinity by Wissowa, a lunar goddess by Pettazzoni, a bean-goddess by Latte, and a patroness of digestion by Dumézil".
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The Church–Turing thesis conjectures that there is no effective model of computing that can compute more mathematical functions than a Turing machine. Computer scientists have imagined many varieties of hypercomputers, models of computation that go beyond Turing computability.
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Journal of Bible and Religion, vol. 8, no. 3, 1940, p. 134. However, no Assyrian king by the name of "Jareb" is known to history, which has led to a variety of conjectures about what the phrase refers to.
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He has developed 4-dimensional handlebody techniques, settling conjectures and solving problems about 4-manifolds, such as a conjecture of Christopher Zeeman,S. Akbulut, A solution to a conjecture of Zeeman, Topology, vol.30, no.3, (1991), 513-515.
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181–239; 2006, Practical Certainty and Cosmological Conjectures, in Rahnfeld, M, ed., Gibt es sicheres Wissen?: aktuelle Beiträge zur Erkenntnistheorie, Leipziger Universitätsverlag, Leipzig, pp. 44–59. simplicity,Maxwell, N., 1998, The Comprehensibility of the Universe, Clarendon Press, Oxford, chs.
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However, the general case of evaluating an arbitrary position is known to be NP-hard. There are some open conjectures on the value of some remarkable positions. A one-player puzzle version of the game has also been considered.
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Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.
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She returned to graduate school at the University of Houston and completed a Ph.D. in mathematics there in 1997. Her doctoral supervisor was Siemion Fajtlowicz, with whom she worked on the Graffiti computer program for automatically formulating conjectures in graph theory.
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450 Once Kepler had made the sun, not the Primum Mobile, the cause of planetary motion, however,N. R. Hanson, Constellations and Conjectures (1973) p. 256-7 the Primum Mobile gradually declined into the realm of metaphor or literary allusion.
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Sarah Kent (2007): 'Public Pictures, Private Lives', in Uwe Wittwer - Hail and Snow. Haunch of Venison, Zurich / London, Kunde, Harald (2005). 'Conjectures About What Is Possible', in Uwe Wittwer - Geblendet/Dazzled, Heidelberg: Kehrer Verlag. The works of referenceAlso termed Appropriation Art.
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"Yunnan" has been a place name already before "Yunling Mountains". Modern research gives more conjectures. You Zhong said "Yunnan" means "south of the mountain (Cang Mountain) with clouds". Wu Guangfan said "Yunnan" might be a Loloish or Bai language name.
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The two conjectures are mathematically independent, as there exist spacetimes for which weak cosmic censorship is valid but strong cosmic censorship is violated and, conversely, there exist spacetimes for which weak cosmic censorship is violated but strong cosmic censorship is valid.
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Bernard d'Albi, was born at Saverdun in the diocese of Pamiers in the Pyrenees foothills, south of Toulouse,For other conjectures, see Baluze (1693), I, p. 820 [ed. Mollat (1927), II, p. 324]. and died on 23 November 1350 at Avignon.
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Zygopolis () was a town of ancient Pontus, in the neighbourhood of Colchis mentioned by Strabo. Stephanus of Byzantium conjectures that it was in the territory of the Zygii, which, however, does not agree with Strabo's description. Its site is unlocated.
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It is not much harder to do -dimensional projective space. The number of points of over a field with elements is just . The zeta function is just :. It is again easy to check all parts of the Weil conjectures directly.
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Algebraic geometry likewise uses group theory in many ways. Abelian varieties have been introduced above. The presence of the group operation yields additional information which makes these varieties particularly accessible. They also often serve as a test for new conjectures.
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In developing his approaches to teaching and fencing, Sollee used his understanding of a wide range of subjects, including boxing, martial arts and psychology, and his experience teaching fencing to the blind at the Carroll Center. Sollee taught well over a thousand students at the Carroll Center helping people regain their orientation in space. As part of the effort to work on teaching approaches, Sollee and Johan Harmenberg came up with a new way to think about épée fencing starting with the three "Sollee conjectures". Sollee and his students collaboratively worked on these conjectures and the associated new paradigm.
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That would also be a rule of the bucket view of science. Popper's main methodological rule is that scientists must try to guess and corroborate (or equivalently falsify) bold and useful conjectures and take any falsification as a problem that can be used to start a critical discussion. In other words, the usefulness of falsifiability is that falsifiable conjectures say more, because they prohibit more and, in the case of their falsification, they lead to useful problems, which steer the creative process of science. For Popper, who knew most of section , this is exactly what we should expect from a scientific theory.
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The reason for the request is unknown. Zacour conjectures that King John was finding opposition to the planned crusade, and wanted help; it is difficult to see how Talleyrand could have helped, or why the cardinals would refuse. Zacour also conjectures that the College of Cardinals did not authorize the mission because Talleyrand did not want it to, because he was more interested in his affairs in Naples; it is difficult to see how Talleyrand's influence could have outweighed that of King John and Pope Urban with the cardinals, especially in the matter of a crusade.Zacour (1960), p. 69.
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The first clear sign of a possible generalization from Chow groups to a more general motivic cohomology theory for algebraic varieties was Quillen's definition and development of algebraic K-theory (1973), generalizing the Grothendieck group K0 of vector bundles. In the early 1980s, Beilinson and Soulé observed that Adams operations gave a splitting of algebraic K-theory tensored with the rationals; the summands are now called motivic cohomology (with rational coefficients). Beilinson and Lichtenbaum made influential conjectures predicting the existence and properties of motivic cohomology. Most but not all of their conjectures have now been proved.
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The main claimed application of IUT is to various conjectures in number theory, among them abc, but also more geometric conjectures such as Szpiro's conjecture on elliptic curves and Vojta's conjecture for curves. The first step is to translate arithmetic information on these objects to the setting of Frobenioid categories. It is claimed that extra structure on this side allows one to deduce statements which translate back into the claimed results. One issue with Mochizuki's arguments, which he acknowledges, is that it does not seem possible to get intermediate results in his proof of abc using IUT.
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Together with Paolo Cascini, Christopher Hacon and James McKernan, Birkar settled several conjectures including existence of log flips, finite generation of log canonical rings, and existence of minimal models for varieties of log general type, building upon earlier work of Vyacheslav Shokurov and of Hacon and McKernan.C. Birkar, P. Cascini, C. Hacon, J. McKernan Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), 405–468. In the setting of log canonical singularities, he proved existence of log flips along with key cases of the minimal model and abundance conjectures.
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He also worked on Bloch-Kato conjectures. In 1984 he received the Prix Carrière from the French Academy of Sciences. Beginning in 2002 he was a member of the French Academy of Sciences. In 2002 he was awarded the Gay-Lussac-Humboldt Prize.
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Peter Littelmann at Oberwolfach, 2009 Peter Littelmann is a German mathematician at the University of Cologne working on algebraic groups and representation theory, who introduced the Littelmann path model and used it to solve several conjectures in standard monomial theory and other areas.
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Silbermann later had a falling out with Hebenstreit and was blocked by a royal writ from building any further pantaleons. Stewart Pollens conjectures that in adding the damper-raising stop to the piano, Silberman may have been attempting to partially circumvent this restriction.
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Kumar has made profound and original contributions to commutative algebra and algebraic geometry. He is well known for his contribution settling the Eisenbud-Evans conjectures proposed by David Eisenbud. His work on rational double points on rational surfaces has also been acclaimed.
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Ehlers' research was in the field of general relativity. In particular, he made contributions to cosmology, the theory of gravitational lenses and gravitational waves. His principal concern was to clarify general relativity's mathematical structure and its consequences, separating rigorous proofs from heuristic conjectures.
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"Yunnan" became the common name of this area. Therefore, Yuan Dynasty set "Yunnan Province" after he occupied Dali Kingdom. The province name "Yunnan" continues to this day. Han Dynasty literature did not record the etymology of "Yunnan", so people have many conjectures.
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Conversely, Alexander Beilinson proved that the existence of a category of motives implies the standard conjectures. Additionally, cycles are connected to algebraic K-theory by Bloch's formula, which expresses groups of cycles modulo rational equivalence as the cohomology of K-theory sheaves.
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In mathematics, a Mordellic variety is an algebraic variety which has only finitely many points in any finitely generated field. The terminology was introduced by Serge Lang to enunciate a range of conjectures linking the geometry of varieties to their Diophantine properties.
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When the Court issued a show cause notice to The Pioneer, Nilabh Kishore issued an affidavit on 4 October 2010 stating that "no authorised person in the CBI" had spoken to The Pioneer's correspondent, and that the article was full of "factual infirmities and conjectures".
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Conjectures have been made by scholars who argue that the ancestors of Maldivian people arrived to the Maldives from North West and West India, from Kalibangan between 2500 and 1700 BC and that they formed a distinct ethnic group around the 6th century BC.
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Contemporary observers recorded barometric readings as low as 973 millibars (measured by William Derham in south Essex), but it has been suggested that the storm deepened to 950 millibars over the Midlands. Retrospective analysis conjectures that the storm was consistent with a Category 2 hurricane.
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If X is smooth and proper over k the rigid cohomology groups are the same as the crystalline cohomology groups. The name "rigid cohomology" comes from its relation to rigid analytic spaces. used rigid cohomology to give a new proof of the Weil conjectures.
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Arthur is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case (due to Selberg himself) to general reductive groups, one of the most important tools for research on the Langlands program. He also introduced the Arthur conjectures.
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The geometric Langlands correspondence is a relationship between abstract geometric objects associated to an algebraic curve such as the elliptic curves illustrated above. In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory to the branch of mathematics known as representation theory.Frenkel 2007 Formulated by Robert Langlands in the late 1960s, the Langlands correspondence is related to important conjectures in number theory such as the Taniyama–Shimura conjecture, which includes Fermat's last theorem as a special case. In spite of its importance in number theory, establishing the Langlands correspondence in the number theoretic context has proved extremely difficult.
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The Kazhdan–Lusztig polynomials arise as transition coefficients between their canonical basis and the natural basis of the Hecke algebra. The Inventiones paper also put forth two equivalent conjectures, known now as Kazhdan–Lusztig conjectures, which related the values of their polynomials at 1 with representations of complex semisimple Lie groups and Lie algebras, addressing a long-standing problem in representation theory. Let W be a finite Weyl group. For each w ∈ W denote by be the Verma module of highest weight where ρ is the half-sum of positive roots (or Weyl vector), and let be its irreducible quotient, the simple highest weight module of highest weight .
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These conjectures have since been dubbed the Beilinson-Soulé conjectures; they are intertwined with Vladimir Voevodsky's program to develop a homotopy theory for schemes. In 1984, Beilinson published the paper Higher Regulators and values of L-functions, in which he related higher regulators for K-theory and their relationship to L-functions. The paper also provided a generalization to arithmetic varieties of the Lichtenbaum conjecture for K-groups of number rings, the Hodge conjecture, the Tate conjecture about algebraic cycles, the Birch and Swinnerton-Dyer conjecture about elliptic curves, and Bloch's conjecture about K2 of elliptic curves. Beilinson continued to work on algebraic K-theory throughout the mid-1980s.
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Esther has a romantic interest in Rex Matheson (Mekhi Phifer), who she idealises and looks up to. Despite her feelings, Rex does not appear to notice or reciprocate, actress Alexa Havins conjectures that "he's so blind to her feelings" due to him having "this wall built up around him that it's hard to break through." Phifer commented that Rex sees Esther as a sister and conjectures that Esther's interests in him are partly a result of her sensationalising his work. Despite her highly romanticised idea of field work, Esther is not as skilled in the field as more experienced agents Rex, Jack (John Barrowman) and Gwen.
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From 17 November 1588 until June 1589, he revised the text; until the end of November 1589, he corrected the proofs. Sixtus made the corrections using simple conjectures and working quickly. He used the Codex Carafianus.Carlo Vercellone, Variae lectiones Vulgatae Latinae Bibliorum editionis, Romae 1860, p. XXX.
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If not they may be > ruled out altogether. This razor is sharper than Ockham's: all entities are > ruled out except those which are perceived.Karl Popper, Conjectures and > Refutations: The Growth of Scientific Knowledge, New York: Routledge, 2002, > p. 231. In another essay of the same bookK.
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All the above conjectures and theorems are consequences of the unproven extension of Baker's theorem, that logarithms of algebraic numbers that are linearly independent over the rational numbers are automatically algebraically independent too. The diagram on the right shows the logical implications between all these results.
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In the unbroken line of new > apartments, lining Fifty-seventh Street almost solidly from Second Avenue to > Sutton Place, those who doubted the wisdom of Mrs. Vanderbilt's move have > found a convincing answer to their conjectures as to the ultimate success of > the Sutton Place movement.
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In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, so the periods form a ring. gave a survey of periods and introduced some conjectures about them.
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More generally, every minor-closed graph family is incapable of representing all finite groups by the symmetries of its graphs., Theorem 4.5. László Babai conjectures, more strongly, that each minor-closed family can represent only finitely many non-cyclic finite simple groups., discussion following Theorem 4.5.
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Michael O'Brien, Conjectures of Order: Intellectual Life and the American South, 1810-1860, Chapel Hill, North Carolina: University of North Carolina Press, 2004, Volume 2, p. 127 He would receive honorary LLD. degrees from Delaware college in 1875, and the College of William and Mary in 1878.
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The real Zhang Youliang was actually obsessed with rocks rather than pigeons and once arranged for a team of 300 oxen to drag a rock down from the mountains to adorn his famous garden; Zeitlin conjectures that the author may have confused the names of these two aristocratic aesthetes.
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Exoplanets have been directly observed and remotely sensed, but due to their great distance and proximity to obscuring energy sources (the stars they orbit), there is little concrete knowledge of their composition and geodynamic regime. Therefore, the majority of information and conjectures made about them come from alternative sources.
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1 (2. St.) 57–61. In 1781 J. H Voigt of Gotha, Germany, editor of Magazin fuer das Neueste aus der Physik und Naturgeschichte, a scientific review journal, describes meeting with Giros von Gentilly and the latter's conjectures about color blindness.Palmer, G. 1793. Letter dated June 19, 1793.
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Then we should be able to require the existence of n such that N − F(n) is both positive and a prime number; and with all the fi(n) prime numbers. Not many cases of these conjectures are known; but there is a detailed quantitative theory (Bateman–Horn conjecture).
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In 2006, Huai-Dong Cao and Xi-Ping Zhu published an exposition of Hamilton and Perelman's works, also covering Perelman's first two articles.Huai-Dong Cao and Xi-Ping Zhu. A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow.
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However, James has stolen the painting as Hugh had made it clear to him before his death that he did not want it sold. MacMaster conjectures they have to tell Ellen of the situation. When he visits her the next day, she says the painting will have to go.
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The Georgian scholar Ramin Ramishvili conjectures that the combination of letters ႩႲႽ corresponds to the number 5320 (5000 + 300 + 20, correspondingly Ⴉ [k] + Ⴒ [t] + Ⴝ [č]), which may denote, according to Georgian numerals, the year 284 BC, the alleged date of creation of the first Georgian script.
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Typically the basic/nonbasic employment ratio is about 1:1. Extending by manipulation of data and comparisons, conjectures may be made about population and income. This is a rough, serviceable procedure, and it remains in use today. It has the advantage of being readily operationalized, fiddled with, and understandable.
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Neither "ret" nor "kiń" are in use in contemporary Polish, and the etymology is a matter of guesswork.Załuska and Załuska admit that "these are just our conjectures... and nothing more" (p. 13). Another theory suggests that the name of the district derives from the personal name Retko (or Retka).
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An ordination document issued by David in September 1499 refers to his father as by then already dead. Rabinowitz conjectures that Messer Leon had been with David, and died at Monastir (present-day Bitola in the Republic of Macedonia) in that year. However, Tirosh-Rothschild (p. 253, n.
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A different notion of a P-space has been introduced by Kiiti Morita in 1964, in connection with his (now solved) conjectures (see the relative entry for more information). Spaces satisfying the covering property introduced by Morita are sometimes also called Morita P-spaces or normal P-spaces.
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Some conjectures can be made on the surname Cairano, in particular that it leads one to Cairate in Varese province, which is to this day shortened to Caira in the local dialect.Historical sources provide other variations of the last name of Gasparo. See Zani 2010, p. 102, n.
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Among these schools are ego psychology, object relations, and interpersonal, Lacanian, and relational psychoanalysis. Psychologists such as Hans Eysenck and philosophers including Karl Popper criticized psychoanalysis. Popper argued that psychoanalysis had been misrepresented as a scientific discipline,Karl Popper, Conjectures and Refutations, London: Routledge and Keagan Paul, 1963, pp.
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These are, first, an argument Riccioli called the "physico-mathematical argument", which was related to one of Galileo's conjectures; second, an argument based on what today is known as the "Coriolis effect"; third, an argument based on the appearance of stars as seen through the telescopes of the time.
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Field, Tim. (1995). Bully in Sight: How to Predict, Resist, Challenge and Combat Workplace Bullying, p. 60. Karl Popper coined the concept conventionalist twist or conventionalist stratagem in Conjectures and Refutations with similar use as this fallacy but in the context of the falsifiability of certain scientific theories.
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Other expositions, which have also been widely cited, were written by Huai-Dong Cao and Xi-Ping Zhu, and by Bruce Kleiner and John Lott.Cao, Huai-Dong; Zhu, Xi- Ping. A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow.
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Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
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Accessed at bartleby.com on 9 November 2006. Hanmer's editing, however, was based on his own selection of emendations from the Shakespeare editions of Alexander Pope and Lewis Theobald, along with his own conjectures, without indicating for the reader what was in his source texts and what was editorially corrected.
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A 'theory > of everything' is one of many components necessary for complete > understanding of the universe, but is not necessarily the only one. The > development of macroscopic laws from first principles may involve more than > just systematic logic, and could require conjectures suggested by > experiments, simulations or insight.
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In mathematics, the Weil conjectures were some highly influential proposals by , which led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory. The conjectures concern the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. A variety over a finite field with elements has a finite number of rational points (with coordinates in the original field), as well as points with coordinates in any finite extension of the original field. The generating function has coefficients derived from the numbers of points over the extension field with elements.
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Subsequently, he worked extensively in p-groups and pro-p groups and was among those who solved the coclass conjectures on the structure of such groups. Likewise Shalev used Lie methods to solve problems on fixed points of automorphisms of p-groups, and studied subgroup growth of profinite and discrete groups.
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In arithmetic dynamics, posed conjectures on the Zariski density of non-fibered endomorphisms of quasi-projective varieties and proposed a dynamical analogue of the Manin–Mumford conjecture. In 2018, proved the averaged Colmez conjecture which was shown to imply the André–Oort conjecture for Siegel modular varieties by Jacob Tsimerman.
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Ludwig Wittgenstein (at least in his early period),Ludwig Wittgenstein, Tractatus Logico-Philosophicus, Routledge 2001 [1921]. J. L. Austin,Austin, J. L., 1950, "Truth", reprinted in Philosophical Papers, 3rd ed., Oxford: Oxford University Press 1979, 117–33. and Karl PopperKarl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, 1963.
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The Philharmonic Society insisted on the date and hired the English cellist Leo Stern without consulting Dvořák. The composer then at first refused to come for the concert. "Berger was horrified and greatly embarrassed," as the concert had already been advertised. Clapham conjectures that Wihan released Dvořák from his promise.
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In 1986 ruins of 4th- to 6th- century baths were found in Ashkelon. The bath houses are believed to have been used for prostitution. The remains of nearly 100 mostly male infants were found in a sewer under the bathhouse, leading to conjectures that prostitutes had discarded their unwanted newborns there.
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Zarefsky pioneered a policy debate judging paradigm called "hypothesis testing," which spells out how debate judges can draw metaphorically upon the scientific method's process of weighing scientific conjectures and refutations.David Zarefsky. "Argument as Hypothesis-testing." In David A. Thomas (Ed.), Advanced Debate: Readings in Theory, Practice and Teaching (pp. 427–437).
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Mathematical statements have their own moderately complex taxonomy, being divided into axioms, conjectures, propositions, theorems, lemmas and corollaries. And there are stock phrases in mathematics, used with specific meanings, such as "", "" and "without loss of generality". Such phrases are known as mathematical jargon. The vocabulary of mathematics also has visual elements.
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These give the first non-trivial cases of the Weil conjectures (proved by Hasse). If is an elliptic curve over a finite field with elements, then the number of points of defined over the field with elements is , where and are complex conjugates with absolute value . The zeta function is : .
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1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
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In mathematics, Vojta's conjecture is a conjecture introduced by about heights of points on algebraic varieties over number fields. The conjecture was motivated by an analogy between diophantine approximation and Nevanlinna theory (value distribution theory) in complex analysis. It implies many other conjectures in Diophantine approximation, Diophantine equations, arithmetic geometry, and mathematical logic.
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In 2001, the proof of the local Langlands conjectures for GLn was based on the geometry of certain Shimura varieties. In the 2010s, Peter Scholze developed perfectoid spaces and new cohomology theories in arithmetic geometry over p-adic fields with application to Galois representations and certain cases of the weight-monodromy conjecture.
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In 2008, Ngô Bảo Châu proved the "fundamental lemma", which was originally conjectured by Langlands and Shelstad in 1983 and being required in the proof of some important conjectures in the Langlands program.Ngô Bảo Châu, "Le lemme fondamental pour les algèbres de Lie", Publications Mathématiques de l'IHES, t. 111 (2010), 1–169.
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The Discourse does not attempt to offer clear proofs of Galileo's conjectures, (unlike his Letters on Sunspots or Discourse on Floating Bodies); instead it focuses on arguments which undermine Grassi's contentions, forcing him to examine the phenomenon of comets more thoroughly and produce more substantial evidence for his argument that they are real.
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Mozart had health problems throughout his life, suffering from smallpox, tonsillitis, bronchitis, pneumonia, typhoid fever, rheumatism, and gum disease.For a thorough survey of Mozart's health history, with an M.D.'s proposed diagnoses, see . Whether these played any role in his demise cannot be determined. Conjectures as to what killed Mozart are numerous.
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Euler made the first conjectures about biquadratic reciprocity.Euler, Tractatus, § 456 Gauss published two monographs on biquadratic reciprocity. In the first one (1828) he proved Euler's conjecture about the biquadratic character of 2. In the second one (1832) he stated the biquadratic reciprocity law for the Gaussian integers and proved the supplementary formulas.
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Daurat is described by Eduard Fraenkel as "the true initiator of the study of Greek poetry in France". His pupils, including Joseph Justus Scaliger, were responsible for circulating the numerous textual conjectures made by Daurat, especially in Aeschylus' Agamemnon, which Daurat himself left unpublished.E. Fraenkel, Aeschylus: Agamemnon, volume 1, pp. 34–35.
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The French Wikipedia article conjectures the name comes from Jacques Bizard, but both Jacques Cartier and Jacques Bizard have not been named Saints. There is a street named "St. Jacques" in the city of Montreal dated 1672. There is also a land area called the Saint-Jacques Escarpment on the island of Montreal.
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His principal scholarly work is the Codex Fabrianus definitionum forensium (1609), a report of the decisions of his court organised after the Justinian Code. Favre's other research, conjectures about the Justinian code in which he endeavours to separate the Justinian insertions from the classical Roman texts, is still valued by scholars today.
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The simplest example (other than a point) is to take to be the projective line. The number of points of over a field with elements is just (where the "" comes from the "point at infinity"). The zeta function is just :. It is easy to check all parts of the Weil conjectures directly.
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The conjectures for (b) are called the Bloch–Kato conjectures for special values (for Spencer Bloch and Kazuya Kato – NB this circle of ideas is distinct from the Bloch–Kato conjecture of K-theory, extending the Milnor conjecture, a proof of which was announced in 2009). For the sake of greater clarity, they are also called the Tamagawa number conjecture, a name arising via the Birch–Swinnerton-Dyer conjecture and its formulation as an elliptic curve analogue of the Tamagawa number problem for linear algebraic groups.Matthias Flach, The Tamagawa Number Conjecture (PDF) In a further extension, the equivariant Tamagawa number conjecture (ETNC) has been formulated, to consolidate the connection of these ideas with Iwasawa theory, and its so-called Main Conjecture.
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Further analyzed by Maurice A. Finocchiaro, "Newton's Third Rule of Philosophizing: A Role for Logic in Historiography", Isis 65:1 (Mar. 1974), pp. 66–73. Similarly in Optics he conjectures that God created matter as "solid, massy, hard, impenetrable, movable particles", which were "...even so very hard as never to wear or break in pieces".
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All these conjectures can be formulated for more general fields in place of Q: algebraic number fields (the original and most important case), local fields, and function fields (finite extensions of Fp(t) where p is a prime and Fp(t) is the field of rational functions over the finite field with p elements).
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As one can postulate tests that could be applied, given enough time and space, then these ideas should be seen as scientific hypotheses. These are conjectures and perhaps can only be considered as social and maybe political philosophy; they may have implications for theology, or thealogy as Zell- Ravenheart and Isaac Bonewits put it.
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This is sometimes known as the extended Goldbach conjecture. The strong Goldbach conjecture is in fact very similar to the twin prime conjecture, and the two conjectures are believed to be of roughly comparable difficulty. The Goldbach partition functions shown here can be displayed as histograms, which informatively illustrate the above equations. See Goldbach's comet.
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Algebraic K-theory is a topological construction that assigns spaces (ultimately spectra) to rings, schemes, and other non-topological input. It has connections with important questions in high-dimensional topology, notably the conjectures of Novikov and Borel. Carlsson has proved, jointly with E. Pedersen and B. Goldfarb Novikov's conjecture for large classes of groups.
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The Bunyakovsky conjecture generalizes Dirichlet's theorem to higher-degree polynomials. Whether or not even simple quadratic polynomials such as (known from Landau's fourth problem) attain infinitely many prime values is an important open problem. The Dickson's conjecture generalizes Dirichlet's theorem to more than one polynomial. The Schinzel's hypothesis H generalizes these two conjectures, i.e.
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The Macdonald polynomials are now named after him. The Macdonald conjectures from 1982 also proved most influential. Macdonald was elected a Fellow of the Royal Society in 1979. He was an invited speaker in 1970 at the International Congress of Mathematicians (ICM) in Nice and a plenary speaker in 1998 at the ICM in Berlin.
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Apparently not finished. # Too Good to be True, with Henry Chettle and Richard Hathwaye, November 1601-January 1602. # Love Parts Friendship, with Henry Chettle, May 1602. E. K. Chambers conjectures that this play was published in 1605 as The Trial of Chivalry. # Merry as May be, with John Day and Richard Hathwaye, November 1602.
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In 2011, André received the Prix Paul Doistau–Émile Blutet of the Académie des Sciences. In 2015, he was elected as a Member of the Academia Europaea. He was an invited speaker at the 2018 International Congress of Mathematicians in Rio de Janeiro and gave a talk titled Perfectoid spaces and the homological conjectures.
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With Waldspurger, Moeglin completed the proof of the local Gan–Gross–Prasad conjecture for generic L-packets of representations of orthogonal groups in 2012. She did much work on the programme of James Arthur to classify automorphic representations of classical groups, and she was invited to present Arthur's ultimate solution to his conjectures at the Bourbaki seminar.
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Just as the André–Oort conjecture can be seen as a generalisation of the Manin–Mumford conjecture, so too the André–Oort conjecture can be generalised. The usual generalisation considered is the Zilber–Pink conjecture, an open problem which combines a generalisation of the André–Oort conjecture proposed by Richard Pink. and conjectures put forth by Boris Zilber...
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A third theory, promulgated by a San Diego news article about Xia's American descendants, conjectures that Xia was killed by nationalists for his Chinese translations of the Bible. Xia was replaced by Gao Fengchi as general manager and Zhang Yuanji as manager. Xia Ruifang is now regarded as "China's first publisher" who founded the country's first "modern publishing company".
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Approximate measurements have been calculated based on the surviving marble plinth, with the tops of the columns reaching 13 meters above the Rostra floor, excluding the statue heights. Although insufficient evidence remains to make similar conjectures about the columns at the eastern Rostra, it is reasonable to suppose that the eastern monument would have been of similar proportions.
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Other than his Conjectures and a poorly regarded genealogy (published posthumously), none of Clarke's antiquarian work survives. Feeling a conspiracy against him, Clarke stopped paying his dues to the Society of Antiquaries, and was finally kicked out in 1765. In 1762, he retired to Elm, serving as a vicar, where he remained for the rest of his life.
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Conversely, it is shown by Yoshifumi Tsuchimoto (2005), and independently by , that the Jacobian conjecture for 2N variables implies the Dixmier conjecture for N dimension. A self-contained and purely algebraic proof of the last implication is also given by who also proved in the same paper that these two conjectures is equivalent to Poisson conjecture.
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The Costa surface evolves from a torus, which is deformed until the planar end becomes catenoidal. Defining these surfaces on rectangular tori of arbitrary dimensions yields the Costa surface. Its discovery triggered research and discovery into several new surfaces and open conjectures in topology. The Costa surface can be described using the Weierstrass zeta and the Weierstrass elliptic functions.
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Mike and Ike is a brand of fruit-flavored candies that were first introduced in 1942 by the company Just Born, Inc. The origin of the candy's name remains unknown, but there are many conjectures. Mike and Ikes were originally all fruit flavored but now come in several different varieties which have been introduced over the years.
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This required ordination to the priesthood, but he requested a delay of five years; he was granted two. On 6 December 1437 he was also granted the privilege of holding more than one benefice at a time.Groër, p. 274, who conjectures that the source of the benefice was Cardinal Giuliano Cesarini, a close friend of Cardinal Castiglione.
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Ephyra () was a village of Sicyonia, in the north of the Peloponnese, mentioned by Strabo, along with the river Selleeis, as situated near Sicyon. Ludwig Ross conjectures that some ruins situated upon a hill about 20 minutes southeast of Suli represent the Sicyonian Ephyra,Ludwig Ross, Reisen im Peloponnes, p. 56. but modern writers say it is unlocated.
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Avidius Cassius, commandant of Legio III Gallica, returning veterans, was promoted to Consul. He claimed descent from the Seleucids of Macedonia. New coins and medals were issued in Macedonia on Alexandrian themes. Pratt conjectures that the manuscript in storage, by this time damaged and partly destroyed, was published finally, accounting for the previous lack of references to it.
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This requires the concept of the length of a module, denoted here by \ell_R, and the assumption that : \ell _R((R/P)\otimes(R/Q)) < \infty. If this idea were to work, however, certain classical relationships would presumably have to continue to hold. Serre singled out four important properties. These then became conjectures, challenging in the general case.
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Jacobi confirms Isherwood's story and further accuses Rolfe of performing various services to the Nazi regime. He even conjectures that Rolfe allowed Jews to deposit their money in his bank and then turned over their information to the Gestapo. Jacobi relates that it was not uncommon for Nazi leaders to reward such informants with valuable property, including art.
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Another Ottoman document, from c. 1821, mentions Vakhtang as khan of Imereti. Khomeriki conjectures that the Ottomans, vying with Russia for influence in western Caucasus, recognized the exiled Imeretian prince as a legitimate ruler of his country. During his exile, Vakhtang was in correspondence with anti-Russian opposition and sought allies in both Turkey and Iran.
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There exist numerous topologies on any given finite set. Such spaces are called finite topological spaces. Finite spaces are sometimes used to provide examples or counterexamples to conjectures about topological spaces in general. Any set can be given the cofinite topology in which the open sets are the empty set and the sets whose complement is finite.
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It is unclear whether this representation means that sacred trees might be replaced with artificial or pictorial ones. The apertures were paved over in the time of Augustus, an event that may explain Ovid's vestigia.Rabun Taylor, "Roman Oscilla: An Assessment," in RES: Anthropology and Aesthetics 48 (2005), pp. 91–92. Taylor conjectures that oscilla were hung from such trees.
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Further such examples arise in Zariski surface theory. He also conjectures that the Kodaira vanishing theorem is false for surfaces in characteristic p. In the third paper, he gives an example of a normal surface for which Kodaira vanishing fails. The first example of a smooth surface for which Kodaira vanishing fails was given by Michel Raynaud in 1978.
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Furniture expert Luke Beckerdite calls Harding "one of the most important carvers active in Philadelphia during the first half of the eighteenth century." He conjectures that the carver Nicholas Bernard either was trained or influenced by him.Luke Beckerdite and Alan Miller, "A Table's Tale: Craft, Art, and Opportunity in Eighteenth-Century Philadelphia," American Furniture (Chipstone Foundation, 2004).
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Anthony Wood (Athenæ Oxon. i. 309) conjectures that he was born near Caversham, where his eldest brother Thomas had lands of inheritance, and died in 6 Edward VI, but was descended from the Brighams of Brigham in Yorkshire. Now one Anthony Brigham was made bailiff of the king's manor of Caversham in 1543 (Pat. 35 Hen.
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In empirical studies of three-dimensional problem solving, Bryan Lawson found architects employed solution-focused cognitive strategies, distinct from the problem-focused strategies of scientists.Lawson, Bryan. 1979. "Cognitive Strategies in Architectural Design". Ergonomics, 22, 59–68 Nigel Cross suggests that 'Designers tend to use solution conjectures as the means of developing their understanding of the problem'.
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In the 1930s G. A. Hedlund proved that the horocycle flow on a compact hyperbolic surface is minimal and ergodic. Unique ergodicity of the flow was established by Hillel Furstenberg in 1972. Ratner's theorems provide a major generalization of ergodicity for unipotent flows on the homogeneous spaces of the form Γ \ G, where G is a Lie group and Γ is a lattice in G. In the last 20 years, there have been many works trying to find a measure-classification theorem similar to Ratner's theorems but for diagonalizable actions, motivated by conjectures of Furstenberg and Margulis. An important partial result (solving those conjectures with an extra assumption of positive entropy) was proved by Elon Lindenstrauss, and he was awarded the Fields medal in 2010 for this result.
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In May 2020 it was announced that he would be assuming the title chaire de combinatoire at the College de France beginning in October 2020, though he intends to continue to reside in Cambridge and maintain a part-time affiliation at the University, as well enjoy the privileges of his life Fellowship of Trinity College. Gowers initially worked on Banach spaces. He used combinatorial tools in proving several of Stefan Banach's conjectures in the subject, in particular constructing a Banach space with almost no symmetry, serving as a counterexample to several other conjectures.1998 Fields Medalist William Timothy Gowers from the American Mathematical Society With Bernard Maurey he resolved the "unconditional basic sequence problem" in 1992, showing that not every infinite-dimensional Banach space has an infinite- dimensional subspace that admits an unconditional Schauder basis.
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The objectives of experimental mathematics are "to generate understanding and insight; to generate and confirm or confront conjectures; and generally to make mathematics more tangible, lively and fun for both the professional researcher and the novice". The uses of experimental mathematics have been defined as follows: #Gaining insight and intuition. #Discovering new patterns and relationships. #Using graphical displays to suggest underlying mathematical principles.
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The practice is found in other sources in a civilian context.Rüpke, The Roman Calendar, p. 28, citing Juvenal 6.442–443 and Livy 26.5.9. Jörg Rüpke conjectures that the tubae were played monthly "to fortify the waning moon (Luna)", one nundinal cycle after the full moon of the Ides, since the Roman calendar was originally lunar.Rüpke, The Roman Calendar, p. 28.
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In number theory, Shanks is best known for his book Solved and Unsolved Problems in Number Theory. Hugh Williams described it as "a charming, unconventional, provocative, and fascinating book on elementary number theory." It is a wide-ranging book, but most of the topics depend on quadratic residues and Pell's equation. The third edition contains a long essay on "judging conjectures".
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Shefali Chandan writing in Jano conjectures that the emotions behind the circumstances that led to the ethnic cleansing of Bellingham in 1907, in which white mobs went door to door to locate Indian immigrants and forced their expulsion, resulting in the entire community numbering about 200 leaving the town for good, found expression in the feature article written less than a year ago.
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However, the strong and sharp three exponentials conjectures are implied by their four exponentials counterparts, bucking the usual trend. And the three exponentials conjecture is neither implied by nor implies the four exponentials conjecture. The three exponentials conjecture, like the sharp five exponentials conjecture, would imply the transcendence of eπ² by letting (in the logarithmic version) λ1 = iπ, λ2 = −iπ, and γ = 1\.
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Euler's interest in number theory can be traced to the influence of Christian Goldbach, his friend in the St. Petersburg Academy. A lot of Euler's early work on number theory was based on the works of Pierre de Fermat. Euler developed some of Fermat's ideas and disproved some of his conjectures. Euler linked the nature of prime distribution with ideas in analysis.
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He made a series of conjectures on class field theory. The concepts were highly influential, and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol of local class field theory. Results were mostly proved by 1930, after work by Teiji Takagi.This work established Takagi as Japan's first mathematician of international stature.
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Murray conjectures that people today do not accept Aristotle's statement about character and plot because to modern people, the most memorable things about tragedy plays are often the characters.Murray (1916), p. 52. However, Murray does concede that Aristotle is correct in that "[t]here can be no portrayal of character [...] without at least a skeleton outline of plot".Murray (1916), p. 53.
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It is also known that a group of cohomological dimension 2 has a 3-dimensional Eilenberg−MacLane space. In 1997, Mladen Bestvina and Noel Brady constructed a group G so that either G is a counterexample to the Eilenberg–Ganea conjecture, or there must be a counterexample to the Whitehead conjecture; in other words, not both conjectures can be true.
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Steven G. Krantz ("Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical", American Mathematical Society, 2002) also lists some conjectures. However, Cartan and Ferrand quote Henri Baruk, who was the medical head of the asylum where Bloch was confined. Bloch told Baruk that the murders were a eugenic act, in order to eliminate branches of his family affected by mental illness.
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The notion of conjectures has maintained a long history in the Industrial Organization theory ever since the introduction of Conjectural Variations Equilibria by Arthur Bowley in 1924Bowley, A. L. (1924). The Mathematical Groundwork of Economics, Oxford University Press. and Ragnar Frisch (1933)Frisch R. 1951 [1933]. Monopoly – Polypoly – The concept of force in the economy, International Economic Papers, 1, 23–36.
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A Passage to Infinity : Medieval Indian Mathematics from Kerala and Its Impact is a book by George Gheverghese Joseph chronicling the social and mathematical origins of the Kerala school of astronomy and mathematics. The book discusses the highlights of the achievements of Kerala school and also analyses the hypotheses and conjectures on the possible transmission of Kerala mathematics to Europe.
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The origin of the name Lygourio is unknown and there are only conjectures. According to an opinion, the name Lygourio derives from the corruption of the word Elaiogyrion that means olive factory. In antiquity, in this place there was the ancient city Lessa which was referred by Pausanias. During 4th century B.C. near Lessa was located the sanctuary Asklipieio of Epidaurus.
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After 1581, the procedures took place before either the Crown Tribunal or the Lithuanian Tribunal. Norman Davies conjectures that this practice was among the factors leading to the establishment of a unique Polish practice of heraldic families (, "heraldic clans", by Davies). It is also asserted that this practice led to development of extensive personal archiving and archive research among Polish nobility.
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He stayed at Cambridge, working on finite groups. Norton was one of the authors of the ATLAS of Finite Groups. He constructed the Harada–Norton group and in 1979 together with John Conway proved there is a connection between the Monster group and the j-function in number theory. They dubbed this "monstrous moonshine", and made some conjectures later proved by Richard Borcherds.
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46), and appears to have been the first who discovered the true cause of the yearly inundations of the Nile. (Diod. i. 41.) An Agatharchides, of Samos, is mentioned by Plutarch, as the author of a work on Persia, and one περὶ λίθων. J.A. Fabricius, however, conjectures that the true reading is Agathyrsides, not Agatharchides. (Dodwell in Hudson's Geogr. Script.
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In mathematics, the Quillen–Lichtenbaum conjecture is a conjecture relating étale cohomology to algebraic K-theory introduced by , who was inspired by earlier conjectures of . and proved the Quillen–Lichtenbaum conjecture at the prime 2 for some number fields. Voevodsky, using some important results of Markus Rost, has proved the Bloch–Kato conjecture, which implies the Quillen–Lichtenbaum conjecture for all primes.
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From 1969 to 1972 he was a professor ordinarius at the Goethe-Universität Frankfurt am Main. From 1972 he was a professor ordinarius at the University of Mannheim, where he retired in 2003 as professor emeritus. His research deals with algebraic and arithmetic geometry and non-archimedean function theory. He wrote with Eberhard Freitag a textbook on the Weil conjectures and étale cohomology.
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A Thousand Barrels a Second: The Coming Oil Break Point and the Challenges Facing an Energy Dependent World is a 2007 book by Canadian energy economist and columnist Peter Tertzakian that describes the multiple pressures forcing an upending of oil’s dominant role in the global energy supply mix and conjectures about how economic, social and technological innovation will drive the inevitable adjustment process.
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The Cournot–Nash model is the simplest oligopoly model. The model assumes that there are two "equally positioned firms"; the firms compete on the basis of quantity rather than price and each firm makes an "output of decision assuming that the other firm's behavior is fixed."This statement is the Cournot conjectures. Kreps, D.: A Course in Microeconomic Theory page 326.
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Nancy Van Norman Baer conjectures that it developed from a solo called Fear designed and danced by Nijinsky in Kiev in 1919, and inspired by the dynamic movements of a Samurai warrior. In discussion, Nijinska mentions a Japanese influence on her early choreographic works, one source being a collection of prints purchased in 1911.Baer (1986). Guignol de Lyon. ;iv.
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"Characteristically, Nijinska would have refused to become involved with politics or intrigue."Baer (1986), p.66 (two quotes re dismissal, 1939 World's Fair in NY). From interviews Baer heard of conjectures that Nijinska was dismissed because of her life-long familiarity with Russia, now Soviet Russia. [In September 1939 in alliance with the Nazis the Soviets would invade Poland.]Cf.
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Evidence indicates that there was 6 to 8.5 km long Diolkos paved trackway, which transported boats across the Isthmus of Corinth in Greece from around 600 BC.Verdelis, Nikolaos: "Le diolkos de L'Isthme", Bulletin de Correspondance Hellénique, Vol. 81 (1957), pp. 526–529 (526)Cook, R. M.: "Archaic Greek Trade: Three Conjectures 1. The Diolkos", The Journal of Hellenic Studies, Vol.
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Azbel was a theoretical physicist. His areas of study included the quantum physics of electrons in metals, and he made the first prediction of cyclotron resonance in metals, now widely known as the Azbel-Kaner resonance. In an important 1964 article, Azbel made conjectures about the nature of the Harper spectrum which contributed to the discovery of the Hofstadter butterfly in 1974.
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Oria was a prosperous locale before the Muslim conquest; Barbara Kreutz thus conjectures that Matera resisted Louis while Oria welcomed him: the former thus was razed.Kreutz, 172, n26. The capture of the cities is referred to both in Erchempert and Lupus Protospatharius. This may have severed communications between Bari and Taranto, the other pole of Muslim power in southern Italy.
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He has been on the Yale University faculty since 1963, and became emeritus in 1996. He introduced the Tamagawa numbers, which are measures for algebraic groups over algebraic number fields. These measures play an essential role in conjectures on arithmetic algebraic geometry, such as those of Spencer Bloch and Kazuya Kato. Tamagawa's doctoral students included Doris Schattschneider and Audrey Terras.
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In the church of St. George in Domeniko, which occupies the site of the ancient Cyretiae, Leake noticed an inscribed stone, on which the name of Apollodorus is followed by a word beginning ΕΡΗ, which he conjectures with much probability may be the place called Eritium by Livy.Leake, Northern Greece, vol. iv. pp. 310, 313. Modern scholars treat Eritium as unlocated.
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194 and that he thought that most English words are traceable to Gaelic,Anatoly Liberman (2009), 'THE ETYMOLOGY OF 'BRAIN' AND COGNATES', Nordic Journal of English Studies, p. 46 which is certainly not true. Liberman also described MacKay's 1877 dictionary as "full of the most fanciful conjectures", noting that MacKay "was hauled over the coals by his contemporaries and never taken seriously".
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Miller argues that the rapid increases in brain size would have occurred by a positive feedback loop resulting in a Fisherian runaway selection for larger brains. Tor Nørretranders, in The Generous Man conjectures how intelligence, musicality, artistic and social skills, and language might have evolved as an example of the handicap principle, analogously with the peacock's tail, the standard example of that principle.
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Still, philosophical perspectives, conjectures, and presuppositions, often overlooked, remain necessary in natural science.Hugh G Gauch Jr, Scientific Method in Practice (Cambridge: Cambridge University Press, 2003), pp 71–73 Systematic data collection, including discovery science, succeeded natural history, which emerged in the 16th century by describing and classifying plants, animals, minerals, and so on. Today, "natural history" suggests observational descriptions aimed at popular audiences.
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The Langlands conjectures imply, very roughly, that if G is a reductive algebraic group over a local or global field, then there is a correspondence between "good" representations of G and homomorphisms of a Galois group (or Weil group or Langlands group) into the Langlands dual group of G. A more general formulation of the conjectures is Langlands functoriality, which says (roughly) that given a (well behaved) homomorphism between Langlands dual groups, there should be an induced map between "good" representations of the corresponding groups. To make this theory explicit, there must be defined the concept of L-homomorphism of an L-group into another. That is, L-groups must be made into a category, so that 'functoriality' has meaning. The definition on the complex Lie groups is as expected, but L-homomorphisms must be 'over' the Weil group.
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In number theory, the Stark conjectures, introduced by and later expanded by , give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When K/k is an abelian extension and the order of vanishing of the L-function at s = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units. and Cristian Dumitru Popescu gave extensions of this refined conjecture to higher orders of vanishing.
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Notwithstanding this (or conjectures that the balloon might have landed in the Spanish Sahara) no confirmed trace of Light Heart or Gatch was ever found, after the Ore Meridian's reported sighting on 21 February. The US Department of Defense and the Spanish Army conducted extensive search operations both at sea off West Africa and in the Spanish Sahara. Search operations were called off in mid-March 1974.
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Karl Popper,Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, 1963. ("Popper professes to be anti- conventionalist, and his commitment to the correspondence theory of truth places him firmly within the realist's camp.") and Gustav BergmannGustav Bergmann, Logic and Reality, Madison: University of Wisconsin Press, 1964; Gustav Bergmann, Realism: A Critique of Brentano and Meinong, Madison: University of Wisconsin Press, 1967. espoused metaphysical realism.
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Epiphanius states that little is known of the sect, and conjectures that the name either comes from them possibly holding a belief that angels created the world, or else that they believed that they were so pure as to be angels. Citing Epiphanius, and expanding, St. Augustine supposes they are called Angelici because of an extravagant worship of angels, and such as tended to idolatry.
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Victor Ufnarovski and Bo Åhlander have detailed the function's connection to famous number-theoretic conjectures like the twin prime conjecture, the prime triples conjecture, and Goldbach's conjecture. For example, Goldbach's conjecture would imply, for each k > 1 the existence of an n so that D(n) = 2k. The twin prime conjecture would imply that there are infinitely many k for which D^2(k) = 1.
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Vladimir Alexandrovich Voevodsky (; , 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He is also known for the proof of the Milnor conjecture and motivic Bloch–Kato conjectures and for the univalent foundations of mathematics and homotopy type theory.
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In 2009, he solved together with Michael Hill and Michael Hopkins the Kervaire invariant 1 problem for large dimensions. Ravenel has written two books, the first on the calculation of the stable homotopy groups of spheres and the second on the Ravenel conjectures, colloquially known among topologists respectively as the green and orange books (though the former is no longer green, but burgundy, in its current edition).
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Bernhard Riemann made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he investigated the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.
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A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. described the abc conjecture as "the most important unsolved problem in Diophantine analysis". The abc conjecture originated as the outcome of attempts by Oesterlé and Masser to understand the Szpiro conjecture about elliptic curves,. which involves more geometric structures in its statement than the abc conjecture.
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Thacker conjectures that these were Dutch specialists. The lock was rebuilt of masonry in 1870. Originally the lock was attended (or not - according to some accounts) by the miller, but there is reference to a (deserted) lock house in 1865.Fred. S. Thacker The Thames Highway: Volume II Locks and Weirs 1920 - republished 1968 David & Charles The present lock keeper's house dates from 1913.
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Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.
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Little is known about this painter. He is supposed to have been a pupil of Antonio of Murano, though conjectures by critics vary about him and his work. The probability is that he did little alone, but was one of the assistants in the Vivarini workshop. His use of tempera is similar to the school of Murano, flat, light, and with little or no shade.
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His corrections are often hasty and false, but a surprisingly large proportion of them have since received confirmation from manuscripts, and, though his merits as a Grecian lie mainly in his conjectures, his realism is felt in this sphere also; his German translations especially show more freedom and practical insight, more feeling for actual life, than is common with the scholars of that age.
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I. Rassegna di Etruscologia by A. Neppi Modona, the first page of which is found at . Picking up this theme, Bonfante (2002) states:Page 3. An additional elaboration conjectures that the Etruscans werePallottino, page 52, who says that he relies on Alfredo Trombetti and Giacomo Devoto. In 1942, the Italian historian Massimo Pallottino published a book entitled The Etruscans (which would be released in English in 1955).
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The Whitehead conjecture is equivalent to the conjecture that every sub- presentation of an aspherical presentation is aspherical. In 1997, Mladen Bestvina and Noel Brady constructed a group G so that either G is a counterexample to the Eilenberg–Ganea conjecture, or there must be a counterexample to the Whitehead conjecture; in other words, it is not possible for both conjectures to be true.
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Hardgrave conjectures that the Nadars of Southern Travancore migrated there from Tirunelveli in the 16th century after the invasion of Tirunelveli by the Raja of Travancore. Like their Tirunelveli counterparts, the Nadars of Travancore were mostly palmyra climbers. However, a significant number of Nadars were subtenants to Nair or Vellalar landlords. These aristocratic Nadars called themselves Nadans and some of them had direct control over their lands.
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According to Jacob Barth, who was lecturer in Hebrew at the Hildesheimer Rabbinical Seminary, al- comes directly from the Arabic negating particle, lā. He conjectures that lā became al- through a process of metathesis. That is to say, the lām and the alif swapped positions. It is noteworthy that the negation denoted by lā and the definiteness denoted by al- are in stark contrast to each other.
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"Breslin is Given 2-Week Suspension". The New York Times. Author and former FBI agent Robert K. Ressler has stated that Breslin "baited Berkowitz and irresponsibly contributed to the continuation of his murders" by trying to sell sensationalist newspapers. In Ressler's book Whoever Fights Monsters, Ressler condemns Breslin and the media for their involvement in encouraging serial killers by directing their activity with printed conjectures.
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In the first version of the AKS primality test paper, a conjecture about Sophie Germain primes is used to lower the worst case complexity from to . A later version of the paper is shown to have time complexity which can also be lowered to using the conjecture. Later variants of AKS have been proven to have complexity of without any conjectures or use of Sophie Germain primes.
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PrimeGrid is a volunteer distributed computing project which searches for very large (up to near-world-record size) prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing (BOINC) platform. PrimeGrid offers a number of subprojects for prime-number sieving and discovery. Some of these are available through the BOINC client, others through the PRPNet client.
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The conjecture was proposed by William , and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print. Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery.
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This place has been identified by some Assyriologists with the land of Mash, a district between Judea and Babylonia, and the traces of nomadic or seminomadic life and thought found in and give some support to the hypothesis. Heinrich Graetz, followed by Bickell and Cheyne, conjectures that the original reading is המשל ("Ha-Moshel," = "the collector of proverbs"). The true explanation is still uncertain.
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Dwork received his Ph.D. at Columbia University in 1954 under direction of Emil Artin (his formal advisor was John Tate); Nick Katz was one of his students.. For his proof of the first part of the Weil conjectures, Dwork received (together with Kenkichi Iwasawa) the Cole Prize in 1962.Memorial article – by Nick Katz and John Tate. He received a Guggenheim Fellowship in 1964.
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These pumps allow the inside of the embryo to fill with blastocoelic fluid, which supports the further growth of life. The blastomere is considered totipotent. That is, blastomeres are capable of developing from a single cell into a fully fertile adult organism. This has been demonstrated through studies and conjectures made with mouse blastomeres, which have been accepted as true for most mammalian blastomeres as well.
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Weil realized that to prove such a connection one needed a new cohomology theory, but neither he nor any other expert saw how to do this until such a theory was found by Grothendieck. This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.
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The ground of his objection does not appear; Stoughton conjectures that the other congregation was of the independent sort. His preaching was unwelcome. The citizens walked up and down the cloisters all sermon-time, and the constables had to be called in. About this time Burges invested his property in the purchase of alienated church lands, including the manor of Wells and the deanery which he rebuilt.
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In topology, the Tychonoff plank is a topological space defined using ordinal spaces that is a counterexample to several plausible-sounding conjectures. It is defined as the topological product of the two ordinal spaces [0,\omega_1] and [0,\omega], where \omega is the first infinite ordinal and \omega_1 the first uncountable ordinal. The deleted Tychonoff plank is obtained by deleting the point \infty = (\omega_1,\omega).
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Thus, the physics postulations and conjectures made by Dumbleton and his Oxford contemporaries were primarily done without any application of physical experimentation. Dumbleton, along with the other three Merton philosophers, received the moniker 'Calculators' for their adherence to mathematics and logical disputation when solving philosophical and theological problems.Robert Pasnau (ed.) and Christina Van Dyke (2nd ed.). The Cambridge History of Medieval Philosophy (Vol. II).
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While some books supporting similar libertarian and anarcho-capitalist views offer support in terms of morality or natural rights, Friedman (although he explicitly denies being a utilitarian)Second Edition, pg. 165 here argues largely in terms of the effects of his proposed policies. Friedman conjectures that anything done by government costs at least twice as much as a privately provided equivalent.Second edition, p. 85.
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This is notable because no similar structures from this period, North of the Alps have yet been found. Because no other information about the use of the building has been passed down, only conjectures can be offered as to the function of the pool. One possibility is that the building was used for recreation, and that the water storage area was a swimming pool.
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The classical, geometric theory of Solomon Lefschetz was recast in purely algebraic terms, in SGA7. This was for the requirements of its application in the context of l-adic cohomology; and eventual application to the Weil conjectures. There the definition uses derived categories, and looks very different. It involves a functor, the nearby cycle functor, with a definition by means of the higher direct image and pullbacks.
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In 1992, he computed all solutions to the inverse Fermat equation. The Cohen–Lenstra heuristics is a set of precise conjectures about the structure of class groups of quadratic fields that are partially named after him. Three of his brothers, Arjen Lenstra, Andries Lenstra, and Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is the former director of the Netherlands Centrum Wiskunde & Informatica (CWI).
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The conjecture was proposed by , and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print. Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery.
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In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them over the next few years. Intersection cohomology was used to prove the Kazhdan–Lusztig conjectures and the Riemann–Hilbert correspondence. It is closely related to L2 cohomology.
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Vanamali Mishra composed a refutation of the Bramhananda Saraswati's work and the controversy eventually died down. Stoker conjectures that the strong responses Vyasatirtha received were due to the waning power of Advaita in the Vijayanagara empire coupled by the fact that as an administrator of the mathas, Vyasatirtha enjoyed royal patronage. Vyasatirtha's disciple Vijayendra Tirtha has authored a commentary on the Nyayamruta called Laghu Amoda.
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Theophilus Lindsey, a rector at Catterick, Yorkshire, became one of Priestley's few friends in Leeds, of whom he wrote: "I never chose to publish any thing of moment relating to theology, without consulting him."Priestley, Autobiography, 98; see also Schofield (1997), 163. Although Priestley had extended family living around Leeds, it does not appear that they communicated. Schofield conjectures that they considered him a heretic.
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If Heath-Brown's conjecture is true, the problem is decidable. In this case, an algorithm could correctly solve the problem by computing n modulo 9, returning false when this is 4 or 5, and otherwise returning true. Heath-Brown's research also includes more precise conjectures on how far an algorithm would have to search to find an explicit representation rather than merely determining whether one exists.
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This work led in turn, in the winter of 1966–67, to the now well known conjectures making up what is often called the Langlands program. Very roughly speaking, they propose a huge generalization of previously known examples of reciprocity, including (a) classical class field theory, in which characters of local and arithmetic abelian Galois groups are identified with characters of local multiplicative groups and the idele quotient group, respectively; (b) earlier results of Martin Eichler and Goro Shimura in which the Hasse–Weil zeta functions of arithmetic quotients of the upper half plane are identified with -functions occurring in Hecke's theory of holomorphic automorphic forms. These conjectures were first posed in relatively complete form in a famous letter to Weil, written in January 1967. It was in this letter that he introduced what has since become known as the -group and along with it, the notion of functoriality.
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In mathematics, the André–Oort conjecture is an open problem in Diophantine geometry, a branch of number theory, that builds on the ideas found in the Manin–Mumford conjecture, which is now a theorem. A prototypical version of the conjecture was stated by Yves André in 1989. and a more general version was conjectured by Frans Oort in 1995.. The modern version is a natural generalisation of these two conjectures.
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Searchlight view: Expectations and predispositions turn into conjectures that act like a searchlight and lead to observations (not shown). Popper proposed to replace the bucket view of science with what he called the searchlight view of science. In that view, Popper wrote, there is no reason why any methodology should work. It is easy, Popper said, to imagine universes where no methodology can work or even only exist.
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Bold hypothesis or bold conjecture is a concept in the philosophy of science of Karl Popper, first explained in his debut The Logic of Scientific Discovery (1935) and subsequently elaborated in writings such as Conjectures and Refutations: The Growth of Scientific Knowledge (1963). The concept is nowadays widely used in the philosophy of science and in the philosophy of knowledge. It is also used in the social and behavioural sciences.
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18, 19 and 20. These were derived from Inca sources. The Spanish histories of Jerónimo de Vivar, Crónica y relación copiosa y verdadera de los reinos de Chile and Vicente Carvallo y Goyeneche, Descripción Histórico Geografía del Reino de Chile, Tomo I, Capítulo I mention it also. Historian Osvaldo Silva conjectures instead the battle occurred much after Tupac Inca Yupanqui's conquest of northern Chile with 1532 being a possible date.
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"Britain's Balance of Payments in the Century before Waterloo: New Estimates, Controlled Conjectures", Economic History Review, February 1995, pp. 46 67. “The Role of Assignats during the French Revolution: Evil or Rescuer?” (with Francois Crouzet), Journal of European Economic History, April 1995, pp. 7‑40. “Did Foreign Capital Flows Finance the Industrial Revolution? A reply”, Economic History Review, February 1997 "Mercantilism" Oxford Encyclopedia of Economic History, Oxford University Press, 2003, vol.
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913) conjectures it is because of the conflict between the manuscripts, Ughelli preferring the reading of the Vatican manuscript, which gives the diocese as "Avellanensis". But then Mansi, who endorses the judgment of Ughelli in omitting Godefridus from the list of bishops of Atella, asks, "Quae haec sedes?" (What is this diocese?) [There is no diocese of Avella or Avellana. Paul Fridolin Kehr accepts the manuscript reading of "Atellanensis" (pp.
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The Sumerian king list is an ancient text in the Sumerian language listing kings of Sumer, including several foreign dynasties. Some of the earlier dynasties may be mythical; the historical record does not open up before the first archaeologically attested ruler, Enmebaragesi (c. 2600 BCE), while conjectures and interpretations of archaeological evidence can vary for earlier events. The best-known dynasty, that of Lagash, is omitted from the kinglist.
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The Iitaka conjecture states that the Kodaira dimension of a fibration is at least the sum of the Kodaira dimension of the base and the Kodaira dimension of a general fiber; see for a survey. The Iitaka conjecture helped to inspire the development of minimal model theory in the 1970s and 1980s. It is now known in many cases, and would follow in general from the minimal model and abundance conjectures.
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Based on certain conjectures of Miguel Catalan about rotational dynamics, his disciple and biographer Gabriel Barceló, years later, developed the Theory of Dynamic Interactions. The Government of the Comunidad de Madrid (Autonomous Region of Madrid) awards the Miguel Catalán Investigation Award in Science since 2005, to honor Catalán's memory. The award recognizes outstanding life accomplishments in research and science. The award winners each receive a medal, a citation and 42,000 Euros.
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They were soon assured by the widening channel that they were correct in their conjectures. In order to make progress upstream, Donelson rigged his boat, the Adventure, with a small sail made out of a sheet. To prevent ill effects from any sudden gust of wind, a man was stationed at each lower corner of this sail with instructions to loosen it when the breeze became too strong.
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Lionelli was born to a Slovene mother and an Italian father in the town of Sveti Križ (now Vipavski Križ) in the Vipava Valley, County of Gorizia. A recent theory conjectures that he was actually born as Ivan Hrobat, the illegitimate son of Katarina Hrobat and a nobleman of the Lanthieri family, and that the surname Lionelli was purchased to avoid embarrassment.Kmecl, Matjaž, Marjan Krušič, & Kazimir Rapoša. 1997. Zakladi Slovenije.
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The Tenure of Kings and Magistrates is a book by John Milton, in which he defends the right of people to execute a guilty sovereign, whether tyrannical or not. In the text, Milton conjectures about the formation of commonwealths. He comes up with a kind of constitutionalism but not an outright anti- monarchical argument. He gives a theory of how people come into commonwealths and come to elect kings.
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In 1982, he was appointed the McVickar Professor of Political Economy at Columbia. During the early 1980s, he wrote an introductory textbook synthesizing contemporary economics knowledge. The book, Political Economy, was published in 1985 but had limited classroom adoption. In the 1980, Phelps increased collaboration with European universities and institutions, including Banca d'Italia (where he spent most of his 1985–86 sabbatical and Observatoire français des conjectures économiques (OFCE).
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Conjectures on the identities of the artists have been many. Lhote tells that some have believed them to belong to the black populations ancestral to the Mandinka and the Hausas. But the Tuareg, the Egyptians and the ancestors of the Berbers have also been invoked. They have also been thought to have been the Cro-Magnons, the husbandmen and farmers of Asiatic origin, the Harratines, the Proto-Libyans and the Bushmen.
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Marine Lieutenant Hamilton, Midshipman Campbell, Midshipman Byron, and Captain Cheap were the only survivors.Byron, John (1768), pp. 71–124 Before handing over the English to Spanish authorities Martín Olleta's party stopped somewhere south of Chiloé Island to hid all iron objects, likely to avoid have them confiscated. Scholar Ximena Urbina conjectures that Martín Olleta must have lived close to the Spanish and heard from other natives of the wreckage.
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In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29, 1976 in a letter to David Kazhdan as an analogue of the usual Fourier transform. It was used by Gérard Laumon to simplify Deligne's proof of the Weil conjectures.
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Beneath the second 1 of that date a 2 is clearly visible, indicating it was executed in 1612, 8 years after Oxford's death, when Hamersley was 47 years old. Above the date is written aetatis suae.47 (aged 47). He had not, at that time, been granted his coat of arms, and art historian William Pressly conjectures that they were either included in anticipation of the honour, or painted in later.
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The complex is oriented with a north-south axis, but with an accuracy deviation of about 11°. One notable feature of this complex is an inner wall known as "White Wall" made out of limestone covered with red mason's lines and graffiti. It remain unknown whether Sekhemkhet's complex would include any mortuary temples or other features also found in Djoser's complex. Its unfinished state presents difficulty for such conjectures.
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They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most of the named 1-variable orthogonal polynomials as special cases. Koornwinder polynomials are Macdonald polynomials of certain non-reduced root systems. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.
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Based on legend, some people said that the Lumbee tribe, based in North Carolina, were descendants of the Croatan and survivors of the Lost Colony of Roanoke Island. For over a hundred years, historians and other scholars have been examining the question of Lumbee origin. Although there have been many explanations and conjectures, two theories persist. In 1885, Hamilton McMillan, a local historian, and state legislator proposed the "Lost Colony" theory.
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There are conjectures about whether del Ferro worked on a solution to the cubic equation as a result of Luca Pacioli's short tenure at the University of Bologna in 1501–1502. Pacioli had previously declared in Summa de arithmetica that he believed a solution to the equation to be impossible, fueling wide interest in the mathematical community. It is unknown whether Scipione del Ferro solved both cases or not.
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Carlo Rovelli, "The First Scientist, Anaximander and his Legacy" (Yardley: Westholme, 2011).Daniel W. Graham, "Explaining the Cosmos: The Ionian Tradition of Scientific Philosophy" (Princeton, NJ: Princeton University Press, 2006). Karl Popper calls this idea "one of the boldest, most revolutionary, and most portentous ideas in the whole history of human thinking."Karl Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge" (New York: Routledge, 1998), pg 186.
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And let us demand the same of others. Let us explain that studying cultural psychology is no joke, not something to do at odd moments or among other things, and not grounds for every new person’s own conjectures". In: 1930,Cf. self-criticism of 1930: "In the process of development, and in the historical development in particular, it is not so much the functions which change (these we mistakenly studies before).
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The decomposition theorem, a far- reaching extension of the hard Lefschetz theorem decomposition, requires the usage of perverse sheaves. Hodge modules are, roughly speaking, a Hodge- theoretic refinement of perverse sheaves. The geometric Satake equivalence identifies equivariant perverse sheaves on the affine Grassmannian Gr_G with representations of the Langlands dual group of a reductive group G - see . A proof of the Weil conjectures using perverse sheaves is given in .
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He has constructed various beautiful examples of topological spaces, e.g. an acyclic, 3-dimensional continuum which admits a fixed point free homeomorphism onto itself; also 2-dimensional, contractible polyhedra which have no free edge. His topological and geometric conjectures and themes stimulated research for more than half a century. Borsuk received his master's degree and doctorate from Warsaw University in 1927 and 1930, respectively; his Ph.D. thesis advisor was Stefan Mazurkiewicz.
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The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function. One can then ask the same question about the zeros of these L-functions, yielding various generalizations of the Riemann hypothesis.
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It is difficult to determine what methodology the Oxford 'Calculators' used when they were conjecturing and postulating theorems by way of abstraction (i.e., without empirical investigation). This criticism is not expressly made toward Dumbleton's conjectures but more broadly aimed at the methodology of the whole group of Mertonian physicists. One suggestion is that they may have been trying to create a mathematical picture of the Aristotelian world-view.
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Conjectures of a Guilty Bystander p. 285. Eastern traditions, for Merton, were mostly untainted by this type of thinking and thus had much to offer in terms of how to think of and understand oneself. Having studied the Desert Fathers and other Christian mystics, Merton found many parallels between the language of these Christian mystics and the language of Zen philosophy.Solitary Explorer: Thomas Merton's Transforming Journey p. 105.
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He collaborated with Pierre Deligne on the developing a motivic interpretation of Don Zagier's polylogarithm conjectures. From the early 1990s onwards, Beilinson worked with Vladimir Drinfeld to rebuild the theory of vertex algebras. After some informal circulation, this research was published in 2004 in a form of a monograph on chiral algebras. This has led to new advances in conformal field theory, string theory and the geometric Langlands program.
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Other results and conjectures involving graph minors include the graph structure theorem, according to which the graphs that do not have H as a minor may be formed by gluing together simpler pieces, and Hadwiger's conjecture relating the inability to color a graph to the existence of a large complete graph as a minor of it. Important variants of graph minors include the topological minors and immersion minors.
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Yum-Tong Siu (; born May 6, 1943 in Guangzhou, China) is the William Elwood Byerly Professor of Mathematics at Harvard University. Siu is a prominent figure in the mathematics of several complex variables. His research interests involve the intersection of complex variables, differential geometry, and algebraic geometry. He has resolved various conjectures by applying estimates of the complex Neumann problem and the theory of multiplier ideal sheaves to algebraic geometry.
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Fine, p. 225 Pavlov, however, conjectures that Aldimir's domain dates to 1298, long after George's reign. Unlike the neighbouring principality of Smilets at Kopsis, Aldimir remained loyal to the Bulgarian government and ensured that his domain retained its ties to the capital Tarnovo. Fine describes Aldimir's lands as spanning the region from modern Sliven in the east to Kazanlak or Karlovo in the west, just south of the Balkan Mountains.
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In the years since Boyd's articles appeared, his thesis has been largely dismissed as "ungrounded conjectures"; nevertheless, the theory has been widely publicized in a popular American textbook: James West Davidson and Mark Hamilton Lytle, After the Fact: The Art of Historical Detection (Boston: McGraw Hill, 1982 [sixth edition, 2010]).Dennis Kent Anderson and Godfrey Tryggve Anderson, "The Death of Silas Deane: Another Opinion," New England Quarterly 57 (1984), 98-105.
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Torretti, Philosophy of Physics (Cambridge U P, 1999), p 221: "Twentieth-century positivists would maintain, of course, that the rules of inductive logic are not meant to preside over the process of discovery, but to control the validity of its findings". Practicing what Popper had preached—conjectures and refutations—neopositivism ran its course, catapulting its chief rival, Popper, initially a contentious misfit, to carry the richest philosophy out of interwar Vienna.
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Ross used his salary from a year at the shop to enroll for one term at the University of Chicago in Moore's course. Moore gave Ross special attention, knowing his untraditional background, and arranged for Ross to attend the topology class as the sole undergraduate. In Moore's teaching style, he would propose a conjecture and task the students with proving it. Students could respond with counter-conjectures that they would defend.
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Inconsistencies and conflicting verses are even present within the same script, such as the Manusmriti. Some ancient Indian texts suggest artha are instruments that enable satisfaction of desires; some include wealth, some include power, and some such as the bhakti schools include instruments to love God. Some of this, suggests Krishna, reflects differences in human needs. Perhaps, conjectures Krishna, artha is just a subset of kama and karma.
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The famous problems of David Hilbert stimulated further development, which led to the reciprocity laws, and proofs by Teiji Takagi, Phillip Furtwängler, Emil Artin, Helmut Hasse and many others. The crucial Takagi existence theorem was known by 1920 and all the main results by about 1930. One of the last classical conjectures to be proved was the principalisation property. The first proofs of class field theory used substantial analytic methods.
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He left two conjectures, both known as Artin's conjecture. The first concerns Artin L-functions for a linear representation of a Galois group; and the second the frequency with which a given integer a is a primitive root modulo primes p, when a is fixed and p varies. These are unproven; in 1967, Hooley published a conditional proof for the second conjecture, assuming certain cases of the Generalized Riemann hypothesis.
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Landau's fourth problem asked whether there are infinitely many primes which are of the form p=n^2+1 for integer n. (The list of known primes of this form is .) The existence of infinitely many such primes would follow as a consequence of other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture. , this problem is open. One example of near-square primes are Fermat primes.
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Despite his advocacy of empiricism and his many correct conjectures about atomism and the nature of the physical world, Lucretius concludes his first book stressing the absurdity of the (by then well-established) spherical Earth theory. While Epicurus left open the possibility for free will by arguing for the uncertainty of the paths of atoms, Lucretius viewed the soul or mind as emerging from arrangements of distinct particles.
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Abstract Folkard (1892) similarly identifies Lucullus's cherry as a cultivated variety. He states that it was planted in Britain a century after its introduction into Italy, but "disappeared during the Saxon period". He notes that in the fifteenth century "Cherries on the ryse" (i.e. on the twigs) was one of the street cries of London, but conjectures that these were the fruit of "the native wild Cherry, or Gean-tree".
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This was one of the clues leading to the Weil conjectures. Note that in the limit the order of goes to 0! - but under the correct procedure (dividing by ) we see that it is the order of the symmetric group (See Lorscheid's article) - in the philosophy of the field with one element, one thus interprets the symmetric group as the general linear group over the field with one element: .
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He made some famous contributions to modern analytic number theory. In a single short paper, the only one he published on the subject of number theory, he investigated the zeta function that now bears his name, establishing its importance for understanding the distribution of prime numbers. The Riemann hypothesis was one of a series of conjectures he made about the function's properties. In Riemann's work, there are many more interesting developments.
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Anabelian geometry is a theory in number theory, which describes the way in which the algebraic fundamental group G of a certain arithmetic variety V, or some related geometric object, can help to restore V. The first traditional conjectures, originating from Alexander Grothendieck and introduced in Esquisse d'un Programme were about how topological homomorphisms between two groups of two hyperbolic curves over number fields correspond to maps between the curves. These Grothendieck conjectures were partially solved by Hiroaki Nakamura and Akio Tamagawa, while complete proofs were given by Shinichi Mochizuki. Before anabelian geometry proper began with the famous letter to Gerd Faltings and Esquisse d'un Programme, the Neukirch–Uchida theorem hinted at the program from the perspective of Galois groups, which themselves can be shown to be étale fundamental groups. More recently, Mochizuki introduced and developed a so called mono-anabelian geometry which restores, for a certain class of hyperbolic curves over number fields, the curve from its algebraic fundamental group.
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Hypsicrates the historian was a Greek writer in Rome who flourished in the 1st century BC. His work does not survive, but scholars have conjectures about the writer and his work. He was associated probably with Pontus and wrote a history of the area that was possibly used by Strabo. He may be the same Hypsicrates who served as a slave for Julius Caesar and was freed by Caesar in 47 BC.
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A related conjecture of Barnette states that every cubic polyhedral graph in which all faces have six or fewer edges is Hamiltonian. Computational experiments have shown that, if a counterexample exists, it would have to have more than 177 vertices.. The intersection of these two conjectures would be that every bipartite cubic polyhedral graph in which all faces have four or six edges is Hamiltonian. This was proved to be true by .
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Liberman seeks to build an exhaustive purview of previous conjectures and hypotheses on word origins. His team has collected tens of thousands of articles on etymology from hundreds of journals, book chapters, and Festschriften, which feed his works. His books in this area include Etymology for Everyone: Word Origins and How We Know Them (2005) and A Bibliography of English Etymology (2009). He has also published articles on individual words and groups of related words.
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See Hacohen, 2000. Popper dedicated his Conjectures and Refutations to Hayek. For his part, Hayek dedicated a collection of papers, Studies in Philosophy, Politics, and Economics, to Popper and in 1982 said that "ever since his Logik der Forschung first came out in 1934, I have been a complete adherent to his general theory of methodology".See Weimer and Palermo, 1982 Popper also participated in the inaugural meeting of the Mont Pelerin Society.
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129 (1997), no. 3, pp. 445–470 Bestvina and Brady developed a version of discrete Morse theory for cubical complexes and applied it to study homological finiteness properties of subgroups of right-angled Artin groups. In particular, they constructed an example of a group which provides a counter-example to either the Whitehead asphericity conjecture or to the Eilenberg−Ganea conjecture, thus showing that at least one of these conjectures must be false.
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The next day, Sovetsky Sport in its editorial admitted that its journalists, who wrote the sensational article two weeks earlier, had to use "conjectures" to provide details of this tragedy. At the same time, the editors expressed their satisfaction over the worldwide response evoked by their article. In a special press conference in Moscow in August 1989, the Moscow Prosecutor's Office confirmed that there had been 66 fatalities in the Luzhniki disaster.
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Popper Conjectures and Refutations, Part I, 3. titled "Three Views Concerning Human Knowledge", Popper argues that Berkeley is to be considered as an instrumentalist philosopher, along with Robert Bellarmine, Pierre Duhem and Ernst Mach. According to this approach, scientific theories have the status of serviceable fictions, useful inventions aimed at explaining facts, and without any pretension to be true. Popper contrasts instrumentalism with the above mentioned essentialism and his own "critical rationalism".
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Laurent Lafforgue (; born 6 November 1966) is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and analysis,D Mackenzie (2000) Fermat's Last Theorem's First Cousin, Science 287(5454), 792-793. and in particular proved the Langlands conjectures for the automorphism group of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas.
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Jean-Luc Brylinski (born in 1951) is a French-American mathematician. Educated at the Lycée Pasteur and the École Normale Supérieure in Paris, after an appointment as researcher with the C. N. R. S., he became a Professor of Mathematics at Pennsylvania State University. He proved the Kazhdan–Lusztig conjectures with Masaki Kashiwara. He has also worked on gerbes, cyclic homology, Quillen bundles, and geometric class field theory, among other geometric and algebraic topics.
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The station had a single-storey building on the eastern side of the track. No details of the station's facilities have been published, though the standard work conjectures there may have been a siding. In common with Festiniog and Tan-y-Manod stations, the only published photographs were taken from a distance, they lend the buildings the appearance of corrugated iron. The sole close-up photo is of the line's northern terminus - .
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Scientific theories are testable and make falsifiable predictions.Popper, Karl (1963), Conjectures and Refutations, Routledge and Kegan Paul, London, UK. Reprinted in Theodore Schick (ed., 2000), Readings in the Philosophy of Science, Mayfield Publishing Company, Mountain View, Calif. Thus, it is a mark of good science if a discipline has a growing list of superseded theories, and conversely, a lack of superseded theories can indicate problems in following the use of the scientific method.
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Rota's excluded minors conjecture is one of a number of conjectures made by mathematician Gian-Carlo Rota. It is considered to be an important problem by some members of the structural combinatorics community. Rota conjectured in 1971 that, for every finite field, the family of matroids that can be represented over that field has only finitely many excluded minors.. A proof of the conjecture has been announced by Geelen, Gerards, and Whittle.
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Conjectures for the final fate of the black hole include total evaporation and production of a Planck-mass- sized black hole remnant. Such Planck-mass black holes may in effect be stable objects if the quantized gaps between their allowed energy levels bar them from emitting Hawking particles or absorbing energy gravitationally like a classical black hole. In such case, they would be weakly interacting massive particles; this could explain dark matter.
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Werner has recently seen the Yeti on his island, and conjectures that he was marooned there by melting winter ice. He introduces the others to a mute Native American manservant named Laughing Crow. The group have dinner, which is again "gin sung," then go to sleep after one of the students, Tom, sings a song about the Yeti. The next day, the professor and his students begin their search in the woods of the island.
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Koutschan is working on computer algebra, particularly on holonomic functions, with applications to combinatorics, special functions, knot theory, and physics. Together with Doron Zeilberger and Manuel Kauers, Koutschan proved two famous open conjectures in combinatorics using large scale computer algebra calculations. Both proofs appeared in the Proceedings of the National Academy of Sciences. The first concerned a conjecture formulated by Ira Gessel on the number of certain lattice walks restricted to the quarter plane.
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Let X be a smooth projective variety over a number field. The Bloch-Kato conjecture on values of L-functions predicts that the order of vanishing of an L-function of X at an integer point is equal to the rank of a suitable motivic cohomology group. This is one of the central problems of number theory, incorporating earlier conjectures by Deligne and Beilinson. The Birch–Swinnerton-Dyer conjecture is a special case.
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He wisely conjectures that a handy mermaid will bring guests. With Ethel clad in appropriate costume, and seated upon the rocks in true mermaid fashion, her father persuades the reporter of the local paper to take a look at the phenomenon. The newspaper man is greatly impressed with the spectacle and obtains a photo of the mermaid, which he publishes. The mermaid gains wide publicity - and vacationists arrive from near and far to see her.
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He adds that the early Irish form of the name Gododdin is Fortudán., The Gododdin, Appendix 1: Gododdin and Manaw Gododdin. John Koch (Celtic Culture, 2005) incorporates some of Skene's material on Manaw (and credits Skene for it), including an independent view of the historical record (reaching the same general conclusions as Skene), but also asserting conjectures as though they were facts (e.g., asserting that the "Iudeu" mentioned in the Historia Brittonum was at Stirling).
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The weak and the strong cosmic censorship hypotheses are two conjectures concerned with the global geometry of spacetimes. The weak cosmic censorship hypothesis asserts there can be no singularity visible from future null infinity. In other words, singularities need to be hidden from an observer at infinity by the event horizon of a black hole. Mathematically, the conjecture states that, for generic initial data, the maximal Cauchy development possesses a complete future null infinity.
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These conjectures allow dating the genesis of the retable in 1470 to 1480s. In the event that the purchaser of the altar was a Hussite captain Jakoubek of Vřesovice, who died in 1467, dating emergence retable it can be shifted to the 1460s. The Church of St. Wenceslas (Roudníky), for whose altar it was intended, is already mentioned as a parish in 1352, and was rebuilt in the Gothic style in 1486.
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1719–1736; LBNL-44481.I. S. Kotsireas, and K. Karamanos, "Exact Computation of the bifurcation Point B4 of the logistic Map and the Bailey–Broadhurst Conjectures", I. J. Bifurcation and Chaos 14(7):2417–2423 (2004) Integer relation algorithms are combined with tables of high precision mathematical constants and heuristic search methods in applications such as the Inverse Symbolic Calculator or Plouffe's Inverter. Integer relation finding can be used to factor polynomials of high degree.
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Paul Erdős famously asked the question of whether any set that does not contain arbitrarily long arithmetic progressions must necessarily be small. He offered a prize of $3000 for the solution to this problem, more than for any of his other conjectures, and joked that this prize offer violated the minimum wage law.Carl Pomerance, Paul Erdős, Number Theorist Extraordinaire. (Part of the article The Mathematics of Paul Erdős), in Notices of the AMS, January, 1998.
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The book contains a new technical result in describing the Turing completeness of the Rule 110 cellular automaton. Very small Turing machines can simulate Rule 110, which Wolfram demonstrates using a 2-state 5-symbol universal Turing machine. Wolfram conjectures that a particular 2-state 3-symbol Turing machine is universal. In 2007, as part of commemorating the book's fifth anniversary, Wolfram's company offered a $25,000 prize for proof that this Turing machine is universal.
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I. Kroupova, IS MU diploma thesis 2015, p.10 Peter and Iona Opie mention various conjectures that link the character Georgie Porgie to British historical figures, including King George I and George Villiers, 1st Duke of Buckingham, but without the slightest evidence,The Oxford Dictionary of Nursery Rhymes (Oxford University Press, 2nd edition, 1997), pp.185–6 and such unsubstantiated claims have been copied in other works of reference to this day.
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1 – 32, 1971 the nonexistence of Suslin lines. Ronald Jensen proved that CH does not imply the existence of a Suslin line.Devlin, K., and H. Johnsbraten, The Souslin Problem, Lecture Notes on Mathematics 405, Springer, 1974 Existence of Kurepa trees is independent of ZFC, assuming consistency of an inaccessible cardinal.Silver, J., The independence of Kurepa's conjecture and two-cardinal conjectures in model theory, in Axiomatic Set Theory, Proc. Symp, in Pure Mathematics (13) pp.
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In mathematics, crystalline cohomology is a Weil cohomology theory for schemes X over a base field k. Its values Hn(X/W) are modules over the ring W of Witt vectors over k. It was introduced by and developed by . Crystalline cohomology is partly inspired by the p-adic proof in of part of the Weil conjectures and is closely related to the algebraic version of de Rham cohomology that was introduced by Grothendieck (1963).
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Those solutions that are not exact are called non-exact solutions. Such solutions mainly arise due to the difficulty of solving the EFE in closed form and often take the form of approximations to ideal systems. Many non-exact solutions may be devoid of physical content, but serve as useful counterexamples to theoretical conjectures. Al Momin argues that Kurt Gödel's solution to these equations do not describe our universe and are therefore approximations.
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Scientific theories are distinguished from hypotheses, which are individual empirically testable conjectures, and from scientific laws, which are descriptive accounts of the way nature behaves under certain conditions. Theories guide the enterprise of finding facts rather than of reaching goals, and are neutral concerning alternatives among values. A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.
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Various conjectures have been made as to the personality of the author, but nothing certain has been established. The chronicle itself, particularly in its second part, has some importance, and was first edited by Marquard Freher in Rerum Germanicarum Scriptores, I, 411-52 (Frankfurt-am-Main, 1600); 2nd ed., 1634; again by Gewold (Ingolstadt, 1618); later by Struve (Strasbourg, 1717), and finally by Böhmer-Huber in Fontes rerum Germanicarum, IV (1868), 507-68.
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The Mǐ () were the royal house of the states of Chu and Kui (夔) during the later Zhou dynasty. They claimed descent from Zhuanxu via his grandson Jilian, whom they credited with founding their dynasty. The Chu Lexicon at the University of Massachusetts conjectures that it was a native Chu word whose meaning was "bear", explaining the cadet members of the family recorded with the surname Xiong (Chinese: "bear").University of Massachusetts.
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List of Fellows of the American Mathematical Society, retrieved 2013-07-07. Rudin is best known in topology for her constructions of counterexamples to well-known conjectures. In 1958, she found an unshellable triangulation of the tetrahedron. Most famously, Rudin was the first to construct a Dowker space, which she did in 1971, thus disproving a conjecture of Clifford Hugh Dowker that had stood, and helped drive topological research, for more than twenty years.
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The house was again restored, 1931–32, overseen by Fiske Kimball, director of the Philadelphia Museum of Art. New historical research debunked Watson's and Westcott's conjectures about when the house had been built -- Kimball dated it "after 1703 and before 1715." PMA took on administration of the house, operating it as a small museum exhibiting Queen Anne style furniture and decorative arts objects."Our Story: 1930 - 1940," from Philadelphia Museum of Art.
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670–674 > But the main difference reflects the philosophy above: we are interested not > only in theorems and proofs but also in the way in which they have been or > can be reached. Note that we do value proofs: experimentally inspired > results that can be proved are more desirable than conjectural ones. > However, we do publish significant conjectures or explorations in the hope > of inspiring other, perhaps better-equipped researchers to carry on the > investigation.
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A flype move. The Tait flyping conjecture can be stated: > Given any two reduced alternating diagrams D_1 and D_2 of an oriented, prime > alternating link: D_1 may be transformed to D_2 by means of a sequence of > certain simple moves called flypes. The Tait flyping conjecture was proved by Thistlethwaite and William Menasco in 1991. The Tait flyping conjecture implies some more of Tait's conjectures: > Any two reduced diagrams of the same alternating knot have the same writhe.
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Weddington Castle Weddington Castle, or Weddington Hall, was a manor house in the village Weddington, Nuneaton in Warwickshire. Evolving from a Royal Hunting Lodge in the ancient village of Weddington to become an extensive fortified Hall set amidst landscaped gardens, this centuries-old building was demolished in 1928 to make way for a housing estate. Earliest references to Weddington Castle date from 1566, when it was mentioned in a suit. Only conjectures can be made about its history.
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Theodor Siegl conjectures that the landscaped background may have been the last element to be painted, possibly in as late as May 1880.Siegl, pp. 79–81. Once resolved to show the horses' hooves frozen in motion, Eakins was confronted with the problem of the coach's wheels. In the sketch, he blurred the spokes of the wheels, the traditional way for artists to indicate motion, but this conflicted with his intention to show an instantaneous view of the hooves.
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Goldfeld's research interests include various topics in number theory. In his thesis,Goldfeld, Dorian, Artin's conjecture on the average, Mathematika, 15 1968 he proved a version of Artin's conjecture on primitive roots on the average without the use of the Riemann Hypothesis. In 1976, Goldfeld provided an ingredient for the effective solution of Gauss' class number problem for imaginary quadratic fields.Goldfeld, Dorian, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer. Ann.
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Neither provided any proof. Luce's and Duroiselle's conjectures have never been verified or reconciled. In the 1960s, Tha Myat, a self-taught linguist, published books showing the Pyu origin of the Burmese script. But Tha Myat's books, written in Burmese, never got noticed by Western scholars. Per Aung-Thwin, as of 2005 (his book was published in 2005), there had been no scholarly debate on the origins of the Burmese script or the present-day Mon script.
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Brynjúlfur, "Um Höfðaletur," p. 37. There are many conjectures about the derivation of the name höfðaletur, but no definite evidence exists.Brynjúlfur, "Um Höfðaletur," pp. 39-40 mentions three theories: that the name refers to its being "capital" letters, although lowercase letters are sometimes found; that it refers to the decoration in the "heads" of the letters; and that it was invented in a settlement called Höfði, but says that its origins, name, and age are all mysteries.
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The force mediators for these are other hadrons called mesons. Although in the normal phase of QCD single gluons may not travel freely, it is predicted that there exist hadrons that are formed entirely of gluons — called glueballs. There are also conjectures about other exotic hadrons in which real gluons (as opposed to virtual ones found in ordinary hadrons) would be primary constituents. Beyond the normal phase of QCD (at extreme temperatures and pressures), quark–gluon plasma forms.
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Evidence indicates that there was a 6 to 8.5 km long Diolkos paved trackway, which transported boats across the Isthmus of Corinth in Greece from around 600 BC.Verdelis, Nikolaos: "Le diolkos de L'Isthme", Bulletin de Correspondance Hellénique, vol. 81 (1957), pp. 526–529 (526)Cook, R. M.: "Archaic Greek Trade: Three Conjectures 1. The Diolkos", The Journal of Hellenic Studies, vol. 99 (1979), pp. 152–155 (152)Drijvers, J.W.: "Strabo VIII 2,1 (C335): Porthmeia and the Diolkos", Mnemosyne, vol.
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He published his article Conjectures on the Union of the Soul and Body in the Journal in 1703, supporting the views of Gottfried Wilhelm Leibniz. The journal was seen as biased in its discussions of politics and religion due to its association with the Jesuits. The Memoires de Trevoux inspired the launch of various rival journals, but none lasted for long. In 1733 the Duke of Maine, tired of constant complaints, removed his protection from the editors.
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He was the son of Paul Asen, and brother of Simonis and Theodora Asanina. In 1441, his sister Theodora married the Despot Demetrios Palaiologos, with whose career Matthew's destiny was intertwined. Bulgarian historian Ivan Bozhilov conjectures that Matthew must have been born in the first years of the 15th century, but before c. 1405. Matthew first appears in September 1423, when he was sent along with his brother-in-law as an envoy to King Sigismund of Hungary.
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Here Ravenel uses localization in the sense of Aldridge K. Bousfield in a crucial way. All but one of the Ravenel conjectures were proved by Ethan Devinatz, Michael J. Hopkins and Jeff Smith not long after the article got published. Frank Adams said on that occasion: In further work, Ravenel calculates the Morava K-theories of several spaces and proves important theorems in chromatic homotopy theory together with Hopkins. He was also one of the founders of elliptic cohomology.
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In 16.3–4, the Epistle of Barnabas reads: As commonly interpreted, this passage places the Epistle after the destruction of the Second Temple in AD 70. It also places the Epistle before the Bar Kochba Revolt of AD 132, after which there could have been no hope that the Romans would help to rebuild the temple. The document must therefore come from the period between the two Jewish revolts. Attempts at identifying a more precise date are conjectures.
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Later on she examines the nature of leonine entities from Sirius called Paschats which, conjectures Hope, through the lion goddess Bastet were worshiped in Egypt.Murry Hope, The Sirius Connection. Shaftesbury, England 1996. . Particularly in The Gaia Dialogues (1995), Hope defends the natural world asserting that the Earth (Gaia) is a conscious being, a living entity who is shifting its magnetic poles as part of a plan to defend itself from desolation caused by its human children.
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It is here that Edmonds first presented his findings on defining a class of algorithms that could run more efficiently. Most combinatorics scholars, during this time, were not focused on algorithms. However Edmonds was drawn to them and these initial investigations were key developments for his later work between matroids and optimization. He spent the years from 1961 to 1965 on the subject of NP versus P and in 1966 originated the conjectures NP ≠ P and NP ∩ coNP = P.
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In either June,Potter 2004, p.243. Gallus saw to the deification of Decius on June 24, 251 July,Herwig Wolfram, Die Goten und ihre Geschichte, C. H. Beck Verlag, München, 2001, p.33. or AugustSouthern 2001, p.308. She conjectures August as the date of Herennius Etruscus proclamation to the rank of Augustus, then the battle could not take place before that point of 251, the Roman army engaged the Scythians under Cniva near Abritus.
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One of the common objections to intelligent design being accepted as valid science is that ID proponents have published no scientific papers in the peer-reviewed scientific literature in support of their conjectures. The ruling in the 2005 Dover trial, Kitzmiller v. Dover Area School District, found that intelligent design had not been tested by the process of being published in a peer- reviewed scientific journal and was not supported by any peer-reviewed research, data or publications.Kitzmiller v.
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The conjecture was proved in 1994 by Henning Haahr Andersen, Jens Carsten Jantzen and Wolfgang Soergel for sufficiently large group-specific characteristics (without explicit bound) and later by Peter Fiebig for a very high explicitly stated bound. Williamson found several infinite families of counterexamples to the generally suspected validity limits of Lusztig's conjecture. He also found counterexamples to a 1990 conjecture of Gordon James on symmetric groups. His work also provided new perspectives on the respective conjectures.
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Glynn accuses Sayre of erroneously making her sister a feminist heroine, and sees Watson's The Double Helix as the root of what she calls the "Rosalind Industry". She conjectures that the stories of alleged sexism would "have embarrassed her [Rosalind Franklin] almost as much as Watson's account would have upset her", and declared that "she [Rosalind] was never a feminist."Glynn, p. 158. Klug and Crick have also concurred that Franklin was definitely not a feminist.
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HR forms the basis for the artificial intelligence program HRL (the "L" in honour of Imre Lakatos), developed by Alison Pease, Simon Colton, Alan Smaill and John Lee. HRL generates software "student" agents, which are given information with which they attempt to make inferences. It evaluates how "interesting" the inferences are and sends those that are sufficiently interesting to a "teacher" agent. The teacher arranges group discussion amongst the students and may request further modification of conjectures.
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Baglione provided no further explanation about the reasons and circumstances of the rejection but modern scholarship has put forward several theories and conjectures. The first versions of the paintings were obviously acquired by Giacomo Sannesio, secretary of the Sacra Consulta and an avid collector of art. The first Conversion of Saint Paul ended up in the Odescalchi Balbi Collection. It is a much brighter and more Mannerist canvas, with an angel-sustained Jesus reaching down towards a blinded Paul.
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Here "humanism is inextricable from rationalism", and "it is the rationalism of the characters – and the writer – that makes them emotional and human". Miéville further said that despite the extensive use of mathematics, physics and language in the stories, they are infused with a "profound humanism" that makes "the most abstruse philosophical conjectures ... resonant and emotional". The Guardian ranked Stories of Your Life and Others 80 in its list of 100 Best Books of the 21st Century.
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Mrowka's work combines analysis, geometry, and topology, specializing in the use of partial differential equations, such as the Yang-Mills equations from particle physics to analyze low-dimensional mathematical objects. Jointly with Robert Gompf, he discovered four- dimensional models of space-time topology. In joint work with Peter Kronheimer, Mrowka settled many long-standing conjectures, three of which earned them the 2007 Veblen Prize. The award citation mentions three papers that Mrowka and Kronheimer wrote together.
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Moscow, 1978, pp. 59–68. criticized Az i Ya, characterizing Suleymenov's etymological and paleography conjectures as amateurish. Linguists such as Zaliznyak pointed out that certain linguistic elements in Slovo dated from the 15th or 16th centuries, when the copy of the original manuscript (or of a copy) had been made. They noted this was a normal feature of copied documents, as copyists introduce elements of their own orthography and grammar, as is known from many other manuscripts.
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In number theory, Dixon's factorization method (also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method. Unlike for other factor base methods, its run-time bound comes with a rigorous proof that does not rely on conjectures about the smoothness properties of the values taken by polynomial. The algorithm was designed by John D. Dixon, a mathematician at Carleton University, and was published in 1981.
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" However, Anderson conceded that Grade "was not a man you could argue with. If he said "No", you had to accept that he wouldn't change his mind."Archer and Hearn, p. 184. Of Grade's decision, La Rivière conjectures, "No one knows what was running through [his] mind ... but given the ease with which the 'Unwinese' element could have been removed [from] the series, it seems probable that he simply didn't like a lot of what he was seeing.
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The complexities of all integers up to some threshold can be calculated in total time . Algorithms for computing the integer complexity have been used to disprove several conjectures about the complexity. In particular, it is not necessarily the case that the optimal expression for a number is obtained either by subtracting one from or by expressing as the product of two smaller factors. The smallest example of a number whose optimal expression is not of this form is 353942783.
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Macintyre developed a first-order model theory for intersection theory and showed connections to Alexander Grothendieck's standard conjectures on algebraic cycles. Macintyre has proved many results on the model theory of real and complex exponentiation. With Alex Wilkie he proved the decidability of real exponential fields (solving a problem of Alfred Tarski) modulo Schanuel's conjecture from transcendental number theory. With Lou van den Dries he initiated and studied the model theory of logarithmic-exponential series and Hardy fields.
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Experimental mathematics is the use of computers to generate large data sets within which to automate the discovery of patterns which can then form the basis of conjectures and eventually new theory. The paper "Experimental Mathematics: Recent Developments and Future Outlook" describes expected increases in computer capabilities: better hardware in terms of speed and memory capacity; better software in terms of increasing sophistication of algorithms; more advanced visualization facilities; the mixing of numerical and symbolic methods.
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As an editor, while making many false conjectures, he was responsible for clearing many long-standing errors in the traditional texts. His comments when original, are mainly lexicographical. Other works include an anti-Latin theological pamphlet. A selection from his works under the title of Manuelis Moschopuli opuscula grammatica was published by F. N. Titze (Leipzig, 1822); see also Karl Krumbacher, Geschichte der byzantinischen Litteratur (1897) and M. Treu, Maximi monachi Planudis epistulae (1890), p. 208\.
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The opening of cylinder A also shows similarities to the openings of other myths with the destinies of heaven and earth being determined. Various conjectures have been made regarding the supposed contents of an initial cylinder. Victor Hurowitz suggested it may have contained an introductory hymn praising Ningirsu and Lagash. Thorkild Jacobsen suggested it may have explained why a relatively recent similar temple built by Ur-baba (or Ur-bau), Gudea's father-in-law "was deemed insufficient".
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The octahedron is one of the most well-known examples of a spindle. Unfortunately, the Hirsch conjecture is not true in all cases, as shown by Francisco Santos in 2011. Santos' explicit construction of a counterexample comes both from the fact that the conjecture may be relaxed to only consider simple polytopes, and from equivalence between the Hirsch and d-step conjectures. In particular, Santos produces his counterexample by examining a particular class of polytopes called spindles.
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The sea was supposed to be connected to the Pacific Ocean by at least one strait. Many different conjectures about the sea's shape, size, and position appeared on maps of the period. Belief in the sea's existence derived from writings describing two voyages of discovery, one by an Admiral Bartholomew de Fonte, and one by Juan de Fuca. De Fuca's voyage might have happened, but his account is now known to have contained many distortions and confabulations.
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Many of these extrapolations draw on his personal nautical background without supporting evidence. Menzies claims that knowledge of Zheng He's discoveries was subsequently lost because the mandarin bureaucrats of the Ming imperial court feared that the costs of further voyages would ruin the Chinese economy. He conjectures that when the Yongle Emperor died in 1424 and the new Hongxi Emperor forbade further expeditions, the mandarins hid or destroyed the records of previous exploration to discourage further voyages.
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Homeopathy. Brooks discusses the work of researcher Madeleine Ennis involving a homeopathic solution which once contained histamine but was diluted to the point where no histamine remained. Brooks conjectures that the results might be explained by some previously unknown property of water. Brooks supports the investigation of documented anomalies even though he is critical of the practice of homeopathy in general, as are many of the scientists he cites, such as Martin Chaplin of South Bank University.
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Bulwer Lytton wrote that, as a young college student, he and his classmates would > rush every Saturday afternoon for the Literary Gazette, [with] an impatient > anxiety to hasten at once to that corner of the sheet which contained the > three magical letters L.E.L. And all of us praised the verse, and all of us > guessed at the author. We soon learned it was a female, and our admiration > was doubled, and our conjectures tripled.Quoted in Thomson (1860), 152.
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79 but in return, Ludwig required that his current Munich Kapellmeister, Hermann Levi, should conduct the festival. Wagner objected on the grounds of Levi's Jewish faith; Parsifal, he maintained, was a "Christian" opera. Both he and Cosima were vehement anti-Semites; Hilmes conjectures that Cosima inherited this in her youth, from her father, from Carolyne zu Sayn-Wittgenstein, probably from Madame Patersi and, a little later, from Bülow, "an anti-Semite of the first order".Hilmes, p.
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Bernard Morris Dwork (May 27, 1923 – May 9, 1998) was an American mathematician, known for his application of p-adic analysis to local zeta functions, and in particular for a proof of the first part of the Weil conjectures: the rationality of the zeta-function of a variety over a finite field. The general theme of Dwork's research was p-adic cohomology and p-adic differential equations. He published two papers under the pseudonym Maurizio Boyarsky.
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Grothendieck's discovery of the ℓ-adic étale cohomology, the first example of a Weil cohomology theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student Pierre Deligne. Grothendieck's large-scale approach has been called a "visionary program." The ℓ-adic cohomology then became a fundamental tool for number theorists, with applications to the Langlands program.R. P. Langlands, Modular forms and l-adic representations, Lecture Notes in Math. 349.
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He picked up another credited Weil conjecture, around 1967, which later under pressure from Serge Lang (resp. of Serre) became known as the Taniyama–Shimura conjecture (resp. Taniyama–Weil conjecture) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference. His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.
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The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity. Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be observed from the rest of spacetime. Singularities that are not so hidden are called naked. The weak cosmic censorship hypothesis was conceived by Roger Penrose in 1969 and posits that no naked singularities exist in the universe.
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In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A. Horn who proposed it in 1962. It provides a vast generalization of such conjectures as the Hardy and Littlewood conjecture on the density of twin primes or their conjecture on primes of the form n2 + 1; it is also a strengthening of Schinzel's hypothesis H.
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Neither identified sources nor analogues for Beowulf can be definitively proven, but many conjectures have been made. These are important in helping historians understand the Beowulf manuscript, as possible source-texts or influences would suggest time- frames of composition, geographic boundaries within which it could be composed, or range (both spatial and temporal) of influence (i.e. when it was "popular" and where its "popularity" took it). There are Scandinavian sources, international folkloric sources, and Celtic sources.
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They are intellectually compatible and have a budding, mutual romantic interest. Mandrake considers the pair his competitors, and he sabotages their efforts by approaching revived patients before they can. Mandrake's method is to ask mellifluous leading questions of the patients and thereby taint their self-reported NDEs; this causes Joanna and Richard hardship in finding un-interviewed volunteers for their own study. The reader later learns that two of their volunteers are liars, which also corrupts their conjectures.
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Cinderella was initially developed by Jürgen Richter-Gebert and Henry Crapo and was used to input incidence theorems and conjectures for automatic theorem proving using the binomial proving method by Richter-Gebert. The initial software was created in Objective-C on the NeXT platform. In 1996, the software was rewritten in Java from scratch by Jürgen Richter-Gebert and Ulrich Kortenkamp. It still included the binomial prover, but was not suitable for classroom teaching as it still was prototypical.
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While arXiv does contain some dubious e-prints, such as those claiming to refute famous theorems or proving famous conjectures such as Fermat's Last Theorem using only high-school mathematics, a 2002 article which appeared in Notices of the American Mathematical Society described those as "surprisingly rare". arXiv generally re-classifies these works, e.g. in "General mathematics", rather than deleting them; however, some authors have voiced concern over the lack of transparency in the arXiv screening process.
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Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures. Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways. The logical structure of the Disquisitiones (theorem statement followed by proof, followed by corollaries) set a standard for later texts. While recognising the primary importance of logical proof, Gauss also illustrates many theorems with numerical examples.
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The most common alternative theory suggested that the name originated when Portuguese or Spanish explorers, having explored the northern part of the continent and unable to find gold and silver, wrote ("nothing here" in Portuguese), or ("Cape Nothing" in Spanish) on that part of their maps. An alternative explanation favoured by philologist Marshall Elliott linked the name to the Spanish word "cañada", meaning "glen" or "valley"."Further Conjectures as to the Origin of the Name 'Canada'". The New York Times, September 5, 1908.
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Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite or infinite. The Lenstra–Pomerance–Wagstaff conjecture asserts that there are infinitely many Mersenne primes and predicts their order of growth. It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes congruent to 3 (mod 4).
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He sincerely practices Indian religions, including Hinduism, Sikhism, Christianity and Islam, attempting to find "God", to no avail. He later discovers that Tapasvi has his remote, who claims it was a gift from God and refuses to return it. Jaggu promises PK that she will recover his remote and he can go back home. PK conjectures that Tapasvi and other godmen must be dialing a "wrong number" to communicate with God and are advising the public to engage in meaningless rituals.
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He had the atrium of Old St. Peter's Basilica paved with large blocks of white marble, and restored other churches of Rome, notably the church of St. Euphemia on the Appian Way and the Basilica of St. Paul Outside the Walls.Duchesne, Liber Pontificalis I, p. 348, who conjectures in note 2 that the church in question was not the Basilica, but instead a small church commemorating the parting of Peter and Paul on their way to execution. Mann, pp. 20-21.
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Let R \to S be a local homomorphism of complete local domains. Then there exists an R-algebra BR that is a balanced big Cohen–Macaulay algebra for R, an S-algebra B_S that is a balanced big Cohen- Macaulay algebra for S, and a homomorphism BR → BS such that the natural square given by these maps commutes. # Serre's Conjecture on Multiplicities. (cf. Serre's multiplicity conjectures.) Suppose that R is regular of dimension d and that M \otimes_R N has finite length.
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During the latter part of the 1950s, the foundations of algebraic geometry were being rewritten; and it is here that the origins of the topos concept are to be found. At that time the Weil conjectures were an outstanding motivation to research. As we now know, the route towards their proof, and other advances, lay in the construction of étale cohomology. With the benefit of hindsight, it can be said that algebraic geometry had been wrestling with two problems for a long time.
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Partition theory is ubiquitous in mathematics with connections to the representation theory of the symmetric group and the general linear group, modular forms, and physics. Thus, Subbarao's conjectures, though seemingly simple, will generate fundamental research activity for years to come. He also researched special classes of divisors and the corresponding analogues of divisor functions and perfect numbers, such as those arising from the exponential divisors ("e-divisors") which he defined. Many other mathematicians have published papers building on his work in these subjects.
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Grant Morrison's run on Animal Man conjectures that all characters which were once published by DC Comics but are no longer active are sent to a dimension called "Limbo", where they remain until they are revived by returning to active publication. Characters never remember being in Limbo. In Animal Man Vol. 1 #25, Animal Man becomes the first character to visit Limbo while still "current" and encounters a large number of old Golden Age and Silver Age DC comic book characters.
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In fact, Galileo's water clock (described above) provided sufficiently accurate measurements of time to confirm his conjectures. Later research, however, has validated the experiments. The experiments on falling bodies (actually rolling balls) were replicated using the methods described by Galileo, and the precision of the results was consistent with Galileo's report. Later research into Galileo's unpublished working papers from 1604 clearly showed the reality of the experiments and even indicated the particular results that led to the time-squared law.
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The novel then flashes 80 years into the future. Spock is still at Kirk's gravesite when the bright flash of phaser fire illuminates the night sky directly above him, where the U.S.S. Farragut is orbiting the planet, leading salvage operations of the crashed remains of the U.S.S. Enterprise NCC-1701-D. One stream of phaser fire is consistent with starfleet-type weaponry, and the other is green, clearly alien in origin. Spock conjectures that the Farragut is engaged in combat.
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Menocchio (Domenico Scandella, 1532–1599) was a miller from Montereale Valcellina, Italy, who was tried for heresy by the Roman Inquisition for his unorthodox religious views and then was burnt at the stake in 1599. The 16th- century life and mediaeval religious beliefs of Menocchio are known from the records of the Inquisition, and are the subject of The Cheese and the Worms (1976) by Carlo Ginzburg,Levine, D., & Vahed, Z. (2001). Ginzburg's Menocchio: Refutations and Conjectures. Histoire sociale/Social History, 34(68).
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Near Mount Phylleium Strabo places a city Phyllus, noted for a temple of Apollo Phylleius. Statius calls this city Phylli.Stat. Theb. 4.45. William Smith conjectures that the town of Iresiae mentioned by Livy, is perhaps a false reading for Peiresiae; however, modern scholars treat the town as distinct from Peiresiae and suggest the site is to be found in Magnesia not at Peiresiae. Under its later name, Peiresia, the town was a polis (city- state), and minted silver coins with the legend «ΠΕΙΡΑΣΙΕΩΝ».
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The provinces fashioned from the Macedonian Empire were difficult to govern, always on the point of rebellion. The work of Curtius, Pratt conjectures, was not politically appropriate because it would have encouraged independence. The earliest opportune moment was the year 167, when the campaign of the emperor Marcus Aurelius against the Parthian Empire had failed, and the returning troops were in bad morale and infected with the Antonine Plague. The emperor attempted to build national pride among the former Macedonian states.
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Work on the temple was finished by Lepidus on the site of the Curia Hostilia, which had been restored by Sulla, destroyed by fire in 52 BC,During the riots that broke out during the funeral of Publius Clodius Pulcher. and demolished by Caesar in 44 BC.Cassius Dio 44.5.2, with Dio's conjectures about the motivations and rivalries involved (on which see also Richardson, A New Topographical Dictionary, pp. 102–103). This temple seems not to have existed by the time of Hadrian.
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Edward Young's Conjectures on Original Composition (1759) was the most significant reformulation of "genius" away from "ability" and toward the Romantic concept of "genius" as seer or visionary. His essay influenced the Sturm und Drang German theorists, and these influenced Coleridge's Biographia Literaria. The Romantics saw genius as superior to skill, as being far above ability. James Russell Lowell would say "talent is that which is in a man's power: genius is that in whose power a man is" (quoted in Brogan).
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They are reviled in texts written centuries later, particularly by Tamil Hindu scholars. This has led to the inference that the Kalabhra rulers may have ended grants to Hindu temples and persecuted the Brahmins, and supported Buddhism and Jainism during their rule. However, the textual support for these conjectures is unclear. In support of their possible Jaina patronage, is the 10th-century Jain text on grammar which quotes a poem that some scholars attribute to Acchuta Vikkanta, a Kalabhra king.
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Common conjectures are "south of colorful clouds" () and "south of Yun Range (Yunling)" (). Some annals in Ming Dynasty, for example Dian Lüe () and Yunnan General Annals (), record the first conjecture. But modern historian Tan Qixiang disagrees with this; he states that is a superficial explanation of the literal meaning. It is totally wrong for the second conjecture because the name "Yunling Mountains" first appeared in Tang Dynasty (618 - 907) literature, but "Yunnan" first appeared in Han Dynasty (202 BC–220 AD).
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Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures. Algebraic geometry has traditionally meant the understanding of geometric objects, such as algebraic curves and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of ring theory. In this approach, the properties of a geometric object are related to the properties of an associated ring.
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Davidson, Adventures in Unhistory: Conjectures on the Factual Foundations of Several Ancient Legends. Unaware of the explanation offered by modern science (i.e. that these insects had lived in times when the climate of northern Europe was much warmer, their bodies preserved unchanged in the amber) the Greeks came up with the idea that the coldness of northern countries was due to the cold breath of Boreas, the North Wind. So if one travelled "beyond Boreas" one would find a warm and sunny land.
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Sarehole Mill Sarehole () is an area in Hall Green, Birmingham, England. Historically in Worcestershire,Gazetteer of British Counties it was a small hamlet in the larger parish, and manor, of YardleyAcocks Green Local History Society , which was transferred to Birmingham in 1911. Birmingham was classed as part of Warwickshire until 1974, and since then has been part of the West Midlands. W. H. Duignan's Worcestershire Place Names conjectures that the name derives from Old English Syrfe, "Service tree", and hyll, "Hill".
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Somewhat surprisingly, these conjectures have been shown to be connected to a number of questions in other fields, notably in harmonic analysis. For instance, in 1971, Charles Fefferman was able to use the Besicovitch set construction to show that in dimensions greater than 1, truncated Fourier integrals taken over balls centered at the origin with radii tending to infinity need not converge in Lp norm when p ≠ 2 (this is in contrast to the one-dimensional case where such truncated integrals do converge).
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A 'higher' regulator refers to a construction for a function on an algebraic -group with index that plays the same role as the classical regulator does for the group of units, which is a group . A theory of such regulators has been in development, with work of Armand Borel and others. Such higher regulators play a role, for example, in the Beilinson conjectures, and are expected to occur in evaluations of certain -functions at integer values of the argument. See also Beilinson regulator.
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In 1992 David Epstein, Klaus Peters and Silvio Levy set up the journal Experimental Mathematics, with scope the use of computers in pure mathematics. At the time the Notices of the American Mathematical Society was running a "Computers and Mathematics" section, launched in 1988. The particular focus of the "experimental mathematics" included in the journal was the computer-assisted development of mathematical conjectures. The traditional context in pure mathematics was that "journals only publish theorems"; in this area A K Peters innovated.
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This conjecture was named after him. Under the Petersson metric it is shown that we can define the orthogonality on the space of modular forms as the space of cusp forms and its orthogonal space and they have finite dimensions. Furthermore, we can concretely calculate the dimension of the space of holomorphic modular forms, using the Riemann-Roch theorem (see the dimensions of modular forms). used the Eichler–Shimura isomorphism to reduce the Ramanujan conjecture to the Weil conjectures that he later proved.
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The more general Ramanujan–Petersson conjecture for holomorphic cusp forms in the theory of elliptic modular forms for congruence subgroups has a similar formulation, with exponent where is the weight of the form. These results also follow from the Weil conjectures, except for the case , where it is a result of . The Ramanujan–Petersson conjecture for Maass forms is still open (as of 2016) because Deligne's method, which works well in the holomorphic case, does not work in the real analytic case.
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So one can talk about a sheaf of sets on a site, a sheaf of abelian groups on a site, and so on. The definition of sheaf cohomology as a derived functor also works on a site. So one has sheaf cohomology groups Hj(X, E) for any object X of a site and any sheaf E of abelian groups. For the étale topology, this gives the notion of étale cohomology, which led to the proof of the Weil conjectures.
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He conjectures that publication of the work was meant as an honor to Giustini; it "represents a gesture of magnificent presentation to a royal musician, rather than an act of commercial promotion." While many performances of his large-scale sacred works are documented, all of that music is lost, with the exception of fragments such as scattered arias. Giustini's fame rests on his publication of his set of piano pieces, although they seem to have attracted little interest at the time.
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A year later Angelo is released from prison and is shocked to find that Jack is alive when he should be dead. Jack informs him that he has obtained the same room from the previous year and invites Angelo back with him. Angelo conjectures that because he cannot die Jack is an embodiment of the devil, and stabs him. When Jack revives again, Angelo allows him to be taken to a butcher's shop where a crowd of people repeatedly kill him.
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In March 1793 two Saint Malo merchants fitted her out and commissioned her as the privateer corvette Duguay-Trouin. A 1793 prospectus from her owners advertised her as having "steel sheathing", which Demerliac conjectures might have been an armour belt at her waterline. On her first cruise in 1793 under Captain Dufresne Le Gué, she captured two merchant vessels, Bonne Espérence and the 520 ton (bm) of London. Albermarle was returning to London from Bombay and Duguay-Trouin set her into Morlaix.
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The circumstances under which Seneca's tragedies were performed are however unclear; scholarly conjectures range from minimally staged readings to full production pageants. More popular than literary theatre was the genre-defying mimus theatre, which featured scripted scenarios with free improvization, risqué language and jokes, sex scenes, action sequences, and political satire, along with dance numbers, juggling, acrobatics, tightrope walking, striptease, and dancing bears.Potter (1999), p. 257. Unlike literary theatre, mimus was played without masks, and encouraged stylistic realism in acting.
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In 1999, David published a paper with Francesco Pappalardi which proved that the Lang–Trotter conjecture holds in most cases. She has shown that for several families of curves over finite fields, the zeroes of zeta functions are compatible with the Katz–Sarnak conjectures. She has also used random matrix theory to study the zeroes in families of elliptic curves. David and her collaborators have exhibited a new Cohen–Lenstra phenomenon for the group of points of elliptic curves over finite fields.
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There is no mention of Tacitus suffering such a condition, but it is possible that this refers to a brother—if Cornelius was indeed his father.Syme, 1958, p. 60, 613; Gordon, 1936, p. 149; Martin, 1981, p. 26 The friendship between the younger Pliny and Tacitus leads some scholars to conclude that they were both the offspring of wealthy provincial families.Syme, 1958, p. 63 The province of his birth remains unknown, though various conjectures suggest Gallia Belgica, Gallia Narbonensis or Northern Italy.
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He also collaborated with David Mumford on a new description of the moduli spaces for curves. Their work came to be seen as an introduction to one form of the theory of algebraic stacks, and recently has been applied to questions arising from string theory. But Deligne's most famous contribution was his proof of the third and last of the Weil conjectures. This proof completed a programme initiated and largely developed by Alexander Grothendieck lasting for more than a decade.
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Supernovae reach their maximum brightness in only 20 days, and then take much longer to fade away. Researchers had initially conjectured that SCP 06F6 might be an extremely remote supernova; relativistic time dilation might have caused a 20-day event to stretch out over a period of 100 days. But this explanation now seems unlikely. Other conjectures that have been advanced involve a collision between a white dwarf and an asteroid, or the collision of a white dwarf with a black hole.
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He was born on 20 March 1680Hans Volkmann, Emanuele d'Astorga, Leipzig 1911, p. 44 in Augusta, Sicily. No authentic account of Astorga's life can be successfully constructed from the obscure and confusing evidence that has been until now handed down, although historians have not failed to indulge many pleasant conjectures. According to Volkmann his father, a baron of Sicily, took an active part in the attempt to throw off the Spanish yoke, but was betrayed by his own soldiers and publicly executed.
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Falsificationism's demarcation falsifiable grants a theory the status scientific—simply, empirically testable—not the status meaningful, a status that Popper did not aim to arbiter.Karl Popper, ch 4, subch "Science: Conjectures and refutations", in Andrew Bailey, ed, First Philosophy: Fundamental Problems and Readings in Philosophy, 2nd edn (Peterborough Ontario: Broadview Press, 2011), pp 338–42. Popper found no scientific theory either verifiable or, as in Carnap's "liberalization of empiricism", confirmable,Godfrey-Smith, Theory and Reality (U Chicago P, 2003), p 57–59.
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Thus, if Caecina Severus did break a siege of Sirmium, he would have pursued the retreating Breuci until they made a last stand.Radman-Livaja, I., Dizda, M., Archaeological Traces of the Pannonian Revolt 6–9 AD: Evidence and Conjectures, Veröffentlichungen der Altertumskommiion für Westfalen Landschaftsverband Westfalen-Lippe, Band XVIII, p. 49 The Dalmatians marched on Salona (in Dalmatia, on the Adriatic coast) but there Bato was defeated and wounded. He sent other men forward who ravaged the coast down to Apollonia.
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Meyendorff posits that the target of Byzantine monks in general and Palamas in particular was actually "secular philosophy" and so-called "Hellenic wisdom". He conjectures that the validity of Greek philosophy remained an open question in Byzantine society precisely because the Byzantines were "Greek-speaking" and "Greek- thinking". In stark contrast to this Hellenic culture, Byzantine monastic thought continually emphasized that theirs was a "faith preached by a Jewish Messiah" and that their destiny was to become a "new Jerusalem".
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ICM 1932 Paul Althaus Smith (May 18, 1900June 13, 1980) was an American mathematician. His name occurs in two significant conjectures in geometric topology: the Smith conjecture, which is now a theorem, and the Hilbert–Smith conjecture, which was proved in dimension 3 in 2013. Smith theory is a theory about homeomorphisms of finite order of manifolds, particularly spheres. Smith was a student of Solomon Lefschetz at the University of Kansas, moving to Princeton University with Lefschetz in the mid-1920s.
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Recently with Manfred Einsiedler, Philippe Michel and Akshay Venkatesh, he studied distributions of torus periodic orbits in some arithmetic spaces, generalizing theorems by Hermann Minkowski and Yuri Linnik. Together with Benjamin Weiss he developed and studied systematically the invariant of mean dimension introduced in 1999 by Mikhail Gromov. In related work he introduced and studied the small boundary property and stated fundamental conjectures. Among his co-authors are Jean Bourgain, Manfred Einsiedler, Philippe Michel, Shahar Mozes, Akshay Venkatesh and Barak Weiss.
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Atwill conjectures that there were no swine captured because they had all run into the river. The Gospel narratives of Luke 10:38-42 and John 12:2-3 describe a dinner just after Lazarus has been raised from the dead. "They made him a supper", John says, and "Mary has chosen the good portion." Atwill sees this as a macabre cannibalistic double entendre, and a parallel to Wars 6.3, in which Josephus describes a woman named Mary who is pierced by famine.
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Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 11–14 October 2003, Cambridge, MA, IEEE Computer Society, pp. 438–449. Most researchers believe that this is indeed the case. However, Alon, Shpilka and Chris Umans have recently shown that some of these conjectures implying fast matrix multiplication are incompatible with another plausible conjecture, the sunflower conjecture.Alon, Shpilka, Umans, On Sunflowers and Matrix Multiplication Freivalds' algorithm is a simple Monte Carlo algorithm that, given matrices , and , verifies in time if .
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Some conjectures can be made based on toponyms, but they cannot be verified. There is no guarantee that the intermediate phases between those old Italic languages and Indo-European will be found. The question of whether Italic originated outside Italy or developed by assimilation of Indo- European and other elements within Italy, approximately on or within its current range there, remains. An extreme view of some linguists and historians is that there is no such thing as "the Italic branch" of Indo-European.
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Bishop Raynerius de Casulo died two or three days before Christmas 1312.Sanclemente, pp. 129-130, conjectures that it was several days before Christmas Eve, since (according to him) bishops were laid out for viewing by the people for several days before interment. This was not the case, however, for popes or for most persons, clerical or lay. The prelimary meeting to summon electors to a meeting to elect his successor met on 15 February 1313, and fixed 17 February as the day of the election.
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According to the Jewish philosopher and professor Menachem Kellner's study on Maimonidean texts (1991), a ger toshav could be a transitional stage on the way to becoming a "righteous alien" (, ger tzedek), i.e. a full convert to Judaism. He conjectures that, according to Maimonides, only a full ger tzedek would be found during the Messianic era. Furthermore, Kellner criticizes the assumption within Orthodox Judaism that there is an "ontological divide between Jews and Gentiles", which he believes is contrary to what the Torah teaches.
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Once again, the Cretan Mantinada often figures prominently in the words to such songs. One explanation of the origin of the word tambahaniotika is that they come from the eponymous district area of Greek city of Patras Ταμπαχανιώτικα. Also, various conjectures are advanced to explain the meaning and origin of the term tabachaniotika. Kostas Papadakis believes that it comes from tabakaniotikes (ταμπακανιώτικες), which may mean places where hashish ( 'tobacco') was smoked while music was performed, as was the case with the tekédes (τεκέδες; pl.
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Eda Kranakis, an expert on early American suspension bridges, conjectures that Finley would have had access in Philadelphia to information about European bridges.Kranakis, p. 23. Fayette County commissioners proposed the bridge in a March 1801 letter to the Westmoreland County board of commissioners. (Jacob's Creek forms part of the boundary between the counties.) The contract with Finley was signed in April, with each county committing to half of the $600 (US$ with inflation) cost, and specifying that the bridge be completed by December 15.
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North attracted the attention of Francis Wise and other antiquaries by An Answer to a Scandalous Libel intituled The Impertinence and Imposture of modern Antiquaries displayed, published anonymously in 1741, a reply to William Asplin. In 1752 he published Remarks on some Conjectures (London), in answer to a paper by Charles Clarke on a coin found at Eltham. In this pamphlet North discussed the standard and purity of early English coins. He corresponded with the numismatist Patrick Kennedy on the coins of Carausius and Allectus.
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In 1931 Egon Friedell summed it up: "Crassus becomes a speculator in the manner of Louis Philippe, the brothers Gracchus are Socialist leaders, and the Gauls are Indians, etc." Friedell, Kulturgeschichte der Neuzeit (1931), at III: 270. A major recent event in Germany was the failure of the 1848–1849 Revolution, while in Mommsen's Roman History his narration of the Republic draws to a close with the revolutionary emergence of a strong state executive in the figure of Julius Caesar. Carr conjectures as follows.
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Probably in JulyHerwig Wolfram, Die Goten und ihre Geschichte, C. H. Beck Verlag, München, 2001, p.33. or AugustSouthern 2001, p.308. She conjectures August as the date of Herennius Etruscus proclamation to the rank of Augustus, then the battle could not take place before that point of 251, the Roman army engaged the Scythians under Cniva near Abritus. The strengths of the belligerent forces are unknown, but we know that Cniva divided his forces into three units, with one of these parts concealed behind a swamp.
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This project was set up in order to try to solve the Erdős discrepancy problem. It was active for much of 2010 and had a brief revival in 2012, but did not end up solving the problem. However, in September 2015, Terence Tao, one of the participants of Polymath5, solved the problem in a pair of papers. One paper proved an averaged form of the Chowla and Elliott conjectures, making use of recent advances in analytic number theory concerning correlations of values of multiplicative functions.
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These papers provided the first systematic treatment of topology and revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, founding the field of algebraic topology.Dieudonné 1989: 15–35. Poincaré's papers introduced the concepts of the fundamental group and simplicial homology, provided an early formulation of the Poincaré duality theorem, introduced the Euler–Poincaré characteristic for chain complexes, and raised several important conjectures, including the celebrated Poincaré conjecture, which was later proven as a theorem. The 1895 paper coined the mathematical term "homeomorphism".
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Later Voevodsky proved the general Bloch–Kato conjecture.Voevodsky (2010) The starting point for the proof is a series of conjectures due to and . They conjectured the existence of motivic complexes, complexes of sheaves whose cohomology was related to motivic cohomology. Among the conjectural properties of these complexes were three properties: one connecting their Zariski cohomology to Milnor's K-theory, one connecting their etale cohomology to cohomology with coefficients in the sheaves of roots of unity and one connecting their Zariski cohomology to their etale cohomology.
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As to the presumption judicis or hominis, it is denoted by the following: #It is called vehement, when the probability is very strongly supported by most urgent conjectures. Thus, a birth would be held illegitimate, which took place eleven months after a husband's decease. A vehement presumption is considered equivalent to a full proof in civil causes of not too great importance. As to whether it should have sufficient effect in criminal causes to produce the condemnation of an accused person, canonists do not agree.
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Frank Morgan (2012) "Math Finds the Best Doughnut", The Huffington Post Martin Schmidt claimed a proof in 2002, but it was not accepted for publication in any peer-reviewed mathematical journal (although it did not contain a proof of the Willmore conjecture, he proved some other important conjectures in it). Prior to the proof of Marques and Neves, the Willmore conjecture had already been proved for many special cases, such as tube tori (by Willmore himself), and for tori of revolution (by Langer & Singer).
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However, alternative assumptions can be made. Suppose you have two firms producing the same good, so that the industry price is determined by the combined output of the two firms (think of the water duopoly in Cournot's original 1838 account). Now suppose that each firm has what is called the "Bertrand Conjecture" of −1. This means that if firm A increases its output, it conjectures that firm B will reduce its output to exactly offset firm A's increase, so that total output and hence price remains unchanged.
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Paul Erdős ( ; 26 March 1913 – 20 September 1996) was a renowned Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. He was known both for his social practice of mathematics (he engaged more than 500 collaborators) and for his eccentric lifestyle (Time magazine called him The Oddball's Oddball). He devoted his waking hours to mathematics, even into his later years—indeed, his death came only hours after he solved a geometry problem at a conference in Warsaw.
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27 et seq.), he released in the year of his accession, the imprisoned king Jehoiachin, invited him to his table, clothed him with royal raiment, and elevated him above all other captive kings that were in Babylon. Tiele, Cheyne, and Hommel are of the opinion that perhaps Neriglissar, Evil-merodach's brother-in-law, who is praised for his benevolence, was instrumental in the freeing of the Judean king. Grätz, on the other hand, conjectures the influence of the Jewish eunuchs (referring to Jer. xxxix. 7 and Daniel).
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Using estimates on Kloosterman sums he was able to derive estimates for Fourier coefficients of modular forms in cases where Pierre Deligne's proof of the Weil conjectures was not applicable. It was later translated by Jacquet to a representation theoretic framework. Let be a reductive group over a number field F and H\subset G be a subgroup. While the usual trace formula studies the harmonic analysis on G, the relative trace formula a tool for studying the harmonic analysis on the symmetric space .
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In the decades of the 1970s and 1980s, the Ahmadiyya Community continued to attract small, though significant number of converts from among the African American populations. In spite of the rise of Muslim immigrant populations from the Middle East, the Community continued to be an exemplary multi-racial model in the changing dynamics of American Islam, which was often wrought with challenges of diversity, and conjectures of racial superiority. It has been argued that it had the potential for partial acculturation along class lines.
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An example of an incomplete sum is the partial sum of the quadratic Gauss sum (indeed, the case investigated by Gauss). Here there are good estimates for sums over shorter ranges than the whole set of residue classes, because, in geometric terms, the partial sums approximate a Cornu spiral; this implies massive cancellation. Auxiliary types of sums occur in the theory, for example character sums; going back to Harold Davenport's thesis. The Weil conjectures had major applications to complete sums with domain restricted by polynomial conditions (i.e.
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The song's line "I'll probably never see you again" appears in Delaney's kitchen sink realism play A Taste of Honey and The Lion in Love. Morrissey paraphrased the line "Everything depends upon how near you stand next to me" from the 1974 Leonard Cohen song "Take This Longing". Goddard conjectures that the song's title was inspired by the 1947 detective novel Hand in Glove by Ngaio Marsh. The lyrics are also quoted in the coda of "Pretty Girls Make Graves", another song from the band's first album.
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114 He then had little more to publish on the subject; but the emergence of Hilbert modular forms in the dissertation of a student means his name is further attached to a major area. He made a series of conjectures on class field theory. The concepts were highly influential, and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol of local class field theory. Results were mostly proved by 1930, after work by Teiji Takagi.
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After Henry's death (1547), Joye returned to England. In May 1548, he published a translation of a book by Andreas Osiander about conjectures of the end of the world, in which he projected the end of the world between 1585 and 1625. In 1549, Joye debated the question of the preferred punishment of adulterers with John Foxe. In September 1549, Joye was given the Rectory of Blunham, Bedfordshire by Sir Henry Grey of Flitton, and in 1550 he was appointed Rector of Ashwell, Hertfordshire.
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In mathematics, in the field of group theory, especially in the study of p-groups and pro-p-groups, the concept of powerful p-groups plays an important role. They were introduced in , where a number of applications are given, including results on Schur multipliers. Powerful p-groups are used in the study of automorphisms of p-groups , the solution of the restricted Burnside problem , the classification of finite p-groups via the coclass conjectures , and provided an excellent method of understanding analytic pro-p-groups .
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Robert Phelan Langlands, (; born October 6, 1936) is an American-Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory,D Mackenzie (2000) Fermat's Last Theorem's First Cousin, Science 287(5454), 792-793. for which he received the 2018 Abel Prize. He is an emeritus professor and occupies Albert Einstein's office at the Institute for Advanced Study in Princeton.
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Small Proth primes (less than 10200) have been used in constructing prime ladders, sequences of prime numbers such that each term is "close" (within about 1011) to the previous one. Such ladders have been used to empirically verify prime-related conjectures. For example, Goldbach's weak conjecture was verified in 2008 up to 8.875·1030 using prime ladders constructed from Proth primes. (The conjecture was later proved by Harald Helfgott.) Also, Proth primes can optimize den Boer reduction between the Diffie-Hellman problem and the Discrete logarithm problem.
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It led to many results within the Zimmer Program, although many of the main conjectures remain open. In addition to Margulis, Zimmer was greatly influenced by the work of Mikhail Gromov on rigid transformation groups and he extended and connected Gromov's theory to the Zimmer Program. Zimmer collaborated with a number of mathematicians to apply the ideas from the Zimmer Program to other areas of mathematics. His collaboration with Alexander Lubotzky applied some of these ideas to arithmetic results on fundamental groups of manifolds.
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The behavior of algebraic cycles ranks among the most important open questions in modern mathematics. The Hodge conjecture, one of the Clay Mathematics Institute's Millenium Prize Problems, predicts that the topology of a complex algebraic variety forces the existence of certain algebraic cycles. The Tate conjecture makes a similar prediction for étale cohomology. Alexander Grothendieck's standard conjectures on algebraic cycles yield enough cycles to construct his category of motives and would imply that algebraic cycles play a vital role in any cohomology theory of algebraic varieties.
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Mauros first appears in the sources in relation to Kuber's plot to conquer Thessaloniki in c. 686–687. From the testaments of contemporaneous historians, it is apparent that Mauros was a well-respected figure among the population ruled by Kuber, which consisted of Bulgars and Sermesianoi (Byzantine refugees from Sirmium on the Sava)Curta, p. 106 who had settled in Macedonia. Bulgarian historian Plamen Pavlov conjectures that Mauros may have been the kavhan (first minister) or ichirgu-boil (general of the highest rank) of Kuber.
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As a corollary he proved the celebrated Ramanujan–Petersson conjecture for modular forms of weight greater than one; weight one was proved in his work with Serre. Deligne's 1974 paper contains the first proof of the Weil conjectures. Deligne's contribution being to supply the estimate of the eigenvalues of the Frobenius endomorphism, considered the geometric analogue of the Riemann hypothesis. It also led to the proof of Lefschetz hyperplane theorem and the old and new estimates of the classical exponential sums, among other applications.
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It is worth noting here a subtle difference between the maximum- parsimony criterion and the ME criterion: while maximum-parsimony is based on an abductive heuristic, i.e., the plausibility of the simplest evolutionary hypothesis of taxa with respect to the more complex ones, the ME criterion is based on Kidd and Sgaramella-Zonta's conjectures that were proven true 22 years later by Rzhetsky and Nei. These mathematical results set the ME criterion free from the Occam's razor principle and confer it a solid theoretical and quantitative basis.
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The letter was first published in French. The essay remained unavailable in the United States until the 1920s. Although the exact origins of the term are uncertain, it was perhaps so-called because it was first noted in regions inhabited by American Indians, or because the Indians first described it to Europeans, or it had been based on the warm and hazy conditions in autumn when American Indians hunted. In addition to such conjectures, a great depth of Native American folklore is attributed to describing this phenomenon.
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The Riemann hypothesis can be generalized by replacing the Riemann zeta function by the formally similar, but much more general, global L-functions. In this broader setting, one expects the non-trivial zeros of the global L-functions to have real part 1/2. It is these conjectures, rather than the classical Riemann hypothesis only for the single Riemann zeta function, which account for the true importance of the Riemann hypothesis in mathematics. The generalized Riemann hypothesis extends the Riemann hypothesis to all Dirichlet L-functions.
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In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space for which there are only finitely many points. While topology has mainly been developed for infinite spaces, finite topological spaces are often used to provide examples of interesting phenomena or counterexamples to plausible sounding conjectures. William Thurston has called the study of finite topologies in this sense "an oddball topic that can lend good insight to a variety of questions".
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Bianxiang (變相) refers to the transformation of a Buddhist sutra into a pictorial representation. That bianwen is extricably linked to bianxiang is not disputed, but the precise nature of the relationship remains undetermined. Professor Bai Huawen of Peking University speculates that bianwen was performed in combination with bianxiang pictures, and that the text was in effect a prosimetric literary script of the performance. He further conjectures that in addition to painted scrolls, wall-paintings and painted banners were also used in conjunction with bianwen for performances.
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A projective spherical variety is a Mori dream space. Spherical embeddings are classified by so-called colored fans, a generalization of fans for toric varieties; this is known as Luna-Vust Theory. In his seminal paper, develops a framework to classify complex spherical subgroups of reductive groups; he reduces the classification of spherical subgroups to wonderful subgroups. He works out completely the case of groups of type A and conjectures that the combinatorial objects (homogeneous spherical data) he introduces indeed provide a combinatorial classification of spherical subgroups.
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He has stated on Goodreads that his favourite novels are Anthony Powell's saga A Dance to the Music of Time. He has also published two humour books entitled What Pooh Might Have Said to Dante (2012) and If Research Were Romance and other Implausible Conjectures (2013), compiling book reviews originally written by him for the Goodreads.com social website. He has also written the humorous books The New Adventures of Socrates: An Extravagance and Everything You Need to Know to Write a Work of Satire in Trump's America.
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Accessed online 14 August 2008. A June 2007 piece in the Seattle Times states that the "genre-flouting" group have been praised by virtually all media in Seattle who cover popular music, but have yet to get geographically broader attention, partly (it conjectures) because their 2007 appearance at South by Southwest in Austin, Texas has been their only non-Seattle-area performance to date.Jonathan Zwickel, C'mon, America, the Saturday Knights are a hip-hop marvel, Seattle Times, June 27, 2008. Accessed online 14 August 2008.
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The planar GFF is also the limit of the fluctuations of the characteristic polynomial of a random matrix model, the Ginibre ensemble, see . The structure of the discrete GFF on any graph is closely related to the behaviour of the simple random walk on the graph. For instance, the discrete GFF plays a key role in the proof by of several conjectures about the cover time of graphs (the expected number of steps it takes for the random walk to visit all the vertices).
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Based on a 1978 observation by mathematician John McKay, Conway and Norton formulated the complex of conjectures known as monstrous moonshine. This subject, named by Conway, relates the monster group with elliptic modular functions, thus bridging two previously distinct areas of mathematics—finite groups and complex function theory. Monstrous moonshine theory has now been revealed to also have deep connections to string theory.Monstrous Moonshine conjecture David Darling: Encyclopedia of Science Conway introduced the Mathieu groupoid, an extension of the Mathieu group M12 to 13 points.
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He argues that even the telephone can be regarded as an online experience in some circumstances, and that the blurring of the distinctions between the uses of various technologies (such as PDA versus mobile phone, internet television versus internet, and telephone versus Voice over Internet Protocol) has made it "impossible to use the term online meaningfully in the sense that was employed by the first generation of Internet research". Slater asserts that there are legal and regulatory pressures to reduce the distinction between online and offline, with a "general tendency to assimilate online to offline and erase the distinction," stressing, however, that this does not mean that online relationships are being reduced to pre-existing offline relationships. He conjectures that greater legal status may be assigned to online relationships (pointing out that contractual relationships, such as business transactions, online are already seen as just as "real" as their offline counterparts), although he states it to be hard to imagine courts awarding palimony to people who have had a purely online sexual relationship. He also conjectures that an online/offline distinction may be seen by people as "rather quaint and not quite comprehensible" within 10 years.
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The first series depicts Caroline's marriage to John (Tony Gardner, pictured) coming to an end. Caroline is established as a successful career woman with a background in academia, holding a chemistry degree from Oxford University. The BBC's official website noted that though her marriage is disintegrating by the start of the first series, her career is "going from strength to strength". Explaining how her character ended up married to John (Tony Gardner), Lancashire conjectures that Caroline had been "charmed by his love of words" and that he had been "a romantic who balanced her out".
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The L-group is used heavily in the Langlands conjectures of Robert Langlands. It is used to make precise statements from ideas that automorphic forms are in a sense functorial in the group G, when k is a global field. It is not exactly G with respect to which automorphic forms and representations are functorial, but LG. This makes sense of numerous phenomena, such as 'lifting' of forms from one group to another larger one, and the general fact that certain groups that become isomorphic after field extensions have related automorphic representations.
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They do that through the creativity or "good judgment" of the scientists only. For Popper, the required non deductive component of science never had to be an inductive methodology. He always viewed this component as a creative process beyond the explanatory reach of any rational methodology, but yet used to decide which theories should be studied and applied, find good problems and guess useful conjectures. Quoting Einstein to support his view, Popper said that this renders obsolete the need for an inductive methodology or logical path to the laws.
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The fate of the invention, mentioned in Kybalchych's last letter, proved to be as tragic as that of its 27-year-old creator. Kibalchich’s design was buried in the archives of Police Department, but the tsar authorities failed to consign the name of the inventor and his idea to oblivion. The trial and execution of the Narodniks had wide repercussions around the world. Much was said and written about Kibalchich’s design abroad and all kinds of conjectures were made about the essence of the invention and its subsequent fate.
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Applying the Tannakian formalism, one concludes that Mnum is equivalent to the category of representations of an algebraic group G, known as the motivic Galois group. The motivic Galois group is to the theory of motives what the Mumford–Tate group is to Hodge theory. Again speaking in rough terms, the Hodge and Tate conjectures are types of invariant theory (the spaces that are morally the algebraic cycles are picked out by invariance under a group, if one sets up the correct definitions). The motivic Galois group has the surrounding representation theory.
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Between 1956 and 1957, Yutaka Taniyama and Goro Shimura posed the Taniyama–Shimura conjecture (now known as the modularity theorem) relating elliptic curves to modular forms. This connection would ultimately lead to the first proof of Fermat's Last Theorem in number theory through algebraic geometry techniques of modularity lifting developed by Andrew Wiles in 1995. In the 1960s, Goro Shimura introduced Shimura varieties as generalizations of modular curves. Since the 1979, Shimura varieties have played a crucial role in the Langlands program as a natural realm of examples for testing conjectures.
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This was the first of the three major expansions, each related to one of the principal characters. As the focus of his attention shifted from one to another of these three principals, he modified the plot and thematic emphasis. Because Melville never entirely finished the revisions, critics have been divided as to where the emphasis lay and to Melville's intentions. After Melville's death, his wife Elizabeth, who had acted as his amanuensis on other projects, scribbled notes and conjectures, corrected spelling, sorted leaves and, in some instances, wrote over her husband's faint writing.
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Greek mathematician Euclid (holding calipers), 3rd century BC, as imagined by Raphael in this detail from The School of Athens (1509–1511) Mathematics (from Greek: ) includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature.
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Langlands generalized the idea of functoriality: instead of using the general linear group GL(n), other connected reductive groups can be used. Furthermore, given such a group G, Langlands constructs the Langlands dual group LG, and then, for every automorphic cuspidal representation of G and every finite-dimensional representation of LG, he defines an L-function. One of his conjectures states that these L-functions satisfy a certain functional equation generalizing those of other known L-functions. He then goes on to formulate a very general "Functoriality Principle".
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Given two reductive groups and a (well behaved) morphism between their corresponding L-groups, this conjecture relates their automorphic representations in a way that is compatible with their L-functions. This functoriality conjecture implies all the other conjectures presented so far. It is of the nature of an induced representation construction—what in the more traditional theory of automorphic forms had been called a 'lifting', known in special cases, and so is covariant (whereas a restricted representation is contravariant). Attempts to specify a direct construction have only produced some conditional results.
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In mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced by Émile Picard for complex surfaces in his book , and extended to higher dimensions by . It is a complex analog of Morse theory that studies the topology of a real manifold by looking at the critical points of a real function. extended Picard–Lefschetz theory to varieties over more general fields, and Deligne used this generalization in his proof of the Weil conjectures.
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His other works include the Castigationes (commentaries) of Cicero's family letter, and editions of works by Varro, Cato, Aeschylus, Sallust, Aristotle, Euripides's Electra and others. His edition of Aeschylus (1557) was the first printed edition to include the whole of the Agamemnon, as the earlier editors of Aeschylus Francesco Robortello and Adrianus Turnebus had only had lines 1-310 and 1067-1159 available to them. Vettori made very few textual conjectures in this edition, but Henricus Stephanus, who printed it, added an appendix with some further corrections.E. Fraenkel, Aeschylus: Agamemnon, volume 1, pp. 34-35.
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The earliest known documented outbreak of unexplained livestock deaths occurred in early 1606 "...about the city of London and some of the shires adjoining. Whole slaughters of sheep have been made, in some places to number 100, in others less, where nothing is taken from the sheep but their tallow and some inward parts, the whole carcasses, and fleece remaining still behind. Of this sundry conjectures, but most agree that it tendeth towards some fireworks." The outbreak was noted in the official records of the Court of James I of England.
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Clark's first and only numismatic work, Some conjectures relative to a very antient piece of money (1751), which incorrectly identified a recently discovered coin, proved to be an utter failure. It was refuted swiftly and unsympathetically, by numismatist George North, who correctly identified the coin as a common Peny-yard pence. Even if some unassociated conclusions were true, Clarke was humiliated, feeling his "reputation and character" damaged by North's response. Clarke attempted some later publications, including a bitter refutation of one of North's works, but none ever came to fruition.
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It is argued that most firms do not conduct this type of analysis systematically enough. Instead, many enterprises operate on what is called "informal impressions, conjectures, and intuition gained through the tidbits of information about competitors every manager continually receives." As a result, traditional environmental scanning places many firms at risk of dangerous competitive blindspots due to a lack of robust competitor analysis.(Fleisher & Bensoussan, 2007) It is important to conduct the competitor analysis at various business stages to provide the best possible product or service for customers.
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Applying this, the authors compute the second line of the Adams–Novikov spectral sequence and establish the non-triviality of a certain family in the stable homotopy groups of spheres. In all of this, the authors use work by Jack Morava and themselves on Brown–Peterson cohomology and Morava K-theory. In the second paper, Ravenel expands these phenomena to a global picture of stable homotopy theory leading to the Ravenel conjectures. In this picture, complex cobordism and Morava K-theory control many qualitative phenomena, which were understood before only in special cases.
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He contributed to p-adic Hodge theory, logarithmic geometry (he was one of its creators together with Jean-Marc Fontaine and Luc Illusie), comparison conjectures, special values of zeta functions including the Birch-Swinnerton- Dyer conjecture and Bloch-Kato conjecture on Tamagawa numbers, Iwasawa theory. A special volume of Documenta Mathematica was published in honor of his 50th birthday, together with research papers written by leading number theorists and former students it contains Kato's song on Prime Numbers. In 2005 Kato received the Imperial Prize of the Japan Academy for "Research on Arithmetic Geometry".
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Aside from Susan, the only client with any substantial connection to that hospital is Jack Ennis, an inventor who had unsuccessfully tried to persuade the staff to use a new X-ray machine he had designed. Wolfe conjectures that he set the bomb as revenge for this rejection, learned that Heller might have become suspicious enough to call in Wolfe, and killed him. As Ennis is placed under arrest, Archie reassures Susan that he is guilty, and a jury reaches the same conclusion at his trial two months later.
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When this way of argumentation was dropped, the ability to understand the results were lost as well. Thus Russo conjectures that the definitions of elementary geometric objects were introduced in Euclid's Elements by Heron of Alexandria, 400 years after the work was completed. More concretely, Russo shows how the theory of tides must have been well-developed in Antiquity, because several pre-Newtonian sources relay various complementary parts of the theory without grasping their import or justification (getting the empirical facts wrong but the theory right). Hellenistic science was focused on the city of Alexandria.
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However, Popper criticised what he saw as Kuhn's relativism.K R Popper (1970), in I Lakatos & A Musgrave (eds.) (1970), at p. 56. Also, in his collection Conjectures and Refutations: The Growth of Scientific Knowledge (Harper & Row, 1963), Popper writes, Another objection is that it is not always possible to demonstrate falsehood definitively, especially if one is using statistical criteria to evaluate a null hypothesis. More generally it is not always clear, if evidence contradicts a hypothesis, that this is a sign of flaws in the hypothesis rather than of flaws in the evidence.
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One Yugoslav border guard was seriously wounded in the clash. According to the Israeli historian Shaul Shay, the ambush represented the first clash of the Kosovo War between the VJ and foreign mujahideen. The Human Rights Watch advisor Fred C. Abrahams conjectures that the mujahideen may have deliberately been led into a trap by the KLA as part of a plan to reduce the influence of Islamic extremists within the organization's ranks. Later in the day, 19 KLA fighters were wounded when the VJ shelled an arms smuggling route near the site of the ambush.
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Proving a bound strictly greater than 1/2 for the dimension of the distance set in the case of compact planar sets with Hausdorff dimension at least one would be equivalent to resolving several other unsolved conjectures. These include a conjecture of Paul Erdős on the existence of Borel subrings of the real numbers with fractional Hausdorff dimension, and a variant of the Kakeya set problem on the Hausdorff dimension of sets such that, for every possible direction, there is a line segment whose intersection with the set has high Hausdorff dimension..
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Early in the twenty-first century he proved two of Saffari's conjectures, the phase problem and the near orthogonality conjecture. In 2007, working with Borwein, Ferguson, and Lockhart, he settled Littlewood's Problem 22. He is an expert on ultraflat and flat sequences of unimodular polynomials, having published papers on the location of zeros for polynomials with constrained coefficients, and on orthogonal polynomials. He has also made significant contributions to the integer Chebyshev problem, worked with Harvey Friedman on recursion theory, and, together with Borwein, disproved a conjecture made by the Chudnovsky brothers.
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Most of the interest in the topic is due to the AdS/CFT correspondence where there is a number of conjectures relating higher spin theories to weakly coupled conformal field theories. It is important to note that only certain parts of these theories are known at present (in particular, standard action principles are not known) and not many examples have been worked out in detail except some specific toy models (such as the higher spin extension of pure Chern-Simons, Jackiw-Teitelboim, selfdual (chiral) and Weyl gravity theories).
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Seymour continued to work with Chudnovsky, and obtained several more results about induced subgraphs, in particular (with Cornuéjols, Liu, Vuskovic) a polynomial-time algorithm to test whether a graph is perfect, and a general description of all claw-free graphs. Most recently, in a series of papers with Alex Scott and partly with Chudnovsky, they proved two conjectures of András Gyárfás, that every graph with bounded clique number and sufficiently large chromatic number has an induced cycle of odd length at least five, and has an induced cycle of length at least any specified number.
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In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both in terms of results and conjectures. Most of these can be posed for an abelian variety A over a number field K; or more generally (for global fields or more general finitely-generated rings or fields).
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First passage percolation is one of the most classical areas of probability theory. It was first introduced by John Hammersley and Dominic Welsh in 1965 as a model of fluid flow in a porous media. It is part of percolation theory, and classical Bernoulli percolation can be viewed as a subset of first passage percolation. Most of the beauty of the model lies in its simple definition (as a random metric space) and the property that several of its fascinating conjectures do not require much effort to be stated.
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The condition of having no fixed prime divisor is certainly effectively checkable in a given case, since there is an explicit basis for the integer-valued polynomials. As a simple example, : x^2 + 1 has no fixed prime divisor. We therefore expect that there are infinitely many primes : n^2 + 1 This has not been proved, though. It was one of Landau's conjectures and goes back to Euler, who observed in a letter to Goldbach in 1752 that n^2 + 1 is often prime for n up to 1500.
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The attributions of Pashkov House and lesser projects to Bazhenov, backed by a sketchy paper trail, deductions and conjectures, are uncertain to the point where his life and work became subject of conspiracy theories.For example, Even his place of birth and the location of Bazhenov's grave are unknown. His life story, as reconstructed by Igor Grabar and popularized by the historians of the Soviet period, is regarded by modern critics as the "Bazhenov myth", and even most recent academic researchGerchuk, 2001 fails to replace this myth with a reliable biography.
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The main conjecture of Iwasawa theory (now a theorem due to Barry Mazur and Andrew Wiles) is the statement that the Kubota–Leopoldt p-adic L-function and an arithmetic analogue constructed by Iwasawa theory are essentially the same. In more general situations where both analytic and arithmetic p-adic L-functions are constructed (or expected), the statement that they agree is called the main conjecture of Iwasawa theory for that situation. Such conjectures represent formal statements concerning the philosophy that special values of L-functions contain arithmetic information.
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Little is known about Shi. Traditionally, it was believed that he was a teacher of Luo Guanzhong, the editor or author of Romance of the Three Kingdoms, another of the Four Great Classical Novels. The recent Chinese scholar Ge Liangyan writes that little is known about Luo, and about Shi even less. Late Ming and early Qing scholars claimed that Shi lived near the end of the Yuan dynasty and that he was a native of Hangzhou, but they may have been echoing each other or citing the conjectures that they did not endorse.
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In 1970, Ringbom succeeded his father as professor of art history at Åbo Akademi University. Ringbom became the first scientist who has supposed an existence of a connection between early abstract art and occultism. He published his conjectures in an article "Art in 'The Epoch of the Great Spiritual': Occult Elements in the Early Theory of Abstract Painting" (1966) and in a book The Sounding Cosmos: A Study in the Spiritualism of Kandinsky and the Genesis of Abstract Painting (1970). According to WorldCat, he had written 93 works.
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More precisely, the Langlands conjectures associate an automorphic representation of the adelic group GLn(AQ) to every n-dimensional irreducible representation of the Galois group, which is a cuspidal representation if the Galois representation is irreducible, such that the Artin L-function of the Galois representation is the same as the automorphic L-function of the automorphic representation. The Artin conjecture then follows immediately from the known fact that the L-functions of cuspidal automorphic representations are holomorphic. This was one of the major motivations for Langlands' work.
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Algebraic K-groups are used in conjectures on special values of L-functions and the formulation of a non-commutative main conjecture of Iwasawa theory and in construction of higher regulators.Lemmermeyer (2000) p.385 Parshin's conjecture concerns the higher algebraic K-groups for smooth varieties over finite fields, and states that in this case the groups vanish up to torsion. Another fundamental conjecture due to Hyman Bass (Bass' conjecture) says that all of the groups Gn(A) are finitely generated when A is a finitely generated Z-algebra.
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Elizabeth Woodville was born about 1437, possibly in October,No record of Elizabeth's birth survives. She was the product of a secret marriage between Richard Woodville, a prominent English gentleman, and Jacquetta of Luxembourg, the aristocratic eldest daughter of Peter I of Luxembourg, Count of Saint-Pol, Conversano and Brienne. The marriage caused a scandal when it came to public notice and the couple were fined, and, on 24 October 1437, pardoned for marrying without royal permission. David Baldwin conjectures that the pardon coincided with the birth of Elizabeth Woodville, the couple's firstborn child.
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One cause of concern for some people is that Tonga hasn't signed the Convention on the Elimination of All Forms of Discrimination Against Women (CEDAW), an important international treaty that the vast majority of countries have signed. There are several conjectures as to why Tonga has refrained from signing. Some people think the land ownership issues where only men can own land are the problem. Others say Tongans need to focus on becoming a full democracy because that would give women more voice in the government and likely improve their position as a result.
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In algebraic number theory, an equivariant Artin L-function is a function associated to a finite Galois extension of global fields created by packaging together the various Artin L-functions associated with the extension. Each extension has many traditional Artin L-functions associated with it, corresponding to the characters of representations of the Galois group. By contrast, each extension has a unique corresponding equivariant L-function. Equivariant L-functions have become increasingly important as a wide range of conjectures and theorems in number theory have been developed around them.
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Karl Popper, ch 4, subch "Science: Conjectures and refutations", in Andrew Bailey, ed, First Philosophy: Fundamental Problems and Readings in Philosophy, 2nd edn (Peterborough Ontario: Broadview Press, 2011), pp. 338–42. Popper regarded scientific hypotheses to be unverifiable, as well as not "confirmable" under Rudolf Carnap's thesis.Peter Godfrey-Smith, Theory and Reality: An Introduction to the Philosophy of Science (Chicago: University of Chicago Press, 2005), pp. 57–59. He also found non-scientific, metaphysical, ethical and aesthetic statements often rich in meaning and important in the origination of scientific theories.
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Andronicus () was an Ancient Macedonian who is first mentioned in the war against Antiochus III the Great in 190 BCE, as the governor of Ephesus.Livy, Ab Urbe Condita Libri xxxvii. 13. He is spoken of in 169 as one of the generals of Perseus of Macedon, and was sent by him to burn the dock-yards at Thessalonica, which he delayed doing, wishing to gratify the Romans, according to Diodorus Siculus, or thinking that the king would relent of his purpose, as Livy conjectures. Andronicus was shortly afterwards put to death by Perseus.
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The first application of the omega and agemo subgroups was to draw out the analogy of regular p-groups with abelian p-groups in . Groups in which Ω(G) ≤ Z(G) were studied by John G. Thompson and have seen several more recent applications. The dual notion, groups with [G,G] ≤ ℧(G) are called powerful p-groups and were introduced by Avinoam Mann. These groups were critical for the proof of the coclass conjectures which introduced an important way to understand the structure and classification of finite p-groups.
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Effects of European infectious diseases and conquest, and assimilation by larger native tribes, led to native abandonment of the settlement long before English explorers arrived in the region in the 17th century. De Soto's 1540 expedition noted the Chalaque already in the area at the time. According to some modern-day conjectures, the Cherokee, an Iroquoian-speaking people, migrated into western North Carolina from northern areas around the Great Lakes and used some of the former Mississippian village sites. English, Scots-Irish and German immigrants arrived in the 18th century.
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The field of Diophantine approximation deals with the cases of Diophantine inequalities. Here variables are still supposed to be integral, but some coefficients may be irrational numbers, and the equality sign is replaced by upper and lower bounds. The single most celebrated question in the field, the conjecture known as Fermat's Last Theorem, was solved by Andrew Wiles, using tools from algebraic geometry developed during the last century rather than within number theory where the conjecture was originally formulated. Other major results, such as Faltings's theorem, have disposed of old conjectures.
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Continuing the tradition of Vedanta, he authored a commentary on Nyaya Sudha of Jayatirtha called Vagvajra which, according to Sharma, "is a lucid and attractive commentary in 3500 granthas". He also adds that despite the exhaustive exposition and the graceful style, his role as a Haridasa eclipsed his scholarly work. He is often considered as the pioneer of Dasa Sahitya with his simple worded and spiritual hymns synchronised to music. Jackson conjectures that the simple and rural beginnings of Sripadaraya coupled with an intimate connection with his vernacular language influenced his poetry.
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Felleisen conjectures, Matthias Felleisen, LL1 mailing list posting that these three categories make up the primary legitimate uses of macros in such a system. Others have proposed alternative uses of macros, such as anaphoric macros in macro systems that are unhygienic or allow selective unhygienic transformation. The interaction of macros and other language features has been a productive area of research. For example, components and modules are useful for large-scale programming, but the interaction of macros and these other constructs must be defined for their use together.
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User definitions in the programming language that satisfy a definitional principle extend the theory in a way that maintains the theory's logical consistency. The core of ACL2's theorem prover is based on term rewriting, and this core is extensible in that user-discovered theorems can be used as ad-hoc proof techniques for subsequent conjectures. ACL2 is intended to be an "industrial strength" version of the Boyer–Moore theorem prover, NQTHM. Toward this goal, ACL2 has many features to support clean engineering of interesting mathematical and computational theories.
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Victor Gershevich (Grigorievich) Kac (; born 19 December 1943) is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discoveredStephen Berman, Karen Parshall "Victor Kac and Robert Moody — their paths to Kac–Moody-Algebras", Mathematical Intelligencer, 2002, Nr.1 Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.
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In number theory, Gillies' conjecture is a conjecture about the distribution of prime divisors of Mersenne numbers and was made by Donald B. Gillies in a 1964 paper in which he also announced the discovery of three new Mersenne primes. The conjecture is a specialization of the prime number theorem and is a refinement of conjectures due to I. J. Good and Daniel Shanks. The conjecture remains an open problem: several papers give empirical support, but it disagrees with the widely accepted (but also open) Lenstra–Pomerance–Wagstaff conjecture.
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William Blackstone wrote, in 1765, "The reason of [this] appellation Sir Edward Coke offers many conjectures; but there is one which seems more probable than any that he has given us: viz. that these purchases being usually made by ecclesiastical bodies, the members of which (being professed) were reckoned dead persons in law, land therefore, holden by them, might with great propriety be said to be held in mortua manu. [in dead hands]."William Blackstone, Commentaries on the Laws of England, Volume I, "Of the Rights of Persons".
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A break in research while he was involved in trying to meet 1960s student activism halfway caused him (by his own description) difficulties in picking up the threads afterwards. He wrote on modular forms and modular units, the idea of a 'distribution' on a profinite group, and value distribution theory. He made a number of conjectures in diophantine geometry: Mordell–Lang conjecture, Bombieri–Lang conjecture, Lang–Trotter conjecture, and the Lang conjecture on analytically hyperbolic varieties. He introduced the Lang map, the Katz–Lang finiteness theorem, and the Lang–Steinberg theorem (cf.
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The editio princeps was printed in 1474 in Rome by Georg Sachsel and Bartholomaeus Golsch, which broke off at the end of Book 26. The next edition (Bologna, 1517) suffered from its editor's conjectures upon the poor text of the 1474 edition; the 1474 edition was pirated for the first Froben edition (Basle, 1518). It was not until 1533 that the last five books of Ammianus' history were put into print by Silvanus Otmar and edited by Mariangelus Accursius. The first modern edition was produced by C.U. Clark (Berlin, 1910–1913).
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In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by that for a finite set of linear forms , , ..., with , there are infinitely many positive integers for which they are all prime, unless there is a congruence condition preventing this . The case k = 1 is Dirichlet's theorem. Two other special cases are well-known conjectures: there are infinitely many twin primes (n and 2 + n are primes), and there are infinitely many Sophie Germain primes (n and 1 + 2n are primes). Dickson's conjecture is further extended by Schinzel's hypothesis H.
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A 3-manifold with a Riemannian metric of constant positive sectional curvature is covered by the 3-sphere, moreover the group of covering transformations are isometries of the 3-sphere. If the original 3-manifold had in fact a trivial fundamental group, then it is homeomorphic to the 3-sphere (via the covering map). Thus, proving the elliptization conjecture would prove the Poincaré conjecture as a corollary. In fact, the elliptization conjecture is logically equivalent to two simpler conjectures: the Poincaré conjecture and the spherical space form conjecture.
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Befitting the single historical mention of the Novantae by Ptolemy, many historians have largely included the Novantae im passim in their works, if they are mentioned at all. William Forbes Skene (Celtic Scotland, 1886) briefly relates their notice in Ptolemy, adding his conjectures as to the possible locations of towns, though not with any conviction., Celtic Scotland John Rhys (Celtic Britain, 1904) mentions the Novantae in passing, without any detailed discussion., Celtic Britain Local Galwegian historians, writing histories of their own home territory, provide a similarly scant treatment.
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Unlike von Neumann–Bernays–Gödel set theory (NBG) and Morse–Kelley set theory (MK), ZFC does not admit the existence of proper classes. A further comparative weakness of ZFC is that the axiom of choice included in ZFC is weaker than the axiom of global choice included in NBG and MK. There are numerous mathematical statements undecidable in ZFC. These include the continuum hypothesis, the Whitehead problem, and the normal Moore space conjecture. Some of these conjectures are provable with the addition of axioms such as Martin's axiom or large cardinal axioms to ZFC.
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In theoretical physics, unparticle physics is a speculative theory that conjectures a form of matter that cannot be explained in terms of particles using the Standard Model of particle physics, because its components are scale invariant. Howard Georgi proposed this theory in two 2007 papers, "Unparticle Physics" and "Another Odd Thing About Unparticle Physics". His papers were followed by further work by other researchers into the properties and phenomenology of unparticle physics and its potential impact on particle physics, astrophysics, cosmology, CP violation, lepton flavour violation, muon decay, neutrino oscillations, and supersymmetry.
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On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide counterexamples to conjectures, showing the boundaries of possible theorems. Of course, one can easily find regular spaces that are not T0, and thus not Hausdorff, such as an indiscrete space, but these examples provide more insight on the T0 axiom than on regularity. An example of a regular space that is not completely regular is the Tychonoff corkscrew. Most interesting spaces in mathematics that are regular also satisfy some stronger condition.
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Born on 9 November 1859 in Ugilt near Hjørring, Classen was the daughter of the forester Henrich Wilhelm Claussen and his wife Ane Hedevig Cortsen. She grew up near the village of Børglum between Hjørring and Frederikshavn as her father worked on the Børglum Abbey estate. Claussen showed an early interest in art, sketching scenes of the surrounding countryside from the age of eight. After her father died when she was 14, she was inspired to start writing poetry in a collection she titled Gisninger (Conjectures) in which she documented her religious and existential ideas.
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Kefeng Liu (Chinese: 刘克峰; born 12 December 1965), is a Chinese-American mathematician who is known for his contributions to geometric analysis, particularly the geometry, topology and analysis of moduli spaces of Riemann surfaces and Calabi-Yau manifolds. He is a professor of mathematics at University of California, Los Angeles, as well as the Executive Director of the Center of Mathematical Sciences at Zhejiang University. He is best-known for his collaboration with Bong Lian and Shing-Tung Yau in which they establish some enumerative geometry conjectures motivated by mirror symmetry.
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For a projective variety X, the study of holomorphic maps C → X has some analogy with the study of rational points of X, a central topic of number theory. There are several conjectures on the relation between these two subjects. In particular, let X be a projective variety over a number field k. Fix an embedding of k into C. Then Lang conjectured that the complex manifold X(C) is Kobayashi hyperbolic if and only if X has only finitely many F-rational points for every finite extension field F of k.
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More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group G(AF), for an algebraic group G and an algebraic number field F, is a complex- valued function on G(AF) that is left invariant under G(F) and satisfies certain smoothness and growth conditions. Poincaré first discovered automorphic forms as generalizations of trigonometric and elliptic functions. Through the Langlands conjectures automorphic forms play an important role in modern number theory.
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The judge insists unreasonably that the police Commissioner and Carabinieri should give him cast iron evidence if he is to proceed with any case, as in his view all he heard were conjectures. The estranged widow and son of the ambassador arrive and the extent of the family rift is evident. They appear to have relied on the local parish priest Don Cricco to oversee the mainly abandoned family properties in the area. The film ends with an accident in which the Inspector and Brigadiere exchange pistol shots, killing the Inspector.
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Bishop Fraser's opponents said of him that, "Omnipresence was his forte, and omniscience his foible", reflecting his restless activity in preaching the gospel, reform and activity in civil society. He was a common sight on the streets of Manchester, hurrying to address workers of all kinds several times a day. He was a vocal opponent of Charles Darwin’s ideas and in an address of 1871 said that they were, “merely guesses, conjectures, and inferences resting upon remote analogies”.Bishop Fraser on faith and Darwinism, Preston Chronicle 29 April 1871, page 2.
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Theodore Allen Slaman (born April 17, 1954) is a professor of mathematics at the University of California, Berkeley who works in recursion theory. Slaman and W. Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is logically equivalent to second order arithmetic. They showed that the Bi- interpretability Conjecture is equivalent to there being no nontrivial automorphism of the Turing degrees. They also exhibited limits on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable.
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Inter-universal Teichmüller theory (abbreviated as IUT) is the name given by mathematician Shinichi Mochizuki to a theory he developed in the 2000s, following his earlier work in arithmetic geometry. According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve". The theory was made public in a series of four preprints posted in 2012 to his website. The most striking claimed application of the theory is to provide a proof for various outstanding conjectures in number theory, in particular the abc conjecture.
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Inter-universal Teichmüller theory is a continuation of Mochizuki's previous work in arithmetic geometry. This work, which has been peer-reviewed and well-received by the mathematical community, includes major contributions to anabelian geometry, and the development of p-adic Teichmüller theory, Hodge–Arakelov theory and Frobenioid categories. It was developed with explicit references to the aim of getting a deeper understanding of abc and related conjectures. In the geometric setting, analogues to certain ideas of IUT appear in the proof by Bogomolov of the geometric Szpiro inequality.
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Since verse 14, the samech verse, contains the word "נֹּפְלִ֑ים" (the fallen), the Talmud conjectures that King David foresaw the destruction ("fall") of Israel and omitted a verse starting with nun, while nevertheless hinting to it in the next verse (c.f. the pattern of verse 12, ending with "מַלְכוּתֽוֹ" (His kingship), and verse 13, starting with "מַֽלְכוּתְךָ֗" (Your kingship)). The explanation may not satisfy modern readers (it did not satisfy Rabbi David Kimhi of the 13th centuryJacobson, Bernhard S., The Weekday Siddur (2nd Engl. ed., 1978, Tel-Aviv, Sinai) p 94.
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Victoria was aware that Conroy intended her to reward Victoire and her sister Jane with positions once she became queen. The princess also felt insulted that Conroy often boasted that his daughters "were as high as her". Victoire appears in the princess' journals and watercolours as a person "frequently noted but never analyzed," in contrast with Victoria's writings of her governess Louise Lehzen, for instance. Carolly Erickson conjectures that had Victoire been "warm and friendly" to the princess, the "lonely" Victoria would have liked rather than disliked and distrusted her.
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Fig. 11: Relations between mathematical spaces: locales, topoi etc In Grothendieck's work on the Weil conjectures, he introduced a new type of topology now called a Grothendieck topology. A topological space (in the ordinary sense) axiomatizes the notion of "nearness," making two points be nearby if and only if they lie in many of the same open sets. By contrast, a Grothendieck topology axiomatizes the notion of "covering". A covering of a space is a collection of subspaces that jointly contain all the information of the ambient space.
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One of the two papers containing the published proof of Fermat's Last Theorem is a joint work of Taylor and Andrew Wiles. In subsequent work, Taylor (along with Michael Harris) proved the local Langlands conjectures for GL(n) over a number field. A simpler proof was suggested almost at the same time by Guy Henniart, and ten years later by Peter Scholze. Taylor, together with Christophe Breuil, Brian Conrad and Fred Diamond, completed the proof of the Taniyama–Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction.
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According to the initial translation of the Eran inscription (by John Faithful Fleet in 1888), Bhanugupta participated to a non-specific battle in 510 CE (Line 5). This translation was the basis for various conjectures about a possible encounter with Toramana, the Alchon Huns ruler. It has been suggested that Bhanugupta was involved in an important battle of his time, and suffered important losses, possibly against the Hun invader Toramana, whom he may or may not have defeated in 510.Ancient Indian History and Civilization by Sailendra Nath Sen p.
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Sam and his daughter Sally, proprietors of the Black Bull Inn, are awaiting the arrival of guests when an elderly German professor stops to make enquiries. The inn is booked out; he asks unusual questions about the people staying at the inn, but his conjectures appear to be wrong. Shortly after he is turned away, the three women they had been expecting cancel their bookings by telephone. Sally is annoyed at the cancellation, but almost immediately they receive another telephone call from Mr and Mrs Ormund, a wealthy couple who book two rooms.
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In 1836 Darwin used his Red Notebook to record field observations during the last stages of his Beagle voyage, from May to 25 September. Page 113 mentions a meeting with Richard Owen, after the ship's return to England in October. Later notes mention discussions with other experts, including the geographer Sir Woodbine Parish, geologists Charles Lyell and Roderick Murchison, and the conchologist James De Carle Sowerby. Darwin also took brief notes on what he was reading, reminders on planned publications including his Journal of the voyage, and his developing "theories", "conjectures", and "hypotheses".
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Meanwhile, analysing a sample of the meat, Torchwood's resident medic Owen Harper (Burn Gorman) conjectures that it is being used for human consumption. Rhys texts Gwen asking for her to come home. He attempts to get her to confess to being at the crash site by questioning her on the police response to the lorry crash, but she is evasive. After following Gwen from home, Rhys sees her meeting up with her boss Jack Harkness near the invisible lift in Roald Dahl Plass and follows them to a warehouse on the outskirts of Cardiff.
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Everett used his time to write a book on European affairs, published in 1821 as Europe; or, A General Survey of the Present Situation of the Principal Powers; with Conjectures on Their Future Prospects. In it Everett described the Netherlands as "a decayed and decaying nation" whose creation had been an error and predicted that it would eventually disappear in the sea. After Adams became president in 1825, he appointed Everett minister to Spain, from 1825–1829. As ambassador to Spain, Everett maintained the United States' concern with Cuba as a nearby slaveholding colony.
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Thereafter she held temporary positions at Harvard University, the University of Chicago and University of Minnesota before joining the University of Utah in 1996. More recently, she has spent time at the Institute for Advanced Study in 2010 as a visitor and in 2017 as a member as well as at the Mathematical Sciences Research Institute in 2014 and 2018 as part of programs on perfectoid spaces and the homological conjectures, respectively. As of 2015 she was directrice de recherches at CNRS, based at École normale supérieure de Lyon.
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In 1971 she emigrated from the Soviet Union to Israel and she taught at the Hebrew University from 1971 until 1975. She began to work with Rufus Bowen at Berkeley and later emigrated to the United States and became a professor of mathematics at Berkeley. Her work included proofs of conjectures dealing with unipotent flows on quotients of Lie groups made by S. G. Dani and M. S. Raghunathan. For this and other work, she won the John J. Carty Award for the Advancement of Science in 1994.
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In 1900, Jacques Hadamard observed that Huygens' principle was broken when the number of spatial dimensions is even. From this, he developed a set of conjectures that remain an active topic of research. In particular, it has been discovered that Huygens' principle holds on a large class of homogenous spaces derived from the Coxeter group (so, for example, the Weyl groups of simple Lie algebras). The traditional statement of Huygens' principle for the D'Alembertian gives rise to the KdV hierarchy; analogously, the Dirac operator gives rise to the AKNS hierarchy.
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She conjectures that there is an element, wæsse, perhaps Old English, that signifies very specifically "land by a meandering river which floods and drains quickly", and her examples are primarily Midland and northern. This seems to fit the Erewash perfectly. A good example of the meandering character of the river will be seen around Gallows Inn Playing Fields, Ilkeston, where rapid flooding and draining occur frequently. As it meanders through Toton and Long Eaton the river splits into two sections; the main course veers to the east and the relief channel flows over a low weir in a straight southerly direction.
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Marx's predictions have been criticized because they have allegedly failed, with some pointing towards the GDP per capita increasing generally in capitalist economies compared to less market oriented economics, the capitalist economies not suffering worsening economic crises leading to the overthrow of the capitalist system and communist revolutions not occurring in the most advanced capitalist nations, but instead in undeveloped regions.Andrew Kliman, Reclaiming Marx's "Capital", Lanham, MD: Lexington Books, p. 208, emphases in original. In his books The Poverty of Historicism and Conjectures and Refutations, philosopher of science Karl Popper criticized the explanatory power and validity of historical materialism.
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Palace finds that Zell called Naomi Eddes every night, proof that she was lying to Palace earlier. When he confronts her, she explains that Zell was addicted to morphine and needed her help getting clean. Palace conjectures that the "12.375" on Zell's box is a percentage—that is, the threshold at which the chance of Maia destroying the Earth became high enough that it would be worth attempting a risky thing he'd always wanted to do: experimenting with drugs. When a computer check finds that Toussaint is the son of a onetime major local drug dealer, Palace returns to question him.
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Prodromus achieved immediate popularity and established Kircher's reputation as a scholar. The first enthusiastic response to the work came from Kircher's fellow Jesuit, Melchior Inchofer, who had been appointed as its censor. Normally censors wrote succinct reports with an opinion as to whether a work posed any doctrinal problems, but Inchofer was expansive in his praise, hailing the book as "a worthy beginning from which we may anticipate what will follow." A more critical note was sounded by Kircher's former mentor Peiresc, who complained of his inaccurate transliterations and warned him that presenting theories and conjectures as established fact would damage his reputation.
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This idea was based on previous conjectured structural decompositions of similar type that would have implied the strong perfect graph conjecture but turned out to be false.; ; ; , section 4.6 "The first conjectures". The five basic classes of perfect graphs that form the base case of this structural decomposition are the bipartite graphs, line graphs of bipartite graphs, complementary graphs of bipartite graphs, complements of line graphs of bipartite graphs, and double split graphs. It is easy to see that bipartite graphs are perfect: in any nontrivial induced subgraph, the clique number and chromatic number are both two and therefore both equal.
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This admission greatly affects Mitchell, who sees it as a sign of kinship. He takes Dexter to his old home and tells him that when he was 10, he startled his sister while spying on her in the shower; she fell and broke the glass door, slicing her femoral artery and bleeding to death. His mother later committed suicide by leaping off a building, leaving him in the care of his abusive father; Dexter conjectures that Mitchell bludgeoned his father to death, accounting for the third victim. For the remainder of the trip Mitchell exhibits sudden mood swings and irrational behavior.
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In the area of modern algebra known as group theory, a Tarski monster group, named for Alfred Tarski, is an infinite group G, such that every proper subgroup H of G, other than the identity subgroup, is a cyclic group of order a fixed prime number p. A Tarski monster group is necessarily simple. It was shown by Alexander Yu. Olshanskii in 1979 that Tarski groups exist, and that there is a Tarski p-group for every prime p > 1075. They are a source of counterexamples to conjectures in group theory, most importantly to Burnside's problem and the von Neumann conjecture.
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Sixtus was helped in his editing work by a few people he trusted, including Toledo and Rocca but excluding the members of the commission and Carafa. Sixtus V took pride in being a very competent text editor. When he was only a minor friar, he had started editing the complete work of St. Ambrose, the sixth and last volume of which was published after he became pope. This edition of the complete work of St. Ambrose produced by Sixtus is regarded as the worst ever published; it "replaced the readings of the manuscripts by the least justified conjectures".
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Zhu collaborated with Cao Huaidong of Lehigh University in verifying Grigori Perelman's proof of the Poincaré conjecture. The Cao–Zhu team is one of three teams formed for this purpose. The other teams were the Tian–Morgan team (Gang Tian of Princeton University and John Morgan of Columbia University) and the Kleiner–Lott team (Bruce Kleiner of Yale University and John Lott of University of Michigan). Zhu and Cao published a paper in the June 2006 issue of the Asian Journal of Mathematics with an exposition of the complete proof of the Poincaré and geometrization conjectures.
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The questioning of theism was not confined to abstract concerns in philosophy, but also developed as modern historical consciousness dawned. This new historical consciousness was presaged in the seventeenth century controversies of Deism where Biblical miracles, and especially Christ's resurrection, were called into doubt. Alongside the debates about miracles came new conjectures about the authorship of the Biblical books, and investigations into possible sub-documents and written sources undergirding the present biblical texts. A further element of controversy for Christians at that time arose in the wake of the theory of evolution as propounded in 1859 by Charles Darwin.
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The Macdonald polynomials P_\lambda are a two-parameter family of orthogonal polynomials indexed by a positive weight λ of a root system, introduced by Ian G. Macdonald (1987). They generalize several other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials. They are known to have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them. introduced a new basis for the space of symmetric functions, which specializes to many of the well-known bases for the symmetric functions, by suitable substitutions for the parameters q and t.
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The second medal at the same congress was received by Laurent Lafforgue In 1998 he gave a plenary lecture (A1-Homotopy Theory) at the International Congress of Mathematicians in Berlin. He coauthored (with Andrei Suslin and Eric M. Friedlander) Cycles, Transfers and Motivic Homology Theories, which develops the theory of motivic cohomology in some detail. From 2002, Voevodsky was a professor at the Institute for Advanced Study in Princeton, New Jersey. In January 2009, at an anniversary conference in honor of Alexander Grothendieck, held at the Institut des Hautes Études Scientifiques, Voevodsky announced a proof of the full Bloch–Kato conjectures.
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Foreman (2003) does not reject Woodin's argument outright but urges caution. Solomon Feferman (2011) has argued that CH is not a definite mathematical problem. He proposes a theory of "definiteness" using a semi-intuitionistic subsystem of ZF that accepts classical logic for bounded quantifiers but uses intuitionistic logic for unbounded ones, and suggests that a proposition \phi is mathematically "definite" if the semi-intuitionistic theory can prove (\phi \lor eg\phi). He conjectures that CH is not definite according to this notion, and proposes that CH should, therefore, be considered not to have a truth value.
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Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others. It can be much easier to show a proposition's truth to follow from another proposition than to prove it independently. A famous network of conditional proofs is the NP-complete class of complexity theory. There is a large number of interesting tasks, and while it is not known if a polynomial- time solution exists for any of them, it is known that if such a solution exists for any of them, one exists for all of them.
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In some occasions, the number of cases is quite large, in which case a brute-force proof may require as a practical matter the use of a computer algorithm to check all the cases. For example, the validity of the 1976 and 1997 brute-force proofs of the four color theorem by computer was initially doubted, but was eventually confirmed in 2005 by theorem-proving software. When a conjecture has been proven, it is no longer a conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem (which resolved the Poincaré conjecture), Fermat's Last Theorem, and others.
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In his dissertation, entitled "The conjectures of Birch and Swinnerton-Dyer for constant abelian varieties over function fields," he proved the conjecture of Birch and Swinnerton–Dyer for constant abelian varieties over function fields in characteristic not equal to zero. He also gave the first example of abelian varieties with finite Tate–Shafarevich group. He then went to study Shimura varieties (certain hermitian symmetric spaces, low-dimensional examples being modular curves) and motives. His students include Piotr Blass, Michael Bester, Matthew DeLong, Pierre Giguere, William Hawkins Jr, Matthias Pfau, Victor Scharaschkin, Stefan Treatman, Anthony Vazzana, and Wafa Wei.
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The ruling family of this confederation may have hailed from the Āshǐnà (阿史那) clan of the West Türkic tribes, although Constantine Zuckerman regards Āshǐnà and their pivotal role in the formation of the Khazars with scepticism. Golden notes that Chinese and Arabic reports are almost identical, making the connection a strong one, and conjectures that their leader may have been Yǐpíshèkuì (Chinese:乙毗射匱), who lost power or was killed around 651. Moving west, the confederation reached the land of the Akatziroi, who had been important allies of Byzantium in fighting off Attila's army.
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Typically, they represent two characters per metope either in action or repose. The interpretations of these metopes are only conjectures, starting from mere silhouettes of figures, sometimes barely discernible, and comparing them to other contemporary representations (mainly vases). There is one theme per side of the building, representing a fight each time: Amazonomachy in the west, fall of Troy in the north, gigantomachy in the east and fight of Centaurs and Lapiths in the south. The metopes have a purely warlike theme, like the decoration of the chryselephantine statue of Athena Parthenos housed in the Parthenon.
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169), following Braancamp Freire, conjectures this award may have been made as early as January 1500. Another royal letter, dated October 1501, gave da Gama the personal right to intervene and exercise a determining role on any future India-bound fleet. Around 1501, Vasco da Gama married Catarina de Ataíde, daughter of Álvaro de Ataíde, the alcaide-mór of Alvor (Algarve), and a prominent nobleman connected by kinship with the powerful Almeida family (Catarina was a first cousin of D. Francisco de Almeida).Catarina de Ataíde's mother, Maria da Silva, was the sister of Beatriz da Silva, mother of Francisco de Almeida.
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Example of Wang tessellation with 13 tiles. In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there exists also a periodic tiling, i.e., a tiling that is invariant under translations by vectors in a 2-dimensional lattice, like a wallpaper pattern. He also observed that this conjecture would imply the existence of an algorithm to decide whether a given finite set of Wang tiles can tile the plane.. Wang proposes his tiles, and conjectures that there are no aperiodic sets.. Presents the domino problem for a popular audience.
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It cannot, however, agree with Mr. Banerji that any of the buildings mentioned by him was erected in the twelfth century for, towards the end of the tenth century, the capital Haruppeswara was, in all probability, abandoned by Brahma Pala. The buildings in Tezpur must therefore belong to the ninth century. Further, the lofty temple the ruins of which he has described in the quotation given above and which, he conjectures was a sun-temple, may be the Himalaya like temple of Hataka Sulin which Vanamala is said to have recrected. In his report for the year 1925-26.
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101 In his 1974 thesis, Gerald Reisner gave a complete characterization of such complexes. This was soon followed up by more precise homological results about face rings due to Melvin Hochster. Then Richard Stanley found a way to prove the Upper Bound Conjecture for simplicial spheres, which was open at the time, using the face ring construction and Reisner's criterion of Cohen–Macaulayness. Stanley's idea of translating difficult conjectures in algebraic combinatorics into statements from commutative algebra and proving them by means of homological techniques was the origin of the rapidly developing field of combinatorial commutative algebra.
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This massive theory is important because, according to various conjectures, spontaneously broken gauges of higher-spins may contain an infinite tower of massive higher-spin particles on the top of the massless modes of lower spins s ≤ 2 like graviton similarly as in string theories. The linearized version of the higher-spin supergravity gives rise to dual graviton field in first order form. Interestingly, the Curtright field of such dual gravity model is of a mixed symmetry, hence the dual gravity theory can also be massive. Also the chiral and nonchiral actions can be obtained from the manifestly covariant Curtright action.
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Borcea had a comprehensive project on the distribution of positive charges and the Hausdorff geometry of complex polynomials. One of the motivations for the project was to bring Sendov’s conjecture into a larger and more natural context. He formulated several interesting conjectures, and in the summer of 2008 he was the driving force of two meetings, one at the American Institute of Mathematics in San Jose, California and the other at the Banff International Research Station together with Dmitry Khavinson, Rajesh Pereira, Mihai Putinar, Edward B. Saff, and Serguei Shimorin. These two encounters were focused on structuring and expanding Julius’ program.
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She wrote that her cell was small, filthy, foul, infested with fleas, and that the rats were so numerous and hungry that they ate her night candle as it burned. She learned to piece together pages for writing from the wrappers on the sugar that she was given, and to make ink for her fowl's quill by capturing the candle's smoke on a spoon. Slowly she adjusted to her plight, ceased longing for revenge or death, and developed a mordant humor. She studied the vermin who were her only companions, recording her observations and conjectures about their instincts.
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He wrote The Search for Society (1989) his "equal time response" to the interpretive anthropology of Clifford Geertz, and The Violent Imagination (1989), a book of essays, verse, satire, drama, and dialogue. Fox was then a Senior Overseas Scholar at St John's College, Cambridge, and wrote a series of related collections of his essays. The first was Reproduction and Succession (1993), relating his part in both the appeal of a Mormon policeman to the Supreme Court and the famous "Baby M" surrogate mother trials in New Jersey. Then followed The Challenge of Anthropology (1994), and Conjectures and Confrontations (1997).
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In mathematics, the Thompson groups (also called Thompson's groups, vagabond groups or chameleon groups) are three groups, commonly denoted F \subseteq T \subseteq V, which were introduced by Richard Thompson in some unpublished handwritten notes in 1965 as a possible counterexample to the von Neumann conjecture. Of the three, F is the most widely studied, and is sometimes referred to as the Thompson group or Thompson's group. The Thompson groups, and F in particular, have a collection of unusual properties which have made them counterexamples to many general conjectures in group theory. All three Thompson groups are infinite but finitely presented.
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The documents also show that Huguet was not paid as originally promised and did not receive his full sum until 1488, when he was still owed 200 lliures. The reasons for the delay are unknown, but there a couple conjectures as to what happened. One is that the Constable Dom Pedro arrived six weeks after the contract was drawn up and engaged Huguet to paint him a retable, which would have taken precedence over that of the guild. It could also be that the guild lost interest or had a lack of finances that temporarily halted the project.
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There are five high-quality dedications to Arimanius found throughout the Roman Empire, but none are on any of the many images of the Mithraic lion-headed figure. The text of the dedications suggest that in a Mithraic context Arimanius was not conceived of as an evil being, however formidable. Gordon remarks: “the real point is surely that we know nothing of any importance about the western Areimanius.” Occultist D.J. Cooper conjectures that the lion-headed figure does not depict a god, but rather symbolically represents the spiritual state achieved in the Leo degree – Mithraism’s “adept” level.
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His superrigidity theorem from 1975 clarified an area of classical conjectures about the characterisation of arithmetic groups amongst lattices in Lie groups. He was awarded the Fields Medal in 1978, but was not permitted to travel to Helsinki to accept it in person, allegedly due to anti-semitism against Jewish mathematicians in the Soviet Union. His position improved, and in 1979 he visited Bonn, and was later able to travel freely, though he still worked in the Institute of Problems of Information Transmission, a research institute rather than a university. In 1991, Margulis accepted a professorial position at Yale University.
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The 1949 Oxford Classical Text by R.A.B. Mynors, partly because of its wide availability, has become the standard text, at least in the English-speaking world. One very influential article in Catullus scholarship, R.G.M. Nisbet's "Notes on the text and interpretation of Catullus" (available in Nisbet's Collected Papers on Latin Literature, Oxford, 1995), gave Nisbet's own conjectural solutions to more than 20 problematic passages of the poems. He also revived a number of older conjectures, going as far back as Renaissance scholarship, which editors had ignored. Another influential text of Catullus poems is that of George P. Goold, Catullus (London, 1983).
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It may have been this closeness that led Nietzsche to claim in his 1888 book Der Fall Wagner (The Case of Wagner) that Wagner's father was Geyer, and to make the pun that "Ein Geyer ist beinahe schon ein Adler" (A vulture is almost an eagle) --Geyer also being the German word for "vulture" and Adler being both a very common Jewish surname and the German word for "eagle". Despite these conjectures on the part of Wagner and Nietzsche, there is no evidence that Geyer was Jewish, and the question of Wagner's paternity is unlikely to be settled without DNA evidence.
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It was one of the pair of "Altieri Claudes", among the most famous and expensive paintings of the day. See Reitlinger, Gerald; The Economics of Taste, Vol I: The Rise and Fall of Picture Prices 1760–1960, Barrie and Rockliffe, London, 1961, and Art and Money , by Robert Hughes. Image of the Raphael, and image of the Claude All that exists in the scene is a procession of individuals, and the narrator conjectures on the rest. The altar and town exist as part of a world outside art, and the poem challenges the limitations of art through describing their possible existence.
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These planes are endlessly repeating ruled Cartesian coordinate system grids, tiled with a single signature pattern that is different for each plane. Higher planes have bright, colourful patterns, whereas lower planes appear far duller. Every detail of these patterns acts as a consistent portal to a different kingdom inside the plane, which itself comprises many separate realms. Bruce notes that the astral may also be entered by means of long tubes that bear visual similarity to these planes, and conjectures that the grids and tubes are in fact the same structures approached from a different perceptual angle.
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Kehr conjectures that Nicastro was built to replace a town which had been destroyed by the Saracens. For a long time, the Greek Rite was in use at Nicastro. The church in the village below the citadel of Nicastro was built and endowed by the Norman Aumberga, the niece of Robert Guiscard and sister of Count Richard Dapifer, the son of Drago. It became the Cathedral of S. Peter. In 1101, Count Richard the Dapifer transferred to the diocese of Nicastro property and chattels which had belonged to Aumberga in the territory between Agarena and Nicastro.
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Street lighting of Sueca-Literato Azorín in 2017 Saragüells, a traditional Valencian costume for the men There are different conjectures regarding the origin of the Falles festival. One suggests that the Falles started in the Middle Ages, when artisans disposed of the broken artefacts and pieces of wood they saved during the winter by burning them to celebrate the spring equinox. Valencian carpenters used planks of wood called parots to hang their candles on during the winter, as these were needed to provide light to work by. With the coming of the spring, they were no longer necessary, so they were burned.
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Hypohamiltonian snarks do not have a partition into matchings of this type, but conjectures that the edges of any hypohamiltonian snark may be used to form six matchings such that each edge belongs to exactly two of the matchings. This is a special case of the Berge–Fulkerson conjecture that any snark has six matchings with this property. Hypohamiltonian graphs cannot be bipartite: in a bipartite graph, a vertex can only be deleted to form a Hamiltonian subgraph if it belongs to the larger of the graph's two color classes. However, every bipartite graph occurs as an induced subgraph of some hypohamiltonian graph..
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Lanford gave the first proof that the Feigenbaum-Cvitanovic functional equation : g(x) = T(g)(x) = (1/\lambda) g(g(\lambda x)), g(0)=1, g(0)<0,\lambda=g(1)<0 has an even analytic solution g and that this fixed point g of the Feigenbaum renormalisation operator T is hyperbolic with a one-dimensional unstable manifold. This provided the first mathematical proof of the rigidity conjectures of Feigenbaum. The proof was computer assisted. The hyperbolicity of the fixed point is essential to explain the Feigenbaum universality observed experimentally by Mitchell Feigenbaum and Coullet-Tresser.
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Dirichlet's theorem on arithmetic progressions, in its basic form, asserts that linear polynomials :p(n) = a + bn with relatively prime integers a and b take infinitely many prime values. Stronger forms of the theorem state that the sum of the reciprocals of these prime values diverges, and that different linear polynomials with the same b have approximately the same proportions of primes. Although conjectures have been formulated about the proportions of primes in higher-degree polynomials, they remain unproven, and it is unknown whether there exists a quadratic polynomial that (for integer arguments) is prime infinitely often.
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In his second monograph on biquadratic reciprocity Gauss displays some examples and makes conjectures that imply the theorems listed above for the biquadratic character of small primes. He makes some general remarks, and admits there is no obvious general rule at work. He goes on to say > The theorems on biquadratic residues gleam with the greatest simplicity and > genuine beauty only when the field of arithmetic is extended to imaginary > numbers, so that without restriction, the numbers of the form a + bi > constitute the object of study ... we call such numbers integral complex > numbers.Gauss, BQ, § 30, translation in Cox, p.
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Larry Laudan concluded, after examining various historical attempts to establish a demarcation criterion, that "philosophy has failed to deliver the goods" in its attempts to distinguish science from non-science—to distinguish science from pseudoscience. None of the past attempts would be accepted by a majority of philosophers nor, in his view, should they be accepted by them or by anyone else. He stated that many well-founded beliefs are not scientific and, conversely, many scientific conjectures are not well- founded. He also stated that demarcation criteria were historically used as in polemical disputes between "scientists" and "pseudo-scientists".
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In his initial work on perfect graphs, Berge made two important conjectures on their structure that were only proved later. The first of these two theorems was the perfect graph theorem of Lovász (1972), stating that a graph is perfect if and only if its complement is perfect. Thus, perfection (defined as the equality of maximum clique size and chromatic number in every induced subgraph) is equivalent to the equality of maximum independent set size and clique cover number. A seven-vertex cycle and its complement, showing in each case an optimal coloring and a maximum clique (shown with heavy edges).
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This model states that the orientation of the cleavage plane at the 8-cell and 16-cell stages determines their later differentiation. There are two main way in which blastomeres typically divide: symmetrically, meaning perpendicular to the apical-basal axis, or asymmetrically, meaning horizontal to the apical-basal axis. Many potential hypotheses and conjectures that attempt to explain why these cells orient themselves the way that they do. Some researchers have stated that early-dividing blastomeres tend to divide asymmetrically, while others have proposed that the orientation of 8-cell stage blastomeres is random and cannot be predicted on a larger scale.
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Lambert took a prominent part in the Committee of Council which drew up instructions to the administrative major-generals. He was the organiser of the system of police which these officers were to control. Samuel Gardiner conjectures that it was through divergence of opinion between the protector and Lambert in connection with these "instructions" that the estrangement between the two men began. At all events, although Lambert had himself at an earlier date requested Cromwell to take the royal dignity, when the proposal to declare Oliver king was started in parliament (February 1657) he at once opposed it.
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Part of the seventh of Hilbert's twenty three problems posed in 1900 was to prove, or find a counterexample to, the claim that ab is always transcendental for algebraic a ≠ 0, 1 and irrational algebraic b. In the address he gave two explicit examples, one of them being the Gelfond–Schneider constant 2. In 1919, he gave a lecture on number theory and spoke of three conjectures: the Riemann hypothesis, Fermat's Last Theorem, and the transcendence of 2. He mentioned to the audience that he didn't expect anyone in the hall to live long enough to see a proof of this final result.
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Witsenhausen (1974) conjectures that the maximum sum of squared distances, among n points with unit diameter in Rd, is attained for a configuration formed by embedding a Turán graph onto the vertices of a regular simplex. An n-vertex graph G is a subgraph of a Turán graph T(n,r) if and only if G admits an equitable coloring with r colors. The partition of the Turán graph into independent sets corresponds to the partition of G into color classes. In particular, the Turán graph is the unique maximal n-vertex graph with an r-color equitable coloring.
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Grothendieck's construction of new cohomology theories, which use algebraic techniques to study topological objects, has influenced the development of algebraic number theory, algebraic topology, and representation theory. As part of this project, his creation of topos theory, a category-theoretic generalization of point-set topology, has influenced the fields of set theory and mathematical logic. The Weil conjectures were formulated in the later 1940s as a set of mathematical problems in arithmetic geometry. They describe properties of analytic invariants, called local zeta functions, of the number of points on an algebraic curve or variety of higher dimension.
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The book was praised for its "trove of compelling observations, anecdotes, and conjectures," for its "nearly encyclopedic" coverage of private techniques in criminal justice, and for elevating the discussion of criminal justice to a higher philosophical plane by redirecting the reader's attention away from social engineering goals like deterrence and rehabilitation toward a focus on justice and individual rights and responsibilities. It was praised for its summary of the role of private contributions to the criminal justice system, such as witness testimony and the bail bondsman system. It was also praised for applying economics, including incentives analysis, to the study of law.
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Karl Popper described the characteristics of a scientific theory as follows:Popper, Karl (1963), Conjectures and Refutations, Routledge and Kegan Paul, London, UK. Reprinted in Theodore Schick (ed., 2000), Readings in the Philosophy of Science, Mayfield Publishing Company, Mountain View, Calif. # It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations. # Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory—an event which would have refuted the theory.
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Stove starts chapter one by clarifying the sort of view that would uncontroversially constitute an irrationalist position regarding science. Stove then advances his reading of the philosophers he is criticising: "Popper, Kuhn, Lakatos, and Feyerabend, are all writers whose position inclines them to deny (A), or at least makes them more or less reluctant to admit it. (That the history of science is not "cumulative", is a point they all agree on)." Popper himself had given a 1963 summary of his thoughts the title "Conjectures and Refutations: The Growth of Scientific Knowledge", seemingly endorsing (A) in almost identical language.
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According to the footnote to the undefinability theorem (Twierdzenie I) of the 1933 monograph, the theorem and the sketch of the proof were added to the monograph only after the manuscript was sent to the printer in 1931. Tarski reports there that, when he presented the content of his monograph to the Warsaw Academy of Science on March 21, 1931, he expressed at this place only some conjectures, based partly on his own investigations and partly on Gödel's short report on the incompleteness theorems "Einige metamathematische Resultate über Entscheidungsdefinitheit und Widerspruchsfreiheit", Akademie der Wissenschaften in Wien, 1930.
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Tait, in 1885, published a table of knots with up to ten crossings, and what came to be known as the Tait conjectures. This record motivated the early knot theorists, but knot theory eventually became part of the emerging subject of topology. These topologists in the early part of the 20th century—Max Dehn, J. W. Alexander, and others—studied knots from the point of view of the knot group and invariants from homology theory such as the Alexander polynomial. This would be the main approach to knot theory until a series of breakthroughs transformed the subject.
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A difficulty, however, arises about the time of the destruction of the smaller temple, from the fact that the forms of the letters and the long vowels in the inscriptions upon the chairs clearly show that those inscriptions belong to an era long subsequent to the battle of Marathon. Christopher Wordsworth considered it ridiculous to suppose that these chairs were dedicated in this temple after its destruction, and hence conjectures that the temple was destroyed towards the close of the Peloponnesian War by the Persian allies of Sparta.William Martin Leake, Demi of Attica, p. 105, et seq.
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The Petersen graph The Petersen graph is an undirected graph with ten vertices and fifteen edges, commonly drawn as a pentagram within a pentagon, with corresponding vertices attached to each other. It has many unusual mathematical properties, and has frequently been used as a counterexample to conjectures in graph theory. The book uses these properties as an excuse to cover several advanced topics in graph theory where this graph plays an important role. It is heavily illustrated, and includes both open problems on the topics it discusses and detailed references to the literature on these problems.
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Five places named Segedunum are known to have existed in the Roman empire, one each in Britain and Germany and three in Gaul. The name Segedunum is known from the Notitia Dignitatum of the 4th century,"Segedunum: History" , Hadrian's Wall website but there is no consensus on its meaning. The various conjectures include "derived from the Celtic for 'powerful' or 'victorious'",Chamberlin, R., "Hadrian’s Wallsend", History Today, Volume: 50 Issue: 8, August 2000 "derived from the [Celtic] words sego ('strength') and dunum ('fortified place')","Segedunum" , roman-britain.org "Romano-British Segedunum 'Strong-fort'",Koch, J.T., Celtic Culture, 2006, and "Celtic sechdun or 'dry hill'".
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Hints at the nature and origins of Opar appear in Philip José Farmer's fictional biography Tarzan Alive: A Definitive Biography of Lord Greystoke (1972). This book attempts to add a high degree of realism and plausibility to the Tarzan stories, including references to Opar. Farmer conjectures on the inhabitants of Opar, and even goes to suggest that the city's populace was on the verge of extinction at the time of the events in the original Tarzan novels. As Edgar Rice Burroughs made clear, there had been cross-breeding with the caveman-like "great ape" humanoids and the adoption of that animalistic language.
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While Simeon's attempt at taking the throne was ill-fated and Stephen Uroš even captured Berat in 1356, John managed to preserve his remaining lands and became independent from both Simeon and Stephen Uroš.Fine, p. 357 The threat of Nikephoros II Orsini, who was gaining ground in Thessaly and Epirus, forced John to request the dispatch of a Venetian warship and an administrator from Venice to take control of his domain, to which the republic obliged. Bulgarian historian Hristo Matanov conjectures that after 1355, John may have minted his own coinage intended for trade with partners outside the inner Balkans.
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Following up his "weak cosmic censorship hypothesis", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with the Belinski–Khalatnikov–Lifshitz conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in general relativity. Also from 1979 dates Penrose's influential Weyl curvature hypothesis on the initial conditions of the observable part of the universe and the origin of the second law of thermodynamics. Penrose and James Terrell independently realised that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation.
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Illustratiom from De ichnographica campi published in Acta Eruditorum, 1763 La perspective affranchie de l'embarras du plan géometral, French edition, 1759 Lambert was the first to introduce hyperbolic functions into trigonometry. Also, he made conjectures regarding non-Euclidean space. Lambert is credited with the first proof that π is irrational by using a generalized continued fraction for the function tan x. Euler believed the conjecture but could not prove that π was irrational, and it is speculated that Aryabhata also believed this, in 500 CE. Lambert also devised theorems regarding conic sections that made the calculation of the orbits of comets simpler.
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Emotionally aware automated portrait painting - Proceedings of the 3rd international conference on Digital Interactive Media in Entertainment and Arts The work has also been the subject of some media attention. Prior to his work on The Painting Fool, Simon worked on the HR tool, a reasoning tool that was applied to discover mathematical concepts. The system successfully discovered theorems and conjectures, some of which were novel enough to become published works.Rise of the Robogeeks - New Scientist Colton's work with HM included the discovery of [refactorable number]s which appeared to be original but turned out to have been previously discovered.
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Many of the exceptional objects in mathematics and physics have been found to be connected to each other. Developments such as the Monstrous moonshine conjectures show how, for example, the Monster group is connected to string theory. The theory of modular forms shows how the algebra E8 is connected to the Monster group. (In fact, well before the proof of the Monstrous moonshine conjecture, the elliptic j-function was discovered to encode the representations of E8.) Other interesting connections include how the Leech lattice is connected via the Golay code to the adjacency matrix of the dodecahedron (another exceptional object).
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Most quantizers are based on the one-dimensional integer lattice, but using multi-dimensional lattices reduces the RMS error. The Leech lattice is a good solution to this problem, as the Voronoi cells have a low second moment. The vertex algebra of the two- dimensional conformal field theory describing bosonic string theory, compactified on the 24-dimensional quotient torus R24/Λ24 and orbifolded by a two-element reflection group, provides an explicit construction of the Griess algebra that has the monster group as its automorphism group. This monster vertex algebra was also used to prove the monstrous moonshine conjectures.
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The 3×3 game can be completely analyzed (strongly solved) and is a win for the first player—a table showing who wins from every possible position is given in Winning Ways, and given this information it is easy to read off a winning strategy. David des Jardins showed in 1996 that the 4×4 and 5×5 games never end with perfect play—both players get stuck shuffling their cars from side to side to prevent the other from winning. He conjectures that this is true for all larger boards. For a 3x3 board, there are 56 reachable positions.
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There were rumors, never substantiated, that Benjamin was impotent and that Natalie was unfaithful. Benjamin's troubled married life has led to speculation that he was gay. Daniel Brook, in a 2012 article about Benjamin, suggests that early biographies read as though "historians are presenting him as an almost farcically stereotypical gay man and yet wear such impervious heteronormative blinders that they themselves know not what they write". These conjectures were not given scholarly weight until 2001, when in an introduction to a reprinting of Meade's biography of Benjamin, Civil War historian William C. Davis acknowledged "cloaked suggestions that he [Benjamin] was a homosexual".
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The sources do agree that Romulus took up residence in the Castel dell'Ovo (Lucullan Villa) in Naples, now a castle but originally built as a grand sea-side house by Lucullus in the 1st century BC, fortified by Valentinian III in the mid-5th century. From here, contemporary histories fall silent. In the History of the Decline and Fall of the Roman Empire, Edward Gibbon notes that the disciples of Saint Severinus of Noricum were invited by a "Neapolitan lady" to bring his body to the villa in 488; Gibbon conjectures from this that Augustulus "was probably no more."Gibbon, p.
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The Math B Regents was often considered one of the most difficult New York State Regents. Math B covered concepts that can be found in trigonometry and advanced algebra, and prepared students for pre-calculus and calculus and reviewed past topics. During their year of study, students learned different theorems, graphed complex numbers and vectors, as well as reviewed topics such as exponential functions, systems of inequalities, and radicals. As the year progressed, students were expected to relate these functions to the real world, create conjectures through their own research, and begin a classroom discussion about these topics.
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V838 Monocerotis (Nova Monocerotis 2002) is a cataclysmic variable - or outburst - star in the constellation Monoceros about 20,000 light years (6 kpc) from the Sun. The previously unknown star was observed in early 2002 experiencing a major outburst, and was possibly one of the largest known stars for a short period following the outburst. Originally believed to be a typical nova eruption, it was then identified as something completely different. The reason for the outburst is still uncertain, but several conjectures have been put forward, including an eruption related to stellar death processes and a merger of a binary star or planets.
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The curve X (like any smooth curve of degree n in P2) has genus (n − 1)(n − 2)/2. It is not known whether there is an algorithm to find all the rational points on an arbitrary curve of genus at least 2 over a number field. There is an algorithm that works in some cases. Its termination in general would follow from the conjectures that the Tate–Shafarevich group of an abelian variety over a number field is finite and that the Brauer–Manin obstruction is the only obstruction to the Hasse principle, in the case of curves.
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Ralph Greenberg (born 1944) is an American mathematician who has made contributions to number theory, in particular Iwasawa theory. He was born in Chester, Pennsylvania) and studied at the University of Pennsylvania, earning a B.A. in 1966, after which he attended Princeton University, earning his doctorate in 1971 under the supervision of Kenkichi Iwasawa. Greenberg's results include a proof (joint with Glenn Stevens) of the Mazur–Tate–Teitelbaum conjecture as well as a formula for the derivative of a p-adic Dirichlet L-function at s=0 (joint with Bruce Ferrero). Greenberg is also well known for his many conjectures.
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In his PhD thesis, he conjectured that the Iwasawa μ- and λ-invariants of the cyclotomic \Z_p-extension of a totally real field are zero, a conjecture that remains open as of September 2012. In the 1980s, he introduced the notion of a Selmer group for a p-adic Galois representation and generalized the "main conjectures" of Iwasawa and Barry Mazur to this setting. He has since generalized this setup to present Iwasawa theory as the theory of p-adic deformations of motives. He also provided an arithmetic theory of L-invariants generalizing his aforementioned work with Stevens.
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He is allowed to stay on the station only because of his ability to establish a telepathic connection with and thereby control Joe, a creature designed to survive the hostile conditions on the Jovian surface. Cornelius conjectures that something in Anglesey's mind rejects or fears Jupiter, and the resulting feedback keeps destroying the delicate equipment. Eventually Cornelius is allowed to share a session with Anglesey during an important part of the mission. A set of autonomous female Jovians, similar to Joe but lacking a human controller such as Anglesey, has been launched from the satellite and will soon land on Jupiter.
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There are topological spaces where taking the associated topos loses information, but these are generally considered pathological. (A necessary and sufficient condition is that the topological space be a sober space.) Conversely, there are topoi whose associated topological spaces do not capture the original topos. But, far from being pathological, these topoi can be of great mathematical interest. For instance, Grothendieck's theory of étale cohomology (which eventually led to the proof of the Weil conjectures) can be phrased as cohomology in the étale topos of a scheme, and this topos does not come from a topological space.
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Heilen, Stephan, 'Ptolemy's Doctrine of the Terms and its Reception', in Jones (2010), pp.65–66. Houlding has also pointed out that differences in tabulated information presented within the Paraphrase and the Commentary "is a telling argument that both cannot be the work of the same author". The Greek Commentary was first printed in 1559 with an accompanying Latin translation by Hieronymus Wolf. This claimed to be based on a heavily corrupted manuscript which required numerous conjectures by a scholarly friend of Wolf, who preferred to remain anonymous rather than face reproaches for "dabbling in this sort of literature".
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Neolithic ashmounds (sometimes termed as cinder mounds) are man-made landscape features found in some parts of southern India (chiefly around Bellary) that have been dated to the Neolithic period (3000 to 1200 BC). They have been a puzzle for long and have been the subject of many conjectures and scientific studies. They are believed to be of ritual significance and produced by early pastoral and agricultural communities by the burning of wood, dung and animal matter. Hundreds of ashmound sites have been identified and many have a low perimeter embankment and some have holes that may have held posts.
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By 29 July, a total of 570 cases and 10 deaths had been reported across 40 states, Washington DC, and New York City. Until late May, no confirmed case had been documented outside the EU/EEA/UK and USA. No suspicious case had been observed in East Asia or Southeast Asia (or in Australia or New Zealand). The absence of documented cases in China and other Asian countries that had already experienced a COVID-19 epidemic led to conjectures regarding the possibility of a significant evolution of the virus, or variations in susceptibility in different populations.
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Vyasatirtha maintained cordial relationships with the royalty, especially Krishnadevaraya, who considered Vyasatirtha as his guru. At Hampi, the new capital of the empire, Vyasatirtha was appointed as the "Guardian Saint of the State" after a period of prolonged disputations and debates with scholars led by Basava Bhatta, an emissary from the Kingdom of Kalinga. His association with the royalty continued after Viranarasimha Raya overthrew Narasimha Raya II to become the emperor. Fernão Nunes observes that "The King of Bisnega, everyday, hears the teachings of a learned Brahmin who never married nor ever touched a woman" which Sharma conjectures is Vyasatirtha.
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While the concept of diffusion is well accepted in general, conjectures about the existence or the extent of diffusion in some specific contexts have been hotly disputed. An example of such disputes is the proposal by Thor Heyerdahl that similarities between the culture of Polynesia and the pre-Columbian civilizations of the Andes are due to diffusion from the latter to the former—a theory that currently has few supporters among professional anthropologists. Heyerdahl's theory of Polynesian origins has not gained acceptance among anthropologists.Robert C. Suggs The Island Civilizations of Polynesia, New York: New American Library, pp.
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Cabernet Franc For many years, the origin of Cabernet Sauvignon was not clearly understood and many myths and conjectures surrounded it. The word "Sauvignon" is believed to be derived from the French sauvage meaning "wild" and to refer to the grape being a wild Vitis vinifera vine native to France. Until recently the grape was rumored to have ancient origins, perhaps even being the Biturica grape used to make ancient Roman wine and referenced by Pliny the Elder. This belief was widely held in the 18th century, when the grape was also known as Petite Vidure or Bidure, apparently a corruption of Biturica.
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Vincent Pilloni (born 1982) is a French mathematician, specializing in arithmetic algebraic geometry and the Langlands program. Pilloni studied at the École Normale Supérieure and received his doctorate in 2009 from Paris 13 University with thesis advisor Jacques Tilouine and thesis Arithmétique des variétés de Siegel. His research deals with, among other topics, the question of how the modularity theorem for elliptic curves over the rational numbers (which led to the proof of Fermat's Last Theorem) can be extended to abelian varieties. With Fabrizio Andreatta and Adrian Iovita, he made significant progress on general modularity conjectures (following Fontaine-Mazur, Langlands, Clozel, and others).
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Stanisław Marcin Ulam (; 3 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapons, discovered the concept of the cellular automaton, invented the Monte Carlo method of computation, and suggested nuclear pulse propulsion. In pure and applied mathematics, he proved some theorems and proposed several conjectures. Born into a wealthy Polish Jewish family, Ulam studied mathematics at the Lwów Polytechnic Institute, where he earned his PhD in 1933 under the supervision of Kazimierz Kuratowski.
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This explains some of the movements in the early days of the Fondom, and resolves the lingering questions about Wore Tad and Wore Gowi which has led to conjectures that either a Wore Tad or a Wore Gowi would have formed the royal household for the Batibo Fondom. What is obvious is that while the successor vacated his father's home for safety, one of his brothers always remained and governed the rest of the family as quarter head under the authority of the successor and Fon who lived apart. R.A.M. Tebo II has engaged on a modernization of the Batibo palace, building new structures and upgrading some old ones.
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Suppose that a mathematician is studying geometry and shapes, and she wishes to prove certain theorems about them. She conjectures that "All rectangles are squares", and she is interested in knowing whether this statement is true or false. In this case, she can either attempt to prove the truth of the statement using deductive reasoning, or she can attempt to find a counterexample of the statement if she suspects it to be false. In the latter case, a counterexample would be a rectangle that is not a square, such as a rectangle with two sides of length 5 and two sides of length 7.
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In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems. Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was in fact the Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it.
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Bulgarian historian Plamen Pavlov conjectures that Ivan the Russian was a Ruthenian born in the Kingdom of Galicia–Volhynia (centred on modern western Ukraine), a hypothesis based only on his ties to Hungary, the western neighbour of Galicia–Volhynia.Павлов. Hungarian sources from 1288 make notice of one Russian named Ivan (Iwan dicto Oroz) as an ally of the ban of Severin, Theodore Vejtehi from the kindred Csanád,Vásáry, p. 124. who was one of the nobles that opposed the rule of Charles I of Hungary in 1316–1317. The land to the south of Severin was governed for Bulgaria by the despot of Vidin, Michael Shishman, a supporter of Vejtehi.
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In mathematics, the Weil conjectures were some highly influential proposals by on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. A variety V over a finite field with q elements has a finite number of rational points, as well as points over every finite field with qk elements containing that field. The generating function has coefficients derived from the numbers Nk of points over the (essentially unique) field with qk elements. Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places.
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From 1995 Shalev developed and applied probabilistic methods to finite groups and (nonabelian) finite simple groups in particular. A formative result in this area shows that almost every pair of elements in a finite simple group generate the group. This result, like many others in the field, were proved by Shalev in collaboration with Martin Liebeck of Imperial College at the University of London. The probabilistic approach led to the solution of many classical problems whose formulation does not involve probability; these problems concern quotients of the modular group, conjectures of Babai and of Cameron on permutation groups, diameters of certain Cayley graphs, Fuchsian groups, random walks, etc.
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Using [volume 15] of Gödel's still-unpublished [working notebooks], John W. Dawson Jr. conjectures that Gödel discovered a proof for the independence of the axiom of choice from finite type theory, a weakened form of set theory, while in Blue Hill in 1942. Gödel's close friend Hao Wang supports this conjecture, noting that Gödel's Blue Hill notebooks contain his most extensive treatment of the problem. On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship.
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Osmond participated in a Native American Church ceremony in which he ingested peyote, regarded by the Native Americans as sacred, not insanity inducing. His hosts were Plains Indians, members of the Red Pheasant Band, and the all-night ceremony took place near North Battleford (in the region of the South Saskatchewan River). Osmond published his report on the experience in Tomorrow magazine, Spring 1961. He reported details of the ceremony, the environment in which it took place, the effects of the peyote, the courtesy of his hosts, and his conjectures concerning the meaning for them of the experience and of the Native American Church.
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The conjecture is known to be true for d\le 4. It is also known to be true for simplicial polytopes: it follows in this case from a conjecture of that every centrally symmetric simplicial polytope has at least as many faces of each dimension as the cross polytope, proven by ... Indeed, these two previous papers were cited by Kalai as part of the basis for making his conjecture. Another special class of polytopes that the conjecture has been proven for are the Hansen polytopes of split graphs, which had been used by to disprove the stronger conjectures of Kalai.. The 3d conjecture remains open for arbitrary polytopes in higher dimensions.
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For his discovery of noncommutative instantons together with Albert Schwarz in 1998, noncommutative monopoles and monopole strings with David Gross in 2000 and for his work with Alexander S. Gorsky on the relations between gauge theories and many-body systems he was awarded the of the French Academy of Sciences in 2004. For his contributions to topological string theory and the ADHM construction he received the Hermann Weyl Prize in 2004. In 2008 together with Davesh Maulik, Andrei Okounkov and Rahul Pandharipande he formulated a set of conjectures relating Gromov–Witten theory and Donaldson–Thomas theory, for which the four authors were awarded the Compositio Prize in 2009.
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In the 1950s, Immanuel Velikovsky propounded catastrophism in several popular books. He speculated that the planet Venus is a former "comet" which was ejected from Jupiter and subsequently 3,500 years ago made two catastrophic close passes by Earth, 52 years apart, and later interacted with Mars, which then had a series of near collisions with Earth which ended in 687 BCE, before settling into its current orbit. Velikovsky used this to explain the biblical plagues of Egypt, the biblical reference to the "Sun standing still" for a day (Joshua 10:12 & 13, explained by changes in Earth's rotation), and the sinking of Atlantis. Scientists vigorously rejected Velikovsky's conjectures.
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Upon Archie's return to the stadium, Wolfe confronts the eight men who have remained in the clubhouse and notes that the assumption that Ferrone drugged the drinks is implausible. Brought into the Giants' organization by Durkin, Ferrone had performed so well that his next year's salary would be increased and he would receive a large bonus if the team won the Series. Instead, Wolfe conjectures that Ferrone caught someone else drugging the drinks and was killed to keep him quiet. The fact that drew his attention is that Durkin had been sitting in the stands from the starting lineup announcement until the time he was called into the clubhouse.
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This work has been generally attributed to Sir Francis Walsingham, and other conjectures have been made as to its authorship. Its original was an anonymous French work, Traité de la Cour, ou Instruction des Courtisans, by Eustache du Refuge, a diplomat and author in the reign of Henry IV of France. The first edition was published in Holland, the second at Paris, but the earliest known to be extant is the third, which appears in two parts at Paris (1619, 8vo: other editions 1622, 1631, and Leyden, 1649). It was reprinted as Le Nouveau Traité de la Cour in 1664 and 1672, and as Le Conseiller d'Estat in 1685.
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In a letter to Hayek in 1944, Popper stated, "I think I have learnt more from you than from any other living thinker, except perhaps Alfred Tarski."Hacohen, 2000 Popper dedicated his Conjectures and Refutations to Hayek. For his part, Hayek dedicated a collection of papers, Studies in Philosophy, Politics, and Economics, to Popper, and in 1982 said, "...ever since his Logik der Forschung first came out in 1934, I have been a complete adherent to his general theory of methodology."Weimer and Palermo, 1982 Popper also had long and mutually influential friendships with art historian Ernst Gombrich, biologist Peter Medawar, and neuroscientist John Carew Eccles.
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Depictions of Kratos and Bia in ancient Greek art are extremely rare. The only known surviving depiction of Kratos and Bia in ancient Greek pottery is on a fragmentary red-figure skyphos by the Meidias Painter, or a member of his circle, that is dated to the end of the fifth century BC and depicts the punishment of Ixion. One of Bia's hands is visible on the wheel that Ixion is bound to, steadying it. H. A. Shapiro conjectures that this is probably a representation of a scene from the lost tragedy Ixion by Euripides, who likely borrowed the figures of Kratos and Bia from Prometheus Bound.
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In computational complexity theory, an integer circuit is a circuit model of computation in which inputs to the circuit are sets of integers and each gate of the circuit computes either a set operation or an arithmetic operation on its input sets. As an algorithmic problem, the possible questions are to find if a given integer is an element of the output node or if two circuits compute the same set. The decidability is still an open question, but there are results on restriction of those circuits. Finding answers to some questions about this model could serve as a proof to many important mathematical conjectures, like Goldbach's conjecture.
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Logunov received, jointly with Eugenia Malinnikova, the 2017 Clay Research Award for their introduction of novel geometric-combinatorial methods for the study of elliptic eigenvalue problems.Clay Research Award 2017 He proved, among other results, an estimate (from above) for Hausdorff measures on the zero sets of Laplace eigenfunctions defined on compact smooth manifolds and an estimate (from below) in harmonic analysis and differential geometry that proved conjectures by Shing-Tung Yau and Nikolai Nadirashvili. In 2018 he received the Salem PrizeSalem Prize 2018 and in 2020 the EMS Prize of the European Mathematical Society.EMS Prize 2020 For 2021 he received the Breakthrough Prize in Mathematics - New Horizons in Mathematics.
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The exact dates of his birth and death are unknown, and not much detail has surfaced concerning his career. Conjectures place him first in the house of the Dominicans at Paris between 1215 and 1220, and later at the Dominican monastery founded by Louis IX of France at Beauvais in Picardy. It is more certain, however, that he held the post of "reader" at the monastery of Royaumont on the Oise, not far from Paris, also founded by Louis IX, between 1228 and 1235. Around the late 1230s, Vincent had begun working on the Great Mirror and in 1244 he had completed the first draft.
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This became known as the Taniyama–Shimura conjecture. In the West, this conjecture became well known through a 1967 paper by André Weil, who gave conceptual evidence for it; thus, it is sometimes called the Taniyama–Shimura–Weil conjecture. By around 1980, much evidence had been accumulated to form conjectures about elliptic curves, and many papers had been written which examined the consequences if the conjecture was true, but the actual conjecture itself was unproven and generally considered inaccessible—meaning that mathematicians believed a proof of the conjecture was probably impossible using current knowledge. For decades, the conjecture remained an important but unsolved problem in mathematics.
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In August 2012 writer and psychologist Patrick Oomens published the book "De zaak Koos H.", in which he questions Koos H. being a serial killer and concludes that he doesn't fit the profile. According to Oomens, that would shed another light on the case and the writer conjectures that the whole case of Koos H. has more characteristics of a cover-up with connections to Operation Gladio. With respect to the 'befriended' psychiatrist, the writer claims to have discovered that the ex-wife of Stolk wasn't a psychiatrist at all, but in reality the first female pilot in the Netherlands who transported the Dutch Royal family in the early '50s.
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The hypothesis aims to define the possible scope of a conjecture of the nature that several sequences of the type : f(n), g(n), \ldots, with values at integers n of irreducible integer-valued polynomials : f(x), g(x), \ldots, should be able to take on prime number values simultaneously, for arbitrarily large integers n. Putting it another way, there should be infinitely many such n for which each of the sequence values are prime numbers. Some constraints are needed on the polynomials. Schinzel's hypothesis builds on the earlier Bunyakovsky conjecture, for a single polynomial, and on the Hardy–Littlewood conjectures and Dickson's conjecture for multiple linear polynomials.
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Armed with such information, they take Heechee Heaven into Earth orbit via FTL travel. The crew become fantastically wealthy from their voyage; Robin, the richest man in the solar system. Happy with his healthy wife, his secure finances, and his slow but certain resolution of the food crisis on Earth, he is still terrified of the Heechee, and where they may have gone. Albert, an AI scientist program written by his wife, conjectures that the Heechee may have hidden themselves inside a black hole, taking advantage of relativistic time dilation to live quiet lives at a much slower rate than outside of the black hole's singularity.
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Nothing is known about his early life except that he served as a minister in the Eastern Ganga Kingdom in Kalinga (modern day Odisha) and later as a regent in the stead of Narasimha Deva II before his ordination as a monk. Information about his life is derived from a hagiography called Narahariyatistotra, Narayana Pandita's Madhva Vijaya and inscriptions from the Srikurmam and Simhachalam temples, all of which attest to his regency. The inscriptions also allude to his expertise in scriptures and swordsmanship. Sharma conjectures from the presence and contents of the inscriptions that post 1281 C.E., he was "the virtual overlord of the country".
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In fact, given that the geometrization conjecture is now settled, the only case needed to be proven for the virtually fibered conjecture is that of hyperbolic 3-manifolds. The original interest in the virtually fibered conjecture (as well as its weaker cousins, such as the virtually Haken conjecture) stemmed from the fact that any of these conjectures, combined with Thurston's hyperbolization theorem, would imply the geometrization conjecture. However, in practice all known attacks on the "virtual" conjecture take geometrization as a hypothesis, and rely on the geometric and group-theoretic properties of hyperbolic 3-manifolds. The virtually fibered conjecture was not actually conjectured by Thurston.
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The first music specifically written for piano dates from this period, the Sonate da cimbalo di piano (1732) by Lodovico Giustini. This publication was an isolated phenomenon; James Parakilas conjectures that the publication was meant as an honor for the composer on the part of his royal patrons. Certainly there could have been no commercial market for fortepiano music while the instrument continued to be an exotic specimen. It appears that the fortepiano did not achieve full popularity until the 1760s, from which time the first records of public performances on the instrument are dated, and when music described as being for the fortepiano was first widely published.
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He has been an active contributor to an ongoing discussion concerning the date of the Buddha's death, and has argued that data supplied in Pali texts composed in Sri Lanka enable us to date that event to about 404 BCE. Whilst an undergraduate, Gombrich helped to edit the volume of papers by Karl Popper entitled "Conjectures and Refutations". Since then, he has followed this method in his research, seeking the best hypothesis available and then trying to test it against the evidence. This makes him oppose both facile scepticism and the quest for a method which can in any way substitute for the simple need for critical thought.
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His colleagues in Jerusalem immediately responded with a letter to the Times on 16 March 1956 refuting his claim. The letter concluded, :"It is our conviction that either he [Allegro] has misread the texts or he has built up a chain of conjectures which the materials do not support."Philip R. Davies, "John Allegro and the Copper Scroll" in One result of this letter seemed to be that his appointment at Manchester was not to be renewed.This was Allegro's view, stated in a letter to John Strugnell dated 6 February 1957, cited in However, in July after several uneasy months the appointment was renewed.
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In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of complex multiplication theory. A shtuka (also called F-sheaf or chtouca) is a sort of generalization of a Drinfeld module, consisting roughly of a vector bundle over a curve, together with some extra structure identifying a "Frobenius twist" of the bundle with a "modification" of it. Drinfeld modules were introduced by , who used them to prove the Langlands conjectures for GL2 of an algebraic function field in some special cases.
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In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.
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Harris makes the point that when writing the cantata, Handel would have recalled his earlier setting, and perhaps borrowed from it. Dean and Knapp provide further example of works in which the Florinda and Daphne music may have re-emerged: the oratorio Il trionfo del Tempo e del Disinganno (1707); the opera Radamisto (1720); and the overture in B flat, HWV336, which Baselt conjectures might have been written as the overture to Florindo. This last-named has been combined with HWV352–354 and HWV356 to form the Suite from the operas Florindo and Daphne, which in 2012 was adapted and recorded by The Parley of Instruments under Peter Holman.
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Journalist Benoît Cachin said that the lyrics evoke with humour and irony the year 2000, on the significance of which many people got lost in conjectures, but which Farmer herself sees as bringing much joy. He noted that in the lyrics, Farmer refers to group U2's rock song "Sunday Bloody Sunday" in the phrase "Bloody lundi". The refrain is addressed to Father Christmas, comparing him to the Messiah, quotes André Malraux (who wrote "le XXIè siècle sera spirituel ou ne sera pas"), mentions the women's magazine Elle, the River Styx in the Greek mythology, and the antidepressant Prozac (in verlan).Cachin, 2006, pp. 130-34.
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He published only Reflections on a Letter writ by a nameless Author to the Reverend Clergy of both Universities, 1697. The tract is excessively rare; from the state of one of the two known copies, Aspland conjectures that most of the impression was accidentally destroyed; it is more probable that it had a purely local circulation. It has a preface by Oliver Heywood (dated 11 March; not included in his works). The Letter to which it is a reply was published in 1694 (dated 10 December), and is a plea by a churchman for moderation towards unitarians; Heywood's preface suggests that it had got into the hands of Frankland's students.
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However, these exceptions are relatively rare. They occur, for example, in the machine learning programs of AI. For the vast bulk of human science both past and present, rules of inductive inference do not exist. For such science, Popper's model of conjectures which are freely invented and then tested out seems to be more accurate than any model based on inductive inferences. Admittedly, there is talk nowadays in the context of science carried out by humans of 'inference to the best explanation' or 'abductive inference', but such so-called inferences are not at all inferences based on precisely formulated rules like the deductive rules of inference.
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Hanson's posthumous works include What I Do Not Believe and Other Essays (1971) and Constellations and Conjectures (1973). He is also known for the essays What I Do Not Believe and The Agnostic's Dilemma, among other writings on belief systems. From Michael Scriven's preface to Hanson's posthumous Perception and Discovery: > In a general sense Hanson continues the application of the Wittgensteinian > approach to the philosophy of science, as Waissman and Toulmin have also > done. But he goes much further than they, exploring questions about > perception and discovery in more detail, and ... tying in the history of > science for exemplification and for its own benefit.
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A jack flag was a small flag, used to distinguish it from the large ensign or pennants. The OED mentions the theory of its derivation from James I or from a leathern jacket but dismisses both: "neither of these conjectures covers the early use of the word". Originally, the jack would have been flown from the bowsprit topmast head: "You are alsoe for this present service to keepe in yor Jack at yor Boultspritt end" (sailing instructions 1633 as quoted in OED2). In 1667 Samuel Pepys, naval administrator and diarist, recorded the Dutch taking the and a man "struck her flag and jacke" -- clearly two different things.
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Historicists believe that prophetic interpretation reveals the entire course of history of the church from the writing of the Book of Daniel, some centuries before the close of the 1st century, to the end of time.Seventh-day Adventist Bible Student's Source Book, No. 1257, p. 775 Historicist interpretations have been criticized for inconsistencies, conjectures, and speculations and historicist readings of the Book of Revelation have been revised as new events occur and new figures emerge on the world scene. Historicism was the belief held by the majority of the Protestant Reformers, including Martin Luther, John Calvin, Thomas Cranmer, and others including John Thomas, John Knox, and Cotton Mather.
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One property he discovered was that the denominators of the fractions of Bernoulli numbers are always divisible by six. He also devised a method of calculating based on previous Bernoulli numbers. One of these methods follows: It will be observed that if n is even but not equal to zero, # is a fraction and the numerator of in its lowest terms is a prime number, # the denominator of contains each of the factors 2 and 3 once and only once, # is an integer and consequently is an odd integer. In his 17-page paper "Some Properties of Bernoulli's Numbers" (1911), Ramanujan gave three proofs, two corollaries and three conjectures.
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Between 1958 and 1963, the work led by Ognenova at the Nesebar site uncovered many significant monuments, including the Temple of Zeus Hiperdeksios, the Botros Temple of Zeus and Hera and others. She also was noted for her epigraphic work with Greek and Latin texts found in Bulgaria. Her study on inscription of the ring found in Ezerovo, and an Illyrian inscription found on a ring from Koman, Albania, allowed Ognenova to conclude that the Illyrian text, despite previous conjectures of its meaninglessness was significant. Tracing the origin of the ring and its shape, she was able to date the ring to the 8th century.
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Shio's tenure is preceded and succeeded by those of the catholicos named David, whom traditional lists of the Georgian prelates, such as those compiled by Michel Tamarati and Roin Metreveli, and that accepted by the Georgian Orthodox Church, identify as David III (1435–1439) and David IV (1443/47–1457), respectively. Some historians, especially Cyril Toumanoff, see in these names one and the same person, David II, a son of King Alexander I. Toumanoff, further, conjectures that Shio was a locum tenens for David II, who was designated by his father to become the prelate of the Georgian church at a very young age.
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The analogous conjectures for all higher dimensions were proved before a proof of the original conjecture was found. After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv. The proof built upon the program of Richard S. Hamilton to use the Ricci flow to attempt to solve the problem. Hamilton later introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way, but was unable to prove this method "converged" in three dimensions.
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In his Or Zarua, the only primary source of information on his life, Isaac ben Moses mentions as his teachers two Bohemian scholars, Jacob ha-Laban and Isaac ben Jacob ha-Laban. Led by a thirst for Talmudic knowledge, he undertook in his youth extensive journeys to the prominent yeshivot of Germany and France. According to Gross he went to Ratisbon first; but S.N. Bernstein conjectures that previously he stopped for a long time at Vienna, and became closely identified with the city, as he is usually quoted as "Isaac of Vienna." From among the many scholars at Ratisbon he selected for his guide the mystic Yehuda ben Samuel HaChasid.
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With little known about Manaw Gododdin, there is little that can be said of it with any authority. Aside from parenthetical references to it as Cunedda's homeland, discussion is scant. William Forbes Skene (The Four Ancient Books of Wales, 1868) has a chapter on "Manau Gododdin and the Picts",, Celtic Scotland, Manau Gododdin and the Picts and later historians either repeat him or cite him, but do not add more. Kenneth Jackson (The Gododdin, 1969) provides the same information as Skene, enhanced by his notice and commentary on some of the speculations and conjectures made by historians in the century since Skene published his work.
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Asín, Escatologia (2d ed., 1943) at Part III: 271-353. and (IV) conjectures how Dante could have known directly of the Muslim literature in translation.Asín, Escatologia (2d ed., 1943) at Part IV: 355-421. Prior to Asín's La Escatologia it was assumed that Dante drew from the long poem the Aeneid by the ancient Roman poet Virgil for the inspiration to create the memorable scenes of the afterlife.In Virgil's Aeneid, Book VI, lines 301-447, the hero Aeneas enters the underworld, and later visits his deceased father Anchises (lines 910-972), who shows Aeneas a vision of the future, and of Rome (lines 973-1219).
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This may suggest that Belgian players were being influenced by a new mode of play emanating from Switzerland in which the Fool is treated like the highest trump as in Troggu. Dummett conjectures that this family of decks, especially those of Viéville's design, originate from the Savoy-Piedmont- Lombardy region and were used until the collapse of the local card manufacturing industry at the end of the 17th century (as described above). Viéville's ordering of the trumps is almost identical to 16th century orders in Pavia and Mondovì. However, no cards from this region before the 18th century are known to have survived to prove or disprove this theory.
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Of these, most still exist in complete or fragmentary form, despite depredations by later Byzantine Emperors, Crusaders, and Ottoman conquerors. Four presently adorn the facade of the main building of the İstanbul Archaeology Museums, including one whose rounded shape led Alexander Vasiliev to suggest attribution to Emperor Julian on the basis of Constantine Porphyrogenitus's description. Vasiliev conjectures that the nine imperial sarcophagi, including one which carries a crux ansata or Egyptian cross, were carved in Egypt before shipment to Constantinople. The tradition was emulated by Ostrogothic King Theodoric the Great (454-526), whose mausoleum in Ravenna still contains a porphyry tub that was used as his sarcophagus.
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It comprises a core set of ideas from Pure Mathematics. These ideas reflect those that would be met early on in a typical A Level Mathematics course: algebra, basic functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration, graphs of functions. In addition, knowledge of the GCSE curriculum is assumed Test of Mathematics for University Admission - Specification for October 2018 retrieved 22 April 2019 . Paper 2: Mathematical Reasoning Paper 2 has 20 multiple-choice questions, with 75 minutes allowed to complete the paper. The second paper assesses a candidate’s ability to justify and interpret mathematical arguments and conjectures, and deal with elementary concepts from logic.
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There is no information about Alexander's early life in the contemporary sources. Indeed, the only hint as to his existence in a Bulgarian source is an anonymous reference in Ephraim's Prayer Canon to the Tsar, where he is only mentioned as “the son of the tsar”. It is uncertain whether Alexander was born to Ivan Shishman's first wife, Kira Maria, or to his second wife, a daughter of Prince Lazar of Serbia (r. 1371–1389).Божилов, pp. 229, 241 Due to Alexander's first-born status, Bulgarian historian Petar Nikov conjectures that at some point before 1395, Alexander was made co-ruler by his father Ivan Shishman.
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Many mathematicians believe these generalizations of the Riemann hypothesis to be true. The only cases of these conjectures which have been proven occur in the algebraic function field case (not the number field case). Global L-functions can be associated to elliptic curves, number fields (in which case they are called Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis is formulated for Dedekind zeta-functions, it is known as the extended Riemann hypothesis (ERH) and when it is formulated for Dirichlet L-functions, it is known as the generalized Riemann hypothesis (GRH).
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The rank of E(Q), that is the number of copies of Z in E(Q) or, equivalently, the number of independent points of infinite order, is called the rank of E. The Birch and Swinnerton- Dyer conjecture is concerned with determining the rank. One conjectures that it can be arbitrarily large, even if only examples with relatively small rank are known. The elliptic curve with biggest exactly known rank is :y2 \+ xy + y = x3 − x2 − x + It has rank 20, found by Noam Elkies and Zev Klagsbrun in 2020. Curves of rank at least 28 are known, but their rank is not exactly known.
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F.W. Walbridge in Library Journal, 70 (November 15, 1945), 1086, said that Brodie had treated her material with "taste, skill, and scholarship". An anonymous review in the New Yorker, 21 (November 24, 1945), 109, commented that Brodie had written about Joseph Smith "entertainingly". Newsweek called Brodie's book "a definitive biography in the finest sense of the word", and Time praised the author for her "skill and scholarship and admirable detachment".. Other reviews were less positive. Brodie was especially annoyed by the review of novelist Vardis Fisher, who accused her of stating "as indisputable facts what can only be regarded as conjectures supported by doubtful evidence".
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Until the late 20th century Michell was considered important primarily because of his work on geology. His most important geological essay, written after the 1755 Lisbon earthquake, was entitled "Conjectures concerning the Cause and Observations upon the Phaenomena of Earthquakes" (Philosophical Transactions, li. 1760). In this paper he introduced the idea that earthquakes spread out as waves through the Earth and that they involve the offsets in geological strata now known as faults. He was able to estimate both the epicentre and the focus of the Lisbon earthquake, and may also have been the first to suggest that a tsunami is caused by a submarine earthquake.
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Aristotle, The Athenian Constitution, 2.17 Nevertheless, the tradition persisted. Four centuries later Plutarch ignored Aristotle's skepticismHomosexuality & Civilization By Louis Crompton, p. 25 and recorded the following anecdote, supplemented with his own conjectures: > And they say Solon loved [Peisistratos]; and that is the reason, I suppose, > that when afterwards they differed about the government, their enmity never > produced any hot and violent passion, they remembered their old kindnesses, > and retained "Still in its embers living the strong fire" of their love and > dear affection.Plutarch, The Lives "Solon" Tr. John Dryden s:Lives (Dryden > translation)/Solon A century after Plutarch, Aelian also said that Peisistratos had been Solon's eromenos.
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Before handing over the English to Spanish authorities Martín Olleta's party stopped somewhere south of Chiloé Island to hide all iron objects, likely to avoid have them confiscated. When Spanish authorities learned that Leutenant Hamilton had been lost in the way north he compelled Olleta to go back south and find him which he actually did. Scholar Ximena Urbina conjectures that Martín Olleta must have lived close to the Spanish and heard from other natives of the wreckage. Thus the rescue was not by chance but an enterprise done with prior knowledge of the Spanish interest in foreigners and of the valuable loot to be found at the wreckage.
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Thales' most famous philosophical position was his cosmological thesis, which comes down to us through a passage from Aristotle's Metaphysics. In the work Aristotle unequivocally reported Thales' hypothesis about the nature of all matter – that the originating principle of nature was a single material substance: water. Aristotle then proceeded to proffer a number of conjectures based on his own observations to lend some credence to why Thales may have advanced this idea (though Aristotle did not hold it himself). Aristotle laid out his own thinking about matter and form which may shed some light on the ideas of Thales, in Metaphysics 983 b6 8–11, 17–21.
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The allied victory at Red Cliffs ensured the survival of Liu Bei and Sun Quan, gave them control of the Yangtze and provided a line of defence that was the basis for the later creation of the two southern states of Shu Han and Eastern Wu. The battle has been called the largest naval battle in history in terms of numbers involved. Descriptions of the battle differ widely and the site of the battle is fiercely debated. Although its location remains uncertain, the majority of academic conjectures place it on the south bank of the Yangtze River, southwest of present-day Wuhan and northeast of Baqiu (present-day Yueyang, Hunan).
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The expedition consequently explored both Cape Cod, but also Martha's Vineyard, which George R. Stewart conjectures that Archer himself named, as Gosnold had a daughter named Martha and there were many grapevines in the area. Martha's Vineyard initially designated a smaller island, before the name was shifted to the larger island referred to as Martha's Vineyard to this day. Archer also recorded and most likely coined many other names from that voyage that are not still used in the present day, including Tucker's Terror and Hill's Hap. His records contain a description of most of the important events of the voyage, including finding and naming Cape Cod.
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In 2004, Everett discovered that the language uses a voiceless bilabially post-trilled dental stop, . He conjectures that the Pirahã had not used that phoneme in his presence before because they were ridiculed whenever non-Pirahã heard the sound. The occurrence of in Pirahã is all the more remarkable considering that the only other languages known to use it are the unrelated Chapacuran languages, Oro Win, and Wari’, spoken some west of the Pirahã area. Oro Win is a nearly extinct language (surviving only as the second language of a dozen or so members of the Wari’ tribe), which was discovered by Everett in 1994.
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However, the proof of Beilinson–Bernstein introduced a method of localization. This established a geometric description of the entire category of representations of the Lie algebra, by "spreading out" representations as geometric objects living on the flag variety. These geometric objects naturally have an intrinsic notion of parallel transport: they are D-modules. Alexander Beilinson (left) and his students In 1982 Beilinson published his own conjectures about the existence of motivic cohomology groups for schemes, provided as hypercohomology groups of a complex of abelian groups and related to algebraic K-theory by a motivic spectral sequence, analogous to the Atiyah–Hirzebruch spectral sequence in algebraic topology.
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In mathematics, a modular Lie algebra is a Lie algebra over a field of positive characteristic. The theory of modular Lie algebras is significantly different from the theory of real and complex Lie algebras. This difference can be traced to the properties of Frobenius automorphism and to the failure of the exponential map to establish a tight connection between properties of a modular Lie algebra and the corresponding algebraic group. Although serious study of modular Lie algebras was initiated by Nathan Jacobson in 1950s, their representation theory in the semisimple case was advanced only recently due to the influential Lusztig conjectures, which have been partially proved.
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His research accomplishments during that period include the celebrated hooklength formula for the dimension of an irreducible representation of a symmetric group, or equivalently the number of standard Young tableaux of a given shape (with J. Sutherland Frame and G. de B. Robinson) and the influential Brauer-Thrall conjectures (with Richard Brauer). For two years, from 1940 to 1942, he was a visiting scholar at the Institute for Advanced Study. During WW II he began to study operations research and development of mathematical models for military applications. From 1957 to 1961 he was the editor-in-chief of Management Science, as successor to C. West Churchman.
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The book is written for a general audience, unlike a follow-up work published by Knorr, Textual Studies in Ancient and Medieval Geometry (1989), which is aimed at other experts in the close reading of Greek mathematical texts. Nevertheless, reviewer Alan Stenger calls The Ancient Tradition of Geometric Problems "very specialized and scholarly". Reviewer Colin R. Fletcher calls it "essential reading" for understanding the background and content of the Greek mathematical problem- solving tradition. In its historical scholarship, historian of mathematics Tom Whiteside writes that the book's occasionally speculative nature is justified by its fresh interpretations, well-founded conjectures, and deep knowledge of the subject.
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Entertainment Weekly conjectures that despite its ratings decline, Fringe survived for five seasons in part because of Fox executive Kevin Reilly's love of the series, and also due to the network's desire to make amends for the science fiction shows it had previously canceled. Across its run the series earned many accolades, though it failed to win major awards. At the Television Critics Awards, Fringe earned a 2009 award that designated it "Outstanding New Program of the Year". Fringe won seven Saturn Awards among fifteen nominations; from 2009–11, Torv won for Best Actress on Television, while Noble won for Best Supporting Actor on Television in 2010.
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Maintaining the proposition that the Blessed Virgin was conceived without sin was heretical, he aroused against him the faculty of the University of Paris. They condemned fourteen propositions from his lectures, warned him, first privately, then publicly, to retract, and when he refused carried the matter to Pierre Orgement, Bishop of Paris, who promulgated a decree of excommunication against all who should defend the forbidden theses. The faculty issued letters condemnatory of Montson's errors and conduct, which Denifle conjectures, from their acerbity of speech, were written by Pierre d'Ailly. Denifle also says Montson would not have been condemned had he not declared the doctrine of the Immaculate Conception heretical.
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Nearly forty years later, in his book Pallen conjectures that if the virus did not "go" to Parker, she must have "gone" to the virus. It is possible that Parker gained unauthorised access to the Smallpox Laboratory, when offering staff photographic film at a discounted price or when seeking advice on photographic materials used in the laboratory experiments. A.M. Walker, reviewing the book for the Journal of Hospital Infection, notes that it is detailed and scholarly while being written for a lay audience. The first three of seven sections in the book provide the reader with historical background on the smallpox disease and its eradication.
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Cassius Dio wrote that in AD 7, Augustus sent Tiberius' nephew Germanicus to Illyricum because Tiberius’ lack of activity made him suspicious that Tiberius was intentionally delaying the war so as to remain under arms as long as possible. Augustus seems to have been displeased with what he must have considered a passive strategy. However, Tiberius was very active and was conducting a war of attrition and counter-insurgency operations. This strategy later proved to be the right one.Radman-Livaja, I., Dizda, M., Archaeological Traces of the Pannonian Revolt 6–9 AD: Evidence and Conjectures, Veröffentlichungen der Altertumskommiion für Westfalen Landschaftsverband Westfalen-Lippe, Band XVIII, p.
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Prime Minister Mari Kiviniemi of the Centre Party had previously been quiet on spending cuts, but when pressed on the issue by the debate's moderator she was rather indiscreet on cutting funding for the public sector and the Defence Forces. However, she still insisted that cuts may not be necessary if the economic growth is sufficiently high in the following years. Cuts on defence spending were supported by most parties, but Timo Soini contested this by saying that national security can not depend on economic conjectures. The crisis concerning the breaches against the campaign funding laws during the previous electoral campaign in 2007 was also discussed.
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Stoker conjectures that this was advantageous to both the king and Vyasatirtha as the establishments of mathas in these newly conquered regions led to political stability and also furthered the reach of Dvaita. Somanatha writes of an incident where Krishnadeva Raya was sent a work of criticism against Dvaita by an Advaita scholar in Kalinga as a challenge. After Vyasatirtha retaliated accordingly, Krishnadeva Raya awarded Vyasatirtha with a ratnabhisheka (a shower of jewels) which Vyasatirtha subsequently distributed among the poor. The inscriptions speak of grants of villages to Vyasatirtha from Krishnadeva Raya around this period, including Bettakonda, where he developed large irrigation systems including a lake called Vyasasamudra.
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Written for flute, clarinet, violin, cello and performer, the piece tells the story of a game, where the musicians start by only playing their instruments, when gradually the performer enters: he is searching for an object on stage, the musicians reveal that they know where it is, but they are teasing him, and the piece ends with the performer frustrated, surrounded by chaos, as the four musicians verbally taunt him. In 2018, she wrote Dangerous Conjectures for the German ensemble Ascolta, which was premiered at ECLAT festival in Stuttgart. In the same year, she also wrote a piece for the German duo leise dröhnung, called Through Hell & High Water.
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It was written by Gerstner about some people not understanding him since he was a child and about one just trying to be themselves in spite of people trying to pinch them. "Creatures in Heaven" conjectures about whether heaven exists, where it is located and what kind of creatures inhabit it. Weikath, who wrote the song, said he tried to capture the essence of old hard rock clubs in the track's intro. "If God Loves Rock 'n' Roll" has the band proposing the theory that God likes rock 'n' roll and heavy metal, or "otherwise he would not have us and all the others do what we are doing", as Grosskopf said.
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Camillo Acquacotta conjectures that it was around 578 that the first epoch of the diocese of Matelica came to an end, as a result of the massive destruction of the Lombard invasions.Acquacotta, p. 43. On 8 July 1785, the diocese of Matelica was revived by Pope Pius VI, its territory was separated from that of the diocese of Fabriano, and it was united aeque principaliter with the Diocese of Fabriano to form the Diocese of Fabriano e Matelica, two dioceses joined by the fact of having one bishop. The Collegiate Church of S. Maria e S. Bartolomeo was erected into a cathedral church, and made immediately subject to the Holy See (Papacy).
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Philosopher of science Karl Popper, in The Poverty of Historicism and Conjectures and Refutations, critiqued such claims of the explanatory power or valid application of historical materialism by arguing that it could explain or explain away any fact brought before it, making it unfalsifiable and thus pseudoscientific. Similar arguments were brought by Leszek Kołakowski in Main Currents of Marxism. In his 1940 essay Theses on the Philosophy of History, scholar Walter Benjamin compares historical materialism to the Turk, an 18th-century device which was promoted as a mechanized automaton which could defeat skilled chess players but actually concealed a human who controlled the machine. Benjamin suggested that, despite Marx's claims to scientific objectivity, historical materialism was actually quasi-religious.
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During the remaining years of the 17th century, Cristofori invented two keyboard instruments before he began his work on the piano. These instruments are documented in an inventory, dated 1700, of the many instruments kept by Prince Ferdinando. Stewart Pollens conjectures that this inventory was prepared by a court musician named Giovanni Fuga, who may have referred to it as his own in a 1716 letter.The inventory is published in Gai 1969. The spinettone, Italian for "big spinet", was a large, multi-choired spinet (a harpsichord in which the strings are slanted to save space), with disposition 1 x 8', 1 x 4';van der Meer 2005, 275 most spinets have the simple disposition 1 x 8'.
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Archie conjectures that Henry may have gone back to the mine shaft. There, Henry begins to investigate the area and comes across a glass item similar to the one Regina found earlier that he puts into his backpack. Archie goes in to search for Henry and finds the boy, but as they try to escape, an aftershock blocks off the main entrance, leaving an injured Archie and Henry trapped. They find an elevator shaft, not knowing that above ground Emma and Regina have taken the suggestion of blasting the main entrance from Marco (Tony Amendola), which results in the elevator carrying Henry and Archie being lowered even further after the blast takes place.
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A culture-based estimate gives the percentage of Mestizos as high as 90%.en el censo de 1930 el gobierno mexicano dejó de clasificar a la población del país en tres categorías raciales, blanco, mestizo e indígena, y adoptó una nueva clasificación étnica que distinguía a los hablantes de lenguas indígenas del resto de la población, es decir de los hablantes de español. Eugenio Derbez Mexican actor, comedian and filmmaker. The use of variated methods and criteria to quantify the number of Mestizos in Mexico is not new: Since several decades ago, many authors have analyzed colonial censuses data and have made different conjectures respecting the ethnic composition of the population of colonial Mexico/New Spain.
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These conditions are the valuing of creativity and the free and open debate that exposed ideas to criticism to reveal those good explanatory ideas that naturally resist being falsified due to their having basis in reality. Deutsch points to previous moments in history, such as Renaissance Florence and Plato's Academy in Golden Age Athens, where this process almost got underway before succumbing to their static societies' resistance to change. The source of intelligence is more complicated than brute computational power, Deutsch conjectures, and he points to the lack of progress in Turing test AI programs in the six decades since the Turing test was first proposed. What matters for knowledge creation, Deutsch says, is creativity.
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The Pythagorean tiling may be generalized to a three- dimensional tiling of Euclidean space by cubes of two different sizes, which also is unilateral and equitransitive. Attila Bölcskei calls this three- dimensional tiling the Rogers filling. He conjectures that, in any dimension greater than three, there is again a unique unilateral and equitransitive way of tiling space by hypercubes of two different sizes.. See also , which includes an illustration of the three-dimensional tiling, credited to "Rogers" but cited to a 1960 paper by Richard K. Guy: . Burns and Rigby found several prototiles, including the Koch snowflake, that may be used to tile the plane only by using copies of the prototile in two or more different sizes.. .
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North responded to these advertisements mockingly in a letter to Andrew Ducarel: In his Conjectures, Clarke had appended a more successful essay: 'Remarks on a dissertation on Oriuna, the supposed wife of Carausius'. "Oriuna" was a name, referenced in the coins of the self-declared Emperor of Britannia, Carausius, whose supposed identity was being hotly debated between numismatists Patrick Kennedy and William Stukeley, with Kennedy proposing her as the emperor's guardian goddess, and Stukeley proposing his wife. Clarke correctly identified the name didn't refer to a person, but was rather a misreading of the Latin word "fortuna" on Carausius' poorly preserved coins. This view was correct, but his vindication here did little to comfort Clarke's ego.
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The Qurayza appear as a tribe of considerable military importance: they possessed large numbers of weaponry, as upon their surrender 1,500 swords, 2,000 lances, 300 suits of armor, and 500 shields were later seized by the Muslims.Heck, "Arabia Without Spices: An Alternate Hypothesis", p. 547-567. Meir J. Kister notes that these quantities are "disproportionate relative to the number of fighting men" and conjectures that the "Qurayza used to sell (or lend) some of the weapons kept in their storehouses". He also mentions that the Qurayza were addressed as Ahlu al-halqa ("people of the weapons") by the Quraysh and notes that these weapons "strengthened their position and prestige in the tribal society".
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In mathematics, a Tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to approximate, in some sense, the category of linear representations of an algebraic group G defined over K. A number of major applications of the theory have been made, or might be made in pursuit of some of the central conjectures of contemporary algebraic geometry and number theory. The name is taken from Tannaka–Krein duality, a theory about compact groups G and their representation theory. The theory was developed first in the school of Alexander Grothendieck. It was later reconsidered by Pierre Deligne, and some simplifications made.
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One of the founding works of algebraic number theory, the Disquisitiones Arithmeticae (Latin: Arithmetical Investigations) is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24. In this book Gauss brings together results in number theory obtained by mathematicians such as Fermat, Euler, Lagrange and Legendre and adds important new results of his own. Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures. Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways.
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In 1958, Shimura generalized the initial work of Martin Eichler on the Eichler–Shimura congruence relation between the local L-function of a modular curve and the eigenvalues of Hecke operators. In 1959, Shimura extended the work of Eichler on the Eichler–Shimura isomorphism between Eichler cohomology groups and spaces of cusp forms which would be used in Pierre Deligne's proof of the Weil conjectures. In 1971, Shimura's work on explicit class field theory in the spirit of Kronecker's Jugendtraum resulted in his proof of Shimura's reciprocity law. In 1973, Shimura established the Shimura correspondence between modular forms of half integral weight k+1/2, and modular forms of even weight 2k.
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Around 1955, Japanese mathematicians Goro Shimura and Yutaka Taniyama observed a possible link between two apparently completely distinct, branches of mathematics, elliptic curves and modular forms. The resulting modularity theorem (at the time known as the Taniyama–Shimura conjecture) states that every elliptic curve is modular, meaning that it can be associated with a unique modular form. It was initially dismissed as unlikely or highly speculative, and was taken more seriously when number theorist André Weil found evidence supporting it, but no proof; as a result the "astounding" conjecture was often known as the Taniyama–Shimura-Weil conjecture. It became a part of the Langlands program, a list of important conjectures needing proof or disproof.
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He had no offspring, and contemporary sources only offer conjectures about his successor, possibly Árni óreiða Magnússon, nephew of Guðmundr gríss Ámundason and son-in-law of the skald Snorri Sturluson. In fact, the sagas narrate that Sturluson caused Magnús's fall: during his first term as lawspeaker, Sturluson convinced the Althing to outlaw (skógarmaðr) Magnús. Despite his title, Magnús was not one of Iceland's more powerful citizens. According to konungsannáll, Magnús obtained the support of the clans Haukdælir, Oddaverjar and Svínfellingar to become bishop of Skálholt in 1236, but he did not obtain the Apostolic Blessing since he did not fulfil the requirements for the position; his candidacy was approved neither by the Norwegian archdiocese nor the Pope.
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In AD 973 Edgar the Peaceful repossessed Braunton for the Crown through an exchange with Glastonbury Abbey, thus retrieving a strategically important estate at the head of a major estuary. Susan Pearce conjectures Pearce, S. 1985: The Early Church in the Landscape: The Evidence from North Devon, in Archaeological Journal Volume 142, 255-275. that the King then placed a number of his thegns here providing each with a landholding which became the small estates which form an arc around Braunton to the north and east. These appear to have been members of three manors within the parish of Braunton, later known as Braunton Dean, Braunton Abbot and Braunton Gorges, of which latter manor Ash was part.
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Writer Joseph Broccoli conjectures that Alice de Janzé and the 1927 shooting served as a source of inspiration for Maria Wallis and the shooting incident in F. Scott Fitzgerald's novel Tender Is the Night (1934),Bruccoli, Joseph Matthew & Baughman, Judith S. (1996). Reader's Companion to F. Scott Fitzgerald's Tender Is the Night. Columbia: University of South Carolina Press, p. 91. Sarah Miles portraying Alice de Janzé in White Mischief (1988) In 1982, Alice de Janzé's life was prominently featured in the investigative non-fiction book White Mischief by journalist James Fox, which examined the events surrounding the murder of Lord Erroll, the Happy Valley set, and their notorious life before and after the event.
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These three properties implied, as a very special case, that the norm residue map should be an isomorphism. The essential characteristic of the proof is that it uses the induction on the "weight" (which equals the dimension of the cohomology group in the conjecture) where the inductive step requires knowing not only the statement of Bloch-Kato conjecture but the much more general statement that contains a large part of the Beilinson-Lichtenbaum conjectures. It often occurs in proofs by induction that the statement being proved has to be strengthened in order to prove the inductive step. In this case the strengthening that was needed required the development of a very large amount of new mathematics.
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The social nature of mathematics is highlighted in its subcultures. Major discoveries can be made in one branch of mathematics and be relevant to another, yet the relationship goes undiscovered for lack of social contact between mathematicians. Social constructivists argue each speciality forms its own epistemic community and often has great difficulty communicating, or motivating the investigation of unifying conjectures that might relate different areas of mathematics. Social constructivists see the process of "doing mathematics" as actually creating the meaning, while social realists see a deficiency either of human capacity to abstractify, or of human's cognitive bias, or of mathematicians' collective intelligence as preventing the comprehension of a real universe of mathematical objects.
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There has been a great deal of controversy concerning the ringing ability of the boulders; conversely, there has been an almost complete lack of testing to support the conjectures. Conditions such as size and shape of the boulders and the way that the boulders are supported or stacked certainly influence the sounds that the boulders make but do not in themselves impart the ringing ability. Although the sound is often described as metallic, it is most likely due to a combination of the density of the rock and a high degree of internal stress. The sound can be duplicated on a small scale by tapping the handle of a ceramic coffee cup.
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It is conjectured that such examples exist for all primes k. , the largest prime for which this is confirmed is k = 19, for this AP-19 found by Wojciech Iżykowski in 2013: :19 + 4244193265542951705·17#·n, for n = 0 to 18. It follows from widely believed conjectures, such as Dickson's conjecture and some variants of the prime k-tuple conjecture, that if p > 2 is the smallest prime not dividing a, then there are infinitely many AP-(p−1) with common difference a. For example, 5 is the smallest prime not dividing 6, so there is expected to be infinitely many AP-4 with common difference 6, which is called a sexy prime quadruplet.
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This information was combined with legitimate historical mentions of the Attacotti to produce inaccurate histories and to make baseless conjectures. For example, Edward Gibbon combined De Situ Britanniae with St. Jerome's description of the Attacotti by musing on the possibility that a 'race of cannibals' had once dwelt in the neighbourhood of Glasgow. These views were echoed in the works of Dutch, French and German authors. Nicolaus Hieronymus Gundling proposed that the exotic appearance and cannibalism of the Scottish people made them akin to the savages of Madagascar. Even as late as the mid-18th century, German authors likened Scotland and its ancient population to the exotic tribes of the South Seas.
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We do not dispute anyone's attained > distance nor declare it impossible that he should have been where he was. We > did not hunt up nameless islands and promontories to tag them with the > surnames ... We did not even erect cenotaphs ... We received no flags, > converted no natives, killed no one ... The object of this report is to > expose a few of the specious pleas, fallacious reasonings, and ill-grounded > conjectures which are called scientific, and to place the subject of > circumpolar exploration on a basis of facts and reasonable probabilities. > One cannot explore the earth's surface from an observatory, nor by > mathematics, nor by the power of logic. It must be done physically.
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Samson has a unique nazirite status called Nazir Shimshon which permitted him to touch dead bodies, since the angel who imposed the status omitted this restriction. Radak conjectures that even without this special status, Samson would be allowed to touch dead bodies while doing God's work defending Israel.Nazir 4b, "The Prophets - The Rubin Edition by Artscroll" Judges 14:18 commentary The prophet Amos later condemned the Israelites for their failure to respect the nazirite vow, along with their failure to hear the prophets: :And I raised up some of your sons as prophets and some of your young men as nazirites; is this not so, O children of Israel? says the Lord.
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Generalizing the ideas of Hermann Weyl from the spectral theory of ordinary differential equations, Harish-Chandra introduced his celebrated c-function c(λ) to describe the asymptotic behaviour of the spherical functions φλ and proposed c(λ)−2 dλ as the Plancherel measure. He verified this formula for the special cases when G is complex or real rank one, thus in particular covering the case when G/K is a hyperbolic space. The general case was reduced to two conjectures about the properties of the c-function and the so-called spherical Fourier transform. Explicit formulas for the c-function were later obtained for a large class of classical semisimple Lie groups by Bhanu-Murthy.
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Eutresis () was a town of ancient Boeotia, mentioned by Homer in the Catalogue of Ships in the Iliad, and said to have been the residence of Amphion and Zethus before they ruled over Thebes.Eustath. ad loc.; In the time of Strabo it was a village in the territory of Thespiae. Stephanus of Byzantium places it on the road from Thespiae to Plataea; but William Martin Leake conjectures that there is an error in the text, and that for Θεσπιῶν (Thespiae) we ought to read Θισβῶν (Thisbe), since there is only one spot in the ten miles between Plataea and Thespiae where any town is likely to have stood, and that was occupied by Leuctra.
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Hence it may be seen that, roughly speaking, the Western or Latin Liturgy went through three phases, which may be called for want of better names the Gallican, the Ambrosian, and the Roman stages. The holders of the theory no doubt recognize that the demarcation between these stages is rather vague, and that the alterations were in many respects gradual. Of the three theories of origin, the Ephesine may be dismissed as practically disproved. To both of the other two the same objection may be urged, that they are largely founded on conjecture and on the critical examination of documents of a much later date than the periods to which the conjectures relate.
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What is true for the generic point is true for "most" points of the variety. In Weil's Foundations of Algebraic Geometry (1946), generic points are constructed by taking points in a very large algebraically closed field, called a universal domain. Although this worked as a foundation, it was awkward: there were many different generic points for the same variety. (In the later theory of schemes, each algebraic variety has a single generic point.) In the 1950s, Claude Chevalley, Masayoshi Nagata and Jean-Pierre Serre, motivated in part by the Weil conjectures relating number theory and algebraic geometry, further extended the objects of algebraic geometry, for example by generalizing the base rings allowed.
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The novel closes with an image of Lemuel holding his bloodied hatchet up. Malone writes that Lemuel will not hit anyone with it or anything else anymore, while the final sentence breaks into semantically open-ended fragments: The majority of the book's text, however, is observational and deals with the minutiae of Malone's existence in his cell, such as dropping his pencil or his dwindling amount of writing lead. Thoughts of riding down the stairs in his bed, philosophical observations, and conjectures constitute large blocks of text and are written as tangential to the story that Malone is set on telling. Several times he refers to a list of previous Beckett protagonists: Murphy, Mercier and Camier, Molloy, and Moran.
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Particular responses to this argument attack both the first and the second premise (1 and 2). It is argued against the first premise that the underdetermination must be strong and/or inductive. It is argued against the second premise that there is evidence for a theory's truth besides observations; for example, it is argued that simplicity, explanatory power or some other feature of a theory is evidence for it over its rivals. A more general response from the scientific realist is to argue that underdetermination is no special problem for science, because, as indicated earlier in this article, all knowledge that is directly or indirectly supported by evidence suffers from it—for example, conjectures concerning unobserved observables.
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In a series of four papers between 2010 and 2012, Jean-Loup Waldspurger proved the local Gan–Gross–Prasad conjecture for tempered representations of special orthogonal groups over p-adic fields. In 2012, Colette Moeglin and Waldspurger then proved the local Gan–Gross–Prasad conjecture for generic non-tempered representations of special orthogonal groups over p-adic fields. In his 2013 thesis, Raphaël Beuzart-Plessis proved the local Gan–Gross–Prasad conjecture for the tempered representations of unitary groups in the p-adic Hermitian case under the same hypotheses needed to establish the local Langlands conjecture. Hongyu He proved the Gan-Gross- Prasad conjectures for discrete series representations of the real unitary group U(p,q).
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Seduction of the Innocent cited overt or covert depictions of violence, sex, drug use, and other adult fare within "crime comics" – a term Wertham used to describe not only the popular gangster/murder-oriented titles of the time, but superhero and horror comics as well. The book asserted that reading this material encouraged similar behavior in children. Comics, especially the crime/horror titles pioneered by EC, were not lacking in gruesome images; Wertham reproduced these extensively, pointing out what he saw as recurring morbid themes such as "injury to the eye".as seen in Jack Cole's "Murder, Morphine and Me" in True Crime Comics #2 (May 1947) Many of his other conjectures, particularly about hidden sexual themes (e.g.
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In algebraic geometry and algebraic topology, branches of mathematics, homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to Fabien Morel and Vladimir Voevodsky. The underlying idea is that it should be possible to develop a purely algebraic approach to homotopy theory by replacing the unit interval , which is not an algebraic variety, with the affine line , which is. The theory requires a substantial amount of technique to set up, but has spectacular applications such as Voevodsky's construction of the derived category of mixed motives and the proof of the Milnor and Bloch-Kato conjectures.
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Some initial conjectures related directly to the satiation of specific and general maternal hunger. These hinged on the idea that prior to parturition mothers ceased to eat and so, immediately after birth they consumed the placenta to satisfy an intense hunger. Further, was the idea of specific hunger in that the maternal figure participated in placentophagy to replenish any resources depleted during pregnancy that were contained within the placenta. This was later disproved by studies on rats and other species showing that a wide range of animals do not typically decrease the amount of food or water taken in prior to delivery, and that rats presented with placenta will consume it regardless of pregnancy or virginity.
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His best-known work is on the homological conjectures, many of which he established for local rings containing a field, thanks to his proof of the existence of big Cohen–Macaulay modules and his technique of reduction to prime characteristic. His most recent work on tight closure, introduced in 1986 with Craig Huneke, has found unexpected applications throughout commutative algebra and algebraic geometry. He has had more than 40 doctoral students, and the Association for Women in Mathematics has pointed out his outstanding role in mentoring women students pursuing a career in mathematics. He served as the chair of the department of Mathematics at the University of Michigan from 2008 to 2017.
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Nevertheless, even scholars sharing Thiele's religious convictions have maintained that there are weaknesses in his argument such as unfounded assumptions and assumed circular reasoning. > In his desire to resolve the discrepancies between the data in the Book of > Kings, Thiele was forced to make improbable suppositions ... There is no > basis for Thiele's statement that his conjectures are correct because he > succeeded in reconciling most of the data in the Book of Kings, since his > assumptions ... are derived from the chronological data themselves > ...Gershon Galil, "The Chronology of the Kings of Israel and Judah" (Brill, > 1996) p.4'The numerous extrabiblical synchronisms he invokes do not always > reflect the latest refinements in Assyriological research (cf. E.2.f below).
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Philippa Gregory is well known for her controversial portrayals of historical characters in her novels. In The Virgin's Lover, Philippa Gregory suggests as facts several things that historians have found reason to dispute, such as the cause of Amy Robsart's death as well as the exact extent of the intimacy between Robert Dudley and Elizabeth I. The book's "Author's Note" cites the uncertainty as to the accuracy of her conjectures and lists her evidence for presuming them true for the sake of telling her story. Robert Dudley is a main character in The Virgin's Lover; many believed he was in love with Queen Elizabeth, despite being married. Amy Robsart, who was Robert Dudley's wife, was found dead in 1560.
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Preface, pages vii–xi Maugham later wrote, '... Otho Stuart, who was a famous [theatrical] manager in his day, had run into difficulties with a play at the Royal Court Theatre, Sloane Square, and he wanted a replacement so that the theatre shouldn't be dark. Aleister Crowley, one of my disreputable friends, introduced me to him... If Lady Federick had failed, I'd made up my mind that I would give up writing.'Avram Davidson, Adventures in Unhistory: Conjectures on the Factual Foundations of Several Ancient Legends, Tor Press (2013) - Google Books Lady Frederick was a success for Stuart and for Maugham. The drama was first at the Court Theatre on 26 October 1907, with Ethel Irving as Lady Frederick.
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Among these are the Anosov—Katok construction of smooth ergodic area-preserving diffeomorphisms of compact manifolds, the construction of Bernoulli diffeomorphisms with nonzero Lyapunov exponents on any surface, and the first construction of an invariant foliation for which Fubini's theorem fails in the worst possible way (Fubini foiled). With Elon Lindenstrauss and Manfred Einsiedler, Katok made important progress on the Littlewood conjecture in the theory of Diophantine approximations. Katok was also known for formulating conjectures and problems (for some of which he even offered prizes) that influenced bodies of work in dynamical systems. The best-known of these is the Katok Entropy Conjecture, which connects geometric and dynamical properties of geodesic flows.
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The concept is named after English mathematician and computer scientist Alan Turing. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing machine. A universal Turing machine can be used to simulate any Turing machine and by extension the computational aspects of any possible real-world computer.A UTM cannot simulate non-computational aspects such as I/O.
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However, the rights that Nozick takes to be fundamental and the basis for regarding them to be such are different from the equal basic liberties included in justice as fairness and Rawls conjectures that they are thus not inalienable. In Lectures on the History of Political Philosophy (2007), Rawls notes that Nozick assumes that just transactions are "justice preserving" in much the same way that logical operations are "truth preserving". Thus, as explained in Distributive justice above, Nozick holds that repetitive applications of "justice in holdings" and "justice in transfer" preserve an initial state of justice obtained through "justice in acquisition or rectification". Rawls points out that this is simply an assumption or presupposition and requires substantiation.
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By the same reasoning, it cannot be either of the places called el Qantara ("bridge") which were just above, and 2 km below, modern Samsat, Turkey, before its old site was also flooded, by the Atatürk Dam. The Barrington Atlas conjectures that it was at Killik, Şanlıurfa Province, Turkey ), on the basis of T.A. Sinclair's Eastern Turkey : an architectural and archaeological survey, which is some 40 km downstream from Samosata, and below the dam. The reasoning here is unclear. Sinclair shows this Killik (which means "Claypit" in Turkish), on his map at IV 172, but all four of his references to the name in his text are to a Killik at , at the headwaters of the Euphrates, near Divriği.
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On 21 January 1939 after 10 weeks and two days on strike the waterside workers at Port Kembla decided to load the pig iron "under protest". The Lyons Government policy of appeasement of Japanese military aggression and opposition to the trade union bans on trade with Japan were not entirely unanimous. External Affairs minister Billy Hughes appears to have attempted to undermine the government policy according to at least one historian, who conjectures this may have been due to Hughes' past links with the Waterside Workers' Federation, being the first President of the union in 1902. The day after the workers at Port Kembla capitulated Billy Hughes delivered a vitriolic speech attacking Japanese militarism and its threat to Australia.
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A constructible sheaf on a variety over a finite field is called pure of weight β if for all points x the eigenvalues of the Frobenius at x all have absolute value N(x)β/2, and is called mixed of weight ≤β if it can be written as repeated extensions by pure sheaves with weights ≤β. Deligne's theorem states that if f is a morphism of schemes of finite type over a finite field, then Rif! takes mixed sheaves of weight ≤β to mixed sheaves of weight ≤β+i. The original Weil conjectures follow by taking f to be a morphism from a smooth projective variety to a point and considering the constant sheaf Ql on the variety.
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Malle does research on linear algebraic groups, finite groups of Lie type and on local-global conjectures in finite-group representation theory, e.g. the Brauer height-zero conjecture, the Alperin weight conjecture, and the McKay conjecture and its block-wise version known as the Alperin-McKay conjecture. Malle's research also deals with the Cohen-Lenstra heuristic of the structure of class groups of quadratic number fields in algebraic number theory, the asymptotic distribution of Galois groups of number fields, and with the inverse problem of Galois theory. In 1993 he began a collaboration with Michel Broué and Jean Michel concerning Spetses (named after the Greek island Σπέτσες where the program was initiated).
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They first went to Nicaea and then, on pretence of change of air and of procuring a cure for his wound, into the East where he was made magister militum. Having traversed Asia Minor, they raised the standard of revolt in 484, when Illus declared Leontius Emperor. Zeno sent an army to fight them, but Illus won, obtained possession of Papurius, released Verina, and induced her to crown Leontius at Tarsus. In 485 Zeno sent against the rebels a fresh army, said to consist of Macedonians and Scythians (Tillemont conjectures, not unreasonably, that these were Ostrogoths) under John the Hunchback, or, more probably, John the Scythian, and Theoderic the Amal, who was at this time consul.
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According to Woudhuysen, 'William Baldwin was instrumental in the creation of Ferrers's largest surviving literary work, his contributions to The Mirror for Magistrates, in which he was also associated with Sir Thomas Chaloner and Thomas Phaer'. Woudhuysen conjectures that Ferrers wrote several pieces for a suppressed edition of The Mirror for Magistrates published about 1554 which survives only in fragments. The 1559 edition includes his tragedies of Tresilian and Thomas of Woodstock, but his other contributions were suppressed in that edition, and not printed until several years later. According to John Stow, Ferrers wrote the part of Richard Grafton's Chronicle (1568–9) dealing with the reign of Queen Mary, an allegation which Grafton denied, but Stow insisted upon.
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The area appears for the first time in texts from 429 in the Chronology of Lérins. The etymology of the place has attracted many assumptions, especially to keep away from the Alemanni, now rejected by scholars for half a century. The old form Alamania, noted in 1182, leaves little doubt and indicates a formation on an ethnic name by the Alemanni (with the suffix -ia) and perpetuates the memory of a colony or a military post of these people present before the great invasions. Among the former conjectures dating from the Franco-German rivalry in the late 19th and the beginning of the 20th century was the denial of a connection between the name of the village and Germany.
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The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory. However, there exist classical solutions to the Einstein equations that allow values of the entropy larger than those allowed by an area law, hence in principle larger than those of a black hole.
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Its energy density and pressure evolve over time. The 2018 paper on swampland conjectures with Agrawal, Obieds and Vafa points to quintessence as being the only option for dark energy in string theory and consistent quantum gravity. Self-interacting dark matter: In 2000, David Spergel and Steinhardt first introduced the concept of strongly self-interacting dark matter (SIDM) to explain various anomalies in standard cold dark models based on assuming dark matter consists of weakly interacting massive particles (also referred to as "WIMPs") In 2014, Steinhardt, Spergel and Jason Pollack have proposed that a small fraction of dark matter could have ultra-strong self-interactions, which would cause the particles to coalesce rapidly and collapse into seeds for early supermassive black holes.
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Additionally, combining both Furtwängler's and Keller's conjectures, Robinson showed that k-fold square coverings of the Euclidean plane must include two squares that meet edge to edge. However, for every k > 1 and every n > 2 there is a k-fold tiling of n-dimensional space by cubes with no shared faces . Once counterexamples to Keller's conjecture became known, it became of interest to ask for the maximum dimension of a shared face that can be guaranteed to exist in a cube tiling. When the dimension n is at most six, this maximum dimension is just n − 1, by Perron's proof of Keller's conjecture for small dimensions, and when n is at least eight, then this maximum dimension is at most n − 2\.
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Kierkegaard discusses the aria in the section "The Immediate Stages of the Erotic, or Musical Erotic" of his Either/Or. He conjectures that the number 1003, the number of Spanish women seduced by Don Giovanni, might be a last remnant of the original legend about Don Giovanni (or Don Juan); moreover, the number 1003 being odd and somewhat arbitrary suggests in Kierkegaard's opinion that the list is not complete and Don Giovanni is still expanding it. The comic sides of this aria have dramatic and ominous undertones. Kierkegaard finds in this aria the true epic significance of the opera: condensing in large groups countless women, it conveys the universality of Don Giovanni as a symbol of sensuality and yearning for the feminine.
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Forrest is referred to by John Knox as "of Linlithgow," and John Foxe describes him as a "young man born in Linlithgow." David Laing, in his edition of Knox's Works, conjectures that he may have been the son of "Thomas Forrest of Linlithgow" mentioned in the treasurer's accounts as receiving various sums for the "bigging of the dyke about the paliss of Linlithgow." Laing also states that the name "Henricus Forrus" occurs in the list of students who became Bachelors of Arts at the University of Glasgow in 1518, but supposes with more likelihood that he was identical with the "Henriccus Forrest" who was a determinant in St. Leonard's College, St. Andrews, in 1526, which would account for his special interest in the fate of Patrick Hamilton.
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Zhang's result set off a flurry of activity in the field, such as the Polymath8 project. If P(N) stands for the proposition that there is an infinitude of pairs of prime numbers (not necessarily consecutive primes) that differ by exactly N, then Zhang's result is equivalent to the statement that there exists at least one even integer k < 70,000,000 such that P(k) is true. The classical form of the twin prime conjecture is equivalent to P(2); and in fact it has been conjectured that P(k) holds for all even integers k. While these stronger conjectures remain unproven, a result due to James Maynard in November 2013, employing a different technique, showed that P(k) holds for some k ≤ 600.
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The last that is ever heard of da Correggio is in 1506 while he was meeting with Pope Julius II in Rome. Da Correggio had just published his De Quercu Iulii Pontificis, Sive De Lapide Philosophico (On the Oak of Pope Julius, or On the Philosopher's Stone), and presented it to the pope. Given da Correggio's state of poverty, Hanegraaff conjectures that De Quercu was a desperate last attempt by da Correggio to secure a source of funding to provide for himself and his family. He appeals to Julius II by mentioning that they had met before face-to-face in Savona (possibly before Julius II was pope), as if attempting to imply a stronger connection between the two men.
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Because of the Mordell–Weil theorem, Faltings's theorem can be reformulated as a statement about the intersection of a curve C with a finitely generated subgroup Γ of an abelian variety A. Generalizing by replacing C by an arbitrary subvariety of A and Γ by an arbitrary finite-rank subgroup of A leads to the Mordell–Lang conjecture, which was proved by . Another higher-dimensional generalization of Faltings's theorem is the Bombieri–Lang conjecture that if X is a pseudo-canonical variety (i.e., a variety of general type) over a number field k, then X(k) is not Zariski dense in X. Even more general conjectures have been put forth by Paul Vojta. The Mordell conjecture for function fields was proved by and by .
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This computing paradigm based upon identical photons sent through a linear-optical network can solve certain sampling and search problems that, assuming a few complexity-theoretical conjectures (that calculating the permanent of Gaussian matrices is #P-Hard and that the polynomial hierarchy does not collapse) are intractable for classical computers. However, it has been shown that boson sampling in a system with large enough loss and noise can be simulated efficiently. The largest experimental implementation of boson sampling to date had 6 modes so could handle up to 6 photons at a time. The best proposed classical algorithm for simulating boson sampling runs in time O(n2^n+mn^2) for a system with n photons and m output modes.
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Both of these statements point to his being of noble birth, and appear strangely at variance with the assertion that he was a mere professional grammarian Grammatodidascalus, a statement which Robert Geier conjectures plausibly enough to refer in fact to Marsyas of Philippi. Suidas, indeed, seems in many points to have confounded the two. The only other fact transmitted to us concerning the life of Marsyas, is that he was appointed by Demetrius Poliorcetes to command one division of his fleet in the Battle of Salamis in Cyprus (306 BC) (Diodorus, xx. 50.). However, this circumstance is alone sufficient to show that he was a person who himself took an active part in public affairs, not a mere man of letters.
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Themes found within Marlowe's literary works have been noted as humanistic with realistic emotions, which some scholars find difficult to reconcile with Marlowe's "anti-intellectualism" and his catering to the taste of his Elizabethan audiences for generous displays of extreme physical violence, cruelty, and bloodshed. Events in Marlowe's life were sometimes as extreme as those found in his dramas. Reports of Marlowe’s death in 1593 were particularly infamous in his day and are contested by scholars today due to a lack of good documentation. Traditionally, the playwright’s death has been blamed on a long list of conjectures, including a bar-room fight, church libel, homosexual intrigue, betrayal by another playwright, and espionage from the highest level: Elizabeth I of England’s Privy Council.
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11th century manuscript of the Hebrew Bible. In the mid-18th century, some scholars started a critical study of doublets (parallel accounts of the same incidents), inconsistencies, and changes in style and vocabulary in the Torah. In 1780 Johann Eichhorn, building on the work of the French doctor and exegete Jean Astruc's "Conjectures" and others, formulated the "older documentary hypothesis": the idea that Genesis was composed by combining two identifiable sources, the Jehovist ("J"; also called the Yahwist) and the Elohist ("E"). These sources were subsequently found to run through the first four books of the Torah, and the number was later expanded to three when Wilhelm de Wette identified the Deuteronomist as an additional source found only in Deuteronomy ("D").
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After his PhD, Williamson was a post-doctoral researcher at the University of Oxford, based at St. Peter's College, Oxford and from 2011 until 2016 he was at the Max Planck Institute for Mathematics. Williamson deals with a geometric representation of group theory. With Ben Elias, he gave a new proof and a simplification of the theory of the Kazhdan–Lusztig conjectures (previously proved in 1981 by both Beilinson–Bernstein and Brylinski–Kashiwara). For this purpose, they built on works by Wolfgang Soergel and developed a purely algebraic Hodge theory of Soergel bimodules about polynomial rings, In this context, they also succeeded in proving the long-standing positive presumption of positivity for the coefficients of the Kazhdan–Lusztig polynomials for Coxeter groups.
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Though it remains uncertain, the book's editor is commonly identified as William Whittingham. Patrick Collinson has made a case for Thomas Wood as the editor, and M. A. Simpson has questioned the assumption that there was a single author behind A Brief Discourse who was part of the debates it concerns. Much of its material must have come to its compiler(s) from other hands, the letters it contains vary in apparent authenticity, and the documentary sources behind it are no longer extant except, in adapted form, parts of John Knox's account of his time in Frankfurt. Noting these things, Simpson conjectures that A Brief Discourse was the product of several editors, the last of whom he believes to have been John Field.
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The oplomachi were a designation or possibly a class of Roman gladiator with relatively little mention in literary sources. They are often identified with the similarly named hoplomachus, but literary mentions do not seem to relate the two, despite the similarity of the names. According to Justus Lipsius, an oplomachus was one of two designations of Samnite; he conjectures that Samnite variants were called oplomachi when matched against a Thracian, and a secutor when facing a retiarii.Roman life and manners under the early empire, 4 Ludwig Friedlaender (1913) p 176 Though historical accounts identify them primarily as an opponent of the Thraex, they appear in a Pompeian list as fighting not only against Thraeces, but against Murmillones and Dimachaeri as well.
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The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. For the purposes of this article, we do not regard mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify (as otherwise no scientific discovery before the late 19th century would count). We begin our timeline at the Bronze Age, as it is difficult to estimate the timeline before this point, such as of the discovery of counting, natural numbers and arithmetic. To avoid overlap with Timeline of historic inventions, we do not list examples of documentation for manufactured substances and devices unless they reveal a more fundamental leap in the theoretical ideas in a field.
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Whether the New Testament contains an individual Antichrist is disputed. The Greek term antikhristos originates in 1 John. The similar term pseudokhristos ("False Messiah") is also first found in the New Testament, but never used by Josephus in his accounts of various false messiahs. The concept of an antikhristos is not found in Jewish writings in the period 500 BC–50 AD. However, Bernard McGinn conjectures that the concept may have been generated by the frustration of Jews subject to often-capricious Seleucid or Roman rule, who found the nebulous Jewish idea of a Satan who is more of an opposing angel of God in the heavenly court insufficiently humanised and personalised to be a satisfactory incarnation of evil and threat.
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To such an host of observations and conjectures, I cannot presume to add any thing, save that of recording an humble opinion in favour of that given by Mr. Horsley. In 1684, when the inclosures between the bridge and town were first ploughed up, many coins of Nerva, Trajan, Hadrian, Constantine, &c.; were found, together with intaglios of agate, and cornelian, the finest coloured urns, and paterae, some wrought in basso relievo, with the workman's name generally impressed on the inside of the bottom; also a discus, or quoit, with an emperor's head embossed upon it. Again, in 1718, two very handsomely moulded altars were dug up, and in 1759, the drawing of another was communicated to the Society of Antiquaries.
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In his mathematical style, Erdős was much more of a "problem solver" than a "theory developer" (see "The Two Cultures of Mathematics" by Timothy Gowers for an in- depth discussion of the two styles, and why problem solvers are perhaps less appreciated). Joel Spencer states that "his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career." This article is a review of Mathematics: Frontiers and Perspectives Erdős never won the highest mathematical prize, the Fields Medal, nor did he coauthor a paper with anyone who did, a pattern that extends to other prizes.From "trails to Erdos" , by DeCastro and Grossman, in The Mathematical Intelligencer, vol.
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800 date, E. Lipinski, "The Nora fragment", Mediterraneo antico 2 (1999:667-71) and for the reconstruction of the text Lipinski2004:234-46), rejecting Cross.. by general Milkaton, son of Shubna, against the Sardinians at the site of TRSS, surely Tarshish; Cross conjectures that Tarshish here "is most easily understood as the name of a refinery town in Sardinia, presumably Nora or an ancient site nearby." He presents evidence that the name PMY ("Pummay") in the last line is a shortened form (hypocoristicon) of the name of Shubna's king, containing only the divine name, a method of shortening “not rare in Phoenician and related Canaanite dialects.”.F. M. Cross, “An Interpretation of the Nora Stone,” Bulletin of the American Schools of Oriental Research 208 (Dec.
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A proof of Fleischner's theorem was announced by Herbert Fleischner in 1971 and published by him in 1974, solving a 1966 conjecture of Crispin Nash-Williams also made independently by L. W. Beineke and Michael D. Plummer.. For the earlier conjectures see Fleischner and . In his review of Fleischner's paper, Nash-Williams wrote that it had solved "a well known problem which has for several years defeated the ingenuity of other graph-theorists".. Fleischner's original proof was complicated. Václav Chvátal, in the work in which he invented graph toughness, observed that the square of a k-vertex-connected graph is necessarily k-tough; he conjectured that 2-tough graphs are Hamiltonian, from which another proof of Fleischner's theorem would have followed.; .
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Some 160 years after Homeopathy and Its > Kindred Delusions, an essay by Oliver Wendell Holmes, we are still debating > whether homeopathy is a placebo or not... Homeopathic principles are bold > conjectures. There has been no spectacular corroboration of any of its > founding principles... After more than 200 years, we are still waiting for > homeopathy "heretics" to be proved right, during which time the advances in > our understanding of disease, progress in therapeutics and surgery, and > prolongation of the length and quality of life by so-called allopaths have > been breathtaking. The true skeptic therefore takes pride in closed > mindedness when presented with absurd assertions that contravene the laws of > thermodynamics or deny progress in all branches of physics, chemistry, > physiology, and medicine.
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Some plausible reasoning methods due to George Polya George Polya in his two volume book titled Mathematics and Plausible Reasoning presents plausible reasoning as a way of generating new mathematical conjectures. To Polya, “a mathematical proof is demonstrative reasoning but the inductive evidence of the physicist, the circumstantial evidence of the lawyer, the documentary evidence of the historian and the statistical evidence of the economist all belong to plausible reasoning”. Polya’s intention is to teach students the art of guessing new results in mathematics for which he marshals such notions as induction and analogy as possible sources for plausible reasoning. The first vole of the book is devoted to an extensive discussion of these ideas with several examples drawn from various field of mathematics.
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The 1829 missionary report does not provide its sources and acknowledges that "no correct idea can be formed of the number of murders occasioned by suttees", then states some of the statistics is based on "conjectures". According to Yang, these "numbers are fraught with problems". William Bentinck, in an 1829 report, stated without specifying the year or period, that "of the 463 satis occurring in the whole of the Presidency of Fort William, 420 took place in Bengal, Behar, and Orissa, or what is termed the Lower Provinces, and of these latter 287 in the Calcutta Division alone". For the Upper Provinces, Bentinck added, "in these Provinces the satis amount to forty three only upon a population of nearly twenty millions", i.e.
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According to the colonial era scholarship, as early as the 6th century, another people called the Mon began to enter the present-day Lower Burma from the Mon kingdoms of Haribhunjaya and Dvaravati in modern-day Thailand. By the mid 9th century, the Mon had founded at least two small kingdoms (or large city-states) centred around Bago and Thaton. The earliest external reference to a Mon kingdom in Lower Burma was in 844–848 by Arab geographers.Hall 1960: 11–12 But recent research shows that there is no evidence (archaeological or otherwise) to support colonial period conjectures that a Mon-speaking polity existed in Lower Burma until the late 13th century, and the first recorded claim that the kingdom of Thaton existed came only in 1479.
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In his paper with Jones, he studied the topology of the moduli space of SU(2) instantons over a 4-sphere. They showed that the natural map from this moduli space to the space of all connections induces epimorphisms of homology groups in a certain range of dimensions, and suggested that it might induce isomorphisms of homology groups in the same range of dimensions. This became known as the Atiyah–Jones conjecture, and was later proved by several mathematicians. Harder and M. S. Narasimhan described the cohomology of the moduli spaces of stable vector bundles over Riemann surfaces by counting the number of points of the moduli spaces over finite fields, and then using the Weil conjectures to recover the cohomology over the complex numbers.
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Luxenberg argues that the Quran was not originally written exclusively in Arabic but in a mixture with Syriac, the dominant spoken and written language in the Arabian peninsula through the eighth century. Luxenberg remarked that scholars must start afresh, ignore the old Islamic commentaries, and use only the latest in linguistic and historical methods. Hence, if a particular Quranic word or phrase seems "meaningless" in Arabic, or can be given meaning only by tortuous conjectures, it makes sense – he argues – to look to Syriac as well as Arabic. Luxenberg also argues that the Quran is based on earlier texts, namely Syriac lectionaries used in Christian churches of Syria, and that it was the work of several generations who adapted these texts into the Quran as known today.
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Christopher Bigsby wrote Arthur Miller: The Definitive Biography based on boxes of papers Miller made available to him before his death in 2005. The book was published in November 2008, and is reported to reveal unpublished works in which Miller "bitterly attack[ed] the injustices of American racism long before it was taken up by the civil rights movement". In his book Trinity of Passion, author Alan M. Wald conjectures that Miller was "a member of a writer's unit of the Communist Party around 1946," using the pseudonym Matt Wayne, and editing a drama column in the magazine The New Masses. In 1999 the writer Christopher Hitchens attacked Miller for comparing the Monica Lewinsky investigation to the Salem witch hunt.
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Comparable revenue assurance activities do occur in other industries, such as with billing of utilities or with the licensing of software, and there are many parallels with financial and operational control activities undertaken by most large businesses. The rationale for why revenue assurance has come to be considered particularly important in telecommunications, unlike other industries, is disputed. Reasonable conjectures are that: (1) the fast pace of change and intense commercial competition increase the likelihood of mistakes; (2) there is significant complexity in determining the combined effect of interacting systems and processes; and (3) the high-volume, low-value nature of transactions amplifies the financial implications of "small" errors. Another conjecture is that revenue assurance is a response to changing market conditions.
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Globe by Jacques de Vau de Claye (1583) showing "Terre de Beac/Locac" as a peninsula of the "Terre Australle". The extent of French knowledge concerning Terra Australis in the mid-16th century is indicated by Lancelot Voisin de La Popelinière, who in 1582 published Les Trois Mondes, a work setting out the history of the discovery of the globe. In Les Trois Mondes, La Popelinière pursued a geopolitical design by using cosmographic conjectures which were at the time quite credible, to theorize a colonial expansion by France into the Austral territories. His country, eliminated from colonial competition in the New World after a series of checks at the hands of the Portuguese and Spanish, could only thenceforward orient her expansion toward this "third world".
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Beginning with the work of J. D. Brown and Marc Henneaux in 1986,Brown and Henneaux 1986 physicists have noticed that quantum gravity in a three-dimensional spacetime is closely related to two-dimensional conformal field theory. In 1995, Henneaux and his coworkers explored this relationship in more detail, suggesting that three-dimensional gravity in anti-de Sitter space is equivalent to the conformal field theory known as Liouville field theory.Coussaert, Henneaux, and van Driel 1995 Another conjecture formulated by Edward Witten states that three-dimensional gravity in anti-de Sitter space is equivalent to a conformal field theory with monster group symmetry.Witten 2007 These conjectures provide examples of the AdS/CFT correspondence that do not require the full apparatus of string or M-theory.
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Theophilus is the name or honorary title of the person to whom the Gospel of Luke and the Acts of the Apostles are addressed (Luke 1:3, Acts 1:1). It is thought that both the Gospel of Luke and Acts of the Apostles were written by the same author, and often argued that the two books were originally a single unified work. Both Luke and Acts were written in a refined Koine Greek, and the name "θεόφιλος" ("Theophilos"), as it appears therein, means friend of GodStrong's G2321 or (be)loved by God or loving GodBauer lexicon, 2nd edition, 1958, page 358 in the Greek language. No one knows the true identity of Theophilus and there are several conjectures and traditions around an identity.
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Some who maintain the 586 date therefore maintain that in this one instance, Ezekiel, without explicitly saying so, switched to the regnal years of Zedekiah, although Ezekiel apparently regarded Jeconiah as the rightful ruler and never names Zedekiah in his writing. Another view is that a later copyist, aware of the 2 Kings passage, modified it and inserted it into the text of Ezekiel. In his study of all biblical texts related to the Babylonian capture of Jerusalem, Young concludes that these conjectures are not necessary, and that all texts related to the fall of Jerusalem in Jeremiah, Ezekiel, 2 Kings, and 2 Chronicles are internally consistent and consistent with the fall of the city in Tammuz of 587 BCE.Rodger C. Young (2004).
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Mathias conjectures that this may have been the first book to be printed in Welsh. Brinley Jones suggests that the dictionary has the appearance of a work-book, devised in the first place for Salesbury's own use. In 1550 his A briefe and a playne introduction, teachyng how to pronounce the letters in the British tong (now commonly called Walsh)... was printed by Robert Crowley. A revised edition was printed "by Henry Denham for Humphrey Toy, at the sygne of the Helmet in Paules church yarde, The. xvij. of May. 1567." A short comparative study of Welsh sounds with Hebrew and Greek is included, plus an examination of the Latin element in Welsh (which he had first examined in the dictionary of 1547).
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Inter- universal Teichmüller theory IV: log-volume computations and set-theoretic foundations, Shinichi Mochizuki, August 2012 These include the strong Szpiro conjecture, the hyperbolic Vojta conjecture and the abc conjecture over every number field. The preprints have not been published. In September 2018, Mochizuki posted a report on his work by Peter Scholze and Jakob Stix asserting that the third preprint contains an irreparable flaw; he also posted several documents containing his rebuttal of their criticism. The majority of number theorists have found Mochizuki's preprints very difficult to follow and have not accepted the conjectures as settled, although there are a few prominent exceptions, including Go Yamashita, Ivan Fesenko, and Yuichiro Hoshi, who vouch for the work and have written expositions of the theory.
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Notable students and members of his company include Stanisław Brzozowski, Ewa Czekalska, Leszek Czarnota, Danuta Kisiel- Drzewinska, Jerzy Kozlowski, Krystyna Marynowska, Stefan Niedzialkowski, Janusz Pieczuro, Paweł Rouba,and Andrzej Szczużewski. Tomaszewski's early work is documented in English in "Tomaszewski's Mime Theatre" by Andrzej Hausbrandt (Poland: Interpress, 1975). Between 1960 and 1966 he collaborated with the Służba Bezpieczeństwa (State Counterintelligence Service), reporting on the activities of his friends and colleagues. He did not receive payment for these activities and Dr. Sebastian Ligarski, the researcher who discovered the dossier on Tomaszewski in the archives of the Wroclaw IPN (Institute of National Remembrance), conjectures that the service blackmailed him either because of his known homosexual tendencies or with the threat of a ban on foreign travel.
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The facial feedback hypothesis, rooted in the conjectures of Charles Darwin and William James, is that one's facial expression directly affects their emotional experience. Specifically, physiological activation of the facial regions associated with certain emotions holds a direct effect on the elicitation of such emotional states, and the lack of or inhibition of facial activation will result in the suppression (or absence altogether) of corresponding emotional states. Variations of the facial feedback hypothesis differ in regards to what extent of engaging in a given facial expression plays in the modulation of affective experience. Particularly, a "strong" version (facial feedback is the decisive factor in whether emotional perception occurs or not) and a "weak" version (facial expression plays a limited role in influencing affect).
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This model does not account for the fluidity of gender asserted by persons like American Psychologist Lisa M. Diamond who explains is not a stable, fixed trait – rather, it is socially constructed and may vary over time for an individual. This model directly contravenes both the notion of gender identity being individual and internal, by explaining its source as social behavior and its manifestation as a desire for congruence with a received notion of gender. It is unclear whether this contradiction occurs as an inconsistency in terminology or as a contradiction of two claims. Other proposed models include that of the Gender Schema Theory, which conjectures that the development of gender identity, is a process of self identification which must precede the ability for "children to label themselves and others as males or females".
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In his plenary address at the International Mathematical Congress in Kyoto (1990), Grigory Margulis outlined a broad program rooted in ergodic theory that allows one to prove number- theoretic results using the dynamical and ergodic properties of actions of subgroups of semisimple Lie groups. The work of D. Kleinbock, G. Margulis and their collaborators demonstrated the power of this novel approach to classical problems in Diophantine approximation. Among its notable successes are the proof of the decades-old Oppenheim conjecture by Margulis, with later extensions by Dani and Margulis and Eskin–Margulis–Mozes, and the proof of Baker and Sprindzhuk conjectures in the Diophantine approximations on manifolds by Kleinbock and Margulis. Various generalizations of the above results of Aleksandr Khinchin in metric Diophantine approximation have also been obtained within this framework.
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In their 1923 paper on the Goldbach Conjecture, Hardy and Littlewood stated a series of conjectures, one of which, if true, would explain some of the striking features of the Ulam spiral. This conjecture, which Hardy and Littlewood called "Conjecture F", is a special case of the Bateman–Horn conjecture and asserts an asymptotic formula for the number of primes of the form ax2 \+ bx + c. Rays emanating from the central region of the Ulam spiral making angles of 45° with the horizontal and vertical correspond to numbers of the form 4x2 \+ bx + c with b even; horizontal and vertical rays correspond to numbers of the same form with b odd. Conjecture F provides a formula that can be used to estimate the density of primes along such rays.
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In the field of mathematics known as representation theory, an L-packet is a collection of (isomorphism classes of) irreducible representations of a reductive group over a local field, that are L-indistinguishable, meaning they have the same Langlands parameter, and so have the same L-function and ε-factors. L-packets were introduced by Robert Langlands in , . The classification of irreducible representations splits into two parts: first classify the L-packets, then classify the representations in each L-packet. The local Langlands conjectures state (roughly) that the L-packets of a reductive group G over a local field F are conjecturally parameterized by certain homomorphisms of the Langlands group of F to the L-group of G, and Arthur has given a conjectural description of the representations in a given L-packet.
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The reasons behind the rejection are covered in more detail in the article on Mosaic authorship. In the mid-18th century, some scholars started a critical study of doublets (parallel accounts of the same incidents), inconsistencies, and changes in style and vocabulary in the Torah. In 1780 Johann Eichhorn, building on the work of the French doctor and exegete Jean Astruc's "Conjectures" and others, formulated the "older documentary hypothesis": the idea that Genesis was composed by combining two identifiable sources, the Jehovist ("J"; also called the Yahwist) and the Elohist ("E"). These sources were subsequently found to run through the first four books of the Torah, and the number was later expanded to three when Wilhelm de Wette identified the Deuteronomist as an additional source found only in Deuteronomy ("D").
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The Hellenist Harrison treats Ovid's long discursive exploration of the political and mythological aspects of Anna Perenna in the Fasti as a "rubbish heap" of "conjectures." The Ides were supposed to be determined by the full moon, reflecting the lunar origin of the Roman calendar. On the earliest calendar, the Ides of March would have been the first full moon of the new year.H.H. Scullard, Festivals and Ceremonies of the Roman Republic (Cornell University Press, 1981), pp. 42–43. H.S. Versnel has argued that adjustments made to the calendar over time caused the Mamuralia to be moved from an original place as the last day of the year (the day before the Kalends of March) to the day before the Ides, causing the Equirria on February 27 to be repeated on March 14.
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Macarius took part in the Council of Nicaea (325), and two conjectures as to the part he played there are worth mentioning. The first is that there was a passage of arms between him and his metropolitan, Eusebius of Caesarea, concerning the rights of their respective sees. The seventh canon of the council — "As custom and ancient tradition show that the bishop of Ælia [Jerusalem] ought to be honoured, he shall have precedence; without prejudice, however, to the dignity which belongs to the Metropolis" — by its vagueness suggests that it was the result of a drawn battle. The second conjecture is that Macarius, together with Eustathius of Antioch, had a good deal to do with the drafting of the Nicene Creed finally adopted by the First Council of Nicæa in 325.
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While many of the puzzling features have still not been fully explained or accounted for (including alleged anachronisms which presume that the date 1548 is the date of composition as opposed to the date of record), and while further tests can be devised, no critics have impugned (i) the integrity and expertise of those who have subjected the document to investigation, or (ii) (subject to reservations over Dibble's lack of access to the original) the reliability and coherence of such tests and investigations as were actually performed or conducted, or (iii) the conclusions drawn from the results of those tests and investigations.Tena; Brading, p. 344; Peralta; cf. Poole (2000) for a brief list of his objections, (2002) where, en passant, he conjectures it to be "most probably a crude nineteenth century forgery", and ibid.
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Bray conjectures that Saloninus's appointment as Caesar, like that of his elder brother, Valerian II, in Illyria, was made at the instigation of Valerian I who was, simultaneously, the senior Emperor (Augustus) and grandfather of the two young Caesars and, as head of the Licinius clan, exercised also the patria potestas over all members of the Imperial family, including his son Gallienus, his co- Emperor (and co-Augustus). Bray suggests that Valerian's motive in making these appointments was securing the succession and establishing a lasting imperial dynasty. We do not know how Valerian envisaged his grandson interacting with the existing governors and military commanders of the Gallic provinces. There is no reason to suppose that he ever thought the thing through as systematically as Diocletian when he established the Tetrarchy some thirty years later.
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The safeguard was required since Astruc's Languedoc homeland was in the frame of the Counter-Reformation, and the Protestant "Camisards" being deported or sent to the galleys was still a very recent memory. In Astruc's own times the writers of the Encyclopédie were working under great pressure and in secret, the Catholic Church not offering a tolerant atmosphere for biblical criticism. That was somewhat ironic, for Astruc saw himself as fundamentally a supporter of orthodoxy; his unorthodoxy lay not in denying Mosaic authorship of Genesis but in his defence of it. In the previous century scholars such as Thomas Hobbes,Astruc, Conjectures sur les memoires originaux dont il paroit que Moyse s'est servi pour composer le livre de la Genese, p. 454, and the "Table des Matieres" (Table of Matters), p. 509.
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Together with Christopher Skinner, Urban proved many cases of Iwasawa–Greenberg main conjectures for a large class of modular forms. As a consequence, for a modular elliptic curve over the rational numbers, they prove that the vanishing of the Hasse–Weil L-function L(E, s) of E at s = 1 implies that the p-adic Selmer group of E is infinite. Combined with theorems of Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if and only if L(E, 1) = 0, a (weak) form of the Birch–Swinnerton-Dyer conjecture. These results were used (in joint work with Manjul Bhargava and Wei Zhang) to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture.
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Rudnick has been studying different aspects of quantum chaos and number theory. He has contributed to one of the discoveries concerning the Riemann zeta function, namely, that the Riemann zeros appear to display the same statistics as those which are believed to be present in energy levels of quantum chaotic systems and described by random matrix theory. Together with Peter Sarnak, he has formulated the Quantum Unique Ergodicity conjectures for eigenfunctions on negatively curved manifolds,Mathematicians Illuminate Deep Connection Between Classical And Quantum Physics, Science Daily and has investigated the question arising from Quantum Chaos in other arithmetic models such as the Quantum Cat map (with Par Kurlberg) and the flat torus (with CP Hughes and with Jean Bourgain). Another interest is the interface between function field arithmetic and corresponding problems in number fields.
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Yet King's musical contribution to the volume was substantial; in the present-day 1991 edition of the Sacred Harp, his name appears on 22 of the tunes as composer, arranger, or co-arranger. Steel describes King as having a distinctive musical style, and describes three of his songs, "Bound for Canaan," "Sweet Canaan," and "Fulfilment" as "classics".Steel (2010, 129) Steel conjectures that King may also have provided the initial financing that would have been needed to persuade the printer (in Philadelphia) to take on the job of producing the book. At the time White was "still establishing himself" as a farmer, but King came from a wealthy family with a large plantation.Steel (2010, 6) The Sacred Harp was first published in 1844; King died 31 August of the same year.
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Michael Ira Rosen (born 7 March 1938 in Brooklyn) is an American mathematician who works on algebraic number theory, arithmetic theory of function fields, and arithmetic algebraic geometry. Rosen earned a bachelor's degree from Brandeis University in 1959 and a PhD from Princeton University in 1963 under John Coleman Moore with thesis Representations of twisted group rings. He is a mathematics professor at Brown University. Rosen is known for his textbooks, especially for the book with co-author Kenneth Ireland on number theory, which was inspired by ideas of André Weil;for example, Weil's essay on Gaussian sums and cyclotomic fields, La cyclotomie jadis et naguère, 1974 this book, A Classical Introduction to Modern Number Theory gives an introduction to zeta functions of algebraic curves, the Weil conjectures, and the arithmetic of elliptic curves.
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Charles Tittle conducted a study of inmate social groups in a Federal hospital serving a large groups of prisoners suffering from narcotics addiction in 1969, in which he compared the experiences of female inmates to those of the males. He found that women were significantly more likely to identify as having a close group of friends; 70% of female respondents said that they had one to five good friends, as compared to 49% of males. Tittle conjectures that these findings indicate that under comparable circumstances, women are more likely to form 'primary group affiliations' while men are more likely to integrate into the overall social organization. He states that male inmate social groups tend to be more symbiotic and to place higher value on individualism than female inmate groups were observed to do.
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Pyusawhti ( , ; also Pyuminhti, ) was a semi-legendary king of Pagan Dynasty of Burma (Myanmar), who according to the Burmese chronicles supposedly reigned from 167 to 242 CE. The chronicles down to the 18th century had reported that Pyusawhti, a descendant of a solar spirit and a dragon princess, was the founder of Pagan—hence, Burmese monarchy. However Hmannan Yazawin, the Royal Chronicle of Konbaung Dynasty proclaimed in 1832 that he was actually a scion of Tagaung Kingdom and traced his lineage all the way to Maha Sammata, the first king of the world in Buddhist mythology.Lieberman 2003: 196 Scholarship conjectures that Pyusawhti the historical figure likely existed in the mid-to- late 8th century, who perhaps came over from the Nanzhao Kingdom as part of the Nanzhao raids of the Irrawaddy valley during the period.
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Suzuki conjectures that the individuals were killed with spears or arrows by enemies who cannibalized their victims (breaking bones in the process) and then threw the remains into the fissure, which had been used as a trash dump (which explains the animal bones). The individuals were rather short (about 1.55 m for the males, 1.40 m for the females) and their cranial capacity was close to the lower end of the range of the latter prehistoric Jōmon (16,000 to 2,000 years ago) and modern Japanese. The teeth were extremely worn out, suggesting an abrasive diet. In one of the mandibles, the two median incisors had been knocked out at the same time, well before death—a custom that is known to have been practiced by the Jōmon people.
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In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety and different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Schemes were introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).Introduction of the first edition of "Éléments de géométrie algébrique". Strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra.
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Skene however, asserted that here "Scots" refers to all of the peoples living north of the firths of Clyde and Forth. In The Tribe in Scotland Aside from the document's intrinsic importance to Scottish history, it is significant in its similarity to corresponding areas both of Irish Brehon law and of Welsh law, which are better-preserved than the laws of medieval southern Scotland, allowing reasonable conjectures to be made regarding the laws and customs of the region, as few historical records exist. The Laws or their precursor were relevant in the early twelfth century, as the Laws of the Four Burghs (Latin: Leges Quatuor Burgorum) explicitly banned parts of it relating to the cro (or weregild). Clause XVII of the Leges Quatuor Burgorum the text of XVII.
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Afterwards, he is reported to have said to a church group, In July 2007, McLeroy was made chairman of the State Board of Education by Texas Governor Rick Perry.Teaching of evolution to go under microscope: Director's departure opens door for changes in Texas' curriculum, Karen Ayres Smith, The Dallas Morning News, December 13, 2007. The Washington Spectator suggests that the goal was to remove Comer prior to the meetings to revise the science standards component of the Texas Essential Knowledge and Skills document, which will influence the design of science textbooks nationwide. The Spectator conjectures that this opportunity will be used by intelligent design supporters to more aggressively press efforts to "teach the controversy", a Discovery Institute program to introduce creationism into the classroom and avoid legal jeopardy.
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Nisa () was a city in ancient Boeotia, mentioned by Homer in the Catalogue of Ships in the Iliad, where the poet applies the epithet "divine" to the city. Given the absence of written material in the more ancient authors about the location in Boeotia of Nisa, Strabo considered possible that the mention by Homer was an error and it was actually the city of Isus, although he cites a Nisa, which no longer existed, near Megara, whose inhabitants had emigrated to form a colony near the Mount Citheron, but in any case both populations were not in Boeotia. Other conjectures replaced the Nisa of the Homeric catalog by Creusa, Pharae or Nysa. The editors of the Barrington Atlas of the Greek and Roman World treat it as unlocated.
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Daedalus' appearance in Homer is in an extended metaphor, "plainly not Homer's invention", Robin Lane Fox observes: "He is a point of comparison and so he belongs in stories which Homer's audience already recognized."Robin Lane Fox, Travelling Heroes in the Epic Age of Homer, 2009:187, 178. In Bronze Age Crete, an inscription (//) has been read as referring to a place at Knossos,"The word da-da-re-jo-de on a has been interpreted as meaning Daidaleionde— "towards" or "into the Daidaleion," and K. Kerenyi conjectures that it may refer to the choros that Daedalus is supposed to have built for Ariadne" (Burns 1974/75:3; the Kerenyi assertion is in an article in Atti e memorie del primo congresso internazionale del micenologia, 1967, vol. II, Rome 1968).
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This is not to say that Merton believed that these religions did not have valuable rituals or practices for him and other Christians, but that, doctrinally, Merton was so committed to Christianity and he felt that practitioners of other faiths were so committed to their own doctrines that any discussion of doctrine would be useless for all involved. He believed that for the most part, Christianity had forsaken its mystical tradition in favor of Cartesian emphasis on "the reification of concepts, idolization of the reflexive consciousness, flight from being into verbalism, mathematics, and rationalization."Conjectures of a Guilty Bystander p. 285. Eastern traditions, for Merton, were mostly untainted by this type of thinking and thus had much to offer in terms of how to think of and understand oneself.
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The term "distant reading" is generally attributed to Franco Moretti and his 2000 article, Conjectures on World Literature. In the article, Moretti proposed a mode of reading which included works outside of established literary canons, which he variously termed "the great unread" and, elsewhere, "the Slaughterhouse of Literature". The innovation it proposed, as far as literary studies was concerned, was that the method employed samples, statistics, paratexts, and other features not often considered within the ambit of literary analysis. Moretti also established a direct opposition to the theory and methods of close reading: "One thing for sure: it cannot mean the very close reading of very few texts—secularized theology, really ('canon'!)—that has radiated from the cheerful town of New Haven over the whole field of literary studies".
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The four Merton ‘Calculators’ were not only well versed in the current issues of philosophy during the fourteenth century; they actually initiated new groundbreaking scientific postulations. John of Dumbleton was no exception. Because he concurred with many of the positions held by William Ockham (1288–1348)—especially the idea that is commonly referred to as Ockham’s razor, which states that the most simplistic explanations are ideal—he may have learned how to succinctly formulate his scientific conjectures. Of Dumbleton’s many scientific theories there is one in particular that is worth mentioning here. By making the assumption that bodies are finite, Dumbleton was able to conjecture that contraction or expansion, as in cases of condensation or rarefaction, does not eliminate any parts of a body; rather, a “denumerable number of parts” always exists.
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Killing's university library did not contain the Scandinavian journal in which Lie's article appeared. (Lie later was scornful of Killing, perhaps out of competitive spirit and claimed that all that was valid had already been proven by Lie and all that was invalid was added by Killing.) In fact Killing's work was less rigorous logically than Lie's, but Killing had much grander goals in terms of classification of groups, and made a number of unproven conjectures that turned out to be true. Because Killing's goals were so high, he was excessively modest about his own achievement. From 1888 to 1890, Killing essentially classified the complex finite-dimensional simple Lie algebras, as a requisite step of classifying Lie groups, inventing the notions of a Cartan subalgebra and the Cartan matrix.
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Stansfield Tower, alt=Prominent structure on a hill One contender is in the civil parish of Blacko, on the site of present-day Malkin Tower Farm; since the 1840s claims have been made that old masonry found in a field wall is from the remains of the building. In The Lancashire Witch-Craze, Jonathan Lumby conjectures that the building was situated on the moors surrounding Blacko Hill, near to an old road between Colne and Gisburn. Local folklore in the parish holds that the remains of Malkin Tower are buried in a field behind the nearby Cross Gaits Inn public house; the tower used to be featured on the inn's sign. The primary evidence supporting this location seems to be that a hollow in the hillside east of the farm is known as Mawkin Hole.
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He is also remembered for his Gaelic Etymology of the Languages of Western EuropeMacKay, Charles, The Gaelic Etymology Of The Languages Of Western Europe, And More Especially Of The English And Lowland Scotch And Of Their Slang, Cant And Colloquial Dialects (1877). and the later Dictionary of Lowland ScotchMacKay, Charles (1888), A Dictionary of Lowland Scotch, London, Whittacker & Co. in which he presented his "fanciful conjectures" that "thousands of English words go back to Scottish Gaelic". The linguist Anatoly LibermanThe author of Word Origins…And How We Know Them, Oxford University Press, USA, 2005, and An Analytic Dictionary of English Etymology: An Introduction, University Of Minnesota Press, 2008. has described MacKay as an "etymological monomaniac" commenting that "He was hauled over the coals by his contemporaries and never taken seriously during his lifetime".
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In higher dimensions, one unifying goal is the Bombieri–Lang conjecture that, for any variety X of general type over a number field k, the set of k-rational points of X is not Zariski dense in X. (That is, the k-rational points are contained in a finite union of lower-dimensional subvarieties of X.) In dimension 1, this is exactly Faltings's theorem, since a curve is of general type if and only if it has genus at least 2. Lang also made finer conjectures relating finiteness of rational points to Kobayashi hyperbolicity.Hindry & Silverman (2000), section F.5.2. For example, the Bombieri–Lang conjecture predicts that a smooth hypersurface of degree d in projective space Pn over a number field does not have Zariski dense rational points if d ≥ n + 2.
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In terms of the completion of some of the underlying Grothendieck program of research, he defined absolute Hodge cycles, as a surrogate for the missing and still largely conjectural theory of motives. This idea allows one to get around the lack of knowledge of the Hodge conjecture, for some applications. The theory of mixed Hodge structures, a powerful tool in algebraic geometry that generalizes classical Hodge theory, was created by applying weight filtration, Hironaka's resolution of singularities and other methods, which he then used it to prove the Weil conjectures. He reworked the Tannakian category theory in his 1990 paper for the "Grothendieck Festschrift", employing Beck's theorem – the Tannakian category concept being the categorical expression of the linearity of the theory of motives as the ultimate Weil cohomology.
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In 1974 at the IHÉS, Deligne's joint paper with Phillip Griffiths, John Morgan and Dennis Sullivan on the real homotopy theory of compact Kähler manifolds was a major piece of work in complex differential geometry which settled several important questions of both classical and modern significance. The input from Weil conjectures, Hodge theory, variations of Hodge structures, and many geometric and topological tools were critical to its investigations. His work in complex singularity theory generalized Milnor maps into an algebraic setting and extended the Picard-Lefschetz formula beyond their general format, generating a new method of research in this subject. His paper with Ken Ribet on abelian L-functions and their extensions to Hilbert modular surfaces and p-adic L-functions form an important part of his work in arithmetic geometry.
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Plan of Vauxhall Gardens, 1826 The Gardens are believed to have opened just before the Restoration of 1660, on property formerly owned by Jane Fauxe, or Vaux, widow, in 1615. Whereas John Nichols in his History of Lambeth Parish conjectures that she was the widow of Guy Fawkes, executed in 1606, John Timbs in his 1867 Curiosities of London states for a fact that there was no such connection, and that the Vaux name derives from one Falkes de Breauté, a mercenary working for King John who acquired the land by marriage. Jane is stated to be the widow of John, a vintner. Curiosities of London John Timbs, 1867, page 745 Perhaps the earliest record is Samuel Pepys' description of a visit he made to the New Spring Gardens on 29 May 1662.
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In mathematics, the Almgren–Pitts min-max theory (named after Frederick J. Almgren, Jr. and his student Jon T. Pitts) is an analogue of Morse theory for hypersurfaces. The theory started with the efforts for generalizing George David Birkhoff's method for the construction of simple closed geodesics on the sphere, to allow the construction of embedded minimal surfaces in arbitrary 3-manifolds.Tobias Colding and Camillo De Lellis: "The min-max construction of minimal surfaces", Surveys in Differential Geometry It has played roles in the solutions to a number of conjectures in geometry and topology found by Almgren and Pitts themselves and also by other mathematicians, such as Mikhail Gromov, Richard Schoen, Shing-Tung Yau, Fernando Codá Marques, André Neves, Ian Agol, among others.Helge Holden, Ragni Piene – The Abel Prize 2008-2012, p. 203.
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They occur, for example, in the machine learning programs of AI. For the vast bulk of human science both past and present, rules of inductive inference do not exist. For such science, Popper's model of conjectures which are freely invented and then tested out seems to me more accurate than any model based on inductive inferences. Admittedly, there is talk nowadays in the context of science carried out by humans of 'inference to the best explanation' or 'abductive inference', but such so-called inferences are not at all inferences based on precisely formulated rules like the deductive rules of inference. Those who talk of 'inference to the best explanation' or 'abductive inference', for example, never formulate any precise rules according to which these so-called inferences take place.
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Duels had been tacitly assumed illegal since a 1614 edict by James I, but often a blind eye was turned. However, prosecution for duelling was a possibility, especially if no seconds or witnesses were present to assure fair play. Adam Nicolson in his book Gentry: Six Hundred Years of a Peculiarly English Class conjectures that despite this, the reason Hobart and Le Neve refused seconds was conversely to avoid any witness for possible prosecution. Some sources suggest that a young servant girl witnessed the duel from nearby bushes;Briggs, Stacia; Connor, Siofra; "Weird Norfolk: The Cawston duel stone and a ghost of Blickling Hall", Eastern Daily Press, 20 October 2017. Retrieved 31 March 2018 reliable sources either don't mention this, or if they do, treat it as folklore.
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Before Hugh Capet, two members of the Robertian family were kings of the Franks, their reigns interspersed between those of the Carolingians: Odo I and Robert I. These first two kings are the sons of Robert the Strong. The origin of the family of the ancestors of Hugh Capet has long been misunderstood and various conjectures have been formulated. In the twentieth century, the work of several historiansKarl Glöckner, Lorsch und Lothringen, Robertiner und Capetinger, Zeitschrift für die Geschichte des Oberrheins, Carlrhue, 1936, t.50, p. 301-354.Karl Ferdinand Werner, Les premiers Robertiens et les premiers Anjou (IXe siècle – Xe siècle), in : Mémoires de la Société des Antiquaires de l’Ouest, 1997 have identified a number of assumptions and near certainty on the history and genealogy of the Robertians.
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Weil suggested that the conjectures would follow from the existence of a suitable "Weil cohomology theory" for varieties over finite fields, similar to the usual cohomology with rational coefficients for complex varieties. His idea was that if is the Frobenius automorphism over the finite field, then the number of points of the variety over the field of order is the number of fixed points of (acting on all points of the variety defined over the algebraic closure). In algebraic topology the number of fixed points of an automorphism can be worked out using the Lefschetz fixed point theorem, given as an alternating sum of traces on the cohomology groups. So if there were similar cohomology groups for varieties over finite fields, then the zeta function could be expressed in terms of them.
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Indologist B.N.K Sharma contends that Vyasatirtha would have been 16 years of age at this time. After the death of Bramhanya Tirtha during the famine of 1475–1476, Vyasatirtha succeeded him as the pontiff of the matha at Abbur and proceeded to Kanchi, which was the centre for Sastric learning in South India at the time, to educate himself on the six orthodox schools of thought, which are: Vedanta, Samkhya, Nyaya, Mimamsa, Vaisheshika and Yoga. Sharma conjectures that the education Vyasatirtha received in Kanchi helped him become erudite in the intricacies and subtleties of Advaita, Visistadvaita, Navya Nyaya and other schools of thought. After completing his education at Kanchi, Vyasatirtha headed to Mulbagal to study the philosophy of Dvaita under Sripadaraja, whom he would consider his guru, for a period of five to six years.
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Based on the geographical locations described in Heungbu-jeon, some scholars have made conjectures about the region in which Heungbu and Nolbu had lived. The research concluded that Heungbu’s hometown is Seongsan-ri, Dong-myeon, in the city of Namwon and that Heungbu became rich while residing near Seong-ri, Ayeong-myeon, in the same city. As Heungbu-jeon originated from a folktale, the claims made by this research are not very realistic. However, the city of Namwon has named the relevant region as Heungbu maeul, or Heungbu Village, and has been making efforts to turn it into a tourist attraction by discovering the hill on which Heungbu had fainted out of hunger and the grave of a person named Bak Chun-bo, whom Heungbu is presumed to have been modeled after.
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Another friend, Gian-Carlo Rota, asserted in a 1987 article that the attack changed Ulam's personality: afterwards, he turned from rigorous pure mathematics to more speculative conjectures concerning the application of mathematics to physics and biology; Rota also cites Ulam's former collaborator Paul Stein as noting that Ulam was sloppier in his clothing afterwards, and John Oxtoby as noting that Ulam before the encephalitis could work for hours on end doing calculations, while when Rota worked with him, was reluctant to solve even a quadratic equation. This assertion was not accepted by Françoise Aron Ulam. By late April 1946, Ulam had recovered enough to attend a secret conference at Los Alamos to discuss thermonuclear weapons. Those in attendance included Ulam, von Neumann, Metropolis, Teller, Stan Frankel, and others.
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Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics. The opinions of mathematicians on this matter are varied. Many mathematiciansSee, for example Bertrand Russell's statement "Mathematics, rightly viewed, possesses not only truth, but supreme beauty ..." in his History of Western Philosophy feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics.
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His reputation does not rest on his numerous editions, often hasty or even made to booksellers' orders, but in his remarks, especially his conjectures. He himself designates the Animadversiones in scriptores Graecos as flos ingenii sui, and in truth these thin booklets outweigh his big editions. Closely following the author's thought he removes obstacles whenever he meets them, but he is so steeped in the language and thinks so truly like a Greek that the difficulties he feels often seem to us to lie in mere points of style. His criticism is empirical and unmethodical, based on immense and careful reading, and applied only when he feels a difficulty; and he is most successful when he has a large mass of tolerably homogeneous literature to lean on, whilst on isolated points he is often at a loss.
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In 2014, Christopher Skinner and Eric Urban proved several cases of the main conjectures for a large class of modular forms. As a consequence, for a modular elliptic curve over the rational numbers, they prove that the vanishing of the Hasse–Weil L-function L(E, s) of E at s = 1 implies that the p-adic Selmer group of E is infinite. Combined with theorems of Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if and only if L(E, 1) = 0, a (weak) form of the Birch–Swinnerton-Dyer conjecture. These results were used (in joint work with Manjul Bhargava and Wei Zhang) to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture.
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Bedaux argues, "if the symbols are disguised to such an extent that they do not clash with reality as conceived at the time ... there will be no means of proving that the painter actually intended such symbolism."Bedaux 1986, 5 He also conjectures that if these disguised symbols were normal parts of the marriage ritual, then one could not say for sure whether the items were part of a "disguised symbolism" or just social reality. Craig Harbison takes the middle ground between Panofsky and Bedaux in their debate about "disguised symbolism" and realism. Harbison argues that "Jan van Eyck is there as storyteller ... [who] must have been able to understand that, within the context of people's lives, objects could have multiple associations", and that there are many possible purposes for the portrait and ways it can be interpreted.
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In theoretical computer science, the Aanderaa–Karp–Rosenberg conjecture (also known as the Aanderaa–Rosenberg conjecture or the evasiveness conjecture) is a group of related conjectures about the number of questions of the form "Is there an edge between vertex u and vertex v?" that have to be answered to determine whether or not an undirected graph has a particular property such as planarity or bipartiteness. They are named after Stål Aanderaa, Richard M. Karp, and Arnold L. Rosenberg. According to the conjecture, for a wide class of properties, no algorithm can guarantee that it will be able to skip any questions: any algorithm for determining whether the graph has the property, no matter how clever, might need to examine every pair of vertices before it can give its answer. A property satisfying this conjecture is called evasive.
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Some nouns have identical singular and plural (zero inflection). Many of these are the names of animals: :bison :buffalo :carp :cod :deer :fish :kakapo (and other Māori- derived words) :moose :neat :pike :salmon :sheep :shrimp :squid :trout As a general rule, game or other animals are often referred to in the singular for the plural in a sporting context: "He shot six brace of pheasant", "Carruthers bagged a dozen tiger last year", whereas in another context such as zoology or tourism the regular plural would be used. Eric Partridge refers to these sporting terms as "snob plurals" and conjectures that they may have developed by analogy with the common English irregular plural animal words "deer", "sheep" and "trout".Partridge, Eric, Usage and Abusage: A Guide to Good English, revised by Janet Whitcut (New York and London: W. W. Norton, 1997), pp. 238–39.
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The Stark conjectures, in the most general form, predict that the leading coefficient of an Artin L-function is the product of a type of regulator, the Stark regulator, with an algebraic number. When the extension is abelian and the order of vanishing of an L-function at s = 0 is one, Stark's refined conjecture predicts the existence of the Stark units, whose roots generate Kummer extensions of K that are abelian over the base field k (and not just abelian over K, as Kummer theory implies). As such, this refinement of his conjecture has theoretical implications for solving Hilbert's twelfth problem. Also, it is possible to compute Stark units in specific examples, allowing verification of the veracity of his refined conjecture as well as providing an important computational tool for generating abelian extensions of number fields.
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Both aspects of Weil's work have steadily developed into substantial theories. Among his major accomplishments were the 1940s proof of the Riemann hypothesis for zeta- functions of curves over finite fields, Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). The so-called Weil conjectures were hugely influential from around 1950; these statements were later proved by Bernard Dwork, Alexander Grothendieck, Michael Artin, and finally by Pierre Deligne, who completed the most difficult step in 1973. Weil introduced the adele ringA. Weil, Adeles and algebraic groups, Birkhauser, Boston, 1982 in the late 1930s, following Claude Chevalley's lead with the ideles, and gave a proof of the Riemann–Roch theorem with them (a version appeared in his Basic Number Theory in 1967).
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Mirror neurons were first reported in a paper published in 1992 by a team of researchers led by Giacomo Rizzolatti at the University of Parma. According to Rizzolati, "Mirror neurons are a specific type of visuomotor neuron that discharge both when a monkey executes a motor act and when it observes a similar motor act performed by another individual." In 2000, Ramachandran made what he called some "purely speculative conjectures" that "mirror neurons [in humans] will do for psychology what DNA did for biology: they will provide a unifying framework and help explain a host of mental abilities that have hitherto remained mysterious and inaccessible to experiments." Ramachandran has suggested that research into the role of mirror neurons could help explain a variety of human mental capacities such as empathy, imitation learning, and the evolution of language.
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In 2005, nearing the end of his investigation, Seracini gave another interview, this time to Guardian reporter John Hooper. Seracini finally published his results in 2006: M. Seracini, "Diagnostic Investigations on the Adoration of the Magi by Leonardo da Vinci" in The Mind of Leonardo – The Universal Genius at Work, exhibit catalogue edited by P. Gauluzzi, Giunti Florence, 2006, pp. 94–101. In the Smithsonian Channel TV program, Da Vinci Detective, Seracini conjectures that, upon seeing the preliminary drawings for the altarpiece they had commissioned, they rejected it due to the sensational scenario presented to them. Fully expecting a traditional interpretation including the three wise men, they were instead confronted with a maelstrom of unrelated, half- emaciated figures surrounding the Christ-Child, as well as a full-blown battle scene in the rear of the picture.
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Comte in the 1830s expounded positivism—the first modern philosophy of science and simultaneously a political philosophyBourdeau, "Auguste Comte", §§ "Abstract" & "Introduction", in Zalta, ed, SEP, 2013.—rejecting conjectures about unobservables, thus rejecting search for causes.Comte, A General View of Positivism (Trübner, 1865), pp 49–50, including the following passage: "As long as men persist in attempting to answer the insoluble questions which occupied the attention of the childhood of our race, by far the more rational plan is to do as was done then, that is, simply to give free play to the imagination. These spontaneous beliefs have gradually fallen into disuse, not because they have been disproved, but because humankind has become more enlightened as to its wants and the scope of its powers, and has gradually given an entirely new direction to its speculative efforts".
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Popper disparages the pseudoscientific, which occurs when an unscientific theory is proclaimed true and coupled with seemingly scientific method by "testing" the unfalsifiable theory—whose predictions are confirmed by necessity—or when a scientific theory's falsifiable predictions are strongly falsified but the theory is persistently protected by "immunizing stratagems", such as the appendage of ad hoc clauses saving the theory or the recourse to increasingly speculative hypotheses shielding the theory. Popper's scientific epistemology is falsificationism, which finds that no number, degree, and variety of empirical successes can either verify or confirm scientific theory. Falsificationism finds science's aim as corroboration of scientific theory, which strives for scientific realism but accepts the maximal status of strongly corroborated verisimilitude ("truthlikeness"). Explicitly denying the positivist view that all knowledge is scientific, Popper developed the general epistemology critical rationalism, which finds human knowledge to evolve by conjectures and refutations.
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Early in 1619, Father Grassi had anonymously published a pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618, which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth, and since it moved in the sky more slowly than the Moon, it must be farther away than the Moon. Grassi's arguments and conclusions were criticised in a subsequent article, Discourse on Comets, published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci, although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures that are now known to be mistaken.
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The son of a Protestant minister who had converted to Catholicism (although the House of Astruc was of medieval Jewish origin), Astruc was educated at Montpellier, one of the great schools of medicine in early modern Europe. His dissertation and first publication, submitted when he was only 19, is on decomposition, and contains many references to recent research on the lungs by Thomas Willis and Robert Boyle. After teaching medicine at Montpellier he became a member of the medical faculty at the University of Paris. His numerous medical writings, or materials for the history of medical education at Montpellier, are now forgotten, but the work published by him anonymously in 1753 has secured for him a permanent reputation. This book, brought out anonymously in 1753, was entitled Conjectures sur les memoires originaux dont il paroit que Moyse s'est servi pour composer le livre de la Genese.
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The identity of Userkaf's parents is uncertain, but he undoubtedly had family connections with the rulers of the preceding Fourth Dynasty. Egyptologist Miroslav Verner proposes that he was a son of Menkaure by one of his secondary queens and possibly a full brother to his predecessor and the last king of the Fourth Dynasty, Shepseskaf. Alternatively, Nicolas Grimal, Peter Clayton and Michael Rice propose that Userkaf was the son of a Neferhetepes, whom Grimal, Giovanna Magi and Rice see as a daughter of Djedefre and Hetepheres II. The identity of Neferhetepes's husband in this hypothesis is unknown, but Grimal conjectures that he may have been the "priest of Ra, lord of Sakhebu", mentioned in Westcar papyrus. Aidan Dodson and Dyan Hilton propose that Neferhetepes was buried in the pyramid next to that of Userkaf, which is believed to have belonged to a woman of the same name.
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A Bao A Qu is a legendary Mewar creature described in Jorge Luis Borges's 1967 Book of Imaginary Beings. Borges claimed to have found it either in an introduction to the Arabian Nights by Richard Francis Burton, or in the book On Malay Witchcraft (1937) by C.C. Iturvuru.The Book of Imaginary Beings, by J.L. Borges, Translated by Andrew Hurley, © 2005 Viking Penguin (original Spanish © 1967 by Editorial Kier, S.A., Buenos Aires under title "El libro de los seres imaginarios") The Burton reference was given in the original Spanish, but it was changed to the Iturvuru reference in the English text, possibly to make it sound more exotic, or as a reference to Borges' friend C. C. Iturburu. The writer Antares conjectures that Borges's tale might be inspired by Orang Asli myth, and that "A Bao A Qu" is a slurring of abang aku meaning "my elder brother".
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Mesgegra's brain-ball has been likened to the táthlum or táthluib "sling- stone", such as the Lugh's sling-stone which was a hardened ball of blood and sand. The one-handed () Mesgegra fighting Connal with a hand tied has been paralleled with Nuada of the Silver Arm and his arm-cutting foe Sreng whose name can mean "cord" or "tug away", as well as with the Norse god Týr who lost one hand in order to bind Fenris wolf. The one-handed figure appears alongside a one-eyed () Eochaid mac Luchta, the king of South Connacht, whose Norse counterpart is Óðinn. Scowcroft conjectures there was some wisdom-gaining underlying theme, similar to Óðinn losing an eye in Mimir's Well, as the strange nut that Mesgegra ate is reminiscent of the hazelnut of water-pool of Segais which imparted wisdom to the Salmon of Knowledge.
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In an Experimentum crucis or "critical experiment" (Book I, Part II, Theorem ii), Newton showed that the color of light corresponded to its "degree of refrangibility" (angle of refraction), and that this angle cannot be changed by additional reflection or refraction or by passing the light through a coloured filter. The work is a vade mecum of the experimenter's art, displaying in many examples how to use observation to propose factual generalisations about the physical world and then exclude competing explanations by specific experimental tests. However, unlike the Principia, which vowed Non fingo hypotheses or "I make no hypotheses" outside the deductive method, the Opticks develops conjectures about light that go beyond the experimental evidence: for example, that the physical behaviour of light was due its "corpuscular" nature as small particles, or that perceived colours were harmonically proportioned like the tones of a diatonic musical scale.
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J. M. Steele, University of Toronto, (review online from Canadian Association of Physicists) of N. Guicciardini's "Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736" (Cambridge UP, 1999), a book which also states (summary before title page) that the "Principia" "is considered one of the masterpieces in the history of science". The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of Mathematical Principles of Natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses."(in French) Alexis Clairaut, "Du systeme du monde, dans les principes de la gravitation universelle", in "Histoires (& Memoires) de l'Academie Royale des Sciences" for 1745 (published 1749), at p.
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He proved theorems on the topology of hyperplane sections of algebraic varieties, which provide a basic inductive tool (these are now seen as allied to Morse theory, though a Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The Picard–Lefschetz formula in the theory of vanishing cycles is a basic tool relating the degeneration of families of varieties with 'loss' of topology, to monodromy. He was an Invited Speaker of the ICM in 1920 in Strasbourg. His book L'analysis situs et la géométrie algébrique from 1924, though opaque foundationally given the current technical state of homology theory, was in the long term very influential (one could say that it was one of the sources for the eventual proof of the Weil conjectures, through SGA 7 also for the study of Picard groups of Zariski surface).
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Walafridus Strabo, who died Abbot of Reichenau in 849, and must therefore have been nearly, if not quite, contemporary with this incident, says nothing about it, but (De Rebus Ecclesiasticis, xxii), speaking of various forms of the Mass, says: "Ambrose, Bishop of Milan, also arranged a ceremonial for the Mass and other offices for his own church and for other parts of Liguria, which is still observed in the Milanese Church". In the eleventh century Pope Nicholas II, who in 1060 had tried to abolish the Mozarabic Rite, wished also to attack the Ambrosian and was aided by St. Peter Damian but he was unsuccessful, and Pope Alexander II his successor, himself a Milanese, reversed his policy in this respect. St. Gregory VII made another attempt, and Le Brun (Explication de la Messe, III, art. I, § 8) conjectures that Landulf's miraculous narrative was written with a purpose about that time.
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Insofar as language helps create the illusion that we know everything there is and that we know how to call it and how to manipulate it, language is a weapon directed against the people. On the other hand we continuously see conjectures or glimpses arise in the common use of language that point to the opposite conclusion (that we do not know what there is and that Reality does not reach so far as to include everything that occurs), and in this sense language, something that anyone can use although no-one can possess it,"(...) el solo inteligente es el lenguaje, que es todos y no es nadie (...)" (A. García Calvo, Análisis de la Sociedad del Bienestar, 2nd ed. Zamora 1995, p. 98). - "(...) el lenguaje popular (...) es la casa de todos, porque no es de nadie y es para cualquiera (...)" (Análisis de la Sociedad del Bienestar, p. 147).
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At about the same time, Vladimir Voevodsky was independently investigating type theory in the context of the search of a language for practical formalization of mathematics. In September 2006 he posted to the Types mailing list "A very short note on homotopy lambda calculus",A very short note on homotopy λ-calculus, by Vladimir Voevodsky, September 27, 2006 PDF which sketched the outlines of a type theory with dependent products, sums and universes and of a model of this type theory in Kan simplicial sets. It began by saying "The homotopy λ-calculus is a hypothetical (at the moment) type system" and ended with "At the moment much of what I said above is at the level of conjectures. Even the definition of the model of TS in the homotopy category is non-trivial" referring to the complex coherence issues that were not resolved until 2009.
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Hobbes first used the mechanics of motion to define principles of human perception, behaviour and reasoning, which were then used to draw the conclusions of his political philosophy (sovereignty, state of nature). In rejecting what he believed were ‘conjectures’ relating to intangible or supernatural objects or realities, Hobbes’s philosophy is drawn from material and physical reality and experience. Höffe explains how Hobbes applied this method to construct his political theory of sovereignty: “…the combination of mathematics and mechanics, is not sufficient on its own… the combination of mathematics and mechanics leads to the metaphor of the state as an “artificial” human being, which is comparable to a machine constructed out of natural human beings; (3) the resoluto-compositive [the recourse to absolutely first principles or elements] method defines and clarifies the nature of this construction: the artificial human being is decomposed into its smallest constituent parts and then recomposed, i.e.
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Alexander Grothendieck's work during the "Golden Age" period at the IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis. His first (pre-IHÉS) discovery in algebraic geometry was the Grothendieck–Hirzebruch–Riemann–Roch theorem, a generalisation of the Hirzebruch–Riemann–Roch theorem proved algebraically; in this context he also introduced K-theory. Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique (EGA) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the étale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it.
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This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality. Diophantine geometry in general is the study of algebraic varieties V over fields K that are finitely generated over their prime fields—including as of special interest number fields and finite fields—and over local fields. Of those, only the complex numbers are algebraically closed; over any other K the existence of points of V with coordinates in K is something to be proved and studied as an extra topic, even knowing the geometry of V. Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers.
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The critic René Girard wrote in Violence and the Sacred (1972) that, despite the rejection of Totem and Taboo by "contemporary criticism", its concept of collective murder is close to the themes of his own work. The historian Peter Gay suggested in Freud: A Life for Our Time (1988) that in Totem and Taboo Freud made conjectures more ingenious than those of the philosopher Jean-Jacques Rousseau. Gay observed that Totem and Taboo was in part an attempt by Freud to outdo his rival Jung, and that the work is full of evidence that "Freud's current combats reverberated with his past history, conscious and unconscious". The critic Harold Bloom asserted in The American Religion (1992) that Totem and Taboo has no greater acceptance among anthropologists than does the Book of Mormon, and that there are parallels between the two works, such as a concern with polygamy.
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A review of the book in the film and popular culture journal Images judges that Hollywood Hex is most successful in the sections covering The Exorcist and Macbeth because of not, "exploiting the subject material but in maintaining distance." Brottman's objective approach to the material gives it an academic and neutral point of view which, in a subject which could easily be sensationalized, is remarked on approvingly in the review. The reviewer, David Ng, comments, "How easy it would have been to sensationalize this material, to cheapen it with tabloidish conjectures, to dilute it with pop psychology, or to kill it with over- analysis... It is a mature book that trusts its readers to extrapolate... freely." Images points out that other films covered by the book are not done in as complete a manner as are Macbeth and The Exorcist, giving the book a somewhat disjointed quality.
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In the story, two scientists and a navy ship investigate two massive pillars of water in the Pacific to discover if they are a natural phenomenon or, as one of the scientists conjectures, created by intelligent beings. His belief is based on another strange recent occurrence in the Pacific: "Lagrange fireballs", spheres of energy which move in a seemingly intelligent manner and appear to be responsible for the disappearance of people in Hawaii. While on the naval ship, more is learned about the pillars: one shoots water far up into the sky, where it enters a cloud-like formation which cannot be successfully entered and studied by aircraft or rockets, because their engines shut off when they try to enter the cloud. After an experiment, they confirm the other water pillar is linked to the first and returns the water back to the ocean.
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Off-beat conjectures at Driekops Eiland Within the archaeological fraternity the site has become important in collegial debates on authorship of rock art in Southern Africa. Amongst rock art specialists there are two principal ideas concerning Driekops Eiland. One of them suggests that whereas sites such as the nearby Wildebeest Kuil, with its profusion of engravings of animals and some human figures, is quintessentially San/hunter-gatherer in character, the site of Driekops Eiland, with its massive preponderance of geometric engravings and very few animals and hardly any human figures, most likely belongs to a different tradition of rock art, now believed to be a separate Khoekhoe herder rock art tradition. This has been a persuasive argument, and the distribution of sites with geometric rock art appears to match the hypothesised migration routes by which herders are thought to have spread through South Africa about 2000 years ago.
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Kirkus Reviews said Stewart "succeed[ed] in illuminating many but not all of some very difficult ideas", and that the book "will enchant math enthusiasts as well as general readers who pay close attention". Robert Schaefer from the New York Journal of Books described "The Great Mathematical Problems" as "both entertaining and accessible", although later noted that "in the end chapters ... explanations of the conjectures get more complicated". Fred Bortz gave the book a positive review in The Dallas Morning News, commenting "few authors are better at understanding their readers than the prolific mathematics writer Ian Stewart" and saying that "anyone who has always loved math for its own sake or for the way it provides new perspectives on important real-world phenomena will find hours of brain-teasing and mind-challenging delight in the British professor’s survey of recently answered or still open mathematical questions".
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Vine of Sodom is the translation of found in the King James and some other translations of the Bible into English, most notably in the Tyndale Bible, which renders it: "Their vines are the vines of Sodom." The Douay-Rheims renders the phrase as, "Their vines are of the vineyard of Sodom," the JPS Tanakh: "The vine for them is from Sodom," and the Revised Standard Version, "For their vine comes from the vine of Sodom." The full verse in the King James Version reads: "For their vine is of the vine of Sodom, and of the fields of Gomorrah: their grapes are grapes of gall, their clusters are bitter." (Hebrew: Kî miggep̄en Səḏōm gap̄nām, ū-miššaḏmōṯ ‘Ǎmōrāh; ‘ănāḇêmōw ‘innəḇê rōwōš, ’aškəlōṯ mərōrōṯ lāmōw.) Among the many conjectures as to this tree, the most probable is that it is the osher (Calotropis procera) of the Arabs, which grows from Jordan to southern Egypt.
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The series explores various Oak Island theories and conjectures through conversations with independent researchers. Persons featured have included Zena Halpern discussing her theory about North African gold and sharing copies of a French map of the island which she claims is dated 1347; J. Hutton Pulitzer discussing his theory of ancient mariner visitations; Petter Amundsen discussing his theory about codes hidden in Shakespearean literature and a secret project involving Sir Francis Bacon and the Rosicrucians; Daniel Ronnstam discussing his theory about the 90 foot stone being a dual cypher containing instructions as how to defeat the money pit flood tunnels with corn; authors Kathleen McGowen and Alen Butler discussing their theory involving the fabled Knights Templar treasure and an alleged relocation of historical religious artifacts to the island; and John O'Brien discussing his theory that the island contains treasures of the Aztec Empire. It has also been suggested by Zena Halpern, without evidence, that the Templars worshipped the Phoenician goddess Tanit.
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The colonial period scholarship's conjectures have been taken as fact, and no one has reviewed the assessments when additional evidence since points to the Burmese script being the parent of Burma Mon. However, no archaeological evidence or any other kind of proof that the Dvaravati and Burma Mon scripts are related exists. The extant evidence shows only that Burma Mon was derived from the Old Burmese script, not Dvaravati.Aung-Thwin 2005: 177–178 (The earliest evidence of the Old Burmese script is securely dated to 1035, while an 18th-century casting of an old Pagan era stone inscription points to 984. The earliest securely dated Burma Mon script is 1093 at Prome while two other "assigned" dates of Old Burma Mon are 1049 and 1086.)Aung-Thwin 2005: 198 However, Aung-Thwin's argument that the Burmese script provided the basis for the Mon script of Burma relies on the general thesis that Mon influence on Burmese culture is overstated.
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A mainstream historian of authorship doubt, Frank Wadsworth, asserted that the "essential pattern of the Baconian argument" consisted of "expressed dissatisfaction with the number of historical records of Shakespeare's career, followed by the substitution of a wealth of imaginative conjectures in their place." In his 1971 essay "Bill and I," author and scientific historian Isaac Asimov made the case that Bacon did not write Shakespeare's plays because certain portions of the Shakespeare canon show a misunderstanding of the prevailing scientific beliefs of the time that Bacon, one of the most intensely educated people of his time, would not have possessed. Asimov cites an excerpt from the last act of The Merchant of Venice, as well as the following excerpt from A Midsummer Night's Dream: ::::...The rude sea grew civil at her song, ::::And certain stars shot madly from their spheres, ::::to hear the sea maid's music. (Act 2, Scene 1, 152–154).
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