The extent to which different denominators capture overlapping sets of irrational numbers is reflected in the number of prime factors the denominators have in common.
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Poor, disadvantaged, not well educated, are denominators common to most.
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This piece is about trying to get to common denominators.
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The new research identifies five common denominators among such organizations.
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For decades, our standard explanation for those who make up our "denominators"—i.e.
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And imagine that your available denominators are the counting numbers 203 to 10.
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The Duffin-Schaeffer conjecture lets you choose an error for each of your denominators.
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Former Republican presidential candidate Chris Christie is pretty good at globbing on to lowest common denominators.
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Meant to be shareable and easily digestible, memes distill things down to their lowest common denominators.
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In terms of common denominators, both cases involved individuals living in Hong Kong's Wong Tai Sin district.
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But there are common denominators, and one encountered ever more frequently is hatred spread over social media.
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On hacking hubs like GBA Temp, fans are rallying to identify common denominators between different banned Switch users.
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So far, messages for and about Latinos are being reduced to common denominators, such as immigration and speaking Spanish.
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Transcendence finds its roots in the African-American experience, but demonstrates the common denominators that are found in every culture.
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In his notes on the project, Young explained his mission in mathematical terms, speaking of primes and denominators and intervals.
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Genetic sequencing is particularly good at this, since it can find common DNA denominators among people of different racial and ethnic origins.
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But unlike many tragedies involving indigenous Canadians, these victims were linked by important common denominators: All were young people from remote towns.
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Proving the Duffin-Schaeffer conjecture is really about understanding exactly how much mileage you're getting out of each of your available denominators.
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Banging from one guardrail to the next, Trump's foreign policy pronouncements seem, like his Twitter feed, entirely unhinged from any common denominators.
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Ars Technica delves further into the math and problems calculating the crash rate if you want to understand the denominators and mileage calculations.
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If you think about the denominators, the differences are relatively small, but they are consequential and important in that these are critical spots.
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No one keeps track of how many people meet these conditions, so two imperfect proxies are normally used as denominators when calculating turnout.
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Is engagement, above all, driving us to lowest common denominators to just have more clicks, and more time, and all of that stuff.
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Or why his first-generation ABC ("American-born Chinese") children were more interested in sports or the humanities than studying fractions and common denominators.
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With every rifle crack, my world flashed in a monochrome of stark, tactical decisions, like life and death reduced to their lowest common denominators.
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European leaders — and Obama Administration envoys — were reduced to highlighting the lowest common denominators of shared history and ideals in giving assurances of continued cooperation.
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This history, along with the common denominators going into the Brexit and Trump victories, likely had a significant impact on one of its northern neighbors.
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"We pay more attention to numerators, such as '16 adverse events,' than we do to denominators, such as 'per million vaccine doses,' " Dr. Buttenheim said.
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Common denominators in the singer's Grammys looks were her high ponytail hairstyle and the various gloves that she paired with each of her dresses or outfits.
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It also isn't really fair to compare Nunavut (population 37,000) to Ontario (13.9 million), for example, where the number of searches will make for vastly different denominators.
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But what if you want your denominators to be drawn from some (still infinite) subset of the whole numbers, like all prime numbers, or all perfect squares?
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The only common denominators found among the victims are that the deaths occurred outdoors, in the early hours and in isolated places like trails and unoccupied streets.
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It would lop $17 billion or so off Citi's common and tangible common equity – the denominators in the all-important return on equity numbers it reports to investors.
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It would lop $17 billion or so off Citigroup's common and tangible common equity — the denominators in the all-important return on equity numbers it reports to investors.
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In places where money comes out of the ground, luck and a willingness to take risks are the main denominators that determine one's future, not talent or education or hard work.
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In their new proof, they create a graph out of their denominators — plotting them as points and connecting the points with a line if they share a lot of prime factors.
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We'll therefore stick to the data we have both good numerators and denominators for to answer an important question: What are your risks if you do get infected with the coronavirus?
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One of the common denominators amongst a lot of these groups is that these people are refugees because of climate-induced disasters, droughts, and famines cause tensions in every part of the world.
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The key to solving the conjecture has been to find a way to precisely quantify the overlap in the sets of irrational numbers approximated by denominators with many small prime factors in common.
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"When a lot of the denominators you have to choose from have a lot of small prime factors then they start to get in the way of each other," said Sam Chow of Oxford.
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Picture it: As the protagonists battle against the evil and oppressive government, the rest of the populace has the wool drawn over their eyes by terrible programs aimed at the lowest of lowest common denominators.
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ROBBINS: THEY STILL HAVE THEIR PRIVATE DATA CENTERS AND NOW THE EXPLOSION AT THE EDGE WITH IOT AND ALL THE DATA BEING CREATED, THE SINGLE PERVASIVE COMMON DENOMINATORS ACROSS ALL OF THAT IS THE NETWORK.
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They highlight the importance of public parks in their role as universal common denominators that serve every person who comes visiting — with a fishing rod, with a ball, a broken picnic table, or nothing at all.
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It said that you can find infinitely many approximating fractions for each irrational number if your denominators can be any whole number, and if you're willing to accept an error that's 1 over the denominator squared.
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The difference is that whereas the VS women always seemed to serve that gaze at its most banal common denominators (sometimes literally, in naughty maid costumes), Rihanna's women own it, manipulate it and crush it between their thighs.
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You can pick different numerators and denominators to get at the same concept — using just wages and salaries instead of total compensation, for example, or dividing by gross domestic product instead of the related concept of national income — but the same basic pattern reveals itself.
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Therefore, the common denominators of suicides and opioid-related overdose deaths are "eroding economic opportunity, evolving approaches to pain treatment, and limited drug treatment," according to Nabarun Dasgupta, PhD, MPH, lead author of Opioid Crisis: No Easy Fix to Its Social and Economic Determinants.
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From makeup and mattresses to wine, cookware, dentistry, and even hospital scrubs, the common denominators for these new brands include adopting a millennial-friendly pastel-tinged, minimalism-adjacent design aesthetic, an abundance of Instagram ads, and a promotion of a workplace culture that prioritizes employee-perks like free snacks and flexible hours.
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The Duffin-Schaeffer conjecture's main claim is that if you want to figure out whether you can approximate nearly all irrational numbers given a set of denominators and allowable error terms, this is the only feature you need to know: whether that infinite sum of measures diverges to infinity or converges to a finite value.
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We know that the video game industry is bigger than the movie industry and the music industry combined, and there have been studies that say it impacts people and studies that says it does not, but I look at the common denominators, as a 60-some-year-old father and grandfather myself, what's changed in this country?
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Koukoulopoulos and Maynard proved that the Duffin-Schaeffer conjecture is indeed true: If you're handed a list of denominators with allowable error terms, you can determine whether you can approximate virtually all irrational numbers or virtually none just by checking whether the corresponding sum of the measures around each fraction diverges to infinity or converges to a finite value.
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With both Balenciaga, where Mr. Gvasalia has been creative director since October 2015, and his own brand, Vetements, the designer has made something of an art form out of appropriating the basic clothing (or high fashion) common denominators that we have long taken for granted and twisting and torquing them into new forms that demand a rethink.
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ISIS and Al Qaeda have long been telling their sympathizers to use a combination of cars and knives, and those appear to be the common denominators in most of these types of attack like back in August in Barcelona when a 22-year-old Spanish citizen drove a van into a crowd of the famed La Rambla shopping district, killing 13, injuring more than 20103.
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This sequence of denominators is a particular Lucas sequence known as the Pell numbers.
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Red auxiliary numbers selected divisors of denominators mp that best summed to numerator mn.
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The decision forbids using factors or denominators in conjunction with p.d.u. (such as "p.d.u./L").
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The Schwinger representation is both useful for making manifest the particle aspect of the propagator, and for symmetrizing denominators of loop diagrams.
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The first building in the village was a hospice house. It was built in 1930, Mátra Association. They were the denominators of the village.
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Gudykunst uses 47 axioms as building blocks for the theorems of AUM. Axioms can be thought of as the lowest common denominators from which all causal theorems are derived.
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Rate equations of this type explicitly account for the interaction of chemical species with catalyst and contain denominators in which terms characteristic of the adsorption of reacting species are presented.
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Similarly, investigators sometimes report the false positive rate (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The total operating characteristic (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used receiver operating characteristic (ROC) and ROC's associated area under the curve (AUC).
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Since there are only finitely many of these equations (the coefficients are bounded), the complete quotients (and also the partial denominators) in the regular continued fraction that represents x must eventually repeat.
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In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
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In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
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One may thus equate numerators with numerators and denominators with denominators, giving Euclid's formula : a = m^2 - n^2 ,\ \, b = 2mn ,\ \, c = m^2 + n^2 with m and n coprime and of opposite parities. A longer but more commonplace proof is given in Maor (2007)Maor, Eli, The Pythagorean Theorem, Princeton University Press, 2007: Appendix B. and Sierpiński (2003). Another proof is given in , as an instance of a general method that applies to every homogeneous Diophantine equation of degree two.
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Farey diagram to F9 represented with circular arcs. In the SVG image, hover over a curve to highlight it and its terms. Farey diagram to F9. Symmetrical pattern made by the denominators of the Farey sequence, F9.
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The remainder of this article is devoted to the subject of simple continued fractions that are also periodic. In other words, the remainder of this article assumes that all the partial denominators ai (i ≥ 1) are positive integers.
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Burnand and Mera have noted that "there is some attempt to show the common denominators of human behavior regardless of 'tribal' affiliations, and there is a clear attempt to represent this through simple musical devices."Conrich; Woods, 2004, p. 58.
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The inch is customarily subdivided in dyadic rather than decimal fractions; similarly, the customary divisions of the gallon into half-gallons, quarts, and pints are dyadic. The ancient Egyptians also used dyadic fractions in measurement, with denominators up to 64..
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Resonances appear as small denominators in the expansion. The existence of resonances and small denominators led to the important question of stability in the planetary problem: do planets, in nearly circular orbits around a star, remain in stable or bounded orbits over time?Chierchia 2010 In 1963, Vladimir Arnold proved using KAM theory a kind of stability of the planetary problem: there exists a set of positive measure of quasiperiodic orbits in the case of the planetary problem restricted to the plane. In the KAM theory, chaotic planetary orbits would be bounded by quasiperiodic KAM tori.
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Del Ferro also made other important contributions to the rationalization of fractions with denominators containing sums of cube roots. He also investigated geometry problems with a compass set at a fixed angle, but little is known about his work in this area.
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It is a version of ITC Galliard with characters that support Central European languages. OpenType features include case sensitive forms, numerators/denominators, fractions, ligatures, lining/old style/proportional/tabular figures, localized forms, ordinals, scientific inferiors, superscript, small caps, diphthongs, stylistic alternates (set 1).
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Even apart from scaling and shifting, there are infinitely many cases, e.g. by considering rational numbers of which the denominators are powers of a given prime number. The translations form a group of isometries. However, there is no pattern with this group as symmetry group.
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Symmetrical pattern made by the denominators of the Farey sequence, F25. In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted by the fraction , and ends with the value 1, denoted by the fraction (although some authors omit these terms). A Farey sequence is sometimes called a Farey series, which is not strictly correct, because the terms are not summed.
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It is a version of Trade Gothic Next with rounded corners and terminals. The family includes nine fonts in three weights (regular, bold, heavy) and three widths and one style (roman). OpenType features include numerators/denominators, fractions, standard/discretionary ligatures, localized forms, sub/superscript, proportional figures.
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This can be proved in almost the same way. First we observe that we can work with numbers in base 10k and omit all denominators that have the given string as a "digit". The analogous argument to the base 10 case shows that this series converges. Now switching back to base 10, we see that this series contains all denominators that omit the given string, as well as denominators that include it if it is not on a "k-digit" boundary. For example, if we are omitting 42, the base-100 series would omit 4217 and 1742, but not 1427, so it is larger than the series that omits all 42s. Farhi considered generalized Kempner series, namely, the sums S(d, n) of the reciprocals of the positive integers that have exactly n instances of the digit d where 0 ≤ d ≤ 9 (so that the original Kempner series is S(9, 0)). He showed that for each d the sequence of values S(d, n) for n ≥ 1 is decreasing and converges to 10 ln 10\.
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According to Grove Music Online, "Western-derived pop styles, whether coexisting with or marginalizing distinctively local genres, have spread throughout the world and have come to constitute stylistic common denominators in global commercial music cultures".P. Manuel, "Pop. Non- Western cultures 1. Global dissemination", Grove Music Online, retrieved 14 March 2010.
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An algebraic number is a number that is a solution of a non-zero polynomial equation in one variable with rational coefficients (or equivalently — by clearing denominators — with integer coefficients). Numbers such as that are not algebraic are said to be transcendental. Almost all real and complex numbers are transcendental.
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The only common use of these subscripts is for the denominators of diagonal fractions, like ½ or the signs for percent %, permille ‰, and basis point ‱. Certain standard abbreviations are also composed as diagonal fractions, such as ℅ (care of), ℀ (account of), ℁ (addressed to the subject), or in Spanish ℆ (cada uno/una, "each one").
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Finally, if needed, one changes the signs of and all coefficients of the primitive part. This factorization may produce a result that is larger than the original polynomial (typically when there are many coprime denominators), but, even when this is the case, the primitive part is generally easier to manipulate for further factorization.
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Can one? Yet, physiognomy tried to be ‘scientific’and came to be devalued. Even in the eighteenth century Lavater tried to reduce the differences among the human faces to certain common denominators and tried to build a system of symbols to interpret it. (Kant considered it too pretentious a task for mere mortals).
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Vulgar fractions with 5 or in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or . There are five exceptional Lie groups.
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There are 8 accredited student organizations in Tarlac Montessori School. These are the Common Denominators' Guild (also referred to as the Math Club), Supreme Student Government (commonly abbreviated as SSG), Debate Society, TMS Chorale, Eco-Warriors Club, The Hark (the official publication of the institution), Technology Club, and the Tarlac Montessori School Scouting Movement.
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Gothic audience, not fratboys. Einsturzende Neubaten walked in through the "gothic" door—Miranda Sex Garden—Cocteau Twins. It's no wonder nobody can agree on what "Gothic" means... depth and dissonance and polite confrontationalism are quite possibly the only denominators.... I just like to play interesting music. It just so happens to be the 'goths' who are listening.
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This formula yields the decomposition for n = 101 in the table. Ahmes was suggested to have converted 2/p (where p was a prime number) by two methods, and three methods to convert 2/pq composite denominators.. Others have suggested only one method was used by Ahmes which used multiplicative factors similar to least common multiples.
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Thus, the diatomic sequence forms both the sequence of numerators and the sequence of denominators of the numbers in the Calkin–Wilf sequence. The function is the number of odd binomial coefficients of the form , ,. and also counts the number of ways of writing as a sum of powers of two in which each power occurs at most twice.
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Thus the difference between and is , in excess; between and , , in deficit; between and , , in excess; and so on. The result being, that by employing this series of differences we can express in another and very simple manner the fractions with which we are here concerned, by means of a second series of fractions of which the numerators are all unity and the denominators successively be the product of every two adjacent denominators. Instead of the fractions written above, we have thus the series: : + − + − ... The first term, as we see, is the first fraction; the first and second together give the second fraction, ; the first, the second and the third give the third fraction , and so on with the rest; the result being that the series entire is equivalent to the original value.
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If the sequence of convergents {xn} approaches a limit the continued fraction is convergent and has a definite value. If the sequence of convergents never approaches a limit the continued fraction is divergent. It may diverge by oscillation (for example, the odd and even convergents may approach two different limits), or it may produce an infinite number of zero denominators Bn.
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By October 16, 2011, about of Texas had burned in a single fire season, equivalent to a square of about . The 2011 Texas wildfires were a series of destructive wildfires in Texas that occurred in the 2011 fire season. During 2011 in Texas, around 31,453 fires had burned "2011 Texas Wildfires: Common Denominators of Home Destruction", tamu.edu, December 2011, webpage (PDF): tamu-TW.
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DST types I–IV are equivalent to real-odd DFTs of even order. In principle, there are actually four additional types of discrete sine transform (Martucci, 1994), corresponding to real-odd DFTs of logically odd order, which have factors of N+1/2 in the denominators of the sine arguments. However, these variants seem to be rarely used in practice.
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This factor has provided a basis to criticize ethnography. Traditionally, the ethnographer focuses attention on a community, selecting knowledgeable informants who know the activities of the community well. These informants are typically asked to identify other informants who represent the community, often using snowball or chain sampling. This process is often effective in revealing common cultural denominators connected to the topic being studied.
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In our usual sign-and-magnitude notation, subtraction involves sign comparison and magnitude comparison, and may require adding or subtracting the magnitudes, just like addition. In our usual fraction notation, subtraction requires finding a common denominator, multiplying, subtracting, and reducing to lowest terms, just like addition. In quote notation, to subtract, just subtract. There are no sign or magnitude comparisons, and no common denominators.
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In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both under discussion, the latter are sometimes termed integral ideals for clarity.
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The font family originally includes 14 fonts in 7 weights, with a complementary italic. OpenType features include numerators/denominators, fractions, ligatures, lining/old style/proportional and tabular figures, superscript, small capitals, stylistic alternates, stylistic sets 1 and 2 (Roman fonts only). Only one width is offered, without condensed or extended designs. OpenType Pro version supports all western European, most central European and many eastern European languages.
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An otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators. For example, 1/1, 5/4, and 3/2 (just major chord) form an otonality because they can be written as 4/4, 5/4, 6/4. This in turn can be written as an extended ratio 4:5:6. Every otonality is therefore composed of members of a harmonic series.
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In this example, it is not difficult to avoid introducing denominators by factoring out 12 before the second step. This can can always be done by using pseudo-remainder sequences, but, without care, this may introduce very large integers during the computation. Therefore, for computer computation, other algorithms are used, that are described below. This method works only if one can test the equality to zero of the coefficients that occur during the computation.
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Gerardo Herrero based his film Las razones de mis amigos (2000) on her third novel La conquista del aire (1998). Francisco Umbral considers her the best writer of her generation. She is a communist, and she has written several articles about Cuba. In the assessment of Luis I. Prádanos, 'the common denominators of Belén Gopegui's work are socio-political engagement and the constant search for updated and original ways to express it.
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The first section, on mathematics, is most focused on what today is most commonly known as number theory: odd numbers, even numbers, prime numbers, perfect numbers, abundant numbers, and other such properties. It contains an account of 'side and diameter numbers', the Pythagorean method for a sequence of best rational approximations to the square root of 2,T. Heath "A History of Greek Mathematics", p.91. the denominators of which are Pell numbers.
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A rational fraction is the quotient (algebraic fraction) of two polynomials. Any algebraic expression that can be rewritten as a rational fraction is a rational function. While polynomial functions are defined for all values of the variables, a rational function is defined only for the values of the variables for which the denominator is not zero. The rational fractions include the Laurent polynomials, but do not limit denominators to powers of an indeterminate.
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The Reut Institute has carried out extensive research regarding the common denominators of all the different countries that have successfully 'leapt' in recent years. It concludes that to leapfrog a country needs to create a shared vision, leadership by a committed elite, 'Inclusive growth', relevant institutions, a labor market suited to cope with rapid growth and changes, growth diagnostics of the country's bottlenecks and focused reforms as well as local and regional development and national mobilization.
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Whether or not a rational number has a terminating expansion depends on the base. For example, in base-10 the number 1/2 has a terminating expansion (0.5) while the number 1/3 does not (0.333...). In base-2 only rationals with denominators that are powers of 2 (such as 1/2 or 3/16) are terminating. Any rational with a denominator that has a prime factor other than 2 will have an infinite binary expansion.
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This contradicts the common meaning of the words that are used, as denominator refers to fractions, and two fractions do not have any greatest common denominator (if two fractions have the same denominator, one obtains a greater common denominator by multiplying all numerators and denominators by the same integer). Historically, other names for the same concept have included greatest common measure.. This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below).
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Born in Lusigny-sur- Barse, France, to Jacques‐Hubert Delaunay and Catherine Choiselat, Delaunay studied under Jean-Baptiste Biot at the Sorbonne. He worked on the mechanics of the Moon as a special case of the three-body problem. He published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. The work hints at chaos in the system, and clearly demonstrates the problem of so- called "small denominators" in perturbation theory.
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Early nationalists tended to ignore Nigeria as the focus of patriotism. Their common denominators tended to be based on newly assertive ethnic consciousness, particularly that of the Yoruba and Igbo. Despite acceptance of European and North American influences, the nationalists were critical of colonialism for its failure to appreciate the antiquity, richness and complexity of indigenous cultures. They wanted self-government, charging that only colonial rule prevented the unshackling of progressive forces in Nigeria and other states.
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Augustin Cauchy read Farey’s letter and published a paper "Démonstration d’un Théorème Curieux sur les Nombres" reproving Haros’ results without acknowledgement. In his paper Cauchy referred to the mediant as "a remarkable property of ordinary fractions observed by M. J. Farey." Thus, an ordered sequence of all vulgar fractions with denominators less than a given value became known as a Farey sequence rather than perhaps more rightfully as either a Chuquet sequence or a Haros sequence.
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Bishop is heard whistling the tune of this particular theme at the beginning and end of the film, making the electric piano theme "a non-diegetic realization of a diegetic source."Conrich; Woods, 2004, p. 56. Burnand and Mera have noted that "there is some attempt to show the common denominators of human behavior regardless of 'tribal' affiliations, and there is a clear attempt to represent this through simple musical devices."Conrich; Woods, 2004, p. 58.
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A similar phenomenon occurs with other numbers, such as 5/5809 (an example found independently by K. S. Brown and David Bailey) which has a 31-term expansion. Although the denominators of this expansion are difficult to compute due to their enormous size, the numerator sequence may be found relatively efficiently using modular arithmetic. describes several additional examples of this type found by Broadhurst, and notes that K. S. Brown has described methods for finding fractions with arbitrarily long expansions.
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Upon clearing denominators, this expression will generate Pythagorean triples. Intriguingly, the arbitrary multiplier of x has become the cornerstone of the generator expression(s). Diophantus II.IX reaches the same solution by an even quicker route which is very similar to the 'generalized solution' above. Once again the problem is to divide 16 into two squares.This solution is II.IX in the numbering of Diophantos of Alexandria: A Study in the History of Greek Algebra, Sir Thomas Little Heath, Cambridge: University of Cambridge Press, 1885.
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Such weightings are inherently valid for use in positional voting systems provided that a legitimate common ratio is employed. Using a common ratio of zero, this form of positional voting has weightings of 1, 0, 0, 0, … and so produces ranking outcomes identical to that for first-past-the-post or plurality voting. Alternatively, the denominators of the above fractional weightings could form an arithmetic progression instead; namely 1/1, 1/2, 1/3, 1/4 and so on down to 1/N.
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COVID numbers in the county-level graphs on this page are based on data from Wisconsin DHS, as of 2020/10/19. County populations used as denominators above are estimates from the Census Bureau as of 2019. To get the numbers from the section on that page, in the section County Population Totals: 2010-2019, follow the link CO-EST2019-ANNRES: Annual Estimates of the Resident Population for Counties: April 1, 2010 to July 1, 2019, and then download the spreadsheet co-est2019-annres-55.xlsx.
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A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance, the classical or naive height over the rational numbers is typically defined to be the maximum of the numerators and denominators of the coordinates (e.g. 3 for the coordinates ), but in a logarithmic scale.
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The above equation is not applicable for vertical and horizontal lines because in these cases one of the intercepts does not exist. Moreover, it is not applicable on lines passing through the pole since in this case, both x and y intercepts are zero (which is not allowed here since x_o and y_o are denominators). A vertical line that doesn't pass through the pole is given by the equation ::r\cos\theta=x_o. Similarly, a horizontal line that doesn't pass through the pole is given by the equation ::r\sin\theta=y_o.
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Students may organize new clubs by presenting a constitution and a list of members to the college administration and the student government for approval. This approval process does not authorize any club to act on behalf of the college, nor does approval indicate any the college's agreement with the club's purpose. The college recognizes over 70 student clubs on campus. A number of student clubs are dedicated to encouraging interest is a specific academic discipline, including the "W&J; Denominators" mathematics club, the Society of Physics Students, and the Pre- Health Professions Society.
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He confirms that these common denominators do not contradict the charter of human rights, but they consist of other foundations such as: respect of motherhood, uplifting of the disenfranchised, importance of child care, and safety of the environment. The aim he often exposes is to avoid all the causes of cultural conflicts that might lead to military stages. His reform-oriented ideas are in phase with those of the two Canadian Will Kymlicka and Charles Taylor. Mgr. Moubarak is in favor of implementing the federal system in Lebanon.
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So we have another thread to start to follow in search for the origin of beehive rocks, diverging from the early medieval period; investigating the story of the Agrian people. Historical studies do not consider the information from Bonfini about the city of Eger to a sufficient degree, however his statements are supported by a series of facts. Accordingly, to Antonio Bonfini, Eger belonged to the domain of Metanastae or Jász or Iazyg people [the Hungarian word “íjász” means archer]. He specifies Agrians as the founders and denominators of the city.
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For example, the first four terms add to 1805/1806, and therefore any Egyptian fraction for a number in the open interval (1805/1806,1) requires at least five terms. It is possible to interpret the Sylvester sequence as the result of a greedy algorithm for Egyptian fractions, that at each step chooses the smallest possible denominator that makes the partial sum of the series be less than one. Alternatively, the terms of the sequence after the first can be viewed as the denominators of the odd greedy expansion of 1/2.
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Problems can occur when calculating the MAPE value with a series of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error, caused by a small deviation in error, can occur. As an alternative, each actual value () of the series in the original formula can be replaced by the average of all actual values () of that series. This alternative is still being used for measuring the performance of models that forecast spot electricity prices.
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For integers, the exponent of the highest power of 2 dividing n gives 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, ... . If 1 is added, or if the 0s are removed, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, ... . The values resemble tick-marks on a 1/16th graduated ruler, hence the name. These values correspond to the restriction of the Thomae function to the dyadic rationals: those rational numbers whose denominators are powers of 2.
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The root of the Stern–Brocot tree corresponds to the number 1. The parent-child relation between numbers in the Stern–Brocot tree may be defined in terms of continued fractions or mediants, and a path in the tree from the root to any other number q provides a sequence of approximations to q with smaller denominators than q. Because the tree contains each positive rational number exactly once, a breadth first search of the tree provides a method of listing all positive rationals that is closely related to Farey sequences.
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Designed by Lynne Yun of Monotype GmbH, this family is based on Trade Gothic Condensed Heavy, but with only capital glyphs for Latin texts. The different fonts can be used over each other in layers to create complex effects.Trade Gothic Display – new multi-layer styles for the popular design font The family include five fonts in one weight and one width, with five different styles inside glyph outlines. OpenType features include case-sensitive forms, numerators/denominators, fractions, standard ligatures, localized forms, sub/superscript, proportional/lining figures, glyph (de)composition, kerning, mark (to mark) positioning.
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It is a peculiar borderland of aesthetics concerning music and everything else in the society in which it is created. Most artists that may be considered neomelodics often have more musical differences between them than common denominators. Neomelodic music is a celebration for those involved and a pejorative term with political implications for those outside. The geographical area that is its homeland consists of every suburb, smalltown, and province between Romanina (Rome, Lazio, Italy) and Catania (Sicily, Italy) with its absolute epicenter in the working-class inner-city and peripherical areas of Naples (Campania, Italy).
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As an application, Bowditch proved that, with a few exceptions of surfaces of small complexity, the action of the mapping class group Mod(S) on C(S) is "acylindrical" and that the asymptotic translation lengths of pseudo-Anosov elements of Mod(S) on C(S) are rational numbers with bounded denominators. A 2007 paper of Bowditch produces a positive solution of the angel problem of John Conway:John H. Conway, "The angel problem" Games of no chance (Berkeley, California, 1994), pp. 3–12, Mathematical Sciences Research Institute Publications, 29, Cambridge University Press, Cambridge, 1996. Bowditch provedB.
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One of the hallmarks of Context-Based Sustainability is its use of Context-Based Metrics (CBMs). Unlike other metrics used to measure, manage and report the sustainability performance of organizations (e.g., absolute and relative/intensity metrics), some CBMs, but not all, take the form of quotients that have two parts to them: 1) denominators that express organization-specific norms for what their impacts on vital capitals must be in order to be sustainable (i.e., equivalent to "allocations" as explained above), and 2) numerators that express their actual impacts on the same capitals.
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Many positive results were proven by Peter Linnell. For example, if the group acting is a free group, then the l^2-Betti numbers are integers. The most general question open as of late 2011 is whether l^2-Betti numbers are rational if there is a bound on the orders of finite subgroups of the group which acts. In fact, a precise relationship between possible denominators and the orders in question is conjectured; in the case of torsion-free groups, this statement generalizes the zero-divisors conjecture.
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Its sequence of numerators (or, offset by one, denominators) is Stern's diatomic series, and can be computed by the fusc function. The Calkin–Wilf tree is named after Neil Calkin and Herbert Wilf, who considered it in their 2000 paper. The tree was introduced earlier by Jean Berstel and Aldo de Luca, Section 6. as Raney tree, since they drew some ideas from a paper by George N. Raney.. Stern's diatomic series was formulated much earlier by Moritz Abraham Stern, a 19th-century German mathematician who also invented the closely related Stern–Brocot tree.
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Amateur radio operators commonly provide local, regional, national, and international emergency / disaster relief communications. The need for interoperability on HF led to the adoption of Automatic Link Establishment ALE open networks by hams. Amateur radio adapted 2G ALE techniques, by using the common denominators of the 2G ALE protocol, with a limited subset of features found in the majority of all ALE radios and controllers. Each amateur radio ALE station uses the operator's call sign as the address, also known as the ALE Address, in the ALE radio controller.
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Largely in the US, but increasingly in other nations, K-12 Mathematics textbooks have reflected the controversies of new math and reform mathematics which have sought to replace traditional mathematics in what have been called the math wars. Traditional texts, still favored in Asia and other areas, merely taught the same time-tested mathematics that most adults have learned. By contrast "progressive" approaches seek to address problems in social inequity with approaches that often incorporate principles of constructivism and discovery. Texts such as TERC and CMP discourage or omit standard mathematics methods and concepts such as long division and lowest common denominators.
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The two-story brick building was built for Mizpah Lodge #39, a Masonic lodge chartered in 1893. It "was one of the masonic "blue" lodges, the common denominators of Masonry inasmuch as it was in such lodges that the initial three degrees - Entered Apprentice, Fellowcraft and Master Mason - were conferred on the candidate." The lodge had 11 charter members, and met in Sheldon's I.O.O.F hall and then in A.O.U.W. halls. It began construction of its own building in 1905 when membership had reached 54 and there were at least seven fraternal organizations in town, with scheduling of meeting times being an issue.
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If such a subset existed, it would form a universal point set that could be used to draw all planar graphs with rational edge lengths (and therefore, after scaling them appropriately, with integer edge lengths). However, Ulam conjectured that dense rational-distance sets do not exist.. According to the Erdős–Anning theorem, infinite non- collinear point sets with all distances being integers cannot exist. This does not rule out the existence of sets with all distances rational, but it does imply that in any such set the denominators of the rational distances must grow arbitrarily large.
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The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1. An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently—by clearing denominators—with integer coefficients). All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as and , are called transcendental numbers.
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Whether created for an exhibition, a film or a public space, Bigert & Bergström's creations have certain common denominators in their forms of expression. Their works are often intended to be experienced through multiple senses; many sculptures exude warmth, vibrations, light and sound, or can be set in motion and change. Their works encourage, and sometimes require viewer- interaction. They are often constructed on a large scale, many times large enough to step into the work and experience it from inside. This angle of having the viewer physically step into the work, has been a feature of the duo’s creations since the very beginning.
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This further mathematical sequence is an example of a harmonic progression. These particular descending rank-order weightings are in fact used in N-candidate positional voting elections to the Nauru parliament. For such electoral systems, the weighting (wn) allocated to a given rank position (n) is defined below; where the value of the first preference is ‘a’. ::wn = a2/(a+(n-1)d) = a/(1+(n-1)d/a) where w1 = a2/(a+(1-1)d) = a For the Nauru (Dowdall) system, the first preference ‘a’ is worth one and the common difference ‘d’ between adjacent denominators is also one.
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But its real triumph, in an age of trimming, of market testing, of self-censorship and lowest common denominators, is not simply to aim insanely high, but to make it to the summit." Criticism centered on the concept of the record; BBC's Chris Jones said that it is "griping vaguely against 'authority and that "too many buzz words obscure incisive meaning". Steve Kandell of Spin wrote that the humor of American Idiot was "sorely missed" and that the energy of the album seemed "directionless". The Guardians Alexis Petridis indicated that "the storyline becomes impossible to follow".
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Then on the unit circle there exists the rational point (a/c, b/c), which, in the complex plane, is just a/c + ib/c, where i is the imaginary unit. Conversely, if (x, y) is a rational point on the unit circle in the 1st quadrant of the coordinate system (i.e. x > 0, y > 0), then there exists a primitive right triangle with sides xc, yc, c, with c being the least common multiple of the denominators of x and y. There is a correspondence between points (a, b) in the x-y plane and points a + ib in the complex plane which is used below.
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The notion of common denominators for several religions and traditions of India further developed from the 12th century CE.; Lorenzen traces the emergence of a "family resemblance", and what he calls as "beginnings of medieval and modern Hinduism" taking shape, at c. 300–600 CE, with the development of the early Puranas, and continuities with the earlier Vedic religion. Lorenzen states that the establishment of a Hindu self- identity took place "through a process of mutual self-definition with a contrasting Muslim Other". According to Lorenzen, this "presence of the Other" is necessary to recognise the "loose family resemblance" among the various traditions and schools.
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Lake San Miguel (named in honor of the city's patron saint) and a rose garden were created to the south of the historic residence, common denominators to most of Thays' public parks. The founder and first President of the University of Tucumán, Doctor Juan Bautista Terán, purchased 20 cast iron, glazed sculptures in France for the park and the planned Liberal Arts campus therein, opened in 1914. Later additions included a campground, a topiary sun dial, the Tucumán Lawn Tennis Club, the Municipal Cultural Center and Sports Complex, the University's Odontology and Physics campuses and the Nasif Estéfano Speedway. The southern three-fourths of the park was never completed, however.
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The coefficients of Ep(x) are rational. We can use either formula for Ep(x) to prove that, unlike ex, all of its coefficients are p-integral; in other words, the denominators of the coefficients of Ep(x) are not divisible by p. A first proof uses the definition of Ep(x) and Dwork's lemma, which says that a power series f(x) = 1 + ... with rational coefficients has p-integral coefficients if and only if f(xp)/f(x)p ≡ 1 mod pZpx. When f(x) = Ep(x), we have f(xp)/f(x)p = e−px, whose constant term is 1 and all higher coefficients are in pZp.
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Roughly fifteen years later in England, Henry Goodwyn set out to create a much more ambitious version of Haros’ table. In particular, Goodwyn wanted to tabulate the decimal values for all irreducible fractions with denominators less than or equal to 1,024. There are 318,963 such fractions. As a warm up and a test of the commercial market for such a table in 1816 he published for private circulation The First Centenary of a Series of Concise and Useful Tables of all the Complete Decimal Quotients, which can arise from dividing a unit, or any whole Number less than each Divisor by all Integers from 1 to 1024.
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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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Followers of the Greek philosopher Pythagoras ( ) discovered that the square root of two cannot be expressed as a fraction of integers. (This is commonly though probably erroneously ascribed to Hippasus of Metapontum, who is said to have been executed for revealing this fact.) In Jain mathematicians in India wrote the "Sthananga Sutra", which contains work on the theory of numbers, arithmetical operations, and operations with fractions. A modern expression of fractions known as bhinnarasi seems to have originated in India in the work of Aryabhatta (), Brahmagupta (), and Bhaskara (). Their works form fractions by placing the numerators () over the denominators (), but without a bar between them.
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A compiled program is typically embedded within a DIV container element or alternatively set to occupy the entire display. The run-time library was specifically built for increased productivity and time-to-market with regards to mobile application development. Smart Pascal reduces development time for JavaScript radically linguistically, by means of Object Pascal and true object oriented programming, and with regards to how the run-time library's class and component system is designed. The RTL interacts with the document object model and JavaScript environment in the same way a native language would interact with an operative system; abstracting common denominators and automating complex tasks.
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Architecture and Design Archive Turkey (ADAT) became active in 2008 under the direction of the historian of modern design in Turkey Gökhan Karakuş as the joint project of GG and Platform Garanti, with the aim of demonstrating the historical development in the fields of architecture and design in Turkey. ADAT treats architecture and design as two main factors that complete each other, and as two separate denominators of a shared practice. Archival work followed two different research methodologies in the fields of architecture and design. Architectural research began with the “senior architects” in Turkey including Cengiz Bektaş, Utarit İzgi, Turgut Cansever, Sedad Hakkı Eldem and Kemali Söylemezoğlu.
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Although one's ethnic identity is a personal project, ultimately, any claim to a Macanese identity is either accepted or refuted by the already existing Macanese community on criteria dependent upon shared cultural heritage and collective notions (these criteria shift with each emerging generation). As Turner and later Bhabka suggest, identity is a layering of experiences unraveled through contact with others and is only decipherable within the social sphere. There are limits to a Macanese identity, and Pina-Cabral and Lourenço (op. cit.), offer a broad- based definition delineated by family and community acceptance as two basic denominators for a tentative definition of the Macanese.
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In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers nontrivially represents zero. In other words, if the equation :Q(x) = 0 has a non-zero real solution, then it has a non-zero rational solution (the converse is obvious). By clearing the denominators, an integral solution x may also be found. Meyer's theorem is usually deduced from the Hasse–Minkowski theorem (which was proved later) and the following statement: : A rational quadratic form in five or more variables represents zero over the field Qp of the p-adic numbers for all p.
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SEDES was incorporated in 1970, its founders coming from different academic, social, professional and political affiliations. They joined to seek societal change by establishing a diverse social activism, organizing political opposition against the Estado Novo regime that ruled Portugal since the 1920s, and encouraging participation in academic associations, Christian organizations and trade union activities. The common denominators inspiring the founders of SEDES were humanism, socio-cultural development and democracy. SEDES held meetings, organized working groups, and facilitated debates in various locations of Portugal; it was the first Portuguese organization to proclaim the advantages of a rapprochement with the European Community and was a pluralistic school of civics.
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Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators.. The name "practical number" is due to . He noted that "the subdivisions of money, weights, and measures involve numbers like 4, 12, 16, 20 and 28 which are usually supposed to be so inconvenient as to deserve replacement by powers of 10." He rediscovered the number theoretical property of such numbers and was the first to attempt a classification of these numbers that was completed by and . This characterization makes it possible to determine whether a number is practical by examining its prime factorization.
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" Jon Casimir of The Sydney Morning Herald said, "It is gratifying, in an entertainment world dominated by market research and common denominators, to see a program that obviously doesn't care if you like it or not." However, he said the characterization of Terrance and Phillip was too thin to be particularly funny, and added that the novelty of the prank is lost in later years. Jakob Von Bayer said the episode continued a long history of South Park Canada-bashing: "South Park has gotten a lot of comic mileage out of Canada over the years. [...] This episode portrays a country full of Bob and Doug McKenzies; Toronto is but a highway town en route to Buffalo.
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He serves as a co-editor of Transactions of the Philological Society and sits on several other editorial boards. He is author of Linguistics Today (Fontana, 1984) and co-author, with Jim Miller, of Syntax: A Linguistic Introduction to Sentence Structure and Syntax: Generative Grammar (Hutchinson, 1981). He was syntax editor for the first edition of the Encyclopedia of Language and Linguistics and was joint editor, with Jim Miller, of A Concise Encyclopedia of Linguistic Theories and A Concise Encyclopedia of Grammatical Categories (Pergamon Press, 1997 and 1998). He was also a joint editor of Common Denominators in Art and Science (Aberdeen University Press, 1983), as well as Language, Reasoning and Inference (Academic Press, 1986).
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The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of z^2 + 4 can be found using difference of two squares: :z^2 + 4 : = z^2 - i^2 \cdot 4 (since i^2 = -1) : = z^2 - (2 i)^2 : = (z + 2 i)(z - 2 i) Therefore, the linear factors are (z + 2 i) and (z - 2 i). Since the two factors found by this method are complex conjugates, we can use this in reverse as a method of multiplying a complex number to get a real number. This is used to get real denominators in complex fractions.
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" Harlan Ellison, writing in March 1977, said: "Lipstick panders to the basest, vilest, lowest possible common denominators of urban fear and lynch logic. It is the sort of film that, if you see it in a ghetto theater filled with blacks, will scare the bejeezus out of you. The animal fury this film unleashes in an audience is terrifying to behold. It gives exploitation a bad name; and it has less to do with rape, which is the commercial hook on which they’ve hung the salability of this bit of putrescence, than it does with the cynicism of Joseph E. Levine, a man who probably has no trouble sleeping with a troubled conscience.
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If all numerators are 1 in a fraction written in this form, and all denominators are different from each other, the result is an Egyptian fraction representation of the number. This notation was also sometimes combined with the composite fraction notation: two composite fractions written next to each other would represent the sum of the fractions. The complexity of this notation allows numbers to be written in many different ways, and Fibonacci described several methods for converting from one style of representation to another. In particular, chapter II.7 contains a list of methods for converting an improper fraction to an Egyptian fraction, including the greedy algorithm for Egyptian fractions, also known as the Fibonacci–Sylvester expansion.
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By the rank–nullity theorem, a system of n vectors (matrix columns) in k linearly independent dimensions (the rank of the matrix is the number of fundamental dimensions) leaves a nullity, p, satisfying (p = n − k), where the nullity is the number of extraneous dimensions which may be chosen to be dimensionless. The dimensionless variables can always be taken to be integer combinations of the dimensional variables (by clearing denominators). There is mathematically no natural choice of dimensionless variables; some choices of dimensionless variables are more physically meaningful, and these are what are ideally used. The International System of Units defines k=7 base units, which are the ampere, kelvin, second, metre, kilogram, candela and mole.
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The perfect fifth of quarter- comma meantone, expressed as a fraction of an octave, is log2 5\. This number is irrational and in fact transcendental; hence a chain of meantone fifths, like a chain of pure 3:2 fifths, never closes (i.e. never equals a chain of octaves). However, the continued fraction approximations to this irrational fraction number allow us to find equal divisions of the octave which do close; the denominators of these are 1, 2, 5, 7, 12, 19, 31, 174, 205, 789 ... From this we find that 31 quarter-comma meantone fifths come close to closing, and conversely 31 equal temperament represents a good approximation to quarter- comma meantone.
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Magic wands commonly feature in works of fantasy fiction as spell-casting tools. Few other common denominators exist, so the capabilities of wands vary wildly. In Joanne K. Rowling's Harry Potter series, the first book of which was published in 1997, personal wands are common, as necessary tools to channel out each character's magic, and they are used as weapons in magical duels, and it is the wand that chooses its owner. A wand is also present in the Children of the Red King series in the possession of Charlie Bone as well as the popular MMORPG World of Warcraft where caster classes such as the mage and warlock use wands offensively.
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However, there is a simpler greedy algorithm that has successfully found Egyptian fractions in which all denominators are odd for all instances x/y (with odd y) on which it has been tested: let u be the least odd number that is greater than or equal to y/x, include the fraction 1/u in the expansion, and continue in the same way with the remaining fraction x/y − 1/u. This method is called the odd greedy algorithm and the expansions it creates are called odd greedy expansions. Stein, Selfridge, Graham, and others have posed the question of whether the odd greedy algorithm terminates with a finite expansion for every x/y with y odd. , this question remains open.
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The mediant is the fraction between two fractions a/c and b/d whose numerator is the sum of the numerators, a+b, and whose denominator is the sum of the denominators, c+d. That is, the mediant of the fractions a/c and b/d is the fraction (a+b)/(c+d). In his paper Haros demonstrated that the mediant is always irreducible and, more importantly for this purposes, if one starts with the sequence of fractions :1/99, 1/98, 1/97, ..., 1/4, 1/3, 1/2, 2/3, 3/4, 5/6, ..., 96/97, 97/98, 98/99 and just keeps applying the rule, only keeping the result if the denominator is less than one-hundred, then they generate all 3,003.
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Prime Minister Najib condemned the church bombings, directed police to increase security at all places of worship, and called for unity amongst the Malaysian people.Farrah Naz Karim (9 January 2010), "PM slams bid to burn churches", New Straits Times The government will hold inter- faith dialogues including prominent religious leaders to find "common denominators of understanding." Tan Sri Dr Koh Tsu Koon, Minister in the Prime Minister's Department, said the government has already met separately with religious groups."Govt to hold inter-faith dialogues to resolve differences of views", The Star, 11 January 2010, Najib visited the church most badly damaged in the attacks, the Protestant Metro Tabernacle church in Kuala Lumpur and promised a grant of RM500,000 to assist with reconstruction.
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The improved understanding of dynamical systems coming from chaos theory helped shed light on what was termed the small denominator problem or small divisor problem. It was observed in the 19th century (by Poincaré, and perhaps earlier), that sometimes 2nd and higher order terms in the perturbative series have "small denominators". That is, they have the general form \psi_n V\phi_m / (\omega_n -\omega_m) where \psi_n, V and \phi_m are some complicated expressions pertinent to the problem to be solved, and \omega_n and \omega_m are real numbers; very often they are the energy of normal modes. The small divisor problem arises when the difference \omega_n -\omega_m is small, causing the perturbative correction to blow up, becoming as large or maybe larger than the zeroth order term.
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Legge's employer, EMI, tolerated his independent ways for many years, but in the 1960s attempts were made to curtail his freedom of choice of repertoire, and finally in 1964 he resigned. His memoirs, edited by Elisabeth Schwarzkopf and published in 1982, set out his disenchantment with EMI and its increasingly powerful internal committees: :I am convinced that in the arts, committees are useless. What is necessary are people like Karajan, Culshaw and me; we know not only how to achieve the best artistic results but how to attract the public and carry out the whole operation with carefully chosen collaborators. Democracy is fatal for the arts; it leads only to chaos or the achievement of new and lower common denominators of quality.
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Rotis serif Rotis semi-serif Rotis semi-sans Rotis sans-serif It is a version of Rotis Sans designed by Monotype Imaging senior designer Robin Nicholas, and freelance designer Alice Savoie. It expands the original with extra three font weights (Light, Semi Bold, and Black) and italics, along with revised letter spacing and kerning, a new set of numerals with similar height to the capitals.Font News: Rotis II Sans, expanded and improved The family includes 14 fonts in seven weights, with complementary italics. OpenType features include access all alternates, case-sensitive forms, numerators/denominators, fractions, standard ligatures, localized forms (OpenType Pro fonts only), proportional/tabular figures, scientific inferiors, superscript/subscript, stylistic alternates, stylistic sets 1, 2 and 3 (OpenType Std fonts only).
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Eventually, the focus on creating blockbusters grew so intense that a backlash occurred, with some critics and film-makers decrying the prevalence of a "blockbuster mentality"Movie Blockbusters - Google Books (pg.108)Heroes, Monsters and Values: Science Fiction Films of the 1970s - Google Books lamenting the death of the author-driven, "more artistic" small-scale films of the New Hollywood era (despite criticism of the praise the latter set of films received). This view is taken, for example, by film journalist Peter Biskind, who wrote that all studios wanted was another Jaws, and as production costs rose, they were less willing to take risks, and therefore based blockbusters on the "lowest common denominators" of the mass market.Peter Biskind: Easy Riders, Raging Bulls: How the Sex-Drugs-And Rock 'N Roll Generation Saved Hollywood.
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His work was based on two important principles, in morphology he chose forms which he regarded as common denominators from which contemporary varieties could be inferred, in lexicography he applied puristic principles and excluded words of Danish or Middle Low German descent when at least some dialects had preserved synonyms inherited from Old Norse. In 1885, Landsmål was adopted as an official written language alongside the Norwegian version of Danish. Knud Knudsen, a teacher, worked instead to adapt the orthography more closely to the spoken Dano- Norwegian koiné known as "cultivated daily speech" (dannet dagligtale). He argued that the cultivated daily speech was the best basis for a distinct Norwegian written language, because the educated classes did not belong to any specific region, they were numerous, and possessed cultural influence.
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DCTs of types I-IV treat both boundaries consistently regarding the point of symmetry: they are even/odd around either a data point for both boundaries or halfway between two data points for both boundaries. By contrast, DCTs of types V-VIII imply boundaries that are even/odd around a data point for one boundary and halfway between two data points for the other boundary. In other words, DCT types I-IV are equivalent to real-even DFTs of even order (regardless of whether N is even or odd), since the corresponding DFT is of length 2(N−1) (for DCT-I) or 4N (for DCT-II/III) or 8N (for DCT-IV). The four additional types of discrete cosine transform correspond essentially to real-even DFTs of logically odd order, which have factors of N ± ½ in the denominators of the cosine arguments.
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L^2-invarianten and those invariants which result from the K-theory of operator algebras. Such invariants arise in generalizations of the Atiyah- Singer index theorem. Schick, with Wolfgang Lück, introduced the strong Atiyah conjecture. Given a discrete group G, the Atiyah conjecture states that the L^2-Betti numbers of a finite CW-complex that has fundamental group G are integers, provided that G is torsion-free; furthermore, in the general case, the L^2-Betti numbers are rational numbers with denominators determined by the finite subgroups of G. In 2007 Schick, with Peter Linnell, proved a theorem which established conditions under which the Atiyah conjecture for a torsion- free group G implies the Atiyah conjecture for every finite extension of G; furthermore, they proved that the conditions are satisfied for a certain class of groups.
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In computer science, specifically information retrieval and machine learning, the harmonic mean of the precision (true positives per predicted positive) and the recall (true positives per real positive) is often used as an aggregated performance score for the evaluation of algorithms and systems: the F-score (or F-measure). This is used in information retrieval because only the positive class is of relevance, while number of negatives, in general, is large and unknown. It is thus a trade-off as to whether the correct positive predictions should be measured in relation to the number of predicted positives or the number of real positives, so it is measured versus a putative number of positives that is an arithmetic mean of the two possible denominators. A consequence arises from basic algebra in problems where people or systems work together.
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Different plants arrange their leaves differently, for instance on alternating sides of the plant stem, or rotated from each other by other fractions of a full rotation between consecutive leaves. In these patterns, rotations by 1/2 of an angle, 1/3 of an angle, 3/8 of an angle, or 5/8 of an angle are common, and it does not appear to be coincidental that the numerators and denominators of these fractions are all Fibonacci numbers. Higher Fibonacci numbers often appear in the number of spiral arms in the spiraling patterns of sunflower seed heads, or the helical patterns of pineapple cells. The theme of Adler's work in this area, in the papers reproduced in this volume, was to find a mathematical model for plant development that would explain these patterns and the occurrence of the Fibonacci numbers and the golden ratio within them.
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The Michigan Murders p. 76 By early April, each of these law enforcement agencies had collectively assigned 20 investigators to work exclusively upon the four homicides.The Michigan Murders p. 77 Little physical evidence existed beyond eyewitness descriptions and forensic reports. Police had noted (and would continue to note) common denominators in the physical characteristics of the victims, and the manner in which they died: all of the victims had been brunette Caucasians; each (excluding Mixer) had been the recipient of extensive violence inflicted with a blunt and/or bladed instrument prior to her murder; each of the victims' bodies had been found within a 15-mile radius of Washtenaw County; and each victim (excluding Mixer) had received knife wounds to the neck. Furthermore, each victim had been found with an item of clothing tied around her neck, and each woman had been menstruating at the time of her death.
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Pan-nationalism (from , "all", and , "nationalism") is a specific term, used mainly in social sciences as a designation for those forms of nationalism that are trying to transcend (overcome) traditional boundaries of basic national identities, in order to create a "higher" pan-national (all-inclusive) identity, based on various common denominators. Pan-nationalism can occur as a specific variant of all common forms of nationalism. In relation to classical state nationalism, pan-nationalism manifests itself through various political movements that are advocating the creation of "higher" (pan-national) forms of political identity, based on a regional or continental grouping of national states (for examples: Pan-Americanism, Pan-Africanism), Pan-Arabism, Pan- Iranism. In terms of ethnic nationalism, pan-nationalism can also manifest itself through specific ethnic movements that are advocating the creation of "higher" (pan-national) forms of common identity that is based on ethnic grouping (for example: Pan-Germanism or Pan-Slavism).
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Written thirty years before Ferdinando Galiani's book on monetary theory, Della Moneta (which may have built upon it), Trade of the World attempted to examine the same problems that prompted Galiani, though he did so in a more primitive way. Among the topics he explicitly identifies and addresses are "Credit, and Its Effects on Trade", "The Balance of Trade", and inflation/deflation, which he refers to as "Accidents that Change the Proportion of Particular Denominators" and "Altering the Denomination of Coin". He goes on to discuss other, non-monetary economic issues, like manufacturing and businesses. The book is subtitled And showing the Pernicious Consequences of CREDIT, and that it destroys the Purpose of National Trade...and thus it's no surprise that Gervaise concludes the special favors granted in mercantilism, essentially protectionism and state-imposed corporate oligopoly and funding, are harmful to the economy and have caused many of the more recent inflation problems.
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The technology of protectionExplosion Protection Techniques can range in price dramatically but where the type of device is rational to use, would typically be from least to most expensive solutions: explosion doors and vents (dependent on quantities and common denominators, either may end up the wise price choice); inerting: explosion suppression; isolation – or combinations of same. To focus on the most cost effective, doors typically have lower release pressure capabilities; are not susceptible to fatigue failures or subject to changing release pressures with changes in temperature, as “rupture membrane” type are; capable of leak tight service; service temperatures of up to 2,000°F; and can be more cost effective in small quantities. Rupture membrane type vents can provide a leak tight seal more readily in most cases; have a relatively broad tolerance on their release pressure and are more readily incorporated into systems with discharge ducts. Discharge Hood with Explosion Relief Panels and Fracture Clip Releases.
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In the sexagesimal system, any fraction in which the denominator is a regular number (having only 2, 3, and 5 in its prime factorization) may be expressed exactly. Shown here are all fractions of this type in which the denominator is less or equal to 60: : = 0;30 : = 0;20 : = 0;15 : = 0;12 : = 0;10 : = 0;7,30 : = 0;6,40 : = 0;6 : = 0;5 : = 0;4 : = 0;3,45 : = 0;3,20 : = 0;3 : = 0;2,30 : = 0;2,24 : = 0;2,13,20 : = 0;2 : = 0;1,52,30 : = 0;1,40 : = 0;1,30 : = 0;1,20 : = 0;1,15 : = 0;1,12 : = 0;1,6,40 : = 0;1 However numbers that are not regular form more complicated repeating fractions. For example: : = 0; (the bar indicates the sequence of sexagesimal digits 8,34,17 repeats infinitely many times) : = 0; : = 0; : = 0;4, : = 0; : = 0; : = 0; : = 0; The fact that the two numbers that are adjacent to sixty, 59 and 61, are both prime numbers implies that fractions that repeat with a period of one or two sexagesimal digits can only have regular number multiples of 59 or 61 as their denominators, and that other non-regular numbers have fractions that repeat with a longer period.
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"Resurgent functions" are divergent power series whose Borel transforms converge in a neighborhood of the origin and give rise, by means of analytic continuation, to (usually) multi-valued functions, but these multi-valued functions have merely isolated singularities without singularities that form cuts with dimension one or greater.Sauzin Resurgent functions and splitting theorem , 2007Boris Sternin, Victor Shatalov Borel-Laplace Transform and Asymptotic Theory: Introduction to Resurgent Analysis , CRC Press 1996Bernard Malgrange Introduction aux travaux de J. Écalle , L'Enseignement Mathématique, 31, 1985, 261-282 Écalle's theory has important applications to solutions of generalizations of Abel's integral equation; the method of resurgent functions provides for such solutions a (Borel) resummation method for dealing with divergent series arising from semiclassical asymptotic developments in quantum theory.Frédéric Pham Introduction à la résurgence quantique, d'après Écalle et Voros, Séminaire Bourbaki 656, 1985/86 He applied his theory to dynamic systems Bernard Malgrange, Travaux d'Écalle et Martinet-Ramis sur les systèmes dynamiques, Séminaire Bourbaki 582, 1981/82 and to the interplay between diophantine small denominators and resonance involved in problems of germs of vector fields.Écalle Singularités non abordables par la géométrie, Ann. Inst.
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