In photosystem I, the quinones on both sides are tightly bound; in photosystem II, they are tightly bound on one side, but loosely bound on the other.
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The problem is the zero lower bound on nominal interest rates.
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The uncertainty kept the dollar range-bound on the euro around $1.1004.
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Rather, the reserve functions as a kind of lower bound on Libra's value.
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If so, my calculation represents an upper bound on the chance Mr. Trump quits.
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The above estimates reflect something of an upper bound on Musk's potential Tesla wealth.
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Let 'em know, "This isn't working for me anymore," then bound on to greener pastures.
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Almost all of the rich world is up against the zero lower bound on interest rates.
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If so, the previous calculation represents a lower bound on the odds Mr. Trump drops out.
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Powell said the Fed still has options open despite falling to its lower bound on rates.
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RNC rules stipulate that most of the delegates are bound on the first ballot of the convention.
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Mr. Holtz-Eakin said that he regarded 0.5 percent as an upper bound on the potential benefits.
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Many mathematicians wondered, however, whether the true bound on cap set size might be much smaller than that.
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These delegates will be bound on the first ballot -- but free to support whomever they like after that.
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So this is a theoretical upper bound on what Trump can accomplish with his attack on Obama's rules.
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Sherri Papini, 34, was found bound on the side of the road outside of Sacramento at 4:30 a.m.
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The remaining 54 delegates are chosen from Pennsylvania's 18 congressional districts — but they're not bound on the first vote.
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The remaining 54 delegates were chosen from Pennsylvania's 18 congressional districts — but they're not bound on the first vote.
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However, the party may well have approached or surpassed a yet-unseen upper bound on the value of fundraising.
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Though parliamentary rules could change ahead of the convention, most delegates would only be bound on the first ballot.
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When China joined the WTO all those years ago, it appeared bound on a course of market-oriented reform.
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Unlike balloting for the presidential nominee, however, delegates are not bound on all ballots for the vice presidential nomination.
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Private spending was depressed; monetary policy was ineffective because we were at the zero lower bound on interest rates.
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On Monday, the actress shared that she was "Rio bound" on Twitter, but she didn't reveal why she was going.
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Kardashian West was bound on that terrifying night and has since greatly reduced her social media presence and public outings.
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Papini was found bound on the side of the road in a tiny town near Sacramento at 4:30 a.m.
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So they're bound on the first ballot but actually there to support Cruz or Kasich or some other unicorn candidate.
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While more than 90 percent are bound on the first vote, it drops to under 50 percent on the second.
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So there tends to be a zero lower bound on wage changes, except in the face of very high unemployment.
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"These results put an upper bound on the number of civilizations transmitting lasers at us while we were observing," said Tellis.
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Typically public health researchers have used 33,000 as the upper bound on the number of deaths caused by flu each year.
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Ryan seems hell bound on destroying the GOP and working against the American people…It's time for Speaker Ryan to resign.
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If all of them approve of Mr. Trump, the resulting estimate would be the upper bound on his partisan approval rating.
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So, the climate sensitivity numbers reported in this paper should be regarded as an upper bound on possible 'Earth System' climate sensitivity.
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They're also currently investigating why the upper bound on working memory hovers around four or five items, and not some other number.
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Given the NLP and basic machine learning methodology of the paper, these numbers should be perceived as a lower bound on disclosures.
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And monetary policymakers are not pressed up against the lower bound on interest rates, at which low inflation becomes a greater threat.
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RNC General Counsel John Ryder presented committee members with a "legal opinion" on why the delegates should be bound on the first ballot.
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Trading across U.S. government bond maturities was range-bound on Wednesday, with yields little changed in spite of gains in the equity market.
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Until the Great Recession, most economists believed that this constraint, like the zero lower bound on interest rates, wasn't that important in practice.
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Revenue Churn matters because as growth slows the impact of churn escalates and provides an upper bound on how big a company can become.
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Johnston later mentioned the lower bound on a couple of websites, but "I don't think anyone really gave it any particular heed," Houston said.
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Those few Republican "moderates" — assuming anything by that name still exists — will have enormous power to set an upper bound on the effort's ambitions.
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Reyes' body was found in a red suitcase, with her hands and feet bound, on the side of the road in Greenwich on Feb. 5.
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In less than an hour, an anonymous person offered an answer — not a complete solution, but a lower bound on the number of episodes required.
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But in a plot twist last month, the Australian science fiction novelist Greg Egan proved a new upper bound on the number of episodes required.
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Within a day or two, he had come up with a new upper bound on the length of the shortest superpermutation for n symbols: n!
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Rules vary state by state, but most delegates who are bound on the first ballot by how their states voted are free in later balloting.
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So it is the presence of the lower bound on policy rates together with a debt overhang that has the potential to create persistently weak recoveries.
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There's still room to improve the bound on cap sets, but in the near term, at least, any further progress is likely to be incremental, Gowers said.
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There are no error bars on the OECD numbers, and there is no attempt to place a lower bound on the size of the global counterfeiting market.
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"The BOJ provides the strongest signal to date that the previously assumed zero lower bound on rates is no longer valid," Deutsche Bank strategist George Saravelos said.
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The effective lower bound on interest rates is a much bigger threat than we realized, and the problem of downward wage rigidity is a bigger deal too.
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The city was bound on this side by a canal, and Bobby's peregrinations tended to bring him, as now, into intermittent contact with this body of water.
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Proofs of HD-PoS may be possible by assuming a bound on the pairwise euclidean distance of the weight vectors or the maximum difference between any two prices.
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The euro also eased back a touch to $1.2346, while the dollar remained tightly bound on the yen at 107.41 yen , still short of recent peaks at 107.78.
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Thus the other study provides a lower bound on expected emissions and warming, and this is indeed lower than the likely range we find, as we would expect.
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Trading across U.S. government bond maturities was range-bound on Wednesday, with yields little changed in spite of gains in the equity market in the last few sessions.
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Many delegates are bound on the first ballot to the winner of their state's primary but are released for following ballots to back the candidate of their choosing.
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Some big changes are afoot for Mobike, the Chinese bike-sharing company that was acquired by IPO-bound on-demand service startup Meituan-Dianping for $2.7 billion last year.
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And I need to rise at four in the morning, looking completely put together, in my elegant workout gear, and my perfect ponytail, bound on down to the bike.
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Yet mathematicians can still try to figure out an upper bound on how big a cap set can be—a number of cards guaranteed to hold at least one set.
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In contrast, as Mr Spieth well knows from his notorious quadruple bogey at Augusta National last year, there is no upper bound on how much damage errant shots can wreak.
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When so much of the world is close to the zero lower bound on interest rates, there are so many more ways for things to go wrong than to go right.
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Though the exact location of the lower bound on interest rates is uncertain, it exists somewhere because the public always has the option of holding cash at a zero nominal return.
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Second, some conservative deficit hawks would likely put an upper bound on the feeding frenzy, insisting on some limits to how much such a bill would add to the national debt.
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Squash is a young man's game; tournament draws are rife with dudes who bound on court, their earbuds leaking Imagine Dragons, eager to go far too fast for far too long.
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In this Monday, July 9, 2018, photo provided by the Northern Territory Department of Tourism and Culture, a large crocodile is bound on a trailer after it was captured near Katherine, Australia.
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"The vehicle went across the grassy area, and into the North Bound on ramp, sliding completely under this trailer and just about out the other side," the department explained in its Facebook post.
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The problem is that a lower bound on interest rates creates a sharp asymmetry in how the economy works: It's relatively easy for the Fed to cool an overheating economy by raising rates.
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Even if the Fed wanted to respect the zero lower bound on the federal funds rate, it probably couldn't, since the yield curve would deeply invert as long-term interest rates turn more negative.
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Gold prices held range-bound on Friday as the dollar trod water after U.S. President Donald Trump sent mixed signals about the prospects for a trade deal with Beijing, while palladium notched a record high.
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And third, it allowed regulators to put in a reserve price — a lower bound on prices, beneath which allowance value could not fall, which served, when needed, as a kind of de facto carbon tax.
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More radically, central banks could give newly printed money directly to households; they could raise the inflation target to boost inflation expectations; or they could abolish physical cash to remove any lower bound on interest rates.
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Linking fiscal policy to inflation, combined with continued BOJ debt purchases to keep yields low, would help overcome the limits posed by the zero lower bound on nominal interest rates, said Sims, a Princeton University economist.
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To avoid that necessity, Ben Bernanke, now a fellow at the Brookings Institution, proposed in 2017 that the Fed should temporarily adopt a level target when the economy runs into the zero lower bound on interest rates.
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A passing motorist discovered Papini bound on the side of a rural road near the tiny town of Yolo, about 25 miles northeast of Sacramento – and a two hour drive from the place she vanished, Bosenko said.
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Just as with interest rates (at least until recently), there is a zero lower bound on a candidate's poll numbers: no one can ever receive less than 553%, no matter how much they are pummeled on the airwaves.
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That gives us an upper bound on how likely all of the natural hazards in the world are to kill us, combined: They have to be unlikely enough that they haven't struck in any of the past 200,000 years.
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Lack of clarity over where a brewing trade spat between the U.S. and Europe is heading kept most major currencies, including the U.S. dollar, range-bound on Wednesday as Juncker traveled to Washington for trade-focused talks with Trump.
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"In order for central banks to overcome the zero lower bound on nominal interest rates, they would need to get rid of cash from society," he said in a speech at an meeting of academics in Nagoya, central Japan.
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There are more elaborate ways of experimentally searching for extra dimension that don't use light and a microscope but they all have in common that they can only give an upper bound on the length of a circular extra dimension.
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And I am confident that if the Fed errs and tips the economy into recession, the consequences will be very serious given that the zero (or perhaps slightly negative) lower bound on interest rates will not allow the normal countercyclical response.
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Previous approaches to getting an upper bound on cap set size used a technique called Fourier analysis, which views the collection of points in a cap set as a combination of waves and looks for the directions in which the collection oscillates.
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You are right to argue that it would be clever for central banks to adopt a temporary price-level target if inflation is too low, the lower bound on interest rates has been reached and a recession hits (Free exchange, October 2146st).
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They then built a polynomial that evaluates to zero on these completion cards, and figured out an ingeniously simple way to split the polynomial into pieces with smaller exponents, which led to a bound on the size of collections with no sets.
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Gold prices were range bound on Tuesday, as lack of concrete details about the interim U.S.-China trade deal kept investors from making firm bets, while palladium was just $2929.46 away from surpassing key $2,000 per ounce level for the first time.
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The approved route would cut a right angle through his property, which is already bound on two sides by roads, blocking the area where he had been planning to build a new structure; the pipeline would also sit just a few feet from his home.
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Given the decline in Republican identification since last November, they find, "the lower bound on Trump's partisan approval rate is much lower" than partisan approval at a comparable point in the Obama presidency and is lower than it was even during Mr. Obama's second term.
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"Low interest rates may eventually take their toll: high-yielding assets will either mature or be prepaid, while at the same time any decrease in interest expenses is limited by the zero lower bound on deposits," Nouy said in an interview with the Eurofi Newsletter on Tuesday.
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"We have learned from the experience in Japan that it is possible to get caught in a vicious cycle of declining inflation expectations, falling inflation and a binding lower bound on nominal interest rates from which it is difficult to escape," ECB Vice President Luis de Guindos said on Thursday.
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We are going to be close to the zero lower bound (on interest rates) forever, a fact which gives central banks less room to boost the economy through traditional rate cuts, but also gives more room for government to borrow, said Julia Coronado, a former Fed staffer and founder of Macropolicy Perspectives consultants.
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Yes, Logan's fate in episode 10 was left undefined — William sends his future brother-in-law off into the sunset, naked and bound on top of a horse — but since Logan was last seen alive onscreen and the fact that William explained his business plans to him, we have to imagine Logan makes it out of Westworld alive.
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This means we can completely specify a symmetry of the square by some arrangement of the four letters A, B, C and D. This is remarkable in and of itself, but it also immediately implies an upper bound on the number of symmetries of the square: There are no more symmetries of the square than there are arrangements of those four letters.
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Since the invention, in 105 CE, of the codex, which Borsuk defines in her handy glossary as "a block of pages bound on one side between covers," the bound book has grown beyond its physical form into a metaphor; we call a new start "turning over a new leaf" (an early reference to book pages) and we read people like open books.
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After holding meetings with Secretary of State Mike PompeoMichael (Mike) Richard PompeoCotton warns China: Crackdown on Hong Kong would be 'grave miscalculation' Pompeo expresses concern over North Korea missile tests Pompeo acknowledges 'places where ISIS is more powerful today' MORE, special representative Stephen Biegun and President Donald TrumpDonald John TrumpFacebook releases audit on conservative bias claims Harry Reid: 'Decriminalizing border crossings is not something that should be at the top of the list' Recessions happen when presidents overlook key problems MORE, the delegation quietly flew out of Dulles, Beijing-bound, on Jan. 19.
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Huxley also improved the known bound on the Dirichlet divisor problem.
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Roughly speaking, differentiability puts a bound on how fast the curve can turn.
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Additionally, Lott showed that if a Riemannian manifold with smooth density arises as a collapsed limit of Riemannian manifolds with an uniform upper bound on diameter and sectional curvature and a uniform lower bound on Ricci curvature, then the lower bound on Ricci curvature is preserved in the limit as a lower bound on Bakry-Émery's Ricci curvature. In this sense, the Bakry-Émery Ricci tensor is shown to be natural in the context of Riemannian convergence theory. In 2002 and 2003, Grigori Perelman posted two papers to the arXiv which claimed to provide a proof for William Thurston's geometrization conjecture, using Richard Hamilton's theory of Ricci flow.Perelman, Grisha.
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However, free energy is also an upper bound on the self-information of outcomes, where the long-term average of surprise is entropy. This means that if a system acts to minimise free energy, it will implicitly place an upper bound on the entropy of the outcomes – or sensory states – it samples.
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Furthermore, if an atom is false in the well-founded model of a program then it does not belong to any of its stable models. Thus the well- founded model of a logic program provides a lower bound on the intersection of its stable models and an upper bound on their union.
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Therefore, the same superlogarithmic dependence on d holds for the lower bound on the equilateral dimension of d-dimensional space.
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Thus, the diameter provides a lower bound on the number of steps this method requires. The Hirsch conjecture, now disproved, suggested a strong bound on how large the diameter could be. Weaker (quasi-polynomial) upper bounds on the diameter are known, as well as proofs of the Hirsch conjecture for special classes of polytope.
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In this version of the problem, it is possible to construct graphs with a non-constant number of linear-sized induced matchings, and this result leads to nearly-tight bounds on the approximation ratio of streaming matching algorithms. The subquadratic upper bound on the Ruzsa–Szemerédi problem was also used to provide an o(3^n) bound on the size of cap sets, before stronger bounds of the form c^n for c<3 were proven for this problem. It also provides the best known upper bound on tripod packing.
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Standard results connect the size of a number and its absolute value, and the combined estimates imply the claimed bound on .
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A bounded wildcard is one with either an upper or a lower inheritance constraint. The bounds can be both class and interface types. Upper bounds are expressed using the extends keyword and lower bounds using the super keyword. An upper bound on a wildcard must be a subtype of the upper bound on the type parameter it is assigned.
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A theoretical upper bound on the speed-up of a single program as a result of parallelization is given by Amdahl's law.
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This allows establishing a lower bound on what other hosts know, and is useful in applications such as checkpointing and garbage collection.
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The karmas are literally bound on account of the stickiness of the soul due to existence of various passions or mental dispositions.
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Everything is getting pot-bound on our patio because he's threatened to dig up my 'useless' flowers if I put them in.
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This limit becomes an upper bound on the number of actors, and with the 1.5 Sun-based JRE the limit was about 6,000.
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In mathematics, the Mestre bound is a bound on the analytic rank of an elliptic curve in terms of its conductor, introduced by .
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923 Recent work (after 2008) includes a lower bound on the inelastic rms cross-section,A.Martin, S.M. Roy, « A lower bound on the inelastic cross-section for pion-pion scattering », Phys. Rev. D, 96 ( 2017), p. 114014 the sign of the real part of the forward scattering amplitudA. Martin, T.T.Wu, « Positivity of the real part of the forward scattering amplitude », Phys.
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Voronoi Treemaps. \- based on Voronoi diagram calculations. The algorithm is iterative and does not give any upper bound on the aspect ratio. Jigsaw Treemaps.
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These bounds are frequently shown using the VC dimension. Of particular prominence is the generalization error bound on boosting algorithms and support vector machines.
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Typically, some sort of line code, such as 8b/10b encoding, is used to put a hard upper bound on the maximum time between transitions.
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It is natural to refer to this as a duality property of extremal length, and a similar duality property occurs in the context of the next subsection. Observe that obtaining a lower bound on EL(\Gamma) is generally easier than obtaining an upper bound, since the lower bound involves choosing a reasonably good \rho and estimating L_\rho(\Gamma)^2/A(\rho), while the upper bound involves proving a statement about all possible \rho. For this reason, duality is often useful when it can be established: when we know that EL(\Gamma)\,EL(\Gamma\,')=1, a lower bound on EL(\Gamma\,') translates to an upper bound on EL(\Gamma).
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Recent data suggest the hydrated sulfenic acid to be the reactive species forming directly from the mono- protonated benzimidazole bound on the surface of the pump.
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Bound on the Wheel is a 1915 American short silent drama film directed by Joe De Grasse and featuring Lon Chaney. The film is now presumed lost.
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In China (only areas using Traditional Chinese), Japan, and Taiwan, literary books are written top-to- bottom, right-to-left, and thus are bound on the right, while text books are written left-to-right, top-to-bottom, and thus are bound on the left. In mainland China the direction of writing and binding for all books was changed to be like left to right languages in the mid-20th century.
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The equilibrium temperature is neither an upper nor lower bound on actual temperatures on a planet. There are several reasons why measured temperatures deviate from predicted equilibrium temperatures.
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In analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of prime numbers in arithmetic progression.
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Her Hawaiian stop was only a brief one for, after 14 months continuous duty outside the continental United States, William P. Biddle was San Francisco bound on 21 March.
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However, recent observations increasing the lower bound on the number of galaxies suggest UV absorption by hydrogen and reemission in near-IR (not visible) wavelengths also plays a role.
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Meshulam's game is a game played on a graph G, that can be used to calculate a lower bound on the homological connectivity of the independence complex of G.
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In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.
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The graphs with any finite bound on the Hadwiger number are sparse, and have small chromatic number. Determining the Hadwiger number of a graph is NP-hard but fixed-parameter tractable.
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In mathematics, the Remez inequality, discovered by the Soviet mathematician Evgeny Yakovlevich Remez , gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev polynomials.
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Since the inclination of the orbit to the line-of-sight is unknown, only a lower bound on the planet's mass can be determined. It has at least 2.3 times Jupiter's mass.
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In potential theory, a branch of mathematics, Cartan's lemma, named after Henri Cartan, is a bound on the measure and complexity of the set on which a logarithmic Newtonian potential is small.
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Faisalabad is bound on the north by Chiniot and Sheikhupura, on the east by Sheikhupura and Sahiwal, on the south by Sahiwal and Toba Tek Singh and on the west by Jhang.
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For some curves there is a smallest number L that is an upper bound on the length of any polygonal approximation. These curves are called and the number L is defined as the .
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A first important result is Gauss's inequality. Gauss's inequality gives an upper bound on the probability that a value lies more than any given distance from its mode. This inequality depends on unimodality.
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Old Fort Park and Golf Course is a 50-acre park and public golf course located in Murfreesboro, Tennessee. Entrance to Old Fort Park. The park grounds include the Civil War era Fortress Rosecrans and two trailheads to the City's Greenway system. The park is bound on two sides by the West Fork of the Stones River and is bound on the east by Lytle Creek, with a small spring fed tributary to the Creek, Springs Branch, bisecting the public park.
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At a more fundamental level, the above equation can be derived from the Machine Repairman queueing model: > Theorem (Gunther 2008): The universal scalability law is equivalent to the > synchronous queueing bound on throughput in a modified Machine Repairman > with state-dependent service times. The following corollary (Gunther 2008 with \beta = 0) corresponds to Amdahl's law: > Theorem (Gunther 2002): Amdahl's law for parallel speedup is equivalent to > the synchronous queueing bound on throughput in a Machine Repairman model of > a multiprocessor.
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"God's Number is 20". Cube20.org Thus 20 is a sharp upper bound on the length of optimal solutions. Mathematician David Singmaster had "rashly conjectured" this number to be 20 in 1980.Singmaster, p.
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This section shows how the backpressure algorithm arises as a natural consequence of greedily minimizing a bound on the change in the sum of squares of queue backlogs from one slot to the next.
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In complex analysis, a field within mathematics, Bloch's theorem gives a lower bound on the size of a disc in which an inverse to a holomorphic function exists. It is named after André Bloch.
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Introduction to Algorithms (Cormen, Leiserson, Rivest, and Stein) 2001, Chapter 2 "Getting Started".In Best-case complexity, it gives the lower bound on the running time of the algorithm of any instances of input.
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In mathematical analysis, the Young's inequality for integral operators, is a bound on the L^p\to L^q operator norm of an integral operator in terms of L^r norms of the kernel itself.
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In cosmological inflation, within the slow-roll paradigm, the Lyth argument places a theoretical upper bound on the amount of gravitational waves produced during inflation, given the amount of departure from homogeneity of the CMB.
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Despite claims that the star has a magnetic field (Butkovskaya & Plachinda [2007]), this didn't hold up under further observation. Neiner et al. (2014) put an upper bound on a dipolar magnetic field strength of about .
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This article introduced the notion of 'stable estimation', and was the first to note that a p-value of 0.05 in the Normal model corresponded to a lower bound on the Bayes Factor of 0.26.
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Extensive searches for axigluons at CERN and Fermilab have placed a lower bound on the axigluon mass of about . Axigluons may be discovered when collisions are studied with higher energy at the Large Hadron Collider.
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In incidence geometry, the De Bruijn–Erdős theorem, originally published by , states a lower bound on the number of lines determined by n points in a projective plane. By duality, this is also a bound on the number of intersection points determined by a configuration of lines. Although the proof given by De Bruijn and Erdős is combinatorial, De Bruijn and Erdős noted in their paper that the analogous (Euclidean) result is a consequence of the Sylvester–Gallai theorem, by an induction on the number of points.
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Construction showing the tight bound for the ring lemma In the geometry of circle packings in the Euclidean plane, the ring lemma gives a lower bound on the sizes of adjacent circles in a circle packing.
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In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code C with block length n, size M and minimum distance d.
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They get a message to the monastery. Kade decides to mass distribute the Nexus 5 instructions. The ERD capture Kade placing him bound on a helicopter. Sam forces her way onto the helicopter, along with Feng.
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The Koch curve. The graph of xsin(1/x). As mentioned above, some curves are non-rectifiable. That is, there is no upper bound on the lengths of polygonal approximations; the length can be made arbitrarily large.
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In the mathematics of coding theory, the Plotkin bound, named after Morris Plotkin, is a limit (or bound) on the maximum possible number of codewords in binary codes of given length n and given minimum distance d.
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MTD(f) derives its efficiency by only performing zero-window alpha-beta searches, with a "good" bound (variable beta). In NegaScout, the search is called with a wide search window, as in AlphaBeta(root, −INFINITY, +INFINITY, depth), so the return value lies between the value of alpha and beta in one call. In MTD(f), AlphaBeta fails high or low, returning a lower bound or an upper bound on the minimax value, respectively. Zero-window calls cause more cutoffs, but return less information - only a bound on the minimax value.
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Concurrently, a significant intermediate conclusion can be drawn from the research thus far. Multisensory stimuli that are bound into a single percept, are also bound on the same receptive fields of multisensory neurons in the SC and cortex.
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The articles by Gil Kalai with a proof of a subexponential upper bound on the diameter of a polyhedron and by Samuel Ferguson on the Kepler conjecture, both published in Discrete & Computational geometry, earned their author the Fulkerson Prize.
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While working for the University of New Hampshire as a lecturer, Zhang submitted an article to the Annals of Mathematics in 2013 which established the first finite bound on gaps between prime numbers, which led to a 2014 MacArthur award.
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The Yilgarn Craton is bound on all sides by younger terranes of various ages, but predominantly of Proterozoic age. The boundaries between the various flanking terranes provide considerable evidence of the post-Archaean events which have involved the Yilgarn Craton.
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On 6 October she was at Kidderpore and on 4 November Calcutta. Homeward bound, on 10 December she was at Saugor. She was Vizagapatam on 17 January 1813 and Masulipatam on 27 January. She was again at Madras on 3 February.
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Sharpsville is located at (40.378949, -86.086632). According to the 2010 census, Sharpsville has a total area of , all land. Sharpsville is bound on the south by Broad Creek a stream that connects Mud Creek going East and Barr Ditch going West.
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Letters, 10, (1963), p. 460 Finally, in 1966 he succeeded in demonstrating the validity of the Froissart bound using local field theory, without postulating the Mandelstam representation.A.Martin, « Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity: », Nuovo Cimento, 42, (1966), p. 930 In the meantime, in 1964, he obtains an absolute bound on the pion-pion scattering amplitude,An absolute bound on the pion pion scattering amplitude, Stanford Preprint ITP-1 (1964) non publié this bound was considerably improved later.B. Bonnier, C Lopez et G.Mennessier, « Improved absolute bounds on the π0π0 amplitude », Physics Letters B, 60, (1), 22 December 1975, p.
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For a polynomial-time list-decoding algorithm to exist, we need the combinatorial guarantee that any Hamming ball of radius pn around a received word r (where p is the fraction of errors in terms of the block length n) has a small number of codewords. This is because the list size itself is clearly a lower bound on the running time of the algorithm. Hence, we require the list size to be a polynomial in the block length n of the code. A combinatorial consequence of this requirement is that it imposes an upper bound on the rate of a code.
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Distance bounding protocols are cryptographic protocols that enable a verifier V to establish an upper bound on the physical distance to a prover P. They are based on timing the delay between sending out challenge bits and receiving back the corresponding response bits. The delay time for responses enables V to compute an upper-bound on the distance, as the round trip delay time divided into twice the speed of light. The computation is based on the fact that electro-magnetic waves travel nearly at the speed of light, but cannot travel faster. Distance bounding protocols can have different applications.
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Three Sophie Calle books with different titling orientations: ascending (left), descending (middle) and upright (right) In languages written from left to right, such as English, books are bound on the left side of the cover; looking from on top, the pages increase counter-clockwise. In right-to-left languages, books are bound on the right. In both cases, this is so the end of a page coincides with where it is turned. Many translations of Japanese comic books retain the binding on the right, which allows the art, laid out to be read right-to-left, to be published without mirror-imaging it.
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Hoods of two different shapes are specified for graduates of the University. Bachelors, and holders of foundation degrees and advanced first degrees (MMath, etc.) wear a hood of black corded rayon in simple shape (actually Burgon shape, denoted [s2] in the Groves system) fully lined and bound on the cowl and neckband with taffeta of the appropriate faculty colour. Holders of graduate degrees wear a hood of a modified Aberdeen shape ([a1] in Groves' system) which the regulations refer to as "special shape". This is fully lined and bound on the cowl and cape with taffeta of the relevant faculty colour.
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The Yilgarn Craton is bound on the western side by the Perth Basin, of Jurassic age, and is separated from this basin by the Darling Fault. The Perth Basin is considered to be a rift fill basin formed on a passive margin.
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Observations of gravitational waves have constrained the Compton wavelength of the graviton to be λg > , which can be interpreted as a bound on the graviton mass mg < . The most recent observations pose a new constraint on λg > for mg < and λg > for mg < .
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The Plaza is bound on the south by Route 3 and Paterson Plank Road, and is accessible via the 78 and 85 local routes, and the 190 and 320 routes, which travel to and from the Port Authority Bus Terminal in Midtown Manhattan.
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In set theory, a nice name is used in forcing to impose an upper bound on the number of subsets in the generic model. It is used in the context of forcing to prove independence results in set theory such as Easton's theorem.
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Xiaonanmen () is a station on Line 9 of the Shanghai Metro. As part of the line's phase 2 easterly extension, it began operation on December 31, 2009. It is the first station in Puxi when travelling southwest-bound on Line 9 from Pudong.
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Hence an interval predictor model can be seen as a guaranteed bound on quantile regression. Interval predictor models can also be seen as a way to prescribe the support of random predictor models, of which a Gaussian process is a specific case .
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This gives a lower bound on the azimuthal velocity of rotation along the star's equator. Tau Puppis is radiating energy from its outer envelope at an effective temperature of around 4,500, giving it the orange hue of a cool, K-type star.
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In the mathematics of coding theory, the Griesmer bound, named after James Hugo Griesmer, is a bound on the length of linear binary codes of dimension k and minimum distance d. There is also a very similar version for non-binary codes.
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It is found by Xia, Zhou and Giannakis that difference sets can be used to construct a complex vector codebook that achieves the difficult Welch bound on maximum cross correlation amplitude. The so- constructed codebook also forms the so-called Grassmannian manifold.
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As of 9 December 2018, the stop is serviced by 4 trains from the Transilien Line R, only Fontainebleau-bound, on Saturdays, Sundays and public holidays (trains leaving at 8:16, 9:38m 10:16, 11:16 from Paris-Gare-de-Lyon).
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Limboor is bound on its side by Lendi river, is one of the important tributaries of the Manjira River. Godavari River has left and right tributaries, Manjira River is one of right side tributaries. It enters Telangana at Kandhakurthi in Nizamabad district.
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Statistics by Govt. of Rajasthan It has an average elevation of 271 metres (889 ft). The district is bound on the north and north west by Sawai Madhopur, Tonk and Bundi districts. The Chambal River separates these districts from Kota district, forming the natural boundary.
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She was homeward bound on 3 November, and arrived at Jacksonville, Florida, on 14 December. Here she was decommissioned and placed in reserve on 19 June 1946. She was struck from the Navy List on 1 August 1965, sold on 29 December 1966 and scrapped.
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Hass is known for proving the equal-volume special case of the double bubble conjecture, for proving that the unknotting problem is in NP, and for giving an exponential bound on the number of Reidemeister moves needed to reduce the unknot to a circle.
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This result is best possible, and significantly improved a previous bound on the same problem by Tatyana Pavlovna Ehrenfest. Despite the prior work of Ehrenfest and Johannes van der Corput on the same problem, Roth was known for boasting that this result "started a subject".
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The expected performance is a result of the random sampling step. The effectiveness of the random sampling step is described by the following lemma which places a bound on the number of F-light edges in G thereby restricting the size of the second subproblem.
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The Campos Basin is bound on the south by the Cabo Frio High, separating the basin from the Santos Basin and on the north by the Vitória High, forming the boundary with the Espírito Santo Basin. Campos Basin contains the Paraiba do Sul River delta.
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The Armenian language dictated which side manuscripts were bound. The language is read from left to right, so the manuscripts were bound on the left.Merian, Sylvie Louise Alice (1993). The Structure of Armenian Bookbinding and its Relation to Near Eastern Bookmaking Traditions (Doctoral Dissertation).
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Lawrence seaway. Ship traffic heading up-bound on the St. Marys River toward Lake Superior passes through the Munuscong Channel on the island's east side, while down-bound traffic to Lake Huron passes through the deepened West Neebish Channel on the island's west side.
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In contrast to sandwich compounds that have parallel cyclopentadienyl rings bound on opposite sides of the metal atom, such as ferrocene, zirconocene and other group 4 metallocenes are bent. Without stabilizing ligands, the Cp2ZrII fragment is unstable and dimerizes to form a fulvalene complex.
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In algebraic geometry, determinantal varieties are spaces of matrices with a given upper bound on their ranks. Their significance comes from the fact that many examples in algebraic geometry are of this form, such as the Segre embedding of a product of two projective spaces.
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In a stable marriage instance chosen to maximize the number of different stable matchings, this number can be at least 2^{n-1}, and us also upper-bounded by an exponential function of (significantly smaller than the naive factorial bound on the number of matchings).
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In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The inequality is named after the Russian mathematician Andrey Kolmogorov.
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Fuller believed that this would lead to ever-increasing standards of living and ever-growing population despite finite resources. Fuller uses Henry Ford's assembly line as an example of how ephemeralization can lead to better products at lower cost with no upper bound on productivity.
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In cryptography, key size or key length is the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper- bound on an algorithm's security (i.e. a logarithmic measure of the fastest known attack against an algorithm), since the security of all algorithms can be violated by brute-force attacks. Ideally, the lower-bound on an algorithm's security is by design equal to the key length (that is, the security is determined entirely by the keylength, or in other words, the algorithm's design doesn't detract from the degree of security inherent in the key length).
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In the example above, the algorithm was guided by the conditional expectation of a random variable F. In some cases, instead of an exact conditional expectation, an upper bound (or sometimes a lower bound) on some conditional expectation is used instead. This is called a pessimistic estimator.
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In probability theory, Bennett's inequality provides an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount. Bennett's inequality was proved by George Bennett of the University of New South Wales in 1962.
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Escambia paid calls to Okinawa and Wakayama Wan to fuel ships at anchor there until leaving Tokyo astern, homeward bound, on 4 November 1945. She was decommissioned on 20 February 1946, struck from the Navy List, and transferred to the Maritime Commission for disposal in June.
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The source coding theorem for symbol codes places an upper and a lower bound on the minimal possible expected length of codewords as a function of the entropy of the input word (which is viewed as a random variable) and of the size of the target alphabet.
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It is a variant of an earlier formula of Smith and Tutte, and was published by de Bruijn and Ehrenfest in the same paper as their work on de Bruijn sequences. Ehrenfest is also known for her proof of a lower bound on low-discrepancy sequences.
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Cadamosto (Kerr, p.220; Ital: p.110; Port: p.27) Cadamosto describes the Wolof (Gilofi) empire, which he notes was bound on the east by the Fula Tekrur/Toucouleur (Tuchusor) and to the south by the Mandinka states of the Gambia River (Gambra)Cadamosto (Kerr, p.
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The bound on the total number of cliques follows easily from the bounds on triangles and K4 subgraphs, and is also stated explicitly by , who provides an Apollonian network as an example showing that this bound is tight. For generalizations of these bounds to nonplanar surfaces, see .
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The Brun sieve establishes an upper bound on the density of primes having the form p=n^2+1: there are O(\sqrt x/\log x) such primes up to x. It then follows that almost all numbers of the form n^2+1 are composite.
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It is rotating rapidly, with a projected rotational velocity of 125 km/s giving a lower bound on the azimuthal velocity along the star's equator. The effective temperature of the photosphere is nearly 10,000 K and the star has expanded to nearly five times the radius of the Sun.
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Princess Charlotte of Wales left the Downs on 8 June 1829 under the command of Captain Christopher Biden. She reached Kedgeree on 22 September. She left Saugor, homeward bound, on 6 February 1830 and reached St Helena on 10 June. She arrived at The Downs on 2 August.
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Death Ray was a British magazine devoted to science fiction and fantasy in all its forms, especially media-related topics and novels. It was published every two months, with the first issue going on sale in May 2007. Typical issues were 132 pages, perfect bound, on glossy paper.
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The Symmetric hypergraph theorem is a theorem in combinatorics that puts an upper bound on the chromatic number of a graph (or hypergraph in general). The original reference for this paper is unknown at the moment, and has been called folklore.R. Graham, B. Rothschild, J. Spencer. Ramsey Theory.
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Because the feasible space only shrinks as information is added, the objective value for the master function can be thought of as an upper bound on the objective function of the overall problem. Bender's Decomposition is applicable to problems with a largely block-diagonal structure, as shown below.
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If there exists a circulation, looking at the max-flow solution would give the answer as to how much goods have to be sent on a particular road for satisfying the demands. The problem can be extended by adding a lower bound on the flow on some edges.
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Ireland's fifth victim was a Maltese chef named Emanuel Spiteri, aged 41, whom he had met at the Coleherne pub. Spiteri was persuaded to be cuffed and bound on his bed. Once more, Ireland demanded his PIN but did not obtain it. He again used a noose to kill.
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A series of publications by Schmitt-Grohe, Jess Benhabib and Martin Uribe between 2001-2002 seek to address what they considered a gap in the current literature on stabilization policy. Citing that the current research on monetary policy regimes with interest rate feedback rules lacked in that they only considered local dynamics, meaning small fluctuations around the proposed equilibrium, and that they do not take into account the zero lower bound on nominal interest rates. These simplifications had thus far lead to a single, unique steady state equilibrium, near the targeted inflation rate. Schmitt-Grohe's research deviated mainly in its loosening of these local dynamics and its consideration of a zero lower bound on nominal interest rates.
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The weak duality theorem says that, for each feasible solution x of the primal and each feasible solution y of the dual: cTx ≤ bTy. In other words, the objective value in each feasible solution of the dual is an upper-bound on the objective value of the primal, and objective value in each feasible solution of the primal is a lower-bound on the objective value of the dual. This implies: > maxx cTx ≤ miny bTy In particular, if the primal is unbounded (from above) then the dual has no feasible solution, and if the dual is unbounded (from below) then the primal has no feasible solution. The weak duality theorem is relatively simple to prove.
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He is both a puzzle historian and a composer of puzzles, and many of his puzzles have been published in newspapers and magazines. In combinatorial number theory, Singmaster's conjecture states that there is an upper bound on the number of times a number other than 1 can appear in Pascal's triangle.
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Anao is east of the provincial capitol and nestling on the Tarlac-Nueva Ecija border. Located in the north-eastern part of Tarlac, it is bound on the north by San Manuel, in the east by Nampicuan, on the south by Ramos and on the west by Paniqui and Moncada.
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Amalu Bay in National park Service Area. National Park map of Tutuila Island. The National Park of American Samoa in Tutuila was established in 1988 for preserving its perfect terrestrial and marine environment. It covers an area of and is bound on the north coast between Fagasa and Afono villages.
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Ari Lennox began uploading her music on the internet in 2009. She released her debut mixtape, Five Finger Discount, and debut EP, Ariography, in 2013. In 2014, she independently released the single "Bound". On July 21, 2015, she was featured on Omen's album Elephant Eyes on the track "Sweat it Out".
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The Macken, 2017, 4. site is located to the northern end of Elizabeth Bay Road, Elizabeth Bay. It is a wedge-shaped site, occupying a prominent position on Macleay Point sloping down towards Elizabeth Bay. The site is bound on the south by a high stonewall to Elizabeth Bay Road.
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This allows Dijkstra's algorithm to be performed in the same time bound on graphs with edges and vertices, and leads to a linear time algorithm for minimum spanning trees, with the assumption for both problems that the edge weights of the input graph are machine integers in the transdichotomous model.
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Non-adaptive group-testing algorithms tend to assume that the number of defectives, or at least a good upper bound on them, is known. This quantity is denoted d in this section. If no bounds are known, there are non- adaptive algorithms with low query complexity that can help estimate d.
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In the simplest case this leads to least squares approximation. Approximation theory studies how to find the best approximation to a given function by another function from some predetermined class, and how good this approximation is. This clearly yields a bound on how well the interpolant can approximate the unknown function.
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P is a discretised circle (a Bresenham circle), so interpolation is used for intermediate diameters to give a more isotropic response. Since any computation gives an upper bound on the \min, the horizontal and vertical directions are checked first to see if it is worth proceeding with the complete computation of c.
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Many attempts were made to extend this result to higher dimensions, d>1, The Lieb–Robinson bound was utilized by Hastings and by Nachtergaele-Sims in a proof of the Lieb–Schultz–Mattis Theorem for higher-dimensional cases. The following bound on the gap was obtained: :\gamma_L\leq c\log (L)/L. .
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This means that any requirement on the filter's locality also implies a bound on its frequency function's width. Consequently, it may not be possible to simultaneously meet requirements on the locality of the filter's impulse response function as well as on its frequency function. This is a typical example of contradicting requirements.
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If this is true, it would be tight: in his 1964 paper, Černý exhibited a class of automata (indexed by the number n of states) for which the shortest reset words have this length. In 2011 Trahtman published a proofA.N. Trahtman. Modifying the Upper Bound on the Length of Minimal Synchronizing Word. Lect.
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Counterexamples to this conjecture were later discovered, but the possibility that a finite bound on toughness might imply Hamiltonicity remains an important open problem in graph theory. A simpler proof both of Fleischner's theorem, and of its extensions by , was given by ,; . and another simplified proof of the theorem was given by .; .
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The presence of tidal bundles depends on the presence of spring and neap tides, which can only occur in three-body gravitational systems (the Earth, the Sun and the Moon). Therefore, the earliest time from which tidal bundles can be identified gives a conclusive lower bound on the age of the Moon.
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In 1898 Borsa, Romania, Darla leads a blindfolded Angelus to a young gypsy woman bound on the floor. With Darla watching, he morphs and bites her inner thigh. In the present day, Angel attempts to convince the gang member he saved to testify. At a club, Faith dances and parties with various men.
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Benzyl phthalate plasticizer and polyvinyl butyral binder have been shown to be helpful in preparing nanoparticle slurries. Once the tape casting process has been carried out, the characterization of the green ITO tapes showed that optimal transmission went up to about 75%, with a lower bound on the electrical resistance of 2 Ω·cm.
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This is a semi- numeric method which supposes that the number of equations is equal to the number of variables. This method is relatively old but it has been dramatically improved in the last decades. This method divides into three steps. First an upper bound on the number of solutions is computed.
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Atlas sailed from Portsmouth on 7 March 1829, bound for Bombay and China. She reached Bombay on 3 July and Singapore on 9 September; she arrived at Whampoa on 9 February 1830. Homeward bound, on 3 April Atlas encountered , which had been badly damaged in a gale. Atlas chaperoned Bridgewater to Madras.
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In probability theory, the Chung–Erdős inequality provides a lower bound on the probability that one out of many (possibly dependent) events occurs. The lower bound is expressed in terms of the probabilities for pairs of events. Formally, let A_1,\ldots,A_n be events. Assume that \Pr[A_i]>0 for some i.
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It remains open whether the exact clique-width, or a tighter approximation to it, can be calculated in fixed-parameter tractable time, whether it can be calculated in polynomial time for every fixed bound on the clique-width, or even whether the graphs of clique-width four can be recognized in polynomial time.
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The plain is bound on the north by the Himalayas, which feed its numerous rivers and are the source of the fertile alluvium deposited across the region by the two river systems. The southern edge of the plain is marked by the Chota Nagpur Plateau. On the west rises the Iranian Plateau.
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McDonalds Mill is an unincorporated community in the northeastern section of Montgomery County, Virginia. Located approximately 10 miles east of Blacksburg, Virginia along State Route 785, McDonalds Mill lies at the floor of the Catawba Valley and is bound on the south by Paris Mountain and to the north by Gallion Ridge.
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In the theory of optimal binary search trees, the interleave lower bound is a lower bound on the number of operations required by a binary search tree (BST) to execute a given sequence of accesses. Several variants of this lower bound have been proved. This article is based on one of the variants.
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The district is mountainous and limited by the Morskoy, Khamar-Daban, Ulan- Burgas and Golondin ranges. It is bound on the northeast by the shores of Lake Baikal and by the left bank of the Selenga River in the southwestern part. The Turka and Itantsa are other important rivers of the area.
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Between 22 May 1944 and 15 May 1945, Fowler made six voyages to escort convoys from New York, Norfolk, and Boston to ports in northern Africa, guarding men and supplies destined for the operations in Italy and southern France. The fifth such voyage, between 1 February and 16 March 1945, was marked by the presence of submarines both outward and homeward bound. On 17 February, west of Gibraltar, two of the merchantmen were torpedoed, but both were brought safely into Gibraltar, one after Fowler had stood by to screen while a tug came out to help. Two days out of Oran homeward bound on 28 February, Fowler picked up a sound contact, and made an urgent attack which brought debris to the surface.
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The cover is bound on green cloth, with a height of An edition with "fancy boards" sold for two shillings and sixpence,Pomo, pg. 19. and an edition with the plates mounted on cloth sold for an extra shilling.Hutton, pg. 23. A Dutch edition translated by Hugo Suringar Leeuwarden of Spectropia was published in 1866.
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The city, located on the Lower River Rouge which bisects the city, is bound on the north by Glenwood Road, the west by Hannan Road, the south by Van Born Road, and on the east by Merriman Road. According to the United States Census Bureau, the city has a total area of , all land.
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Mariner 10's ultraviolet observations have established an upper bound on the exospheric surface density at about 105 particles per cubic centimeter. This corresponds to a surface pressure of less than 10−14 bar (1 nPa).Domingue, 2007, pp. 162–163 The temperature of Mercury's exosphere depends on species as well as geographical location.
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Another kind of constraint, which appears in coding theory, especially in error correcting codes and signal processing (for example compressed sensing), consists in an upper bound on the number of variables which may be different from zero. In error correcting codes, this bound corresponds to the maximal number of errors that may be corrected simultaneously.
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The intuition behind the CDF-based approach is that bounds on the CDF of a distribution can be translated into bounds on statistical functionals of that distribution. Given an upper and lower bound on the CDF, the approach involves finding the CDFs within the bounds that maximize and minimize the statistical functional of interest.
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"If we continue using this interpretation of events, it may be very difficult for the U.S. to ever move off of the zero lower bound on nominal interest rates. This could be a looming disaster for the United States," he said."Inflation Targeting in the USA," speech by James Bullard on Feb. 6, 2012.
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The city is bound on the southwest by the Oyster River (the boundary between West Haven and Milford since colonial times), northwest by Orange, north by New Haven and northeast by the West River, which divides West Haven and New Haven. To the east is New Haven Harbor and to the south is Long Island Sound.
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The Fannes-Audenaert inequality is a mathematical bound on the difference between the von Neumann entropies of two density matrices as a function of their trace distance. It was proved by Koenraad M. R. Audenaert in 2007Koenraad M. R. Audenaert, "A sharp continuity estimate for the von Neumann entropy", J. Phys. A: Math. Theor. 40 8127 (2007).
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Typical results for globular clusters are that they may be as old as 12.7 billion years. This is in contrast to open clusters which are only tens of millions of years old. The ages of globular clusters place a bound on the age limit of the entire universe. This lower limit has been a significant constraint in cosmology.
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While (Hare, Hare) remains a Nash equilibrium, it is no longer risk dominant. Nonetheless many would call this game a stag hunt. 100px In addition to the pure strategy Nash equilibria there is one mixed strategy Nash equilibrium. This equilibrium depends on the payoffs, but the risk dominance condition places a bound on the mixed strategy Nash equilibrium.
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Where the desired pose is known a priori and the robot is moved from a given pose. The main aim of the paper is to determine the upper bound on the positioning error due to image noise using a convex- optimization technique. E. Malis and P. Rives. Robustness of image-based visual servoing with respect to depth distribution errors.
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Machine epsilon gives an upper bound on the relative error due to rounding in floating point arithmetic. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject of computational science. The quantity is also called macheps or unit roundoff, and it has the symbols Greek epsilon \epsilon or bold Roman u, respectively.
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The analysis of GW170104 yielded a new upper bound on the mass of gravitons, if gravitons are massive at all. The graviton's Compton wavelength is at least , or about 1.6 light-years, corresponding to a graviton mass of no more than . This Compton wavelength is about times greater than the gravitational wavelength of the GW170104 event.
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An individual with average consumption of $50,000 would be willing to pay $100 to eliminate fluctuations. This is still a very small amount compared to the implications of long run growth on income. One way to get an upper bound on the degree of risk aversion is to use the Ramsey model of intertemporal savings and consumption.
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It is spinning rapidly with a projected rotational velocity of about . This is a lower bound on the azimuthal velocity along the star's equator. The secondary component, Delta Aquilae B, is a smaller star with about 67% of the Sun's mass and an estimated 61% of the radius of the Sun. It may be a K-type star.
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Homeward bound, she was at Saugor, homeward bound, on 22 January 1833 and reached St Helena on 22 June. She was almost home when a gale drove her onshore on 1 September at Berck, near Boulogne-sur-Mer, with the loss of four of her 30 crew. She was so damaged she had to be abandoned.
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5702 (September 2009) pp. 1003–1010 that computes multiple independent Minimum Spanning Forests and then stitches them together. This enables parallel processing without splitting objects on tile borders. Instead of a fixed weight threshold, an initial connected-component labeling is used to estimate a lower bound on the threshold, which can reduce both over- and undersegmentation.
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The key step is to find a bound on the existential quantifier in a formula (∃x)A(x), producing a bounded existential formula (∃x
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According to the U.S. Census Bureau, the county has an area of , of which is land and (4.3%) is water. Mason County is bound on the south by the Sangamon River, and on the west by the Illinois River. These rivers join at the county's southwest tip. The soil covering much of Mason County is very sandy.
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An offer to contract must be addressed to a person, be sufficiently definite – that is, describe the goods, quantity, and price – and indicate an intention for the offeror to be bound on acceptance.Article 14. The CISG does not appear to recognise common law unilateral contractsSee, for example, Carlill v. Carbolic Smoke Ball Company (1892) 2 QB 484.
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Ennore Creek is a backwater located in Tiruvallur district, Tamil Nadu. The Ennore Creek is bound on the north by the Pulicat Lake and to the south by the Manali marshlands. The Arani River enters the creek's northern edge below Lake Pulicat. To the south, Kosasthalaiyar River and the surplus course of the Puzhal Lake enter the creek.
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The variable radial velocity of this system was announced in 1922 by W. W. Campbell. It is a single-lined spectroscopic binary system with an orbital period of and an eccentricity of 0.38. The value is , where a is the semimajor axis and i is the orbital inclination. This provides a lower bound on the true semimajor axis.
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Griffin et al. (1990) found an orbital period of and an eccentricity of 0.26. The primary has an "a sin i" value of , where a is the semimajor axis and i is the (unknown) orbital inclination. This value provides a lower bound on the actual semimajor axis, which is one half of the longest dimension of their elliptical orbit.
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The vertex-expansion properties of Johnson graphs, as well as the structure of the corresponding extremal sets of vertices of a given size, are not fully understood. However, an asymptotically tight lower-bound on expansion of large sets of vertices was recently obtained.. In general, determining the chromatic number of a Johnson graph is an open problem.
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When agents have cardinality constraints (i.e., for each category of items, there is an upper bound on the number of items each agent an get from this category), the envy- graph algorithm might fail. However, combining it with the round-robin protocol gives an algorithm that finds allocations that are both EF1 and satisfy the cardinality constraints.
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Scoliodon has an elongated, spindle-shaped body tapered at the ends, making it a very fast swimmer. The trunk and tail are laterally compressed, while the head region is dorsoventrally compressed. The entire body is covered by an exoskeleton of placoid scales. The mouth is located on the ventral side and is bound on both sides by jaws.
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Linguist Noam Chomsky, among many others, has argued that the lack of an upper bound on the number of grammatical sentences in a language, and the lack of an upper bound on grammatical sentence length (beyond practical constraints such as the time available to utter one), can be explained as the consequence of recursion in natural language. This can be understood in terms of a recursive definition of a syntactic category, such as a sentence. A sentence can have a structure in which what follows the verb is another sentence: Dorothy thinks witches are dangerous, in which the sentence witches are dangerous occurs in the larger one. So a sentence can be defined recursively (very roughly) as something with a structure that includes a noun phrase, a verb, and optionally another sentence.
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In combinatorial number theory, Singmaster's conjecture states that there is a finite upper bound on the number of times a number other than 1 can appear in Pascal's triangle. Paul Erdős suspected that the conjecture is true, but thought it would probably be very difficult to prove. The empirical evidence is consistent with the proposition that the smallest upper bound is 8\.
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The Perth Basin is bound on the north by the Gascoyne Complex,Cawood, P. A. and Tyler, I. M., 2004. Assembling and reactivating the Proterozoic Capricorn Orogen: lithotectonic elements, orogenies, and significance. Precambrian Research, 128, p. 201–218. Glengarry Basin and Yerrida Basin, which are all part of a middle Proterozoic mobile belt which leads east to the Musgrave Block.
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663 has been used to fix a bound on the date of its author.K. Kunjunni Raja (1980), Contribution of Kerala to Sanskrit Literature, p. 43 S. K. De, in History of Sanskrit Literature co-written with S. N. Dasgupta, mentions this poem in the section on poems with historical themes alongside the later Raghunāthābhyudaya of Rāmabhadrāmbā (which is on Raghunatha Nayaka).Dasgupta, p.
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The circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation also being required for the source and sink (i.e. there are no special nodes). In variants of the problem, there are multiple commodities flowing through the network, and a cost on the flow.
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Kodarma (also spelled as Koderma) is a city and a notified area in Koderma district in the Indian state of Jharkhand. The district is bound on the north by the Nawada district of Bihar, on the south by Hazaribagh district of Jharkhand, on the east by Giridih district of Jharkhand and on the west by the Gaya district of Bihar.
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Ingleside was bounded on the east by the shores of Lake Miccosukee and would have been bound on the west by Blake's mother's Blakely Plantation. Today, the land is County Road 59 (Veterans Memorial Drive). Ingleside's northern boundary would now be Cypress Landing Road and to the south it would have bounded by the streets of Leland Circle and Indigo Lane.
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In mathematics, the Berger-Kazdan comparison theorem is a result in Riemannian geometry that gives a lower bound on the volume of a Riemannian manifold and also gives a necessary and sufficient condition for the manifold to be isometric to the m-dimensional sphere with its usual "round" metric. The theorem is named after the mathematicians Marcel Berger and Jerry Kazdan.
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The torus with minimal Willmore energy, with major radius and minor radius 1 In differential geometry, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by Fernando Codá Marques and André Neves was announced in 2012 and published in 2014.
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Master, previously unaware of this arrangement to kill Blaster, is furious and vows to shut down the refinery and, by extension, Bartertown. Aunty has Blaster killed, Master imprisoned, and Max exiled. He is bound on a horse and sent off in a random direction through the wasteland. When his mount perishes in a sinkhole, Max frees himself and presses on.
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Corran is bound on the north by Killycluggin townland, on the west by Kilnavert and Derrycassan townlands, on the south by Toberlyan and Toberlyan Duffin townlands, and the east by Bellaheady townland in Kildallan Parish. Corran can be entered using the regional R205 road, several minor roads, rural and disused lanes, and the Cavan and Leitrim Railway. The townland covers 146 statute acres.
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In complexity theory, a time-constructible function is a function f from natural numbers to natural numbers with the property that f(n) can be constructed from n by a Turing machine in the time of order f(n). The purpose of such a definition is to exclude functions that do not provide an upper bound on the runtime of some Turing machine.
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160 and 168. and was motivated by the analysis of the simplex method in linear programming, as the diameter of a polytope provides a lower bound on the number of steps needed by the simplex method. The conjecture is now known to be false in general. The Hirsch conjecture was proven for d < 4 and for various special cases,E.g.
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Wait-freedom is the strongest non-blocking guarantee of progress, combining guaranteed system-wide throughput with starvation-freedom. An algorithm is wait-free if every operation has a bound on the number of steps the algorithm will take before the operation completes. Anthony Williams. "Safety: off: How not to shoot yourself in the foot with C++ atomics". 2015\. p. 20.
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Bolinas sits at an elevation of above sea level. It is bound on the northeast by Bolinas Lagoon and Kent Island and on the south by Bolinas Bay and Duxbury Point. According to the United States Census Bureau, the CDP has a total area of , all of it land. The GNIS has cited archaic alternate town-names, including "Ballenas", "Baulenas", "Baulings", and "Bawlines".
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Suppose the primal LP is "Maximize cTx subject to Ax ≤ b, x ≥ 0". Suppose we create a linear combination of the constraints, with positive coefficients, such that the coefficients of x in the constraints are at least cT. This linear combination gives us an upper bound on the objective. The variables y of the dual LP are the coefficients of this linear combination.
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Zirconocene is a hypothetical compound with 14 valence electrons, which has not been observed or isolated. It is an organometallic compound consisting of two cyclopentadienyl rings bound on a central zirconium atom. A crucial question in research is what kind of ligands can be used to stabilize the Cp2ZrII metallocene fragment to make it available for further reactions in organic synthesis.
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Due to the dimension bound on spaces of modular forms, the minimum norm of a nonzero vector of an even unimodular lattice is no greater than ⎣n/24⎦ + 1. An even unimodular lattice that achieves this bound is called extremal. Extremal even unimodular lattices are known in relevant dimensions up to 80, and their non-existence has been proven for dimensions above 163,264.
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Whether this formula produces an infinite quantity of Carmichael numbers is an open question (though it is implied by Dickson's conjecture). Paul Erdős heuristically argued there should be infinitely many Carmichael numbers. In 1994 W. R. (Red) Alford, Andrew Granville and Carl Pomerance used a bound on Olson's constant to show that there really do exist infinitely many Carmichael numbers.
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In 1877, Alexander von Brill determined the sign of the discriminant. Leopold Kronecker first stated Minkowski's theorem in 1882, though the first proof was given by Hermann Minkowski in 1891. In the same year, Minkowski published his bound on the discriminant. Near the end of the nineteenth century, Ludwig Stickelberger obtained his theorem on the residue of the discriminant modulo four.
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Opposition to the new bridge was based on independent evaluations concluding that there would be only slight improvements to traffic congestion city bound on Victoria Road during peak hour while local congestion would worsen. Additionally, parkland on both sides of the new bridge would be reduced and independent environmental studies showed the local environment detrimentally impacted by the new bridge construction.
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A scrum is preparing to engage. The front row consists of two props on either side of the hooker. The number eight can be seen standing up at the back, while the flankers are bound on the side. Number 8 is the only position that does not have a specific name in English and is simply referred to as "number eight" or "eighthman".
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After 4:00 a.m. EST (9:00 UTC), a woman reported to the Ontario Provincial Police in Burlington that she had observed a car travelling at high speed on the Queen Elizabeth Way. A warning was broadcast over police radio. Thirty minutes later, Officer Mike Gula observed a speeding vehicle travelling Niagara-bound on the Queen Elizabeth Way in Vineland.
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Yang's third book, The Price of Productivity: how children learn to break the rules of language (2016), won the Linguistic Society of America's Leonard Bloomfield Award.. This book deals with the acquisition of linguistic rules with exceptions, and proposes a quantifiable upper bound on the number of lexical exceptions that a grammatical rule can tolerate. In 2018, Yang was awarded a Guggenheim Fellowship..
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If a sequence of manifolds converge in the Lipschitz sense to a limit Lipschitz manifold then the SWIF limit exists and has the same limit. Wenger's compactness theorem states that if a sequence of compact Riemannian manifolds, Mj, has a uniform upper bound on diameter, volume and boundary volume, then a subsequence converges SWIF-ly to an integral current space.
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The set with an odd number of factors is just the primes between x1/2 and x, so by the prime number theorem its size is (1 + o(1)) x / ln x. Thus these sieve methods are unable to give a useful upper bound for the first set, and overestimate the upper bound on the second set by a factor of 2.
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A tight lower bound is not known on the number of required additions, although lower bounds have been proved under some restrictive assumptions on the algorithms. In 1973, Morgenstern proved an Ω(N log N) lower bound on the addition count for algorithms where the multiplicative constants have bounded magnitudes (which is true for most but not all FFT algorithms). This result, however, applies only to the unnormalized Fourier transform (which is a scaling of a unitary matrix by a factor of \sqrt N), and does not explain why the Fourier matrix is harder to compute than any other unitary matrix (including the identity matrix) under the same scaling. Pan (1986) proved an Ω(N log N) lower bound assuming a bound on a measure of the FFT algorithm's "asynchronicity", but the generality of this assumption is unclear.
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So, loosely speaking, the use of harmonic coordinates show that Riemannian manifolds can be covered by coordinate charts in which the local representations of the Riemannian metric are controlled only by the qualitative geometric behavior of the Riemannian manifold itself. Following ideas set forth by Jeff Cheeger in 1970, one can then consider sequences of Riemannian manifolds which are uniformly geometrically controlled, and using the coordinates, one can assemble a "limit" Riemannian manifold. Due to the nature of such "Riemannian convergence", it follows, for instance, that up to diffeomorphism there are only finitely many smooth manifolds of a given dimension which admit Riemannian metrics with a fixed bound on Ricci curvature and diameter, with a fixed positive lower bound on injectivity radius. Such estimates on harmonic radius are also used to construct geometrically-controlled cutoff functions, and hence partitions of unity as well.
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The first application of Khovanov homology was provided by Jacob Rasmussen, who defined the s-invariant using Khovanov homology. This integer valued invariant of a knot gives a bound on the slice genus, and is sufficient to prove the Milnor conjecture. In 2010, Kronheimer and Mrowka proved that the Khovanov homology detects the unknot. The categorified theory has more information than the non-categorified theory.
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"The Fireman" novella, which was expanded to become Fahrenheit 451, is set in October 2052. The earliest editions make clear that it takes place no earlier than the year 1960.In early editions of the book, Montag says, "We've started and won two atomic wars since 1960", in the first pages of The Sieve and the Sand. This sets a lower bound on the time setting.
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He introduced the van der Corput lemma, a technique for creating an upper bound on the measure of a set drawn from harmonic analysis, and the van der Corput theorem on equidistribution modulo 1. He became member of the Royal Netherlands Academy of Arts and Sciences in 1929, and foreign member in 1953. He was a Plenary Speaker of the ICM in 1936 in Oslo.
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Prince's Square is a park in Launceston, Tasmania, Australia. Established in 1858 from a disused brickfield it is now an important part of cultural life in Launceston and also a heritage park. The park is known for its symmetrical planning and the bronze gilded Val d'Osne Fountain. The park is bound on all four sides by Elizabeth Street, St John Street, Frederick Street and Charles Street.
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An upper bound on the price can be set through a "safety valve" whereby the issuing authority (e.g. the government) stands ready to issue additional allowances at a set price. A lower bound can also be set through a price floor. Recently economists have begun to explore hybrid carbon taxes where mechanisms are introduced to adjust the tax rate to ensure emission reduction targets are achieved.
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It was also hoped that this change in the election system would energize the base of the party. Starting in 2016, caucus results have become binding when selecting delegates. Acting in accordance with a mandate from the Republican National Committee, the delegates are bound on the first ballot to vote for candidates in proportion to the votes cast for each candidate at the caucus sites.
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Ragged Valley is a valley, in the Diablo Range in Fresno County, California. It was named for the ragged appearance of its surface. It is bound on the east by the Big Blue Hills and on the west by Joaquin Ridge. It extends northwesterly from its mouth at Domengine Creek to the divide between Salt Creek and Cantua Creek where it has its head at .
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After The Long Blondes split in October 2008, Jackson began working a solo record with former Suede guitarist Bernard Butler. Songs included are "Velvet Sofa From No.26", "16 Years" and "Dancing In My Bedroom". In March 2010, she published the track "Homeward Bound" on her Myspace page. Jackson was a guest singer on the Scottish band 1990s' Kickstrasse, on their Kicks album of March 2009.
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Chvátal's art gallery theorem, named after Václav Chvátal, gives an upper bound on the minimal number of guards. It states that \left\lfloor n/3 \right\rfloor guards are always sufficient and sometimes necessary to guard a simple polygon with n vertices. The question about how many vertices/watchmen/guards were needed was posed to Chvátal by Victor Klee in 1973. Chvátal proved it shortly thereafter.
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By modifying the method of de Fraysseix et al., found an embedding of any planar graph into a triangular subset of the grid consisting of 4n2/9 points. A universal point set in the form of a rectangular grid must have size at least n/3 × n/3; ; . A weaker quadratic lower bound on the grid size needed for planar graph drawing was given earlier by .
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Class I MHC molecules bind peptides generated mainly from degradation of cytosolic proteins by the proteasome. The MHC I:peptide complex is then inserted via endoplasmic reticulum into the external plasma membrane of the cell. The epitope peptide is bound on extracellular parts of the class I MHC molecule. Thus, the function of the class I MHC is to display intracellular proteins to cytotoxic T cells (CTLs).
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Kalives town Kalyves lies about 20 km east of Chania in the Apokoronas area and is linked with GR-90 (E65). It is on the coast at the entrance of Souda Bay. It essentially consists of one long road, with houses opening directly on to it, with the occasional alley behind. The town is bound on one side by the sea and the other by low hills.
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Using these coefficients gives the Taylor polynomial of . The Taylor polynomial of degree is the polynomial of degree which best approximates , and its coefficients can be found by a generalization of the above formulas. Taylor's theorem gives a precise bound on how good the approximation is. If is a polynomial of degree less than or equal to , then the Taylor polynomial of degree equals .
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On the other hand, a triply exponential upper bound on a decision procedure for Presburger Arithmetic was proved by Oppen (1978). A more tight complexity bound was shown using alternating complexity classes by . The set of true statements in Presburger arithmetic (PA) is shown complete for TimeAlternations(22nO(1), n). Thus, its complexity is between double exponential nondeterministic time (2-NEXP) and double exponential space (2-EXPSPACE).
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In 1893 Chatham wove its first blanket. The first dozen were bound on a sewing machine by Mrs RL Hubbard. Although Chatham manufactured fabrics for many applications, Chatham Blankets were the only product with the name "Chatham" on them and the thing that the company would be most known for. During the first part of the 19th century, the primary focus of company sales were wool blankets.
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Most internal doors are four panelled, with operable transom windows above, occasionally arched. Half glazed French doors open onto the verandahs from internal rooms. Attached by a walkway to the south elevation of the building is an open elevated pavilion, bound on three sides by round headed arched arcades of three bays each. The rear north wall of the pavilion has two large rectangular openings.
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Leaving Bengal she was at Barrabulla again on 15 September. On 6 October she reached Madras, on 21 October Negapatam, on 17 December Bombay, on 11 April 1782 Tellicherry, on 27 April Calicut, on 6 May Tellicherry again, and on 28 May Bombay again. Homeward bound, on 31 January 1783 Neptune was at St Helena, and she arrived at The Downs on 8 August.
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So to increase load factor, transportation planners try to predict times of low demand, and run reduced schedules or smaller vehicles at these times. This increases passengers' wait times. In many cities, trains and buses do not run at all at night or on weekends. PRT vehicles, in contrast, would only move in response to demand, which places a theoretical lower bound on their average load factor.
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The notion of a nil ideal has a deep connection with that of a nilpotent ideal, and in some classes of rings, the two notions coincide. If an ideal is nilpotent, it is of course nil. There are two main barriers for nil ideals to be nilpotent: # There need not be an upper bound on the exponent required to annihilate elements. Arbitrarily high exponents may be required.
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This can be shown by the isomorphisms {(3,4), (3,4), (3,4)} and {(2,3), (2,3), (2,3)} respectively. Since isotopy classes are disjoint, the number of reduced Latin squares gives an upper bound on the number of isotopy classes. Also, the total number of Latin squares is times the number of reduced squares. Normalize a Cayley table of a quasigroup in the same manner as a reduced Latin square.
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In the nucleus freshly transcribed mRNA molecules are bound on the 5' cap by the nuclear cap- binding complex of Cbc1/Cbc2 in yeast or CBP20/CBP80 in metazoans. These aid in the export of the mRNA and protect it from decapping. They also serve as a marker for the so-called pioneer round of translation when the message is examined by nonsense mediated decay.
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This implies a lower bound on the utility of each coalition, called the core lower bound. According to the UTI doctrine, each country has rights to all water in its region and upstream. These rights are not compatible since their sum is above the total amount of water. However, these rights define an upper bound - the largest utility that a country can hope for.
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The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter position allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. See also Wikipedia article.
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The first linear upper bound on the number of edges of such a graph was established by Lovász et al. . The best known upper bound, 1.428n, was proved by Fulek and Pach. Apart from geometric graphs, Conway's thrackle conjecture is known to be true for x-monotone topological graphs. A topological graph is said to be x-monotone if every vertical line intersects every edge in at most one point.
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Ferrocene is an organometallic compound with the formula . The molecule consists of two cyclopentadienyl rings bound on opposite sides of a central iron atom. It is an orange solid with a camphor-like odor, that sublimes above room temperature, and is soluble in most organic solvents. It is remarkable for its stability: it is unaffected by air, water, strong bases, and can be heated to 400 °C without decomposition.
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While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles. It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton. Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons.
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Closing the gap between the 2n2/9 upper bound and the n2/9 lower bound on drawing area for completions of the nested triangle graph remains an open problem.. Variants of the nested triangles graph have been used for many other lower bound constructions in graph drawing, for instance on area of rectangular visibility representations,. area of drawings with right angle crossings. or relative area of planar versus nonplanar drawings..
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23 who followed Harper to Sherborne whither the latter was bound on a similar mission of resuscitating a moribund school. Such "swarming" in the wake of a charismatic headmaster was typical of the period. Morris and Harper remained lifelong friends. He studied classics at Jesus College, Oxford, graduating in 1856: the first student in thirty years to obtain first-class honours in both his preliminary and his final examinations.
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Finnegan Wake is a merman who is the son of a mermaid. He is shown to be wheelchair bound on land which leads the ghouls to underestimate his abilities. Finnegan is shown to be a daredevil and thrill seeker who doesn't let his disability get in the way of what he wants to do. He was originally referred to as Rider in the webisode, which may be a nickname.
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The lower bound on worst- case running time of output-sensitive convex hull algorithms was established to be Ω(n log h) in the planar case. There are several algorithms which attain this optimal time complexity. The earliest one was introduced by Kirkpatrick and Seidel in 1986 (who called it "the ultimate convex hull algorithm"). A much simpler algorithm was developed by Chan in 1996, and is called Chan's algorithm.
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This measure of contextuality takes values in the interval [0,1], where 0 corresponds to noncontextuality and 1 corresponds to strong contextuality. The contextual fraction may be computed using linear programming. It has also been proved that CF(e) is an upper bound on the extent to which e violates any normalised noncontextuality inequality. Here normalisation means that violations are expressed as fractions of the algebraic maximum violation of the inequality.
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In the mathematical theory of probability, Janson's inequality is a collection of related inequalities giving an exponential bound on the probability of many related events happening simultaneously by their pairwise dependence. Informally Janson's inequality involves taking a sample of many independent random binary variables, and a set of subsets of those variables and bounding the probability that the sample will contain any of those subsets by their pairwise correlation.
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King Alexander I was storm-bound on the island for three days in 1123 and in recognition of the shelter given to him by the hermits, promised to establish a monastic settlement in honour of St Columba. Though the king died before the promise could be fulfilled, his brother David I later founded a priory here for monks of the Augustinian order; the priory was erected into an abbey in 1223.
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Falconwood is a junction on the A2. London bound on the A2 will immediately lead to the A102 (Blackwall Tunnel Approach), and the Blackwall Tunnel under the River Thames to the A12 in East London, unless changing onto the old A2 at the Sun In The Sands junction (Blackheath). The London bound A2 isn't accessible directly from Falconwood. Access is from the Eltham junction with the South Circular (A205).
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In number theory, Størmer's theorem, named after Carl Størmer, gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell equations. It follows from the Thue–Siegel–Roth theorem that there are only a finite number of pairs of this type, but Størmer gave a procedure for finding them all.
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That puts a lower bound on when Serapion the Younger wrote. It is therefore supposed he wrote in the 12th century. It remains possible he wrote in the 13th century because there is no record of the full book anywhere until the late 13th century. On the basis of his name he might have been a Christian because "Serapion" and its Arabic equivalents "Sarafyun" and "Sarabi" is a Greek name.
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The bound on the amplitude of the background waves is called an upper limit. The amplitude of the gravitational wave background is less than the upper limit. Some supermassive black holes binaries may form a stable binary and only merge after many times the current age of the universe. This is called the “final parsec problem;” it is unclear how supermassive black holes approach each other at this distance.
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In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, is an upper bound on the variance σ2 of any bounded probability distribution. Let M and m be upper and lower bounds on the values of any random variable with a particular probability distribution. Then Popoviciu's inequality states: : \sigma^2 \le \frac14 ( M - m )^2. This equality holds precisely when half of the probability is concentrated at each of the two bounds.
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It is bound on the North by Solon, OH; on the west by Twinsburg, on the east by Aurora, and on the South by Twinsburg & Twinsburg Township; within a few minutes of shopping and freeway access. It is primarily a residential community with its own police and fire departments. 83% of Reminderville is a part of the Twinsburg City School District and the balance is part of Aurora City Schools.
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Such a solution is called numeric. A solution is certified if it is provided with a bound on the error of the approximations, and if this bound separates the different solutions. The other way of representing the solutions is said to be algebraic. It uses the fact that, for a zero-dimensional system, the solutions belong to the algebraic closure of the field k of the coefficients of the system.
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In this section, we show achievability of the upper bound on the rate from the last section. A codebook, known to both encoder and decoder, is generated by selecting codewords of length n, i.i.d. Gaussian with variance P-\epsilon and mean zero. For large n, the empirical variance of the codebook will be very close to the variance of its distribution, thereby avoiding violation of the power constraint probabilistically.
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"On the Distribution of the Output Error Burst Lengths for Viterbi Decoding of Convolutional Codes". Curry, S. J.; Harmon, W. D. "A bound on Viterbi decoder error burst length". Single-error-correcting codes alone can't correct such bursts, so either the convolutional code and the Viterbi decoder must be designed powerful enough to drive down errors to an acceptable rate, or burst error- correcting codes must be used.
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55, No. 4 (Jul. 1947) In the region of the Brule, these ridges run nearly exactly east-west, and long, thin lakes lie between them. The valley in which Brule Lake is located is bound on the north by the Misquah Hills, and on the south by another sill peaked by Brule Mountain. Though the distance between these points is only four miles, the valley is six hundred feet deep.
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From parallax measurements, the distance to this star is about . It has an apparent visual magnitude of 2.89, making it easily visible to the naked eye. Beta Canis Minoris has about 3.5 times the Sun's mass and is rotating rapidly with a projected rotational velocity of , which gives a lower bound on the azimuthal rotational velocity along the star's equator. The actual rotation rate may be about once per day.
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Catawba is an unincorporated community in the northern section of Roanoke County, Virginia, United States. Catawba occupies the Catawba Valley bound on the south by the north slope of Catawba Mountain and on the north by several mountains which form the border between Roanoke County and Craig County. The primary road through Catawba is State Route 311. Catawba has a post office with the zip code of 24070.
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Nepenthes argentii, a pitcher plant endemic to Mount Guiting-Guiting in Magdiwang, Romblon. Magdiwang is one of three municipalities in Sibuyan Island, the second largest among the islands of Romblon. It is bound on the west by Cajidiocan, on the south by San Fernando, and on the north by Sibuyan Sea, and to the north-west by Romblon, Romblon. The total land area of Magdiwang is 100.75 km2.
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This gives an upper bound on the absolute values of the eigenvalues of Frobenius, and Poincaré duality then shows that this is also a lower bound. In general Rif! does not take pure sheaves to pure sheaves. However it does when a suitable form of Poincaré duality holds, for example if f is smooth and proper, or if one works with perverse sheaves rather than sheaves as in .
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Detailed measurements made at the Paul Scherrer Institute (PSI) have searched for the exotic muon decay and placed a lower bound on the bilepton mass of about 1 TeV. Studies of muonium- antimuonium conversion, also at PSI, have imposed a similar bound. Higher statistics experiments are planned. The bilepton could alternatively be discovered in electron-electron collisions or in multi TeV proton-proton collisions at the Large Hadron Collider.
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The San Juan Basin is an asymmetrical syncline with three components: the Central Basin Platform, the Four Corners Platform, and the Chaco Slope (a.k.a. the Chaco Homocline). The basin is bound on the northwest by the Hogback Monocline (separating the Central Basin and Four Corners platforms), on the northeast by the Archuleta Anticlinorium, on the east by the Nacimiento Uplift, and on the south by the Zuni Uplift.
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As Schipfe expanded, it became necessary to expand the bridge to accommodate the new traffic. From 1602 to 1605 the bridge was rebuilt with the present dimensions. the bridge was bound on the east by the former Hotel Zum Schwert (now a commercial building), and in the west with a wooden platform made of oak planks. The bridge section between the town hall and the Hauptwache was rebuilt from stone.
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This value provides a lower bound on the true semimajor axis of their orbit. The visible component is an F-type main- sequence star with a stellar classification of F5 V. It is an estimated 1.5 billion years old with 1.3 times the mass of the Sun and 1.7 times the Sun's radius. It is radiating 5.2 times the Sun's luminosity from its photosphere at an effective temperature of 6,732 K.
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The pessimistic, or clean prominence, assumes that the col is as high as it can be, i.e., its elevation is that of the higher contour line nearest the saddle. This gives a lower bound on the possible prominence of the peak, ignoring map error; inaccuracies in mapping lead to further uncertainties and a larger error bound. Optimistic prominence assumes that the col is as low as possible, yielding an upper bound value for the prominence.
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It has been speculated that he may represent Prometheus, who was bound on a mountain and left to be savaged by an eagle as punishment for stealing fire from Mount Olympus.Hughes, 388 All four are hideously ugly.Hughes, 387 The painting's range of color is diminished, as much or even more so than the other black paintings, to ochres and blacks. This reinforces a nocturnal and unreal atmosphere, appropriate to the mythical subject of this work.
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Taluks & Villages - Kollam District The taluk is bound on the north by Kayamkulam, on the east by Kunnathur taluk, on the south by Kollam and on the west by the Arabian Sea. It is one of the fastest developing towns in Kerala and is part of Kollam metropolitan area. Karunagappally is the location of a government engineering college named the College of Engineering Karunagappally, also known as CEK. Europeans called Karunagappally Martha.
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The variable radial velocity of this star was announced in 1911 by W. W. Campbell. It is a single-lined spectroscopic binary in an assumed circular orbit with a period of 111.1 days. The a sin i value for this system is , where a is the semimajor axis and i is the (unknown) orbital inclination. This value provides a lower bound on the true semimajor axis, which in this case is their actual separation.
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Purchasers are particular successors. If the universal or particular distinction is adopted, they should not be bound, but they are bound on the huur gaat voor koop principle. On the first approach, purchasers who did not know of the existence of the lease are not bound if neither the lessee nor anyone else holding under or through him is in occupation. Occupation is an outward sign to prospective purchasers that there is a lease.
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Space complexity is generally expressed as the amount of memory required by an algorithm on an input of size . The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an upper bound on the complexity of the problem solved by this algorithm.
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The series follows a clash of cultures involving two American families brought together by the couple formed by Junior, the valedictorian son of a Latino family, and Molly, the less academic daughter of an Anglo family. The two are finishing high school and Junior is Stanford bound. On graduation day, they discover that Molly is pregnant. The pair decide to get married, forcing a bonding and blending of their two very different families.
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In 2011, the likely presence of a planet in orbit around this star was reported by Byeong-Cheol Lee et al. It was detected using the radial velocity method, based upon measurements made between 2003 and 2010 at the Bohyunsan Optical Astronomy Observatory in Korea. The object has an orbital period of 381 days and an eccentricity of 0.25. The lower bound on this object's mass is about 1.8 times the mass of Jupiter.
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Inspector Garud has Police Inspector Madhavan Kutty (Dileep)as a very corrupt officer, known as Garud(as he is fast as a falcon who would do any dirty work for money. He became Inspector not through the right channel but by paying 15 lakhs as bribe. So he is now bound on getting his money back through bribes. A consignment of arms reaches Kochi meant for LTTE and the villain, Karaikkudy Arumuga Palaniyappa Chettiyar a.k.a.
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Owens Valley is thousands of feet below Wheeler Crest The Wheeler Crest or Wheeler Ridge is a ridge in Mono and Inyo Counties, California. The crest is long, and partially lies in the John Muir Wilderness. The ridge is bound on the west by Rock Creek, on the north by the community of Toms Place, on the east by Round Valley, on the southeast by Gable Creek, and on the southwest by Morgan Creek.
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This is a single-lined spectroscopic binary with a circular orbit and a period of 329.3 days. The a sin i value is , where a is the semimajor axis and i is the orbital inclination to the line of sight. This value provides a lower bound on the actual semimajor axis. The system shows a micro-variability in its brightness, and is a source of X-ray emission with an apparent flux of .
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Riverview Park was an amusement park in Chicago, Illinois which operated from 1904 to 1967. It was located on 74 acres (0.3 km²) in an area bound on the south by Belmont Ave. on the east by Western Ave, on the north by Lane Tech High School, and on the west by the North Branch of the Chicago River. It was in the North Center community area and neighborhood on Chicago's north side.
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Since its peak, brightness dropped smoothly through September 2008 while becoming continuously redder. After September 2008, brightness continued to fall at a lower rate in the optical spectrum but with strong Hα emissions. Further, the optical spectrum is mostly made up of fairly narrow Hydrogen Balmer and Ca II emission lines coupled with strong Ca II H&K; absorption. Research into historical Hubble images provide an accurate upper bound on the progenitor star's brightness.
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Union Street is shown near the southern end of the site, bound on the north and south by buildings owned by Martyn and Coombes. George Atherden's premises are indicated on the southern boundary of Campbell's Lot 2. Arthur Jeffreys died in England in 1861 leaving his interests in the Campbell Estate to his son, John Jeffreys. Primary sources of this period confirm that Lots 9 and 10 remained vacant until the early 1880s.
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The Schottenstein Edition Siddur for Weekdays with an Interlinear Translation. Edited by Menachem Davis, pages 27–31. Brooklyn: Mesorah Publications, 2002. . And many Jews recall God's answering Abraham on Mount Moriah and God's answering his son Isaac when he was bound on top of the altar (as reported in ) as they recite some of the final piyutim that they say each day in penitential Selichot prayers leading up to the High Holy Days.
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A thousand copies were printed and given away. After founding the Guinness Book of Records at 107 Fleet Street, the first 198-page edition was bound on 27 August 1955 and went to the top of the British best seller lists by Christmas. "It was a marketing give away – it wasn't supposed to be a money maker" said Beaver. The following year it launched in the United States, and sold 70,000 copies.
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Amatérská Cave is the longest cave system in the Czech Republic with a length of over 40 km-. The cave system is bound on two main underground streames: Bila voda and Sloupsky potok, (in underground) creating the River Punkva inside Amatérská Cave. The whole system is created by the connection of (semi) separate caves: Nová Rasovna, Pikova Dama, Spiralka, 13C, Amaterska Cave, the Sloupsko-sosuvske Caves, the Punkevni Caves and Macocha Abbys.
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In November 1746, Noble headed to Georgetown "being bound on an expedition against the enemies of the King of Great Britain,". He served at Fort Richmond (Maine). He made his last will, which was proved in the spring of 1747. In it, he named as heirs his brothers, Francis and James, his daughter, Sarah (Noble) Lithgow, and his son Arthur II. He left a large estate, his personal property having been valued at about £8,000.
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The presequence translocase23 (TIM23) is localized to the mitochondrial inner membrane and acts a pore forming protein which binds precursor proteins with its N-terminus. TIM23 acts a translocator for preproteins for the mitochondrial matrix, the inner mitochondrial membrane as well as for the intermembrane space. TIM50 is bound to TIM23 at the inner mitochondrial side and found to bind presequences. TIM44 is bound on the matrix side and found binding to mtHsp70.
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Random sampling by using lots is an old idea, mentioned several times in the Bible. In 1786 Pierre Simon Laplace estimated the population of France by using a sample, along with ratio estimator. He also computed probabilistic estimates of the error. These were not expressed as modern confidence intervals but as the sample size that would be needed to achieve a particular upper bound on the sampling error with probability 1000/1001.
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East Meath () is an area of made up of the electoral divisions of St Mary's (Part) and Julianstown in County Meath. The area is bound on the north by the River Boyne and County Louth, to the south just beyond the River Nanny close to the County Dublin border, to the east by the Irish Sea and to the west by the M1. It has been part of the Dáil constituency of Louth since 2007.
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Though there is technically no upper bound on the number of repetitions that might be needed before the correct answer is obtained, the expected number of repetitions is a constant factor that does not grow with N. Grover's original paper described the algorithm as a database search algorithm, and this description is still common. The database in this analogy is a table of all of the function's outputs, indexed by the corresponding input.
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After a bloody battle Börklüce and his men couldn't flee and moved to the north of the peninsula where they were captured. Börklüce was taken hostage and after a lot of torturing he still insisted on his beliefs and demands. As a result, he was crucified and bound on the back of a camel to be ridiculed and shown around. The dervishes who stayed loyal to him were killed in front of his eyes.
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The middle-aged brothers Butch and Leon - respectively a habitual car thief and a more or less reformed criminal - fetch their wheelchair-bound mother Inez. They set out in a borrowed van for the notorious Parchman prison, where their younger brother Raymond is on death row for murdering a Deputy. En route the brothers and their mother start bickering. Gradually it becomes clear that they are not bound on normal prison visit.
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Taylor's theorem can be used to obtain a bound on the size of the remainder. In general, Taylor series need not be convergent at all. And in fact the set of functions with a convergent Taylor series is a meager set in the Fréchet space of smooth functions. And even if the Taylor series of a function does converge, its limit need not in general be equal to the value of the function .
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Keswick's geographical coordinates are 44.22°N, 79.45°W, and its elevation above sea level is 221m/762 ft. It has a geographical area of 16.25 km² according to Statistics Canada. It is bound on the north by Roches Point, the east by Woodbine Avenue, the south by East Gwillimbury (Ravenshoe Road) and the west by Cook's Bay, part of Lake Simcoe. Included in Keswick is the Keswick Marsh, part of the Holland Marsh.
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Neutrinos oscillate among the flavours as they move. It is hard to determine an exact upper bound on the collective average mass of the three neutrinos (or for any of the three individually). For example, if the average neutrino mass were over 50 eV/c (less than 10 of the mass of an electron), the universe would collapse. CMB data and other methods indicate that their average mass probably does not exceed 0.3 eV/c.
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If the input sequence has steps, then the recursion continues to a depth of , which is also the bound on the parallel running time of this algorithm. The number of steps of the algorithm is , and it can be implemented on a parallel random access machine with processors without any asymptotic slowdown by assigning multiple indices to each processor in rounds of the algorithm for which there are more elements than processors.
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Fairmont Senior has possessed many unique features that fortify its historic nature. An example of this is senior court, which stood by the school's main entrance for many years. This light court was bound on all sides by interior walls of the school, but was not constrained by a ceiling. The opening provided sunlight to the surrounding halls and classrooms, as well as the small glass greenhouse located just inside the court.
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The former fisheries centre, and now Hungry Point Reserve, occupies an area of 3-hectares located at 202 Nicholson Parade at the southernmost tip of Cronulla Peninsula overlooking Salmon Haul Bay and Gunnamatta Bay on Port Hacking. It is also opposite Bundeena in the Royal National Park. It is bound on the north by Darook Park, residential properties fronting Nicholson Parade and Cowra Place, and Salmon Haul Reserve on the north east of the site.
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Demonstration of waterboarding at a street protest during a visit by Condoleezza Rice to Iceland, May 2008 In 2006 and 2007, Fox News and Current TV, respectively, demonstrated a waterboarding technique. In the videos, each correspondent is held against a board by the "interrogators". Christopher Hitchens voluntarily subjected himself to a filmed demonstration of waterboarding in 2008, an experience which he recounted in Vanity Fair. He was bound on a horizontal board with a black mask over his face.
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113, for a bound on the number of distinct labeled unicyclic graphs. That is, if c is a constant with 0 < c < 1/2, and Pc(n) is the probability that choosing uniformly at random among the n-vertex graphs with cn edges results in a pseudoforest, then Pc(n) tends to one in the limit for large n. However, for c > 1/2, almost every random graph with cn edges has a large component that is not unicyclic.
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Naturally, we need to have at least a fraction R of the transmitted symbols to be correct in order to recover the message. This is an information-theoretic lower bound on the number of correct symbols required to perform decoding and with list decoding, we can potentially achieve this information-theoretic limit. However, to realize this potential, we need explicit codes (codes that can be constructed in polynomial time) and efficient algorithms to perform encoding and decoding.
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Out of the many causes of bondage, passion is considered as the main cause of bondage. The karmas are literally bound on account of the stickiness of the soul due to existence of various passions or mental dispositions. The passions like anger, pride, deceit and greed are called sticky (kasayas) because they act like glue in making karmic particles stick to the soul resulting in bandha. Hence the ancient Jain texts talk of subduing these negative emotions: p.
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Five years passed before Social Distortion released their next album, 1988's Prison Bound, on the heels of Ness's recovery from drug addiction. Ness has been sober and clean from heroin since 1985. Furthermore, in the mid-1980s, he briefly was employed as a house painter and assistant speech therapist in an elementary school. Ness performed in the band Easter from 1986–1988 and appeared in the music video for the songs "Slipping Away" and "Lights Out".
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In most of these protocols, an address (whether it is initiator or target) is roughly equivalent to physical device's port. Situations where a single physical port hosts multiple addresses, or where a single address is accessible from one device's multiple ports are not very common, . Even when using multipath I/O to achieve fault tolerance, the device driver switches between different targets or initiators statically bound on physical ports, instead of sharing a static address between physical ports.
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One can formally define functions that are not computable. A well-known example of such a function is the Busy Beaver function. This function takes an input n and returns the largest number of symbols that a Turing machine with n states can print before halting, when run with no input. Finding an upper bound on the busy beaver function is equivalent to solving the halting problem, a problem known to be unsolvable by Turing machines.
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The small books were convenient for soldiers because they fit easily into a cargo pocket. Finished size varied slightly, from to long and from to high. Unlike traditional paperbacks, most of the ASEs were bound on the short side of the text block rather than the long side, due to the printing presses used. A few titles near the end of the series were published in traditional paperback format with the spine on the long side.
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In mathematics, Doob's martingale inequality, also known as Kolmogorov’s submartingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process exceeds any given value over a given interval of time. As the name suggests, the result is usually given in the case that the process is a martingale, but the result is also valid for submartingales. The inequality is due to the American mathematician Joseph L. Doob.
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Gull Island is a small fishing community on the north side of Newfoundland Island, in the Province of Newfoundland and Labrador, Canada. It is situated on Conception Bay on the eastern side of Bay de Verde Peninsula, bound on the north by Burnt Point and on the south by Northern Bay. Gull Island was named for the small rocky, bird nesting island of Gull Island located at . Séan McCann from the band Great Big Sea is from Gull Island.
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Green suffered from racial bigotry throughout his life. After he had purchased his freedom, he was often accosted while he was travelling between his churches, and asked whose slave he was. Since an explanation that he was free would arouse suspicion, he would answer "Mr. Green". In the mid-1850s, on his way to Paris with his wife, Green found his son John, with his hands bound, on his way to being sold "down the river".
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Iona is bound on the north and south by the Kunene and Curoca Rivers, respectively. The climate is noteworthy for the heavy fogs created as the cold, wet air of the Benguela up- welling meets the hot, dry air of the desert. The strong fogs and currents have led to numerous shipwrecks through history. The coast is sometimes called Skeleton Coast after these shipwrecks as well as the numerous skeletons of whales and seals found on the beaches.
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There is no upper bound on k for k-isohedral tilings by certain tiles that are both type 1 and type 2, and hence neither on the number of tiles in a primitive unit. The wallpaper group symmetry for each tiling is given, with orbifold notation in parentheses. A second lower symmetry group is given if tile chirality exists, where mirror images are considered distinct. These are shown as yellow and green tiles in those cases.
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Alwar is a district in the state of Rajasthan in northern India, whose district headquarters is Alwar city. The district covers 8,380 km2. It is bound on the north by Rewari district of Haryana, on the east by Bharatpur district of Rajasthan and Nuh district of Haryana, on the south by Dausa district, and on the west by Jaipur district. As of 2011 it is the third most populous district of Rajasthan (out of 33) after Jaipur and Jodhpur.
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The basin is bound on the south by the Wichita-Amarillo uplift, on the east by the Nemaha uplift, on the north by the Central Kansas uplift, and on the west by the Las Animas arch. Sedimentary rocks from Cambrian through Permian age fill the basin. The sedimentary column is thickest, in excess of , at the southern edge, next to the upfaulted Wichita-Amarillo uplift. The basin has an especially thick section of Pennsylvanian rocks, up to thick.
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In the second of the two papers that introduced these algorithms they are analyzed as encoders defined by finite-state machines. A measure analogous to information entropy is developed for individual sequences (as opposed to probabilistic ensembles). This measure gives a bound on the data compression ratio that can be achieved. It is then shown that there exist finite lossless encoders for every sequence that achieve this bound as the length of the sequence grows to infinity.
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Then a bath of molten lead was prepared; when the apparition of Christ stepped into the cauldron with him, the fire went out and the lead became cold. Pantaleon was now thrown into the sea, loaded with a great stone, which floated. He was thrown to wild beasts, but these fawned upon him and could not be forced away until he had blessed them. He was bound on the wheel, but the ropes snapped, and the wheel broke.
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So the trojan being a mote of dust, m3→0, imposes a lower bound on of 25+√621/2 ≈ 24.9599. And if the star were hyper-massive, m1→+∞, then under Newtonian gravity, the system is stable whatever the planet and trojan masses. And if = , then both must exceed 13+√168 ≈ 25.9615. However, this all assumes a three-body system; once other bodies are introduced, even if distant and small, stability of the system requires even larger ratios.
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The Lyceum is famous for being a center of education, but it was used for numerous other activities including Athenian assembly gatherings, cult practices, and military exercises. Because the Lyceum had to serve many purposes, the building had to have specific structures and developed to accommodate all the activities. The area it was built on had many open spaces with forests. It was bound on the south by the Ilissus river and the north by the mountain Lykabettus.
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The variational Bayesian methods used for model estimation in DCM are based on the Laplace assumption, which treats the posterior over parameters as Gaussian. This approximation can fail in the context of highly non-linear models, where local minima may preclude the free energy from serving as a tight bound on log model evidence. Sampling approaches provide the gold standard; however, they are time consuming and have typically been used to validate the variational approximations in DCM.
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Royal Drive, which was a two-way road that connected with Bloor Street between Broadview Avenue and the Viaduct was re-purposed into a one-way north-bound on-ramp. A pedestrian overpass bridge was constructed to connect the east and west sections of Riverdale Park. The section opened in conjunction with the section of the expressway from the parkway to York Street on November 6, 1964. It was opened ceremonially by Ontario Premier John Robarts.
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Although there is no lower bound on age, FIRST suggests that the program is intended for children 6 or older. After registering a team, the coach guides students to do research by following the Challenge guideline. The team may have a field trip or visit experts to help children to learn more about the topic. Children will then work on their "Show Me" poster and LEGO models to demonstrate their findings according to the instructions in the Challenge.
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Kirkwood is a national historic designated neighborhood on the east side of Atlanta, Georgia, United States. It is a historic streetcar suburb, and was designed by architect Will Saunders. Kirkwood is situated entirely in DeKalb County, bordered by the neighborhoods of Lake Claire, East Lake, Edgewood, and Oakhurst. Kirkwood is bound on the north by DeKalb Avenue, on the south by Memorial Drive and Interstate 20, on the west by Montgomery Street, and on the east by 1st Ave.
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The equilibrium mentioned above is a perfect-information equilibrium and so only strictly holds in idealized conditions where every voter knows every other voter's preference. Thus it provides an upper bound on what can be achieved with rational (self- interested) coordination or knowledge of others' preferences. Since the voters almost surely won't have perfect information, it may not apply to real elections. In that matter, it is similar to the perfect competition model sometimes used in economics.
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The system appears as a single-lined spectroscopic binary with an orbital period of and an eccentricity of 0.38. The a sin i value for the primary is , where a is the semimajor axis and i is the (unknown) orbital inclination. This value provides a lower bound on the actual semimajor axis for the orbit. The primary component is an aging giant star with a stellar classification of , indicating a mild barium star with an underabundance of iron.
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Historically intergenic regions have sometimes been called junk DNA suggesting that they have no function. However, it has been known for a long time that these regions do contain functionally important elements such as promoters and enhancers. In particular, intergenic regions often contain enhancer DNA sequences, which can activate expression of discrete sets of genes over distances of several thousand base pairs. Changes in the proteins bound on enhancers reprogram gene expression and affect the cell phenotype.
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The proof of this tight inequality depends on the so-called (q, p)-norm of the Fourier transformation. (Establishing this norm is the most difficult part of the proof.) From this norm, one is able to establish a lower bound on the sum of the (differential) Rényi entropies, , where , which generalize the Shannon entropies. For simplicity, we consider this inequality only in one dimension; the extension to multiple dimensions is straightforward and can be found in the literature cited.
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In statistics, the Chapman–Robbins bound or Hammersley–Chapman–Robbins bound is a lower bound on the variance of estimators of a deterministic parameter. It is a generalization of the Cramér–Rao bound; compared to the Cramér–Rao bound, it is both tighter and applicable to a wider range of problems. However, it is usually more difficult to compute. The bound was independently discovered by John Hammersley in 1950, and by Douglas Chapman and Herbert Robbins in 1951.
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Transylvania is a historical region that is located in central Romania. Bound on the east and south by its natural borders, the Carpathian mountain range, historical Transylvania extended westward to the Apuseni Mountains. The term sometimes encompasses not only Transylvania proper, but also parts of the historical regions of Crișana and Maramureș, and occasionally the Romanian part of Banat. The region of Transylvania is known for the scenery of its Carpathian landscape and its rich history.
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In 1936 Roland Sprague showed that a part of Pál's cover could be removed near one of the other corners while still retaining its property as a cover. This reduced the upper bound on the area to a \le 0.844137708436. In 1992 Hansen showed that two more very small regions of Sprague's solution could be removed bringing the upper bound down to a \le 0.844137708398. Hansen's construction was the first to make use of the freedom to use reflections.
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A unisecant in this example need not be a tangent line to the circle. This terminology is often used in incidence geometry and discrete geometry. For instance, the Sylvester–Gallai theorem of incidence geometry states that if points of Euclidean geometry are not collinear then there must exist a 2-secant of them. And the original orchard-planting problem of discrete geometry asks for a bound on the number of 3-secants of a finite set of points.
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Federer-Fleming proved that if one has a sequence of integral currents T_i whose supports lie in a compact set K with a uniform upper bound on M(T_i) + M(\partial T_i), then a subsequence converges in the flat sense to an integral current. This theorem was applied to study sequences of submanifolds of fixed boundary whose volume approached the infimum over all volumes of submanifolds with the given boundary. It produced a candidate weak solution to Plateau's problem.
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Chen's theorem proves that for all sufficiently large n, 2n=p+q where p is prime and q is either prime or semiprime.A semiprime is a natural number that is the product of two prime factors. Montgomery and Vaughan showed that the exceptional set (even numbers not expressible as the sum of two primes) was of density zero. The best current bound on the exceptional set is E(x) < x^{0.72} (for large enough x) due to Pintz.
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During this time, he met Kathy Chitty, who was working as a ticket-taker at the club. The two hit it off instantly, but it became clear that Simon desired to perform in London, resulting in an emotional farewell. Following a performance in Liverpool, Simon was waiting for the early morning milk train to London at a railway station. He had been missing Chitty's company and he began to write "Homeward Bound" on a scrap of paper.
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Proofs of the prime number theorem before 1928 and only using the behaviour of the zeta function on the line Re s = 1 (as the 1908 proof of Edmund Landau), also appealed to some bound on the order of growth of the zeta function on this line. Returning to Japan after studying with Dr Wiener, he taught at Osaka University and the Tokyo Institute of Technology. He translated Cybernetics: Or Control and Communication in the Animal and Machine into Japanese.Wiener, N. (1956).
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In 2015, Dutch and German researchers in the EU FP7 ENVISAGE project found a bug in the standard implementation of Timsort. Specifically, the invariants on stacked run sizes ensure a tight upper bound on the maximum size of the required stack. The implementation preallocated a stack sufficient to sort 264 bytes of input, and avoided further overflow checks. However, the guarantee requires the invariants to apply to every group of three consecutive runs, but the implementation only checked it for the top three.
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The law is falsifiable and more useful if we specify an upper bound on melting points or a way to calculate this upper bound. Another example from Maxwell is "All beta decays are accompanied with a neutrino emission from the same nucleus." This is also not falsifiable, because maybe the neutrino can be detected in a different manner. The law is falsifiable and much more useful from a scientific point of view, if the method to detect the neutrino is specified.
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Algorithmic cooling is an algorithmic method for transferring heat (or entropy) from some qubits to others or outside the system and into the environment, which results in a cooling effect. This method uses regular quantum operations on ensembles of qubits, and it can be shown that it can succeed beyond Shannon's bound on data compression. The phenomenon is a result of the connection between thermodynamics and information theory. The cooling itself is done in an algorithmic manner using ordinary quantum operations.
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This process cools some qubits while heating the others. It is limited by a variant of Shannon's bound on data compression and it can asymptotically reach quite close to the bound. A more general method, "irreversible algorithmic cooling", makes use of irreversible transfer of heat outside of the system and into the environment (and therefore may bypass the Shannon bound). Such an environment can be a heat bath, and the family of algorithms which use it is named "heat-bath algorithmic cooling".
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In 2005, the Anglo-Australian Planet Search program announced the discovery of a low-mass planet in orbit around HD 117618. This object was found through measurements of radial velocity variation, which were larger than those produced by the intrinsic jitter of the host star. The best Keplerian fit to the data gave a periodicity of 25.8 days with an eccentricity of around 0.37 and a semimajor axis of . The lower bound on the object's mass was estimated to be .
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After graduation, Baker worked with the Air Ministry on structural problems of airships. At 28, in 1929, he contracted tuberculosis. Upon recovering, he became a Technical Officer with the Structural Steel Research Committee, which was investigating why measured stresses in structural steel bore little resemblance to theoretical ones. During his time in this post, he developed the plastic theory of design, a revolutionary method of design of steel structures which gives a lower bound on the collapse load, and is hence always safe.
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His 1951 paper on the problem was the first to prove a nontrivial upper bound on the area that can be achieved. He eventually published four papers on this problem, the latest in 1976. Roth also made significant progress on square packing in a square. If unit squares are packed into an s\times s square in the obvious, axis-parallel way, then for values of s that are just below an integer, nearly 2s area can be left uncovered.
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Grigoriev,Dima, Karpinski,Marek, and Singer,Michael F., "Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields", SIAM J. Comput., Vol 19, No.6, pp. 1059-1063, December 1990 A low degree PIT has an upper bound on the degree of the polynomial. Any low degree PIT problem can be reduced in subexponential time of the size of the circuit to a PIT problem for depth-four circuits; therefore, PIT for circuits of depth-four (and below) is intensely studied.
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The \Delta-lemma states that every uncountable collection of finite sets contains an uncountable \Delta- system. The \Delta-lemma is a combinatorial set-theoretic tool used in proofs to impose an upper bound on the size of a collection of pairwise incompatible elements in a forcing poset. It may for example be used as one of the ingredients in a proof showing that it is consistent with Zermelo–Fraenkel set theory that the continuum hypothesis does not hold. It was introduced by .
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Duplex print devices, depending on options, software, and printer settings, can print single-sided page to single-sided page (1:1) or double-sided page to double-sided page (2:2). Many can also combine single-sided pages into a double-sided page format (1:2). Double-sided booklet formats (2:2 with a center fold) are also available, depending on optional outputs from the printer. Duplexed documents can be printed to be bound on either the short edge or the long edge.
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A subgroup of a finitely generated group need not be finitely generated. The commutator subgroup of the free group F_2 on two generators is an example of a subgroup of a finitely generated group that is not finitely generated. On the other hand, all subgroups of a finitely generated Abelian group are finitely generated. A subgroup of finite index in a finitely generated group is always finitely generated, and the Schreier index formula gives a bound on the number of generators required.
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EM typically converges to a local optimum, not necessarily the global optimum, with no bound on the convergence rate in general. It is possible that it can be arbitrarily poor in high dimensions and there can be an exponential number of local optima. Hence, a need exists for alternative methods for guaranteed learning, especially in the high-dimensional setting. Alternatives to EM exist with better guarantees for consistency, which are termed moment-based approaches or the so-called spectral techniques.
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In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ2 of any bounded probability distribution on the real line. Suppose a distribution has minimum m, maximum M, and expected value μ. Then the inequality says: : \sigma^2 \le (M - \mu)(\mu - m). \, Equality holds precisely if all of the probability is concentrated at the endpoints m and M. The Bhatia–Davis inequality is stronger than Popoviciu's inequality on variances.
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The West Seventh neighborhood is one of the oldest in Saint Paul. The neighborhood follows along West Seventh Street and is bound on the north by I-35E or the River Bluffs and by the Mississippi River to the South. It formed in the late 1830s from discharged soldiers and other pioneers building houses along the Mississippi River. Later, a boat dock south of Fort Snelling known as the Upper Landing became an important landing spot for dropping off settlers and supplies.
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The Betz limit places an upper bound on the annual energy that can be extracted at a site. Even if a hypothetical wind blew consistently for a full year, no more than the Betz limit of the energy contained in that year's wind could be extracted. Essentially increasing system economic efficiency results from increased production per unit, measured per square meter of vane exposure. An increase in system efficiency is required to bring down the cost of electrical power production.
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This is caused when the cylinder temperature nears the flash point of the charge. At this point, ignition can spontaneously occur before the spark plug fires, causing excessive cylinder pressures. Auto- ignition can be mitigated by using fuels with high auto-ignition resistance (octane rating), however it still puts an upper bound on the allowable peak cylinder temperature. The thermodynamic limits assume that the engine is operating under ideal conditions: a frictionless world, ideal gases, perfect insulators, and operation for infinite time.
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Although the galactic vector potential is very large because the galactic magnetic field exists on very great length scales, only the magnetic field would be observable if the photon is massless. In the case that the photon has mass, the mass term m'A'A would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of . The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.
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The width of a problem is the width of its minimal- width decomposition. While decompositions of fixed width can be used to efficiently solve a problem, a bound on the width of instances does necessarily produce a tractable structural restriction. Indeed, a fixed width problem has a decomposition of fixed width, but finding it may not be polynomial. In order for a problem of fixed width being efficiently solved by decomposition, one of its decompositions of low width has to be found efficiently.
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The Warkentin Farm is located on the northern fringe of Halsted, on the east side of Main Street at East North Street. The property consists of , bound on the south by railroad tracks, the north and east by the Arkansas River, and the west by a grain elevator. The farm complex is clustered near the western end of the property, with fields to the east. Buildings in the farmstead include the house, carriage house, barn, a silo, and a small pump house.
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Without ko, Go is PSPACE-hard. This is proved by reducing True Quantified Boolean Formula, which is known to be PSPACE-complete, to generalized geography, to planar generalized geography, to planar generalized geography with maximum degree 3, finally to Go positions. Go with superko is not known to be in PSPACE. Though actual games seem never to last longer than n^2 moves, in general it is not known if there were a polynomial bound on the length of Go games.
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The Rockhampton Courthouse complex, containing the Supreme Court, Magistrate's Court, District Court, Family Services' building and Government Office building, is located on a level site bound on three sides by East, Fitzroy and Bolsover Streets. The site is prominently located within the city centre at the entrance to the East Street mall, and adjacent to the approach to the Fitzroy Bridge leading to North Rockhampton. The Magistrate's Court, District Court and Family Services' building have been designed in a similar architectural style.
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McKinley neighborhood on Minneapolis’ north side is bound on the north by Dowling Avenue North, on the south by Lowry Avenue North, on the west by Dupont Avenue North and on the east by the Mississippi River. The neighborhood is named for William McKinley, the 25th president of the United States. Many of the homes are two-story, single-family homes with wood frames; bungalows and some small stucco Tudors. Most of the houses were built between 1910 and 1930.
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Input vector- pattern dependent approaches are computationally intensive and are limited to circuit blocks rather than full-chip analysis. Furthermore, these approaches are inherently optimistic, underestimating the voltage drop and thus letting some of the supply noise problems go unnoticed. The vectorless approaches, on the other hand, aim to compute an upper bound on the worst-case drop in an efficient manner. These approaches have the advantage of being fast and conservative, but are sometimes too conservative, leading to overdesign.
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Shaped roughly like an inverted triangle, the country has a long coastline. It is bound on the north by the Caribbean Sea and the Atlantic Ocean, on the east by Guyana, on the south by Brazil, and on the west by Colombia. It has the 55th largest Exclusive Economic Zone of . Its maritime territory borders Trinidad and Tobago, Dominica, the Dominican Republic, Grenada, St. Kitts and Nevis, St. Vincent and the Grenadines, France, the United Kingdom, the Netherlands, and the United States.
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Dependence of temperature on depth in Earth's upper 500 kilometers (black curve). An upper bound on the amount of water in the mantle can be obtained by considering the amount of water that can be carried by its minerals (their storage capacity). This depends on temperature and pressure. There is a steep temperature gradient in the lithosphere where heat travels by conduction, but in the mantle the rock is stirred by convection and the temperature increases more slowly (see figure).
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Each processor may perform a noisy broadcast to all other processors where the received bits may be independently flipped with a fixed probability. The problem is for processor P_0 to determine f(x_1,x_2,\ldots,x_n) for some function f. Saks et al. showed that an existing protocol by Gallager was indeed optimal by a reduction from a generalized noisy decision tree and produced a \Omega(n\log(n)) lower bound on the depth of the tree that learns the input.
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In a sphere of radius R, the entropy in a relativistic gas increases as the energy increases. The only known limit is gravitational; when there is too much energy the gas collapses into a black hole. Bekenstein used this to put an upper bound on the entropy in a region of space, and the bound was proportional to the area of the region. He concluded that the black hole entropy is directly proportional to the area of the event horizon.
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Cipollini's antics are legendary, including showing up to the stage start at the Tour de France dressed in a Julius Caesar-inspired toga complete with an olive wreath, riding on a carriage pulled by his teammates on bicycles. More recently, the entire Saeco team raced a stage of the 2003 Tour de France wearing a Legalize my Cannondale chaingang cycling kit to protest the UCI's lower bound on bike weight which means that their six13 prototype team bikes were underweight and required the installation of additional weight.
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While staying at Chatanati, Goldsborough was struck down by fever and died ‘within some few days after’ 28 November 1693. Before leaving London he made a will, dated 7 March 1691, wherein he described himself as ‘of Bethnall Green, in the county of Middlesex, knight, being bound on a voyage to the East India beyond the seas in the shipp Berkly Castle’ (registered in P. C. C. 12, Bond). Goldsborough was succeeded by Sir John Gayer, who was appointed General of India and based at Bombay.
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In some fields, however, the big O notation (number 2 in the lists above) would be used more commonly than the big Theta notation (items numbered 3 in the lists above). For example, if T(n) represents the running time of a newly developed algorithm for input size n, the inventors and users of the algorithm might be more inclined to put an upper asymptotic bound on how long it will take to run without making an explicit statement about the lower asymptotic bound.
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The number of arithmetic operations is another resource that is commonly used. In this case, one talks of arithmetic complexity. If one knows an upper bound on the size of the binary representation of the numbers that occur during a computation, the time complexity is generally the product of the arithmetic complexity by a constant factor. For many algorithms the size of the integers that are used during a computation is not bounded, and it is not realistic to consider that arithmetic operations take a constant time.
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It is advancing closer to the Earth with a heliocentric radial velocity of −122.7 km/s, and may come as close as in around 643,000 years. This appears to be a single-lined spectroscopic binary system with an orbital period of 130.7 days and an eccentricity of 0.366. It has an "a sin i" value of , where a is the semimajor axis and i is the inclination to the line of sight from the Earth. This value provides a lower bound on the actual semimajor axis.
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The projected semi- major axis of the primary star's orbit is , providing a lower bound on the separation of the stars. The system is around four billion years old. The visible component is an evolved K-type giant star with a stellar classification of ; the suffix notation indicates a mild underabundance of iron in the spectrum. It is probably on the horizontal branch, fusing helium in its core, but may be on the red giant branch fusing hydrogen in a shell around an insert helium core.
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According to a July 2011 interview on the podcast WTF with Marc Maron, Martin had a short-lived marriage with a former high school classmate named Jen. They began dating after high school and got married when he was at NYU Law School and she was attending NYU Medical School. This relationship was further analyzed in his one-man show Spiral Bound. On June 1, 2012, Martin married his long-time girlfriend Rachael Beame in Santa Monica, California, where he has lived since 2009.
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Using pseudo-holomorphic curves, and associated a bigraded abelian group, called knot Floer homology, to each isotopy class of knots. The graded Euler characteristic of knot Floer homology is the Alexander polynomial. While the Alexander polynomial gives a lower bound on the genus of a knot, showed that knot Floer homology detects the genus. Similarly, while the Alexander polynomial gives an obstruction to a knot complement fibering over the circle, showed that knot Floer homology completely determines when a knot complement fibers over the circle.
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Proof pressures are established by the SAAMI, as a percentage of the working pressure, so this places an upper bound on the +P+ pressures of 30–40%. By way of comparison, magnum calibers may be loaded to nearly twice the pressure of the rounds from which they were derived. Overpressure rounds are commonly defensive rounds and are loaded by police and others in need of maximum power in a compact firearm. Accordingly, most overpressure rounds are hollow points or other types of expanding ammunition.
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This alliance, however, was at once destroyed by the execution of Charles I on 30 January 1649, which excited universal horror in Scotland. In the series of tangled incidents which followed, Argyll lost control of the national policy. He describes himself at this period as "a distracted man ... in a distracted time" whose "remedies ... had the quite contrary operation". Argyll supported the invitation from the Covenanters to Charles II to land in Scotland, and gazed upon the captured Montrose, bound on a cart to execution at Edinburgh.
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This star is rotating rapidly, with a projected rotational velocity of 317 km s−1 giving a lower bound on the azimuthal velocity along the equator. As a result, it has a pronounced equatorial bulge, causing the star to assume an oblate spheroidal shape. The equatorial radius is about 30.7% greater than the polar radius. Because of the Doppler effect, this rapid rotation makes the absorption lines in the star's spectrum broaden and smear out, as indicated by the 'n' suffix in the stellar class.
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Like New, the film faced hurdles prior to release with the censor boards insisting on several cuts and Surya's ongoing legal tussles meant the film was delayed. The film opened to mixed reviews in September 2005, with Sify.com labelling it as "adult entertainment" though added he "tries hard to bring his character Shiva to life but has to go miles as far as dialogue delivery and voice modulation goes but has improved leaps and bound on the dancing front".Sify Movies – Review listing. Sify.com.
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The method requires only addition, subtraction, and multiplication, making it very convenient for high-speed computation. (The only divisions are inverses of small integers, which can be precomputed.) Use of a high order—calculating many coefficients of the power series—is convenient. (Typically a higher order permits a longer time step without loss of accuracy, which improves efficiency.) The order and step size can be easily changed from one step to the next. It is possible to calculate a guaranteed error bound on the solution.
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Due to their large heights, this model of equiprobable random trees is not generally used for binary search trees, but it has been applied to problems of modeling the parse trees of algebraic expressions in compiler design, p. 63. (where the above-mentioned bound on Strahler number translates into the number of registers needed to evaluate an expression.) and for modeling evolutionary trees.. In some cases the analysis of random binary trees under the random permutation model can be automatically transferred to the uniform model., p. 70.
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This is often described as adding twigs. By proving that every n-omino is a sequence of twigs, and by proving limits on the combinations of possible twigs, one obtains an upper bound on the number of n-ominoes. For example, in the algorithm outlined above, at each step we must choose a larger number, and at most three new numbers are added (since at most three unnumbered squares are adjacent to any numbered square). This can be used to obtain an upper bound of 6.75.
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Cassandra arrives to help Anita clean up but then, to Anita's surprise, knocks Anita unconscious and delivers her to Raina and Gabriel. With Anita safely bound on the set of Raina's porn films, Cassandra explains that she, Dominic and Sabin are a triumvirate. Cassandra was the lover who convinced Sabin to give up feeding on humans, causing him to develop his degenerative condition. Dominic believed that by sacrificing Jean-Claude's triumvirate, they could heal Sabin, and the three of them came to St. Louis to do so.
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Class X extends class Y to add functionality, either by adding fields or methods to class Y, or by overriding methods of class Y. An interface Z extends one or more interfaces by adding methods. Class X is said to be a subclass of class Y; Interface Z is said to be a subinterface of the interfaces it extends. :Also used to specify an upper bound on a type parameter in Generics. ;`final` :Define an entity once that cannot be changed nor derived from later.
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In 1977, Lee and Weinberg wrote an article about the lower bound on heavy neutrino mass. In this paper, they revealed that if the heavy and stable particles in the early universe which can only be transferred into other particles through the pair annihilation remain as relics after the universe's expansion, then the strength of the interaction should be bigger than 2 GeV. This calculation can be applied to find the amount of the dark matter. This bound is called the Lee-Weinberg bound.
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These highly sensitive instruments were able to put an upper bound on the overall methane abundance at 0.05 p.p.b.v. This nondetection is a major contradiction to what was previously observed with less sensitive instruments and will remain a strong argument in the ongoing debate over the presence of methane in the Martian atmosphere. Furthermore, current photochemical models cannot explain the presence of methane in the atmosphere of Mars and its reported rapid variations in space and time. Neither its fast appearance nor disappearance can be explained yet.
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Although a system can have multiple negative temperature regions and thus have −∞ to +∞ discontinuities. In many familiar physical systems, temperature is associated to the kinetic energy of atoms. Since there is no upper bound on the momentum of an atom, there is no upper bound to the number of energy states available when more energy is added, and therefore no way to get to a negative temperature. However, in statistical mechanics, temperature can correspond to other degrees of freedom than just kinetic energy (see below).
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In the SIMP method a lower bound on the Young's modulus is added, E_0 , to make sure the derivatives of the objective function are non-zero when the density becomes zero. The higher the penalisation factor, the more SIMP penalises the algorithm in the use of non-binary densities. Unfortunately, the penalisation parameter also introduces non-convexitiesvan Dijk, NP. Langelaar, M. van Keulen, F. Critical study of design parameterization in topology optimization; The influence of design parameterization on local minima.. 2nd International Conference on Engineering Optimization, 2010.
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Little Portugal (also known as Portugal Village; Portuguese: Pequeno Portugal / aldeia Portugal) is a neighbourhood and ethnic enclave in Toronto, Ontario, Canada. It is located west of downtown in the "Old" City of Toronto. It is bound on the west by Lansdowne Avenue, on the north by College Street, on the east by Bathurst Street and on the south by the Go Transit and Union Pearson Express railway tracks. The area is mainly residential, with Portuguese businesses along Dundas Street West and College Street.
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One approach is to use special formulations of linear programming problems. Another method involves the use of branch and bound techniques, where the program is divided into subclasses to be solved with convex (minimization problem) or linear approximations that form a lower bound on the overall cost within the subdivision. With subsequent divisions, at some point an actual solution will be obtained whose cost is equal to the best lower bound obtained for any of the approximate solutions. This solution is optimal, although possibly not unique.
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Current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim. Also loop quantum gravity introduces a lower bound on the possible length scales. There have been recent claims that loop quantum gravity may be able to reproduce features resembling the Standard Model. So far only the first generation of fermions (leptons and quarks) with correct parity properties have been modelled by Sundance Bilson-Thompson using preons constituted of braids of spacetime as the building blocks.
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Singmaster's conjecture is a conjecture in combinatorial number theory in mathematics, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times). It is clear that the only number that appears infinitely many times in Pascal's triangle is 1, because any other number x can appear only within the first x + 1 rows of the triangle.
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Note, however, that these confidence limits cannot take systematic error into account. Also, parameter errors should be quoted to one significant figure only, as they are subject to sampling error. When the number of observations is relatively small, Chebychev's inequality can be used for an upper bound on probabilities, regardless of any assumptions about the distribution of experimental errors: the maximum probabilities that a parameter will be more than 1, 2 or 3 standard deviations away from its expectation value are 100%, 25% and 11% respectively.
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The multi-homogeneous Bézout bound on the number of solutions may be used for non-homogeneous systems of equations, when the polynomials may be (multi)-homogenized without increasing the total degree. However, in this case, the bound may be not sharp, if there are solutions "at infinity". Without insight on the problem that is studied, it may be difficult to group the variables for a "good" multi-homogenization. Fortunately, there are many problems where such a grouping results directly from the problem that is modeled.
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The four kasaya are: krodha (anger), lobha (greed), mana (ego) and maya (deceit). Out of the many causes of bondage, emotions or passions are considered as the main cause of bandha or bondage. The karmas are literally bound on account of the stickiness of the soul due to existence of various passions or mental dispositions. p. 112 The passions like anger, pride, deceit and greed are called sticky (kaṣāyas) because they act like glue in making karmic particles stick to the soul resulting in bandha.
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Flounder prepared for her sixth war patrol at Subic Bay from 26 February 1945 to 16 March. Again with a wolfpack, she scouted targets south of Hainan, and on 29 March contacted a large convoy, which was attacked by aircraft before she and her sisters could launch their torpedoes. She closed her war patrol at Saipan on 22 April and headed home for a stateside overhaul. Returning to Pearl Harbor action-bound on the day hostilities ended, Flounder was ordered to the East Coast, and arrived at New York City on 18 September.
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Mulberry is located between Baxter and Mott Streets. It runs north to south, through the center of Little Italy, parallel to Mott Street one block to the east, and is bound on the north by Bleecker Street in NoHo and on the south by Worth Street in Tribeca. Near the southern portion of Mulberry Street, the street enters Chinatown, where the street is lined with Chinese green grocers, butcher stores, and fish mongers. Further south past Bayard Street, on the west side of the street, lies Columbus Park that was created 1897.
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The global state approach was continued in automata theory for finite state machines and push down stack machines including their nondeterministic versions. All of these models have the property of bounded nondeterminism: if a machine always halts when started in its initial state, then there is a bound on the number of states in which it can halt. Hewitt argued that there is a fundamental difference between choices in global state nondeterminism and the arrival order indeterminacy (nondeterminism) of his Actor model. In global state nondeterminism, a "choice" is made for the "next" global state.
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No matter how strange it was to elect a new patriarch while the current was still alive and well, the Serbian Church needed a leader and it set on electing a new patriarch in great haste. Gavrilo's departure meant the downfall of the party within the Serbian Church which was set on establishing closer ties to the West. The other camp, bound on retaining good relations with the Ottoman authorities came to power. As Metropolitan Maksim was one of the most active proponents of this policy he was chosen to the patriarchal throne in Peć.
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In some versions of Ring- LWE there is a security reduction to the shortest-vector problem (SVP) in a lattice as a lower bound on the security. The SVP is known to be NP-hard. Specific ring-LWE systems that have provable security reductions include a variant of Lyubashevsky's ring-LWE signatures defined in a paper by Güneysu, Lyubashevsky, and Pöppelmann. The GLYPH signature scheme is a variant of the Güneysu, Lyubashevsky, and Pöppelmann (GLP) signature which takes into account research results that have come after the publication of the GLP signature in 2012.
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Yitang "Tom" Zhang () (born 1955) is a Chinese-born American mathematician working in the area of number theory. While working for the University of New Hampshire as a lecturer, Zhang submitted an article to the Annals of Mathematics in 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. This work led to a 2014 MacArthur awardYitang Zhang, Mathematician, MacArthur Fellows Program, MacArthur Foundation, September 17, 2014 and his appointment as a professor at the University of California, Santa Barbara.
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They thereby obtained a limiting mass of approximately 0.7 solar masses, which was less than the Chandrasekhar limit for white dwarfs. Taking account of the strong nuclear repulsion forces between neutrons, modern work leads to considerably higher estimates, in the range from approximately 1.5 to 3.0 solar masses. The uncertainty in the value reflects the fact that the equations of state for extremely dense matter are not well known. The mass of the pulsar PSR J0348+0432, at solar masses, puts an empirical lower bound on the TOV limit.
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For high enough noise levels, the same primitives as in the BQSM can be achieved and the BQSM forms a special case of the noisy-storage model. In the classical setting, similar results can be achieved when assuming a bound on the amount of classical (non- quantum) data that the adversary can store. It was proven, however, that in this model also the honest parties have to use a large amount of memory (namely the square-root of the adversary's memory bound). This makes these protocols impractical for realistic memory bounds.
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Three former Federal Reserve officials, Don Kohn, Ben Bernanke and Narayana Kocherlakota, can be seen discussing his proposal for eliminating the lower bound on interest rates here. Many of his blog posts have been translated into Japanese and some into Thai. Kimball is a Unitarian-Universalist lay preacher after having departed from The Church of Jesus Christ of Latter-day Saints (LDS Church) around the age of 40 (circa 2000). He has a special interest outside his professional field of economics in the fields of nutrition and fasting.
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The Range is bound on the north by the Antelope Valley and the Mojave Desert and to the south by the communities of greater Los Angeles area. In the western portion of the San Gabriel Mountain Range, the Sierra Pelona Ridge stretches from approximately Soledad Canyon (14 Freeway and railroad right-of-way), formed by the Santa Clara River. The Sierra Pelona Ridge includes Liebre Mountain, Sawmill Mountain, Grass Mountain, Redrock Peak, Burnt Peak, most of which is part of the Angeles National Forest, but also features several rural communities.
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This in-up-out-down overturning flow is known as the secondary circulation. The Carnot perspective provides an upper bound on the maximum wind speed that a storm can attain. Scientists estimate that a tropical cyclone releases heat energy at the rate of 50 to 200 exajoules (1018 J) per day, equivalent to about 1 PW (1015 watt). This rate of energy release is equivalent to 70 times the world energy consumption of humans and 200 times the worldwide electrical generating capacity, or to exploding a 10-megaton nuclear bomb every 20 minutes.
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The terrestrial (i.e. non-marine) origin of the Jacobsville means that it contains no fossils with which to date the formation and paleocurrent direction cannot be used to determine its age. Additionally, it contains no igneous intrusions to place a lower bound on age, it provides no paleomagnetic data, and few exposures of the sandstone show its stratigraphic relationship to other formations. Because the Jacobsville Formation fills a portion of the rift that formed Lake Superior, it is generally assigned a late Precambrian age in the United States.
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About 8:30 AM Friday, March 16, 2001, Joseph L. Meyer, 33, fled on foot the scene of a non- injury accident near NW 36th and Pennsylvania. About the same time Justin Cornielson was preparing to unload cases of Budweiser beer from a tractor- trailer at the Homeland grocery store at NW 39th and Pennsylvania (Penn). Cornielson had just opened the back of his truck when Meyer climbed into the driver’s seat and started driving off. Oklahoma City Police officers started pursuing the stolen beer truck south bound on Penn.
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Specifically, Wiles presented his proof of the Taniyama–Shimura conjecture for semistable elliptic curves; together with Ribet's proof of the epsilon conjecture, this implied Fermat's Last Theorem. However, it became apparent during peer review that a critical point in the proof was incorrect. It contained an error in a bound on the order of a particular group. The error was caught by several mathematicians refereeing Wiles's manuscript including Katz (in his role as reviewer),Aczel, pp. 128–130. who alerted Wiles on 23 August 1993.Singh, p. 257.
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This is a single-lined spectroscopic binary with an (assumed) circular orbit having a period of only 7.8 days. It has an a sin i value of , where a is the semimajor axis and i is the orbital inclination. Since the sine function can be no larger than one, this provides a lower bound on the true semimajor axis of their orbit. The primary component is an metallic-line (Am) star with the calcium K line of an A3 star, the hydrogen lines of an F1 star, and the metal lines of an F2 star.
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Propositional proof systems can be interpreted as nondeterministic algorithms for recognizing tautologies. Proving a superpolynomial lower bound on a proof system P thus rules out the existence of a polynomial-time algorithm for SAT based on P. For example, runs of DPLL algorithm on unsatisfiable instances correspond to tree-like Resolution refutations. Therefore, exponential lower bounds for tree-like Resolution (see below) rule out the existence of efficient DPLL algorithms for SAT. Similarly, exponential Resolution lower bounds imply that SAT solvers based on Resolution, such as CDCL algorithms cannot solve SAT efficiently (in worst-case).
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The information theoretical lossless compression bound on DSC (the Slepian–Wolf bound) was first purposed by David Slepian and Jack Keil Wolf in terms of entropies of correlated information sources in 1973. They also showed that two isolated sources can compress data as efficiently as if they were communicating with each other. This bound has been extended to the case of more than two correlated sources by Thomas M. Cover in 1975. Similar results were obtained in 1976 by Aaron D. Wyner and Jacob Ziv with regard to lossy coding of joint Gaussian sources.
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In this case, both x and y are odd and z is even. Since (y2, z, x2) form a primitive Pythagorean triple, they can be written : z = 2de : y2 = d2 − e2 : x2 = d2 \+ e2 where d and e are coprime and d > e > 0. Thus, : x2y2 = d4 − e4 which produces another solution (d, e, xy) that is smaller (0 < d < x). As before, there must be a lower bound on the size of solutions, while this argument always produces a smaller solution than any given one, and thus the original solution is impossible.
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Since chromatic number is an upper bound on the order of the maximum clique, the latter invariant is also at most degeneracy plus one. By using a greedy coloring algorithm on an ordering with optimal coloring number, one can graph color a k-degenerate graph using at most k + 1 colors.; . A k-vertex-connected graph is a graph that cannot be partitioned into more than one component by the removal of fewer than k vertices, or equivalently a graph in which each pair of vertices can be connected by k vertex-disjoint paths.
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In computer science, the worst-case complexity (usually denoted in asymptotic notation) measures the resources (e.g. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as n or N). It gives an upper bound on the resources required by the algorithm. In the case of running time, the worst-case time-complexity indicates the longest running time performed by an algorithm given any input of size n, and thus guarantees that the algorithm will finish in the indicated period of time. The order of growth (e.g.
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In that case, the equilibrium real interest rate is given by : r = \rho +\theta g where r is the real (after tax) rate of return on capital (the real interest rate), \rho is the subjective rate of time preference (which measures impatience) and g is the annual growth rate of consumption. r is generally estimated to be around 5% (.05) and the annual growth rate of consumption is about 2% (.02). Then the upper bound on the cost of fluctuations occurs when \theta is at its highest, which in this case occurs if \rho=0.
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An algorithm to determine the minimum number of moves to solve Rubik's Cube was published in 1997 by Richard Korf.Richard E. Korf, "Finding optimal solutions to Rubik's Cube using pattern databases", Proc. Natl. Conf. on Artificial Intelligence (AAAI-97), Providence, Rhode Island, Jul 1997, pp. 700–705. While it had been known since 1995 that 20 was a lower bound on the number of moves for the solution in the worst case, it was proven in 2010 through extensive computer calculations that no configuration requires more than 20 moves.
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Spray and Wait is a routing protocol that attempts to gain the delivery ratio benefits of replication-based routing as well as the low resource utilization benefits of forwarding-based routing. Spray and Wait was developed by researchers at the University of Southern California. It was first presented at the 2005 ACM SIGCOMM conference, under the publication "Spray and Wait: An Efficient Routing Scheme for Intermittently Connected Mobile Networks". Spray and Wait achieves resource efficiency by setting a strict upper bound on the number of copies per message allowed in the network.
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HMS Danae in 1937 In 1923 she was attached to the Special Service Squadron, a naval fleet created for propaganda purposes. The flotilla further consisted of the battlecruisers , and the cruisers , Dragon, Dauntless and , as well as 9 other ships (mostly destroyers), and was bound on a journey around the world. The Squadron left Devonport on 27 November and headed for Freetown in Sierra Leone. Then the task force visited Cape Town, Port Elizabeth, East London and Durban, to where she arrived the last day of the year.
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A key tool for the attack on Coral was the "Gleason crutch", a form of Chernoff bound on tail distributions of sums of independent random variables. Gleason's classified work on this bound predated Chernoff's work by a decade. Toward the end of the war he concentrated on documenting the work of OP-20-G and developing systems for training new cryptographers. In 1950 Gleason returned to active duty for the Korean War, serving as a Lieutenant Commander in the Nebraska Avenue Complex (which much later became the home of the DHS Cyber Security Division).
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The upper bound on the scalability of this system is that no single website can ever utilise more than two servers at once - under this condition all standard LAMP applications will run unmodified. However, it is possible to scale beyond this limit via the use of multi-master database replication - this requires that applications store all variable state information within a database - the database can then be live on many servers, the web application itself must remain static and can be served from as many nodes in the cluster as required.
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The target schema might be the database schema for an object-oriented database as well as a relational database schema, or even an XML schema. Typically, terminology- oriented databases are not bound on a specific database type. Since the information content, which can be stored in object-oriented databases and in relational databases, is identical, data for a terminology-oriented database can be stored theoretically in any type of database as well as in an XML file. Thus, terminology-oriented databases may support several database systems for storing application data.
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Out of the many causes of bondage, emotions or passions are considered as the main cause of bondage. The karmas are literally bound on account of the stickiness of the soul due to existence of various passions or mental dispositions. The passions like anger, pride, deceit and greed are called sticky (kaṣāyas) because they act like glue in making karmic particles stick to the soul resulting in bandha. The karmic inflow on account of yoga driven by passions and emotions cause a long-term inflow of karma prolonging the cycle of reincarnations.
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Current commonly accepted physical theories imply or assume the photon to be strictly massless. If the photon is not a strictly massless particle, it would not move at the exact speed of light, c, in vacuum. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the upper bound on speed that any object could theoretically attain in spacetime.
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In commutative algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a commutative Noetherian ring. The theorem is sometimes referred to by its German name, Krulls Hauptidealsatz (Satz meaning "proposition" or "theorem"). Precisely, if R is a Noetherian ring and I is a principal, proper ideal of R, then each minimal prime ideal over I has height at most one. This theorem can be generalized to ideals that are not principal, and the result is often called Krull's height theorem.
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In the mathematics of graph drawing, the crossing number inequality or crossing lemma gives a lower bound on the minimum number of crossings of a given graph, as a function of the number of edges and vertices of the graph. It states that, for graphs where the number of edges is sufficiently larger than the number of vertices, the crossing number is at least proportional to . It has applications in VLSI design and combinatorial geometry, and was discovered independently by Ajtai, Chvátal, Newborn, and Szemerédi. and by Leighton..
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In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a generalization of the Chernoff bound, which applies only to Bernoulli random variables; for a more intuitive proof, see this note, and a special case of the Azuma–Hoeffding inequality and the McDiarmid's inequality. It is similar to, but incomparable with, the Bernstein inequality, proved by Sergei Bernstein in 1923.
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Since 1997, Toussaint has written articles for Brides magazine, Conde Nast Traveler, Working Woman, Instinct, Gay Financial Network, Outsider Ink, Caribbean Travel and Life and Diversion magazine. He has been an editor at Conde Nast and a three-time guest editor for Francis Ford Coppola's online magazine Zoetrope, and was a full-time columnist for GayWeddings.com. Currently he writes a weekly column and is a theater critic for EDGE magazine, and is the senior editor for GuySpy.com. In 2003, Toussaint wrote an article entitled Outward Bound on same-sex weddings for Brides magazine.
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The fact that the Glauber dynamics converges to the uniform distribution on -colorings naturally raises the question of how quickly it converges. That is, what is the mixing time? A lower bound on the mixing time is the diameter of the space of colorings, the maximum (over pairs of colorings) of the number of steps needed to change one coloring of the pair into the other. If the diameter is exponentially large in the number of vertices in the graph, then the Glauber dynamics on colorings is certainly not rapidly mixing.
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Hilbert's goal of proving the consistency of set theory or even arithmetic through finitistic means turned out to be an impossible task due to Kurt Gödel's incompleteness theorems. However, by Harvey Friedman's grand conjecture most mathematical results should be provable using finitistic means. Hilbert did not give a rigorous explanation of what he considered finitistic and referred to as elementary. However, based on his work with Paul Bernays some experts such as William Tait have argued that the primitive recursive arithmetic can be considered an upper bound on what Hilbert considered finitistic mathematics.
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Khora is a locality in the Ghaziabad district of Uttar Pradesh, India. Its official census population is approximately 190,000 residents (2011), but reports suggest a population closer to 1,000,000 residents inside the city's area of 10 square kilometers. It is located the on NH-24 highway, near Gaziabad and Delhi, and is within the National Capital Region of India. It is bound on the west and southwest by the village of Ghazipur, on the north and northwest by Hindon Canal, on the northeast by Indirapuram (Ghaizabad), and on the east and southeast by Noida.
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This theory was dismissed by fellow scientists, but has found approval more recently through further study into the relationship between gigantism and oxygen availability. If this theory is correct, these insects would have been susceptible to falling oxygen levels and certainly could not survive in our modern atmosphere. Other research indicates that insects really do breathe, with "rapid cycles of tracheal compression and expansion". Recent analysis of the flight energetics of modern insects and birds suggests that both the oxygen levels and air density provide a bound on size.
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Since instructions inside loops can be executed repeatedly, it is frequently not possible to give a bound on the number of instruction executions that will be impacted by a loop optimization. This presents challenges when reasoning about the correctness and benefits of a loop optimization, specifically the representations of the computation being optimized and the optimization(s) being performed.In the book Reasoning About Program Transformations, Jean- Francois Collard discusses in depth the general question of representing executions of programs rather than program text in the context of static optimization.
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A p-box (probability box). A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes. An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x.
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The Wh-word whom is the direct object of the verb likes in each of these sentences. There appears to be no limit on the distance that can separate the fronted expression from its canonical position. In more technical terms, we can say that the dependency relation between the gap (the canonical, empty position) and its filler (the Wh-expression) is unbounded in the sense that there is no upper bound on how deeply embedded within the given sentence the gap may appear. However, there are cases in which this is not possible.
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Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer than are typically made in reversible thermodynamics. It gives an upper bound on the energy that can be derived from a real process that is lower than that predicted by Carnot for a Carnot cycle, and accommodates the exergy destruction occurring as heat is transferred irreversibly. Endoreversible thermodynamics was discovered in simultaneous work by Novikov and Chambadal,Chambadal P (1957) Les centrales nucléaires. Armand Colin, Paris, France, 4 1-58 although sometimes mistakenly attributed to Curzon & Ahlborn.
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Minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. This term is commonly used in the fields of biology, ecology, and conservation biology. MVP refers to the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" is defined as a group of interbreeding individuals in similar geographic area that undergo negligible gene flow with other groups of the species.
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In spectral graph theory, the Alon–Boppana bound provides a lower bound on the second-largest eigenvalue of the adjacency matrix of a d-regular graph, meaning a graph in which every vertex has degree d. The reason for the interest in the second-largest eigenvalue is that the largest eigenvalue is guaranteed to be d due to d-regularity, with the all-ones vector being the associated eigenvector. The graphs that come close to meeting this bound are Ramanujan graphs, which are examples of the best possible expander graphs.
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The powers of three give the place values in the ternary numeral system. In graph theory, powers of three appear in the Moon–Moser bound on the number of maximal independent sets of an -vertex graph, and in the time analysis of the Bron–Kerbosch algorithm for finding these sets. Several important strongly regular graphs also have a number of vertices that is a power of three, including the Brouwer–Haemers graph (81 vertices), Berlekamp–van Lint–Seidel graph (243 vertices), and Games graph (729 vertices).For the Brouwer–Haemers and Games graphs, see .
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Another limitation of Turing machines is that they do not model concurrency well. For example, there is a bound on the size of integer that can be computed by an always-halting nondeterministic Turing machine starting on a blank tape. (See article on unbounded nondeterminism.) By contrast, there are always-halting concurrent systems with no inputs that can compute an integer of unbounded size. (A process can be created with local storage that is initialized with a count of 0 that concurrently sends itself both a stop and a go message.
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On the other hand, using Gabor transform causes an improvement in the clarity and readability of the representation, therefore improving its interpretation and application to practical problems. Consequently, when the signal we tend to sample is composed of single component, we use the WDF; however, if the signal consists of more than one component, using the Gabor transform, Gabor-Wigner distribution function, or other reduced interference TFDs may achieve better results. The Balian–Low theorem formalizes this, and provides a bound on the minimum number of time–frequency samples needed.
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Line 8 platform Oriental Sports Center () formerly known as Jiyang Road () is an interchange station between Lines 6, 8 and 11 of the Shanghai Metro. It is the first cross-platform interchange in Shanghai as well as the southern terminus of Line 6; it is also the first station in Pudong when heading southeast-bound on Line 11 towards . Due to previous constructions on Line 11 and the nearby sports stadium, the station only allowed line transfers and exits to the surface only opened on April 12, 2011.
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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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Observations made between 2001–2003 by the Okayama Planet Search Program showed that Omega Serpentis is undergoing periodic radial velocity variations with a preliminary period estimate of 312.3 days. Following this announcement in 2005, further observations were performed that were best explained by a planet following a Keplerian orbit. This companion has an estimated orbital period of 277 days, a semimajor axis of 1.1 AU, and an eccentricity of 0.1. Since the inclination of the orbit is unknown, only a lower bound on the mass of the planet can be determined.
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A recommended initial value is 64. The time-to-live value can be thought of as an upper bound on the time that an IP datagram can exist in an Internet system. The TTL field is set by the sender of the datagram, and reduced by every router on the route to its destination. If the TTL field reaches zero before the datagram arrives at its destination, then the datagram is discarded and an Internet Control Message Protocol (ICMP) error datagram (11 - Time Exceeded) is sent back to the sender.
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The Municipality of Carmen is geographically located at about the points 124.8 degrees east and 7.2 degrees north. It is bound on the north by the Province of Bukidnon, on the east by the municipalities of Pres. Roxas and Kabacan, on the south by the Province of Maguindanao, and on the west by the Municipality of Aleosan. It is embraced from the north-east, then east, then south by the Mulita and the Rio Grande rivers; from the north-west, then west, then south-west, by the Malitubog and Maridagao rivers.
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As such, the problem of adaptive combinatorial group testing – with a known number or upper bound on the number of defectives – has essentially been solved, with little room for further improvement. There is an open question as to when individual testing is minmax. Hu, Hwang and Wang showed in 1981 that individual testing is minmax when n \leq \lfloor (5d + 1)/2 \rfloor, and that it is not minmax when n > 3d. It is currently conjectured that this bound is sharp: that is, individual testing is minmax if and only if n \leq 3d.
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The Okayama Planet Search team published a paper in 2005 reporting investigations on radial velocity variations observed for a set of class G giants and announcing the detection of a brown dwarf companion in orbit around Upsilon¹ Hydrae. The orbital period for this companion is roughly 4.1 years, and it has a high eccentricity of 0.57. Since the inclination of the orbit to the line-of-sight is unknown, only a lower bound on the mass can be determined. It has at least 49 times the mass of Jupiter.
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The large-scale universe appears isotropic as viewed from Earth. If it is indeed isotropic, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10−5 via observations of the temperature of the CMB. At the scale of the CMB horizon, the universe has been measured to be homogeneous with an upper bound on the order of 10% inhomogeneity, as of 1995.
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The usual type of runner is > from 6 to 7.5 feet long, 6 inches wide, and from 3 to 5 inches thick. A > 6-inch by 6-inch by 4-foot or 5-foot bunk is fastened to each runner by a > bolt. The bunk is placed from 2 to 2.5 feet from the rear end of the > runners. A ring is attached to the center of this bunk and the logs are > bound on the latter by a chain passing around the logs and bunk and through > the ring.
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The St. Petersburg paradox (named after the journal in which Bernoulli's paper was published) arises when there is no upper bound on the potential rewards from very low probability events. Because some probability distribution functions have an infinite expected value, an expected-wealth maximizing person would pay an arbitrarily large finite amount to take this gamble. In real life, people do not do this. Bernoulli proposed a solution to this paradox in his paper: the utility function used in real life means that the expected utility of the gamble is finite, even if its expected value is infinite.
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The main results from Hamburger's prewar research concerned the Hamburger moment problem, which is named after him, and his work on the Carathéodory conjecture, beginning in Berlin in 1922. His work on this topic was published only 20 years later, a reflection of the difficulty of the problem. He attributed the conjecture to Carathéodory and his approach was a reformulation of the conjecture in terms of a bound on the index of an isolated umbilic point of a surface. His attribution remains in place today, and his solution of the Carathéodory conjecture in the real analytic case is regarded as complete.
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The combination of a large neutron star mass, low white dwarf mass (mass ratio ~ 1:11.7) and short orbital period (2 hours and 27 minutes) allows astronomers to test general relativity in a regime of extreme gravitational fields, where it has never been tested before. The result also has implications for the direct detection of gravitational waves and for understanding of stellar evolution. The measured mass of 2.01 \pm 0.04 M_\odot puts an empirical lower bound on the value of the Tolman–Oppenheimer–Volkoff limit. PSR J0348+0432 is also a candidate for a hyperon star, a massive neutron star containing hyperons.
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Phillips performed this song during the 36th Annual Capitol Fourth on July 4, 2012. The song quickly became a song popularly used as backing soundtrack in films, television shows, and commercials after its release. It appeared in the trailer for the film Trouble with the Curve, the trailer for the 2014 Disneynature film Bears, as well as the ending credits of Parental Guidance and Monster Trucks. It was in a television commercial for Extreme Makeover: Home Edition, played at the end of Suburgatory episode "Krampus," and was performed as a mash-up with Simon & Garfunkel's "Homeward Bound" on Glee.
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In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments. The method is often quantitative, in that one can often deduce a lower bound on the probability that the random variable is larger than some constant times its expectation. The method involves comparing the second moment of random variables to the square of the first moment.
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The subject site contains a section of the Parramatta Sand Body and the site of the Military Barracks and Soldiers Garden established in circa 1790. The site is within Robin Thomas Reserve which is located on the eastern fringe of the Parramatta Central Business District. It is bound on the north by George Street, on the west by Harris Street, on the south by Lot 7 DP720779 (formerly part of Hassall Street) and on the east by 153 George Street and Lot 7049 DP 93899 of Robin Thomas Reserve. The bulk of the subject site comprises playing fields.
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Round Trip is the third studio album by power pop/new wave band The Knack that was released by Capitol Records in 1981. It received generally unfavorable critical reviews, but it reached #93 in the Billboard 200 and also contained single "Pay The Devil (Ooo, Baby, Ooo)" (hitting #67 on the Billboard Hot 100). "Boys Go Crazy" was issued as the single from the album in Australia. It was also issued as a follow up single to "Pay the Devil" in the U.S. and was expected to be "chart bound" on the Hot 100, but it did not chart.
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During the execution of Bareiss algorithm, every integer that is computed is the determinant of a submatrix of the input matrix. This allows, using the Hadamard inequality, to bound the size of these integers. Otherwise, the Bareiss algorithm may be viewed as a variant of Gaussian elimination and needs roughly the same number of arithmetic operations. It follows that, for an n × n matrix of maximum (absolute) value 2L for each entry, the Bareiss algorithm runs in O(n3) elementary operations with an O(nn/2 2nL) bound on the absolute value of intermediate values needed.
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Bound on the Wheel was a three act feature. The film is set in the east-side tenements of New York City. Elsie Jane Wilson plays the "embittered" Cora Gertz who lives in a tenement room with her parents, and Lon Chaney plays Tom Coulahan, a "drink-numbed 'good-for-nothing'" who lives on the floor below them with his alcoholic parents. Tom wants to take Cora away with him to live in a place of their own, but his parents create such a fuss that after they are married, Cora agrees to live there with Tom and his parents.
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"Upgrading Eltham to a Premium Station" Newsrail October 1997 page 310 Prior to the works, Bentleigh closely resembled McKinnon station. Also around this time, the underpass was filled in. In 2006, the station's pedestrian level crossing was upgraded, as part of the VicTrack trial of new crossing technology. Additional warning devices were also fitted, with the common red pedestrian sign, as well as an LED light box saying "Another Train Coming", which is lit when either an express train is bound on the southbound line, or when a train is expected after another train on the northbound line.
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Nevertheless, the minimum length of proofs of theorems will remain unbounded, that is, for any natural number n there will still be theorems which cannot be proved in n or fewer steps. If the new axiom schema is not a tautology, then every formula becomes a theorem (which makes the concept of a theorem useless in this case). What is more, there is then an upper bound on the minimum length of a proof of every formula, because there is a common method for proving every formula. For example, suppose the new axiom schema were ((B→C)→C)→B.
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Research on the heritability of IQ inquires into the proportion of variance in IQ that is attributable to genetic variation within a population. "Heritability", in this sense, is a mathematical estimate that indicates an upper bound on how much of a trait's variation within a population can be attributed to genes. There has been significant controversy in the academic community about the heritability of IQ since research on the issue began in the late nineteenth century. Intelligence in the normal range is a polygenic trait, meaning that it is influenced by more than one gene,Alice Marcus. 2010.
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In superconductors, charge can flow without any resistance. It is possible to make pieces of superconductor with a large built-in persistent current, either by creating the superconducting state (cooling the material) while charge is flowing through it, or by changing the magnetic field around the superconductor after creating the superconducting state. This principle is used in superconducting electromagnets to generate sustained high magnetic fields that only require a small amount of power to maintain. The persistent current was first identified by H. Kamerlingh Onnes, and attempts to set a lower bound on their duration have reached values of over 100,000 years.
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The minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. More specifically MVP is the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" refers to the population of a species in the wild. As a reference standard, MVP is usually given with a population survival probability of somewhere between ninety and ninety-five percent and calculated for between one hundred and one thousand years into the future.
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It also gives us a rough estimate that may be good enough for some purposes: if we want to start a store in Chicago that sells piano tuning equipment, and we calculate that we need 10,000 potential customers to stay in business, we can reasonably assume that the above estimate is far enough below 10,000 that we should consider a different business plan (and, with a little more work, we could compute a rough upper bound on the number of piano tuners by considering the most extreme reasonable values that could appear in each of our assumptions).
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Linda Condon is about a wealthy woman—the eponymous heroine—who never learns to have, let alone show, any emotions or, as the narrator puts it, to "lose herself". Although she does not do anybody any harm, in the course of the novel Linda is likened to Siberia, described by her husband as a "woman of alabaster", and calls herself "the most sterile woman alive". Married at 18, she sees herself "in a place of little importance" and at the same time "bound on a journey with a hidden destination". Linda Condon is dedicated to Carl Van Vechten.
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The notion of a nil ideal has a deep connection with that of a nilpotent ideal, and in some classes of rings, the two notions coincide. If an ideal is nilpotent, it is of course nil, but a nil ideal need not be nilpotent for more than one reason. The first is that there need not be a global upper bound on the exponent required to annihilate various elements of the nil ideal, and secondly, each element being nilpotent does not force products of distinct elements to vanish. In a right Artinian ring, any nil ideal is nilpotent.
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Crenarchaeol is a glycerol dibiphantanyl glycerol tetraether (GDGT) biological membrane lipid. It has an distinctive cyclohexane moiety and has been proposed as a specific biomarker for pelagic ammonia-oxidizing archaea (AOA). Structurally, the molecule consists of two long hydrocarbon chains that extend through the cell membrane and are bound on each to glycerol through ether linkage. Crenarchaeol can be preserved for hundreds of millions of years in the environment and is part of the TEX86 paleothermometer, a temperature proxy for sea surface temperatures that has been used to reconstruct paleoclimate through to the middle Jurassic (~160 Ma).
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Lackenby's research contributions include a proof of a strengthened version of the 2 theorem on sufficient conditions for Dehn surgery to produce a hyperbolic manifold, a bound on the hyperbolic volume of a knot complement of an alternating knot, and a proof that every diagram of the unknot can be transformed into a diagram without crossings by only a polynomial number of Reidemeister moves. Lackenby won the Whitehead Prize of the London Mathematical Society in 2003. In 2006, he won the Philip Leverhulme Prize in mathematics and statistics. He was an invited speaker at the International Congress of Mathematicians in 2010.
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Time Unveils the Truth, black and white chalk drawing from 1755, now in the Museum Kunstpalast Jean-Charles Frontier was born in Paris in 1701. He was a pupil of Claude-Guy Hallé, and took the first prize at the Academy in 1728, with a picture of Ezekiel abolishing Idolatry and establishing the Worship of the true God. He was received as an academician in 1744, with the picture Prometheus bound on Caucasus, now in the Louvre. He exhibited at the Salon from 1743 to 1761, and became director of the Academy of Lyon, where he died in 1763.
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Any n-vertex forest has tree- depth O(log n). For, in a forest, one can always find a constant number of vertices the removal of which leaves a forest that can be partitioned into two smaller subforests with at most 2n/3 vertices each. By recursively partitioning each of these two subforests, we can easily derive a logarithmic upper bound on the tree-depth. The same technique, applied to a tree decomposition of a graph, shows that, if the treewidth of an n-vertex graph G is t, then the tree-depth of G is O(t log n).
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Exit 142 to Route 100, east of Saint John An experiment with Sunbury's new A-Trains led to the redesign of highway exit 119. Exit 119-B, west-bound, was widened to allow these longer transport truck configurations to navigate the exit. On the opposite side of the highway, the two east-bound on-ramps were combined into a wider single ramp, again to allow easier navigation for the longer transport trucks to navigate. An east-bound exit was never officially available at exit 128, as it was only a private truck entrance into Strescon's property.
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Different degrees or ratios of anisotropic filtering can be applied during rendering and current hardware rendering implementations set an upper bound on this ratio. This degree refers to the maximum ratio of anisotropy supported by the filtering process. For example, 4:1 (pronounced “4-to-1”) anisotropic filtering will continue to sharpen more oblique textures beyond the range sharpened by 2:1. In practice what this means is that in highly oblique texturing situations a 4:1 filter will be twice as sharp as a 2:1 filter (it will display frequencies double that of the 2:1 filter).
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This is bound on its western side by industrial units and warehouses. The London Borough of Waltham Forest has proposed developing the area around Blackhorse Road railway station to become a gateway to the town. Although bounded by the marshes to the west and parts of Epping Forest to the east, there is little open space in the actual town. There used to be two commons in the town, Church Common, adjacent to St. Mary's Church in Walthamstow Village and Markhouse Common, located off Markhouse Lane (now Markhouse Road) and what is now the western end of Queens Road.
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A Schottky group is called classical if all the disjoint Jordan curves corresponding to some set of generators can be chosen to be circles. gave an indirect and non-constructive proof of the existence of non-classical Schottky groups, and gave an explicit example of one. It has been shown by that all finitely generated classical Schottky groups have limit sets of Hausdorff dimension bounded above strictly by a universal constant less than 2. Conversely, has proved that there exists a universal lower bound on the Hausdorff dimension of limit sets of all non- classical Schottky groups.
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The Kamo River and the Katsura River flow through the district. It is home to several historical places and temples. Minami-ku is roughly bound on the east by the Kamo River, on the west by the Katsura River (although it extends over the Katsura River in some places), on the north by Hachijō Street and the JR Kyoto line (leading into Kyoto station), and on the south by the Meishin Expressway (although it extends over the expressway in some places). The southern portion of Kyoto city (including Minami-ku) is sometimes referred to as Rakunan.
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For all k digits, we need time O(k^3 n^2 \log(B)). The only internal storage needed is r, which is O(k) digits on the kth iteration. That this algorithm does not have bounded memory usage puts an upper bound on the number of digits which can be computed mentally, unlike the more elementary algorithms of arithmetic. Unfortunately, any bounded memory state machine with periodic inputs can only produce periodic outputs, so there are no such algorithms which can compute irrational numbers from rational ones, and thus no bounded memory root extraction algorithms.
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An upper bound on the size of the set of messages can be determined by \delta and \epsilon. Locally decodable codes can also be concatenated, where a message is encoded first using one scheme, and the resulting codeword is encoded again using a different scheme. (Note that, in this context, concatenation is the term used by scholars to refer to what is usually called composition; see ). This might be useful if, for example, the first code has some desirable properties with respect to rate, but it has some undesirable property, such as producing a codeword over a non-binary alphabet.
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188px An enlargeable map of the United Mexican States The following outline is provided as an overview of and topical guide to Mexico: The United Mexican States,The alternative translation Mexican United States is rarely used commonly known as Mexico, is a federal constitutional republic located in North America. Mexico is bound on the north by the United States; on the south and west by the North Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of Mexico.Merriam-Webster's Geographical Dictionary, 3rd ed. Springfield, MA: Merriam-Webster, Inc.
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In the late eighteenth century, slavery prevailed throughout much more than half the lands of North America. Jefferson designed the ordinance to establish from end to end of the whole country a north and south line, at which the westward extension of slavery should be stayed by an impassable bound. On exactly the ninth anniversary of the fight at Concord and Lexington, Richard Dobbs Spaight of North Carolina, seconded by Jacob Read of South Carolina, moved to strike out the fifth article concerning the restriction on the expansion of slavery. The votes of seven states were needed to approve Jefferson's clause.
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Thus, the Gaussian moat problem may be phrased in a different but equivalent form: is there a finite bound on the widths of the moats that have finitely many primes on the side of the origin? Computational searches have shown that the origin is separated from infinity by a moat of width 6.. It is known that, for any positive number k, there exist Gaussian primes whose nearest neighbor is at distance k or larger. In fact, these numbers may be constrained to be on the real axis. For instance, the number 20785207 is surrounded by a moat of width 17.
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Two naturally desirable properties of estimators are for them to be unbiased and have minimal mean squared error (MSE). These cannot in general both be satisfied simultaneously: a biased estimator may have lower mean squared error (MSE) than any unbiased estimator; see estimator bias. Among unbiased estimators, there often exists one with the lowest variance, called the minimum variance unbiased estimator (MVUE). In some cases an unbiased efficient estimator exists, which, in addition to having the lowest variance among unbiased estimators, satisfies the Cramér–Rao bound, which is an absolute lower bound on variance for statistics of a variable.
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Selberg's trace formula shows that for an hyperbolic surface of finite volume it is equivalent to know the length spectrum (the collection of lengths of all closed geodesics on S, with multiplicities) and the spectrum of \Delta. However the precise relation is not explicit. Another relation between spectrum and geometry is given by Cheeger's inequality, which in the case of a surface S states roughly that a positive lower bound on the spectral gap of S translates into a positive lower bound for the total length of a collection of smooth closed curves separating S into two connected components.
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The central value of is higher than the speed of light but, with uncertainty taken into account, is also consistent with a velocity of exactly c or slightly less. This measurement set an upper bound on the mass of the muon neutrino at with 99% confidence. After the detectors for the project were upgraded in 2012, MINOS refined their initial result and found agreement with the speed of light, with the difference in the arrival time of neutrinos and light of −0.0006% (±0.0012%). A similar observation was made, on a much larger scale, with supernova 1987A (SN 1987A).
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Graham's 1975 conjecture on the shape of these polygons was finally proven in 2007.. In another 1975 publication, Graham and Erdős observed that for packing unit squares into a larger square with non-integer side lengths, one can use tilted squares to leave an uncovered area that is sublinear in the side length of the larger square, unlike the obvious packing with axis-aligned squares. Klaus Roth and Bob Vaughan proved that uncovered area at least proportional to the square root of the side length may sometimes be needed; proving a tight bound on the uncovered area remains an open problem.
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If the graph is a metric space then there is an efficient approximation algorithm that finds a Hamiltonian cycle with maximum edge weight being no more than twice the optimum. This result follows by Fleischner's theorem, that the square of a 2-vertex-connected graph always contains a Hamiltonian cycle. It is easy to find a threshold value , the smallest value such that the edges of weight form a 2-connected graph. Then provides a valid lower bound on the bottleneck TSP weight, for the bottleneck TSP is itself a 2-connected graph and necessarily contains an edge of weight at least .
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It has been shown that any solution to the list-labeling problem with a universe polynomial in the number of elements will have insertion and deletion performance no better than \Omega(\log n).. Then, for list-labeling, the above solution is asymptotically optimal. Incidentally, this also proves an \Omega(\log n) lower bound on the amortized rebalancing time of an insertion or deletion in a scapegoat tree. However, this lower bound does not apply to the order-maintenance problem and, as stated above, there are data structures that give worst-case constant time performance on all order-maintenance operations.
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The existence (or otherwise) of this bias and the necessity of correcting for it has become relevant in astronomy with the precision parallax measurements made by the Hipparcos satellite and more recently with the high-precision data releases of the Gaia mission. The correction method due to Lutz and Kelker placed a bound on the true parallax of stars. This is not valid because true parallax (as distinct from measured parallax) cannot be known. Integrating over all true parallaxes (all space) assumes that stars are equally visible at all distances, and leads to divergent integrals yielding an invalid calculation.
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Throughout history, artificial flies constructed of furs, feathers, and threads bound on a hook have been created by anglers to imitate fish prey. The first known mention of an artificial fly was in 200AD in Macedonia. Most early examples of artificial flies imitated common aquatic insects and baitfish. Today, artificial flies are tied with a wide variety of natural and synthetic materials (like mylar and rubber) to represent all manner of potential freshwater and saltwater fish prey to include aquatic and terrestrial insects, crustaceans, worms, baitfish, vegetation, flesh, spawn, small reptiles, amphibians, mammals and birds, etc.
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In order to solve this problem one uses a variation of the circulation problem called bounded circulation which is the generalization of network flow problems, with the added constraint of a lower bound on edge flows. Let G = (V, E) be a network with s,t ∈ V as the source and the sink nodes. For the source and destination of every flight i, one adds two nodes to V, node si as the source and node di as the destination node of flight i. One also adds the following edges to E: # An edge with capacity [0, 1] between s and each si.
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In 2013 it was announced that the hit Scottish comedy Still Game would return for a Glasgow stage show in The Hydro and they could possibly return for another series the usual cast would be still in it including Ford Kiernan and Greg Hemphill with Paul Riley, Mark Cox, Jane McCarry and Gavin Mitchell. In 2016 he played Felix in Journey Bound. On 12 May 2016 it was announced that Still Game would be making a return to BBC1 in late 2016 for a new six-part series. In 2018, it was announced that the ninth series would be the final one.
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There is more than one upper bound on the achievable code rate of linear block codes for multiple phased-burst correction (MPBC). One such bound is constrained to a maximum correctable cyclic burst length within every subblock, or equivalently a constraint on the minimum error free length or gap within every phased-burst. This bound, when reduced to the special case of a bound for single burst correction, is the Abramson bound (a corollary of the Hamming bound for burst-error correction) when the cyclic burst length is less than half the block length.Ling, San, and Chaoping Xing.
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The De Bruijn–Erdős theorem concerns the chromatic numbers of infinite graphs, and shows that (again, assuming the axiom of choice) they can be calculated from the chromatic numbers of their finite subgraphs. It states that, if the chromatic numbers of the finite subgraphs of a graph G have a finite maximum value c, then the chromatic number of G itself is exactly c. On the other hand, if there is no finite upper bound on the chromatic numbers of the finite subgraphs of G, then the chromatic number of G itself must be infinite., Theorem 1, p. 2.
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Despite Kurando's having the strategic advantage of having the sun behind him and Daigorō riding on Ogami's back, a mirror bound on Daigorō's forehead reflects the sun into Kurando's eyes, blinding him long enough for Ogami to slice off Kurando's head. Ogami and Daigorō journey on, never stopping in one place for very long as the Shogun's ninjas are always following them. As they wander, Daigorō recalls how the Shogun's other son Lord Bizen (Taketoshi Naitô) and his men were given orders to kill him. Even though Bizen's men are wearing chain mail beneath their robes, Ogami's skill and blade are too powerful.
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A baseband signal or lowpass signal is a signal that can include frequencies that are very near zero, by comparison with its highest frequency (for example, a sound waveform can be considered as a baseband signal, whereas a radio signal or any other modulated signal is not). A baseband bandwidth is equal to the highest frequency of a signal or system, or an upper bound on such frequencies, for example the upper cut-off frequency of a low-pass filter. By contrast, passband bandwidth is the difference between a highest frequency and a nonzero lowest frequency.
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Ate (minor planet designation: 111 Ate) is a main-belt asteroid that was discovered by the German-American astronomer C. H. F. Peters on August 14, 1870, and named after Ate, the goddess of mischief and destruction in Greek mythology. In the Tholen classification system, it is categorized as a carbonaceous C-type asteroid, while the Bus asteroid taxonomy system lists it as an Ch asteroid. Two stellar occultations by Ate were observed in 2000, only two months apart. The occultation of the star HIP 2559 by 111 Ate was used to determine a chord length of 125.6 ± 7.2 km through the asteroid, giving a lower bound on the maximum dimension.
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This scheme, now known as a Yee lattice, has proven to be very robust, and remains at the core of many current FDTD software constructs. Furthermore, Yee proposed a leapfrog scheme for marching in time wherein the E-field and H-field updates are staggered so that E-field updates are conducted midway during each time-step between successive H-field updates, and conversely. On the plus side, this explicit time-stepping scheme avoids the need to solve simultaneous equations, and furthermore yields dissipation-free numerical wave propagation. On the minus side, this scheme mandates an upper bound on the time-step to ensure numerical stability.
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The state of Kerala experienced tsunami-related damage in three southern densely populated districts, Ernakulam, Alappuzha, and Kollam, due to diffraction of the waves around Sri Lanka. The southernmost district of Thiruvananthpuram, however, escaped damage, possibly due to the wide turn of the diffracted waves at the peninsular tip. Major damage occurred in two narrow strips of land bound on the west by the Arabian Sea and on the east by the Kerala backwaters. The waves receded before the first tsunami with the highest fatality reported from the densely populated Alappad panchayat (including the villages of Cheriya Azhikkal and Azhikkal) at Kollam district, caused by a tsunami.
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FFT algorithms have errors when finite-precision floating-point arithmetic is used, but these errors are typically quite small; most FFT algorithms, e.g. Cooley–Tukey, have excellent numerical properties as a consequence of the pairwise summation structure of the algorithms. The upper bound on the relative error for the Cooley–Tukey algorithm is O(ε log N), compared to O(εN3/2) for the naïve DFT formula, where ε is the machine floating-point relative precision. In fact, the root mean square (rms) errors are much better than these upper bounds, being only O(ε ) for Cooley–Tukey and O(ε ) for the naïve DFT (Schatzman, 1996).
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The efficiency of a kinetic data structure is defined based on the ratio of the number of internal events to external events, thus good runtime bounds can sometimes be obtained by choosing to use a triangulation scheme that generates a small number of external events. For simple affine motion of the points, the number of discrete changes to the convex hull is estimated by \Omega(n^2), thus the number of changes to any triangulation is also lower bounded by \Omega(n^2). Finding any triangulation scheme that has a near-quadratic bound on the number of discrete changes is an important open problem.
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In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász theta function and is commonly denoted by ϑ(G). This quantity was first introduced by László Lovász in his 1979 paper On the Shannon Capacity of a Graph.. Accurate numerical approximations to this number can be computed in polynomial time by semidefinite programming and the ellipsoid method. It is sandwiched between the chromatic number and clique number of any graph, and can be used to compute these numbers on graphs for which they are equal, including perfect graphs.
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Julio Gea-Banacloche (born 1957) is Professor of Physics and currently the Head of Department of Physics at the University of Arkansas. He is notable for his contribution to the field of quantum information, where he has shown that the quantum mechanical nature of the fields used to manipulate the quantum information carriers (qubits) themselves might lead to unpredictable errors in the performance of the quantum logical operations. The lower bound on the size of these errors can be made smaller by increasing the energy of the control system. This has led Gea-Banacloche to predict a minimum energy requirement for quantum computation, which has given rise to some controversy.
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Relying too heavily on heuristics that over-simplify complex decisions. This can include: ; Availability heuristic : Group members rely on information that is readily available. ; Conjunctive bias : When groups are not aware that the probability of a given event occurring is the least upper bound on the probability of that event and any other given event occurring together; thus if the probability of the second event is less than one, the occurrence of the pair will always be less likely than the first event alone. ; Representativeness heuristic : Group members rely too heavily on decision- making factors that seem meaningful but are, in fact, more or less misleading.
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Traditional models of coagulation developed in the 1960s envisaged two separate cascades, the extrinsic (tissue factor (TF)) pathway and the intrinsic pathway. These pathways converge to a common point, the formation of the Factor Xa/Va complex which together with calcium and bound on a phospholipids surface, generate thrombin (Factor IIa) from prothrombin (Factor II). A new model, the cell-based model of anticoagulation appears to explain more fully the steps in coagulation. This model has three stages: 1) initiation of coagulation on TF-bearing cells, 2) amplification of the procoagulant signal by thrombin generated on the TF- bearing cell and 3) propagation of thrombin generation on the platelet surface.
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On lists of integers and floats spreadsort shows a roughly 2–7× runtime improvement for random data on various operating systems. In space performance, spreadsort is worse than most in-place algorithms: in its simplest form, it is not an in- place algorithm, using O(n) extra space; in experiments, about 20% more than quicksort using a c of 4–8. With a cache-aware form (as included in Boost.Sort), less memory is used and there is an upper bound on memory usage of the maximum bin count times the maximum number of recursions, which ends up being a few kilobytes times the size of the key in bytes.
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In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article provides a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since a number of theorems about the analytic structure of the bounded function and its integral transforms can be stated. In particular, Nachbin's theorem may be used to give the domain of convergence of the generalized Borel transform, given below.
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In electrical engineering, uses cliques to analyze communications networks, and use them to design efficient circuits for computing partially specified Boolean functions. Cliques have also been used in automatic test pattern generation: a large clique in an incompatibility graph of possible faults provides a lower bound on the size of a test set.. describe an application of cliques in finding a hierarchical partition of an electronic circuit into smaller subunits. In chemistry, use cliques to describe chemicals in a chemical database that have a high degree of similarity with a target structure. use cliques to model the positions in which two chemicals will bind to each other.
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He descends from the family lineage of Abdul Wahid Khan and Abdul Karim Khan, the founders of Kirana Gharana.The others who left Kairana, many decades ago – The Indian Express He got education in music from his maternal uncles Mashkoor Ali Khan and Mubarak Ali Khan.Melodic downpour – The HinduScintillating Vocal and Sitar leaves the audience spell bound on concluding day of Three day Vocal and Sitar Festival of Pracheen Kala Kendra. – News 'n' At the age of 9, he was described as the biggest sensation of Sawai Gandharva Samelan, following his performance on a special invitation by Bhimsen Joshi on the occasion of his 75th birthday.
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Bertrand's postulate, proven in 1852, states that there is always a prime number between k and 2k, so in particular pn+1 < 2pn, which means gn < pn. The prime number theorem, proven in 1896, says that the average length of the gap between a prime p and the next prime will asymptotically approach ln(p) for sufficiently large primes. The actual length of the gap might be much more or less than this. However, one can deduce from the prime number theorem an upper bound on the length of prime gaps: For every \epsilon > 0, there is a number N such that for all n > N :g_n < p_n\epsilon.
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Many complexity classes are defined using the concept of a reduction. A reduction is a transformation of one problem into another problem. It captures the informal notion of a problem being at least as difficult as another problem. For instance, if a problem X can be solved using an algorithm for Y, X is no more difficult than Y, and we say that X reduces to Y. There are many different types of reductions, based on the method of reduction, such as Cook reductions, Karp reductions and Levin reductions, and the bound on the complexity of reductions, such as polynomial-time reductions or log-space reductions.
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By combining those two kinds of analysis, the tool attempts to give an upper bound on the time required to execute a given task on a given hardware platform. At the low-level, static WCET analysis is complicated by the presence of architectural features that improve the average-case performance of the processor: instruction/data caches, branch prediction and instruction pipelines, for example. It is possible, but increasingly difficult, to determine tight WCET bounds if these modern architectural features are taken into account in the timing model used by the analysis. For example, cache locking techniques can be used for simplifying WCET estimation and providing predictability.
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The pathwidth of any n-vertex cubic graph is at most n/6. The best known lower bound on the pathwidth of cubic graphs is 0.082n. It is not known how to reduce this gap between this lower bound and the n/6 upper bound.. It follows from the handshaking lemma, proven by Leonhard Euler in 1736 as part of the first paper on graph theory, that every cubic graph has an even number of vertices. Petersen's theorem states that every cubic bridgeless graph has a perfect matching.. Lovász and Plummer conjectured that every cubic bridgeless graph has an exponential number of perfect matchings.
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In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation of the sample data or the mean with the standard error. This often leads to confusion about their interchangeability. However, the mean and standard deviation are descriptive statistics, whereas the standard error of the mean is descriptive of the random sampling process. The standard deviation of the sample data is a description of the variation in measurements, while the standard error of the mean is a probabilistic statement about how the sample size will provide a better bound on estimates of the population mean, in light of the central limit theorem.
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By definition, fundamental physical constants are subject to measurement, so that their being constant (independent on both the time and position of the performance of the measurement) is necessarily an experimental result and subject to verification. Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the fine- structure constant might be subject to change over time in proportion of the age of the universe. Experiments can in principle only put an upper bound on the relative change per year. For the fine-structure constant, this upper bound is comparatively low, at roughly 10−17 per year (as of 2008).
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The Anticline Ridge is a ridge, southeast of Joaquin Ridge, declining from its 3,629 foot / 1,106 meter high point, Black Mountain in the north at , to the southeast into low hills bound on the southeast by Los Gatos Creek that divides it from the Guijarral Hills. It is located in the inner California Coast Ranges, in Fresno County, California, east of the town of Coalinga. Anticline Ridge and Guijarral Hills divides Pleasant Valley from the San Joaquin Valley to the east. California State routes 33 and 198, which join together for the stretch through and north of Coalinga, cut across the Coalinga field and cross Anticline Ridge.
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In the field of analysis of algorithms in computer science, the accounting method is a method of amortized analysis based on accounting. The accounting method often gives a more intuitive account of the amortized cost of an operation than either aggregate analysis or the potential method. Note, however, that this does not guarantee such analysis will be immediately obvious; often, choosing the correct parameters for the accounting method requires as much knowledge of the problem and the complexity bounds one is attempting to prove as the other two methods. The accounting method is most naturally suited for proving an O(1) bound on time.
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The sequence of these intervals, labeled by the minimizing function within each interval, forms a Davenport–Schinzel sequence of order s. Thus, any upper bound on the complexity of a Davenport–Schinzel sequence of this order also bounds the number of intervals in this representation of the lower envelope. In the original application of Davenport and Schinzel, the functions under consideration were a set of different solutions to the same homogeneous linear differential equation of order s. Any two distinct solutions can have at most s values in common, so the lower envelope of a set of n distinct solutions forms a DS(n,s)-sequence.
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This is in contrast to many other hash table algorithms, which may not have a constant worst-case bound on the time to do a lookup. Deletions, also, may be performed by blanking the cell containing a key, in constant worst case time, more simply than some other schemes such as linear probing. When a new key is inserted, and one of its two cells is empty, it may be placed in that cell. However, when both cells are already full, it will be necessary to move other keys to their second locations (or back to their first locations) to make room for the new key.
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The motivation of Leighton in studying crossing numbers was for applications to VLSI design in theoretical computer science. Later, realized that this inequality yielded very simple proofs of some important theorems in incidence geometry. For instance, the Szemerédi–Trotter theorem, an upper bound on the number of incidences that are possible between given numbers of points and lines in the plane, follows by constructing a graph whose vertices are the points and whose edges are the segments of lines between incident points. If there were more incidences than the Szemerédi–Trotter bound, this graph would necessarily have more crossings than the total number of pairs of lines, an impossibility.
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Many complexity classes are defined using the concept of a reduction. A reduction is a transformation of one problem into another problem. It captures the informal notion of a problem being at most as difficult as another problem. For instance, if a problem X can be solved using an algorithm for Y, X is no more difficult than Y, and we say that X reduces to Y. There are many different types of reductions, based on the method of reduction, such as Cook reductions, Karp reductions and Levin reductions, and the bound on the complexity of reductions, such as polynomial-time reductions or log-space reductions.
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Most measurements that can be made are relatively insensitive to the outer halo's mass distribution. This is a consequence of Newton's laws, which state that if the shape of the halo is spheroidal or elliptical there will be no net gravitational effect from halo mass a distance r from the galactic center on an object that is closer to the galactic center than r. The only dynamical variable related to the extent of the halo that can be constrained is the escape velocity: the fastest-moving stellar objects still gravitationally bound to the Galaxy can give a lower bound on the mass profile of the outer edges of the dark halo.
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E.W. Dijkstra in 1974 presented the concept of self- stabilization, prompting further research in this area.. His demonstration involved the presentation of self-stabilizing mutual exclusion algorithms. It also showed the first self-stabilizing algorithms that did not rely on strong assumptions on the system. Some previous protocols used in practice did actually stabilize, but only assuming the existence of a clock that was global to the system, and assuming a known upper bound on the duration of each system transition. It was only ten years later when Leslie Lamport pointed out the importance of Dijkstra's work at a 1983 conference called Symposium on Principles of Distributed Computing that researchers .
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Haptotaxis (from Greek ἅπτω (hapto, "touch, fasten") and τάξις (taxis, "arrangement, order")) is the directional motility or outgrowth of cells, e.g. in the case of axonal outgrowth, usually up a gradient of cellular adhesion sites or substrate-bound chemoattractants (the gradient of the chemoattractant being expressed or bound on a surface, in contrast to the classical model of chemotaxis, in which the gradient develops in a soluble fluid.). These gradients are naturally present in the extracellular matrix (ECM) of the body during processes such as angiogenesis or artificially present in biomaterials where gradients are established by altering the concentration of adhesion sites on a polymer substrate.
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If an n-vertex graph has a RAC drawing with straight edges, it can have at most 4n − 10 edges. This is tight: there exist RAC-drawable graphs with exactly 4n − 10 edges. For drawings with polyline edges, the bound on the number of edges in the graph depends on the number of bends that are allowed per edge. The graphs that have RAC drawings with one or two bends per edge have O(n) edges; more specifically, with one bend there are at most 5.5n edges and with two bends there are at most 74.2n edges.. Every graph has a RAC drawing with three bends per edge.
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This places an extremely high lower-bound on the intensity of the flux required to produce the observed force of gravity. Any form of gravitational shielding would represent a violation of the equivalence principle, and would be inconsistent with the extremely precise null result observed in the Eötvös experiment and its successors — all of which have instead confirmed the precise equivalence of active and passive gravitational mass with inertial mass that was predicted by general relativity. For more historical information on the connection between gravitational shielding and Le Sage gravity, see Martins,Martin (1999), secondary sourcesMartins (2002), secondary sources and Borzeszkowski et al.Borzeskkowski et al.
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He realised then that a book supplying the answers to this sort of question might prove successful. Beaver's idea became reality when Guinness employee Christopher Chataway recommended university friends Norris and Ross McWhirter, who had been running a fact-finding agency in London. The twin brothers were commissioned to compile what became The Guinness Book of Records, in August 1954. A thousand copies were printed and given away. After the founding of The Guinness Book of Records office at 107 Fleet Street, London, the first 198-page edition was bound on 27 August 1955 and went to the top of the British best seller lists by Christmas.
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After a race between CERN and Fermilab to discover the top, the accelerator at CERN reached its limits without creating a single top, pushing the lower bound on its mass up to . The Tevatron was (until the start of LHC operation at CERN in 2009) the only hadron collider powerful enough to produce top quarks. In order to be able to confirm a future discovery, a second detector, the DØ detector, was added to the complex (in addition to the Collider Detector at Fermilab (CDF) already present). In October 1992, the two groups found their first hint of the top, with a single creation event that appeared to contain the top.
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A disadvantage of RANSAC is that there is no upper bound on the time it takes to compute these parameters (except exhaustion). When the number of iterations computed is limited the solution obtained may not be optimal, and it may not even be one that fits the data in a good way. In this way RANSAC offers a trade-off; by computing a greater number of iterations the probability of a reasonable model being produced is increased. Moreover, RANSAC is not always able to find the optimal set even for moderately contaminated sets and it usually performs badly when the number of inliers is less than 50%.
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Although, one must bear in mind that these optimal tags are still dominated by the algorithm's survival measure for arbitrarily large t. Moreover, GCM is neither well-suited for use with very short tag-lengths nor very long messages. Ferguson and Saarinen independently described how an attacker can perform optimal attacks against GCM authentication, which meet the lower bound on its security. Ferguson showed that, if n denotes the total number of blocks in the encoding (the input to the GHASH function), then there is a method of constructing a targeted ciphertext forgery that is expected to succeed with a probability of approximately n⋅2−t.
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It is straightforward to turn a proof of Moon and Moser's 3n/3 bound on the number of maximal independent sets into an algorithm that lists all such sets in time O(3n/3).. For a matching bound for the widely used Bron–Kerbosch algorithm, see . For graphs that have the largest possible number of maximal independent sets, this algorithm takes constant time per output set. However, an algorithm with this time bound can be highly inefficient for graphs with more limited numbers of independent sets. For this reason, many researchers have studied algorithms that list all maximal independent sets in polynomial time per output set.
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Kobon triangles generated with 3, 4 and 5 straight line segments. The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura. The problem asks for the largest number N(k) of nonoverlapping triangles whose sides lie on an arrangement of k lines. Variations of the problem consider the projective plane rather than the Euclidean plane, and require that the triangles not be crossed by any other lines of the arrangement.. Saburo Tamura proved that the largest integer not exceeding k(k − 2)/3 provides an upper bound on the maximal number of nonoverlapping triangles realizable by k lines.
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The 2016 Democratic National Convention was held from July 25–28 at the Wells Fargo Center in Philadelphia, with some events at the Pennsylvania Convention Center. The delegates selected the Democratic presidential and vice-presidential nominees and wrote the party platform. A simple majority of 2,383 delegates was needed to win the presidential nomination. (official source tracking active campaigns + adding delegates won on April 26, pending source update) While most of the delegates were bound on the first ballot according to the results of the primaries, a progressively larger number of pledged delegates would have become unbound if the nomination required more than one ballot.
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For comparison, the maximum energies accessible at the Large Hadron Collider are of order 1013 eV, while the Planck scale, at which quantum gravity becomes important and the relevance of quantum field theory itself may be questioned, is 1028 eV. The Higgs boson in the Standard Model of particle physics is described by theory (see Quartic interaction). If the latter has a Landau pole, then this fact is used in setting a "triviality bound" on the Higgs mass. The bound depends on the scale at which new physics is assumed to enter and the maximum value of the quartic coupling permitted (its physical value is unknown).
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In 2013, John Iacono published a paper which uses the geometry of binary search trees to provide an algorithm which is dynamically optimal if any binary search tree algorithm is dynamically optimal. Nodes are interpreted as points in two dimensions, and the optimal access sequence is the smallest arborally satisfied superset of those points. Unlike splay trees and tango trees, Iacono's data structure is not known to be implementable in constant time per access sequence step, so even if it is dynamically optimal, it could still be slower than other search tree data structures by a non-constant factor. The interleave lower bound is an asymptotic lower bound on dynamic optimality.
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Brute-force search for a k-coloring considers each of the k^n assignments of k colors to n vertices and checks for each if it is legal. To compute the chromatic number and the chromatic polynomial, this procedure is used for every k=1,\ldots,n-1, impractical for all but the smallest input graphs. Using dynamic programming and a bound on the number of maximal independent sets, k-colorability can be decided in time and space O(2.4423^n). Using the principle of inclusion–exclusion and Yates’s algorithm for the fast zeta transform, k-colorability can be decided in time O(2^nn) for any k.
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Ten acres in size, St. Michael's has the unusual characteristic of being surrounded on all sides by the backs of buildings, thus making it nearly invisible from the street. It is bound on the north by stores, apartments and office buildings along St. Clair Avenue West, on the west by houses along Foxbar Road, on the south by houses and Toronto Fire Services Station 311 along Balmoral Avenue, and on the east by stores and office buildings along Yonge Street. Entrance to the cemetery is gained through an alley off Yonge Street. The cemetery's octagonal mortuary vault was used to store bodies in the winter until the ground thawed.
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A man, wearing a mask, rides a bicycle in Ocean Park during the COVID-19 pandemic About one kilometer off the beach is the small rocky Island Stone which is also part of the area, measuring about 100 by 50 meters. Ocean Park is bound on the east by Calle Guerrero Noble and its straight extension to the beach, a short piece of Calle Cacique running east to connect to Calle Teniente Rivera, and the connecting piece of Calle Soldado Cruz to Calle Loíza. The southern border runs to Calle Loíza, but excluding same. In the west, it is Calle María Mozco (northern part) and Calle Santa Ana.
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Sachdev argued instead that it is better to examine how rapidly the system loses quantum phase coherence, or reaches local thermal equilibrium in response to general external perturbations. If quasiparticles existed, dephasing would take a long time during which the excited quasiparticles collide with each other. In contrast, states without quasiparticles reach local thermal equilibrium in the fastest possible time, bounded below by a value of order (Planck constant)/((Boltzmann constant) x (absolute temperature)). Sachdev proposed a solvable model of a strange metal (a variant of which is now called the Sachdev-Ye-Kitaev (SYK) model), which was shown to saturate such a bound on the time to reach quantum chaos.
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Dilworth's theorem states that, in any finite partially ordered set, the largest antichain has the same size as the smallest chain decomposition. Here, the size of the antichain is its number of elements, and the size of the chain decomposition is its number of chains. The width of the partial order is defined as the common size of the antichain and chain decomposition. A version of the theorem for infinite partially ordered sets states that, when there exists a decomposition into finitely many chains, or when there exists a finite upper bound on the size of an antichain, the sizes of the largest antichain and of the smallest chain decomposition are again equal.
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The route was first started by The Hongkong and Shanghai Hotels in the 1920s between Blake Pier in Central and the University of Hong Kong by way of Sai Ying Pun, with no route number. On 11 June 1933 CMB took over the route as part of the Hong Kong Island bus service franchise, and given the number 4. In the next year, the Central terminus was moved to the piers of Hongkong and Yaumati Ferry. On 1 April 1935 circular arrangement was implemented, running in anti-clockwise direction, taking Bonham Road and Caine Road for Central bound. On 14 June 1937 service was extended to Queen Mary Hospital, and the circular arrangement was cancelled.
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The same method has also been used to detect planets around stars, in the way that the movement's measurement determines the planet's orbital period, while the resulting radial-velocity amplitude allows the calculation of the lower bound on a planet's mass using the binary mass function. Radial velocity methods alone may only reveal a lower bound, since a large planet orbiting at a very high angle to the line of sight will perturb its star radially as much as a much smaller planet with an orbital plane on the line of sight. It has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit.
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Indeed, if the algorithm can backtrack from a partial solution, part of the search is skipped. The lower the estimated cost, the better the algorithm, as a lower estimated cost is more likely to be lower than the best cost of solution found so far. On the other hand, this estimated cost cannot be lower than the effective cost that can be obtained by extending the solution, as otherwise the algorithm could backtrack while a solution better than the best found so far exists. As a result, the algorithm requires an upper bound on the cost that can be obtained from extending a partial solution, and this upper bound should be as small as possible.
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Joaquin Ridge is a ridge in the Diablo Range in Fresno County, California. The ridge is named for Joaquin Murietta (1830-1853), a California Gold Rush bandit, leader of the Five Joaquins Gang, who used this region as a rendezvous and camp that overlooked the gangs base at the Rancho de Cantua. The ridge is ten miles long, running from its high point at , east of Spanish Lake , eastward to Joaquin Rocks , and then southwestward to near 3,629 foot Black Mountain at the high point on the south southeast trending Anticline Ridge. Joaquin Ridge is bound on the northeast by the Ragged Valley and the Big Blue Hills and on the southwest by Portuguese Canyon.
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Where the branch length in coalescent units (T) is also written in an alternative form: the number of generations (t) divided by twice the effective population size (Ne). Pamilo and Nei also derived the probability of congruence for rooted trees of four and five taxa as well as a general upper bound on the probability of congruence for larger trees. Rosenberg followed up with equations used for the complete set of topologies (although the large number of distinct phylogenetic trees that becomes possible as the number of taxa increases makes these equations impractical unless the number of taxa is very limited). The phenomenon of hemiplasy is a natural extension of the basic idea underlying gene tree-species tree discordance.
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Taking a wright, the most able workman there, he > [Wallace] ordered him to saw the plank in two at the mid streit [middle > stretch], so that no-one might walk over it. He then nailed it up quickly > with hinges, and dirtied it with clay, to cause it to appear that nothing > had been done. The other end he so arranged that it should lie on three > wooden rollers, which were so placed, that when one was out the rest would > fall down. The wright, himself, he ordered to sit there underneath, in a > cradle, bound on a beam, to loose the pin when Wallace let him know by > blowing a horn when the time was come.
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A couple demonstrating the use of a Morrison shelter A Morrison shelter containing a dummy, after the house it was in had been destroyed as a test Steel can either behave elastically or plastically. Elastic deformation is reversible, and with the removal of load the material will return to its original shape, position and stress distribution. Plastic deformation is not reversible, and with the removal of load the material will assume a different shape, position and stress distribution to the one it held originally. Plasticity theory is based on plastic behaviour, and calculates a lower bound on the load that a structure can carry (the load at which it collapses will not be lower than that calculated).
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This allows a structure to be designed so it will always be able to carry the chosen magnitude of load, even if the exact way it does so is not understood. Elasticity theory depends on guessing the way in which a structure works, and the loads it will be subjected to, and designing it to carry those loads in the assumed manner. This ensures it is safe if the structure is well understood, but it may not be safe if the structure carries the loads in a different manner. Therefore, it gives an upper bound on the collapse load (the load at which it collapses will not be higher than that calculated).
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It is located in Gautam Buddh Nagar district of Uttar Pradesh state India. It is about 20 km southeast of New Delhi, northwest of the district headquarters, Greater Noida and northwest of the state capital, Lucknow, 18 km from Connaught Place of New Delhi. It is bound on the west and south-west by the Yamuna River, on the north and north-west by the city of Delhi, on the north-east by the cities of Delhi and Ghaziabad, India and on the north-east, east and south-east by the Hindon River. Sector 62 falls under the catchment area of the Yamuna river and is located on the old river bed.
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The price of stability was first studied by A. Schulzan and N. Moses and was so-called in the studies of E. Anshelevich. They showed that a pure strategy Nash equilibrium always exists and the price of stability of this game is at most the nth harmonic number in directed graphs. For undirected graphs Anshelevich and others presented a tight bound on the price of stability of 4/3 for a single source and two players case. Jian Li has proved that for undirected graphs with a distinguished destination to which all players must connect the price of stability of the Shapely network design game is O(\log n/\log\log n) where n is the number of players.
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Since the toll plaza was opened on 28 September 1987, there were many accident cases which involved brake failure in heavy vehicles due to hard braking when proceeding downhill to the toll plaza. On 7 June 2008, the new Ipoh North toll plaza (South bound) replacing old Jelapang toll plaza opened to traffic, followed by north bound on 15 August 2008. Beginning 11:00 am on 14 July 2009, the Kuala Lumpur–Penang through traffic is now opened to traffic. With the opening of the between Ipoh North (Jelapang) and Ipoh South stretch, highway users are no longer required to stop for toll transactions at the Ipoh North and Ipoh South Toll Plazas.
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It is located in Gautam Buddh Nagar district of Uttar Pradesh state India. It is about 20 km southeast of New Delhi, northwest of the district headquarters, Greater Noida and northwest of the state capital, Lucknow, 18 km from Connaught Place of New Delhi. It is bound on the west and south-west by the Yamuna River, on the north and north-west by the city of Delhi, on the north-east by the cities of Delhi and Ghaziabad, India and on the north-east, east and south-east by the Hindon River. Sector 78 falls under the catchment area of the Yamuna river and is located on land, adjoining the old river bed.
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A string s is compressed to the shortest byte string representing a base-256 big-endian number x in the range [0, 1] such that P(r < s) ≤ x < P(r ≤ s), where P(r < s) is the probability that a random string r with the same length as s will be lexicographically less than s. It is always possible to find an x such that the length of x is at most one byte longer than the Shannon limit, −log2P(r = s) bits. The length of s is stored in the archive header. The arithmetic coder in PAQ is implemented by maintaining for each prediction a lower and upper bound on x, initially [0, 1].
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Continuing East another , the trail becomes uphill again as it connects to the northernmost point of a paved road, Puerto Rico Highway 561, on the right hand side. From this point on the trail starts to head North on a downhill grade but in less than it connects to Trail #3 which leads to the Observation Tower, where there is a sign that reads La Torre ("The Tower"). The trail continuous downhill North-Northwest about until it reaches paved road PR-143, in the vicinity of km 32.6. From this point hikers make a left to walk southwest bound on PR-143 (that is, "West" on PR-143) until reaching the visitors' area at km 32.4.
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Rabun County The first interchange along I-985/US 23/SR 365 in Hall County is Exit 8 at Georgia State Route 347. Though signed only for Sprout Springs Road, the Rankin Smith Interchange (Exit 12) in Flowery Branch also includes Phil Niekro Boulevard. Former rest areas also exists west of Exit 16 (SR 53), which is so close to Exit 17 (SR&13), that southwest-bound ramps are separated by a frontage road, and the northeast-bound on-ramp from Exit 16 goes over the northeast-bound off-ramp from Exit 17. Within Gainesville, US 129 once again joins the concurrency at Exit 22 which is also shared by the southern terminus of US BUS 129.
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It is an open question what is the smallest number :v(n,d), such that any n-variate, non- negative polynomial of degree d can be written as sum of at most v(n,d) square rational functions over the reals. The best known result () is :v(n,d)\leq2^n, due to Pfister in 1967. In complex analysis the Hermitian analogue, requiring the squares to be squared norms of holomorphic mappings, is somewhat more complicated, but true for positive polynomials by a result of Quillen. The result of Pfister on the other hand fails in the Hermitian case, that is there is no bound on the number of squares required, see D'Angelo–Lebl.
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However, Quixadá, south of São Luís–between it and Camalaú–paradoxically had a negative result. To account for the negative Quixadá results, the apparent oblateness (flattening) of Varuna was imposed at a minimum value of approximately 0.56 (aspect ratio c/a ≤ 0.44), corresponding to a minimum polar dimension of approximately , based on the given chord length of . The resulting lower bound on Varuna's polar dimension is approximately equal to Lacerda and Jewitt's lower bound c/a aspect ratio of 0.45, which they previously calculated in 2007. A preliminary conference presentation, given before the Camalaú results were fully analyzed, concluded that the São Luís and Quixadá results together suggested a significantly elongated shape is required for Varuna.
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The Jammu region, one of the two regions of UT of Jammu and Kashmir (the other being the Kashmir Valley), is bound on the north by the Pir Panjal Range of the middle Himalayas, in the south by Punjab, to the east by Ladakh, and close to the west by Pakistan. The lower Himalayan ranges begin behind the town of Jammu, which rests on a slope over above sea level, overlooking and commanding the plain watered by the Chenab, Ravi, Tawi and Ujh rivers. The Jammu region consists of ten districts: Jammu, Kathua, Udhampur, Doda, Poonch, Kishtwar, Reasi, Samba, Ramban and Rajouri. The city of Jammu is the winter capital of the UT of Jammu and Kashmir.
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On August 1, 2011, it was reported that Diablo III would feature two types of auction houses: one where players spend in-game gold and another where players could buy or sell virtual items for real-world money. The real-money auction house was not available in Hardcore mode. Prior to release, Blizzard stated that nearly everything that drops on the ground, including gold, could be traded with other players either directly or through the auction house system. Aside from certain bound on account items, such as the Staff of Herding needed to access the Whimsyshire easter egg, Blizzard stated there would be very few items that would be bound to a particular character and therefore untradable.
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The Polo Grounds was the name of three stadiums in Upper Manhattan, New York City, used mainly for professional baseball and American football from 1880 through 1963. The original Polo Grounds, opened in 1876 and demolished in 1889, was built for the sport of polo. Bound on the south and north by 110th and 112th Streets and on the east and west by Fifth and Sixth (Lenox) Avenues, just north of Central Park, it was converted to a baseball stadium when leased by the New York Metropolitans in 1880. The third Polo Grounds, built in 1890 and renovated after a fire in 1911, is the one generally indicated when the Polo Grounds is referenced.
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In particular, if the number of public bits shared between Alice and Bob are not counted against the communication complexity, it is easy to argue that computing any function has O(1) communication complexity. On the other hand, both models are equivalent if the number of public bits used by Alice and Bob is counted against the protocol's total communication. Though subtle, lower bounds on this model are extremely strong. More specifically, it is clear that any bound on problems of this class immediately imply equivalent bounds on problems in the deterministic model and the private and public coin models, but such bounds also hold immediately for nondeterministic communication models and quantum communication models.
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Her coiffure, known as a coazone, confines her hair smoothly to her head with two bands of it bound on either side of her face and a long plait at the back. Her hair is held in place by a fine gauze veil with a woven border of gold-wound threads, a black band, and a sheath over the plait.Notes for a portrait: the Lady's dress and hairstyle , Grazietta Butazzi, Exhibition notes, 1998 As in many of Leonardo's paintings, the composition comprises a pyramidic spiral and the sitter is caught in the motion of turning to her left, reflecting Leonardo's lifelong preoccupation with the dynamics of movement. The three-quarter profile portrait was one of his many innovations.
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From the beginning of the Tennessee Valley to this point is roughly ; as it runs through East Tennessee the Valley is bound on the east by the Appalachian Mountains (including the Great Smoky Mountains) and on the northwest by the Cumberland Plateau and Cumberland Mountains. After forming the boundary between Alabama and Mississippi for a stretch of , the river reenters Tennessee, where it creates the dividing line between Middle Tennessee and West Tennessee. It empties into the Ohio River in western Kentucky, where it divides the region known as the Jackson Purchase from the rest of Kentucky. Geologically, the eastern portion of the Tennessee Valley consists of many small valleys and ridges within a great valley.
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In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to a receiver. It is also equal to the highest rate at which entanglement can be generated over the channel, and forward classical communication cannot improve it. The quantum capacity theorem is important for the theory of quantum error correction, and more broadly for the theory of quantum computation. The theorem giving a lower bound on the quantum capacity of any channel is colloquially known as the LSD theorem, after the authors Lloyd, Shor, and Devetak who proved it with increasing standards of rigor.
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Captain Ann Campbell is a West Point graduate, the daughter of legendary General "Fighting Joe" Campbell. She is the pride of Fort Hadley until, one morning, her body is found naked and bound on the firing range. Paul Brenner is a member of the Army's elite undercover investigative unit, and the man in charge of this politically explosive case. Teamed with rape specialist Cynthia Sunhill, with whom he once had a tempestuous, doomed affair, Brenner is about to learn just how many people were sexually, emotionally, and dangerously involved with the Army's "golden girl", and how the neatly pressed uniforms and honor codes of the military hide a corruption as rank as Ann Campbell's shocking secret life.
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In estimation theory and statistics, the Cramér–Rao bound (CRB) expresses a lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter, stating that the variance of any such estimator is at least as high as the inverse of the Fisher information. The result is named in honor of Harald Cramér and C. R. Rao, but has independently also been derived by Maurice Fréchet, Georges Darmois, as well as Alexander Aitken and Harold Silverstone. An unbiased estimator which achieves this lower bound is said to be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is therefore the minimum variance unbiased (MVU) estimator.
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Ashton-under- Lyne and neighbouring Oldham viewed from Werneth Low At (53.4941°, −2.1032°), and north-northwest of London, Ashton-under-Lyne stands on the north bank of the River Tame, about above the river. Described in Samuel Lewis's A Topographical Dictionary of England (1848) as situated "on a gentle declivity", Ashton-under-Lyne lies on undulating ground by the Pennines, reaching a maximum elevation of about above sea level. It is east of Manchester city centre, and is bound on all sides by other towns: Audenshaw, Droylsden, Dukinfield, Mossley, Oldham, and Stalybridge, with little or no green space between them. Ashton experiences a temperate maritime climate, like much of the British Isles.
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Possible methods include: the super-ko rule, time control, or placing an upper bound on the number of moves. This is also affected by the scoring method used since territory scoring penalizes extended play after the boundaries of the territories have been settled. Second, how to decide which player won the game; and whether draws (jigo) should be allowed. Possible terms to include in the score are: komi, prisoners captured during the game, stones in dead groups on the board at the end of the game, points of territory controlled by a player but not occupied by their stones, their living stones, the number of passes, and the number of disjoint living groups on the board.
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On the back of the album is an image of all four members of the band together with Jackson Browne and J. D. Souther lying dead and bound on the ground. A posse stands over them, including the producer Glyn Johns (far right in a white hat), manager John Hartmann, road manager Tommy Nixon, artist Boyd Elder (who would be responsible for the skull artwork of Eagles' later albums), roadies, and Gary Burden (far left). The photo is meant to be a reenactment of the historical image of the capture and death of the Dalton Gang. Jackson Browne said that the image on the back cover with the musicians lying dead is when the "whole thing really comes together".
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This theorem has been generalized by to a tight bound on the dimension of the height-three partially ordered sets formed analogously from the vertices, edges and faces of a convex polyhedron, or more generally of an embedded planar graph: in both cases, the order dimension of the poset is at most four. However, this result cannot be generalized to higher-dimensional convex polytopes, as there exist four-dimensional polytopes whose face lattices have unbounded order dimension. Even more generally, for abstract simplicial complexes, the order dimension of the face poset of the complex is at most , where is the minimum dimension of a Euclidean space in which the complex has a geometric realization .
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There is a small portion of lower Charles Village that is sometimes referred to as Koreatown or Little Korea and is home to a number of Korean restaurants, but it has not been officially designated as a Koreatown. This informal Koreatown is bound on the north by 24th Street, on the south by North Avenue, on the west by Maryland Avenue, and on the east by St. Paul Street. Korean international students coming from the nearby Johns Hopkins University provide a constant stream of diners seeking Korean comfort food at the Korean restaurants of Charles Village. A Korean grocery store, the Far East House, formerly existed in Charles Village at 33 W. North Avenue.
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The bisection method consists roughly of starting from an interval containing all real roots of a polynomial, and divides it recursively into two parts until getting eventually intervals that contain either zero or one root. The starting interval may be of the form , where is an upper bound on the absolute values of the roots, such as those that are given in . For technical reasons (simpler changes of variable, simpler complexity analysis, possibility of taking advantage of the binary analysis of computers), the algorithms are generally presented as starting with the interval . There is no loss of generality, as the changes of variables and move respectively the positive and the negative roots in the interval .
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It is Franzel that gets chosen to be the head of the dynasty, as his father, already bound on a wheelchair, is unable to perform his duties. Eventually after Hans Heinrich, with the help of his new loyal adviser, Manager Zbierski known as Wróżka (future-teller) and his secretary Kazimierz, found out that all of the personal saving were sent to Hitler in order to secure the reputation of the Nazi party, he removes Franzel from office and places Conrad in charge. He later makes an announcement about his decision to the workers in the industrial district. Meanwhile, Bolko is arrested in Germany and suspected of fraud and spying on the Gestapo.
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Another application of widest paths arises in the Ford–Fulkerson algorithm for the maximum flow problem. Repeatedly augmenting a flow along a maximum capacity path in the residual network of the flow leads to a small bound, , on the number of augmentations needed to find a maximum flow; here, the edge capacities are assumed to be integers that are at most . However, this analysis does not depend on finding a path that has the exact maximum of capacity; any path whose capacity is within a constant factor of the maximum suffices. Combining this approximation idea with the shortest path augmentation method of the Edmonds–Karp algorithm leads to a maximum flow algorithm with running time .
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The morning after the tragedy, Minister of Interior unexpectedly did not appear at the weekly government meeting, she reported that she was skiing in St. Moritz, Switzerland, and a few days later she appeared with a bound on her arm. Media published photos from the crime scene of the morning after the Baričević's death, showing Ministry of Agriculture State Secretary Sonja Bukovec crying and hugging sister of Baričević. In the parliament, a motion of no confidence (called interpellation in Slovenia) was initiated against the Minister of Agriculture Milan Pogačnik for numerous irregularities in the events related to Baričević's dogs and he the minister resigned. DNA of all three dogs was found on the condom.
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If a family of graphs has bounded treewidth, then it is a subfamily of the partial k-trees, where k is the bound on the treewidth. Families of graphs with this property include the cactus graphs, pseudoforests, series-parallel graphs, outerplanar graphs, Halin graphs, and Apollonian networks. For instance, the series-parallel graphs are a subfamily of the partial 2-trees, and more strongly a graph is a partial 2-tree if and only if each of its biconnected components is series- parallel. The control flow graphs arising in the compilation of structured programs also have bounded treewidth, which allows certain tasks such as register allocation to be performed efficiently on them..
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The global state approach was continued in automata theory for finite-state machines and push down stack machines, including their nondeterministic versions. Such nondeterministic automata have the property of bounded nondeterminism; that is, if a machine always halts when started in its initial state, then there is a bound on the number of states in which it halts. Edsger Dijkstra further developed the nondeterministic global state approach. Dijkstra's model gave rise to a controversy concerning unbounded nondeterminism (also called unbounded indeterminacy), a property of concurrency by which the amount of delay in servicing a request can become unbounded as a result of arbitration of contention for shared resources while still guaranteeing that the request will eventually be serviced.
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Because the only difference between the two games (regular and thoughtful) is the knowledge of card location, all thoughtful games with solutions will also have solutions in Klondike. Since any winnable Klondike game must necessarily be winnable when played thoughtfully, the results on Thoughtful Klondike tells us that 82% is an upper bound on the winnability of regular Klondike when we don't know the location of all cards. The true probability with best play might be much smaller, because the difference between a right and wrong move cannot be known in advance whenever more than one move is possible and some cards are still hidden. Ultimately, very little is known about the winnability of regular Klondike.
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An unpublished study from 1989 on a generalized version of the game on the English board showed that each possible problem in the generalized game has 29 possible distinct solutions, excluding symmetries, as the English board contains 9 distinct 3×3 sub-squares. One consequence of this analysis is to put a lower bound on the size of possible "inverted position" problems, in which the cells initially occupied are left empty and vice versa. Any solution to such a problem must contain a minimum of 11 moves, irrespective of the exact details of the problem. It can be proved using abstract algebra that there are only 5 fixed board positions where the game can successfully end with one peg.
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Most of the interior imagery is behind glass cases, including a dead woman rising off a table, a shaking mummy case, two gorillas, a werewolf popping out from behind foliage, skeletons, and various other horrors, in particular, scenes of a violent and gruesome nature such as a circular saw dismemberment and a man bound on all four limbs begging for help. Suspense is built by relatively long passages of nothing but darkness, strobes that simulate lightning, and sound effects, such as screaming, though some of these are lined with small, impish wall tiles. Little direct influence of Dante Alighieri's Divine Comedy is to be found, though this was not always the case.Coney Island Dark Rides The ride seems to have no particular theme in its current state.
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In principle, the German government followed the line of market- oriented reasoning that the dollar index and the wholesale price index would roughly indicate the true price level in general over the period of high inflation and hyperinflation. In addition, the revaluation was bound on the exchange rate mark and United States dollar to obtain the value of the Goldmark. Finally, the Law on the Revaluation of Mortgages and other Claims of 16 July 1925 (' or ') included only the ratio of the paper mark to the gold mark for the period from January 1, 1918, to November 30, 1923, and the following days. The galloping inflation thus caused the end of a principle, "a mark is worth a mark", which had been recognized, the nominal value principle.
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In mathematics, specifically algebraic topology, semi-locally simply connected is a certain local connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in X. This condition is necessary for most of the theory of covering spaces, including the existence of a universal cover and the Galois correspondence between covering spaces and subgroups of the fundamental group. Most “nice” spaces such as manifolds and CW complexes are semi-locally simply connected, and topological spaces that do not satisfy this condition are considered somewhat pathological. The standard example of a non-semi-locally simply connected space is the Hawaiian earring.
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The size of the separator S constructed in this way is at most √8√n, or approximately 2.83√n. The vertices of the separator and the two disjoint subgraphs can be found in linear time. This proof of the separator theorem applies as well to weighted planar graphs, in which each vertex has a non-negative cost. The graph may be partitioned into three sets A, S, and B such that A and B each have at most 2/3 of the total cost and S has O(√n) vertices, with no edges from A to B.. By analysing a similar separator construction more carefully, shows that the bound on the size of S can be reduced to √6√n, or approximately 2.45√n.
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In addition to its offices, The Plaza at Harmon Meadow has a convention center, a 14-screen Kerasotes Theatres complex, the Meadowlands Exposition Center, The Mall at Mill Creek, and its own post office. The International Council of Shopping Centers lists the mall as having a Gross leasable area (GLA) of .International Council of Shopping Centers: Harmon Meadows , accessed December 2, 2006 The Plaza at Harmon Meadow is bound on the south by Route 3 and Paterson Plank Road. The mall is accessible via the bus lines 78 from Newark, 85 from New Jersey (Jersey City and Union City), and the 190 and 320 interstate bus lines, which travel to and from the Port Authority Bus Terminal in Midtown Manhattan.
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He is also a research associate of the National Bureau of Economics Research. He is a columnist for the online international business magazine Quartz, where his column coauthored with Noah Smith, "There is one key difference between kids who excel at math and those who don't" was the second most popular article in 2013. Other popular columns have focused on education, immigration policy, how to get into PhD programs in economics, geopolitics, gay marriage, sexism in economics, the Reinhart and Rogoff controversy and negative interest rates. On his blog, "Confessions of a Supply Side Liberal," he has been an advocate for eliminating the zero lower bound on nominal interest rates in order to make deep negative interest rates a viable monetary policy option.
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His algorithm uses this generate-and-test approach, but restricts the generated cycles to a small set of O(mn) cycles, called Horton cycles. A Horton cycle is a fundamental cycle of a shortest path tree of the given graph. There are n different shortest path trees (one for each starting vertex) and each has fewer than m fundamental cycles, giving the bound on the total number of Horton cycles. As Horton showed, every cycle in the minimum weight cycle basis is a Horton cycle.. Using Dijkstra's algorithm to find each shortest path tree and then using Gaussian elimination to perform the testing steps of the greedy basis algorithm leads to a polynomial time algorithm for the minimum weight cycle basis.
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In these cases we speak about learning of functions (in terms for instance of regression, neuro-fuzzy system or computational learning) on the basis of highly informative samples. A first effect of having a complex structure linking data is the reduction of the number of sample degrees of freedom, i.e. the burning of a part of sample points, so that the effective sample size to be considered in the central limit theorem is too small. Focusing on the sample size ensuring a limited learning error with a given confidence level, the consequence is that the lower bound on this size grows with complexity indices such as VC dimension or detail of a class to which the function we want to learn belongs.
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However, a key difference is that the dual subgradient algorithm is typically analyzed under restrictive strict convexity assumptions that are needed for the primal variables x(t) to converge. There are many important cases where these variables do not converge to the optimal solution, and never even get near the optimal solution (this is the case for most linear programs, as shown below). On the other hand, the drift-plus- penalty algorithm does not require strict convexity assumptions. It ensures that the time averages of the primals converge to a solution that is within O(1/V) of optimality, with O(V) bounds on queue sizes (it can be shown that this translates into an O(V2) bound on convergence time).
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In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes Shannon's channel capacity for such a communication link, a bound on the maximum amount of error-free information per time unit that can be transmitted with a specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a known power or power spectral density. The law is named after Claude Shannon and Ralph Hartley.
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In computer science, a loop variant is a mathematical function defined on the state space of a computer program whose value is monotonically decreased with respect to a (strict) well-founded relation by the iteration of a while loop under some invariant conditions, thereby ensuring its termination. A loop variant whose range is restricted to the non-negative integers is also known as a bound function, because in this case it provides a trivial upper bound on the number of iterations of a loop before it terminates. However, a loop variant may be transfinite, and thus is not necessarily restricted to integer values. A well-founded relation is characterized by the existence of a minimal element of every non-empty subset of its domain.
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For a finite set of points in the plane the lower bound on the computational complexity of finding the convex hull represented as a convex polygon is easily shown to be the same as for sorting using the following reduction. For the set x_1,\dots,x_n numbers to sort consider the set of points (x_1, x^2_1),\dots,(x_n, x^2_n) of points in the plane. Since they lie on a parabola, which is a convex curve it is easy to see that the vertices of the convex hull, when traversed along the boundary, produce the sorted order of the numbers x_1,\dots,x_n. Clearly, linear time is required for the described transformation of numbers into points and then extracting their sorted order.
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The Downes Memorial clock tower Trinity's campus features a central green known as the Main Quad, designed by famed architect Frederick Law Olmsted. The large expanse of grass is bound on the west by the Long Walk, on the east by the Lower Long Walk, on the north by the Chapel, and on the south by the Cook and Goodwin-Woodward dormitories. While a central green is a feature of many college campuses, Trinity's is notable for its unusually large, rectangular size, running the entire length of the Long Walk and with no walkways traversing it. Trees on the Quad have been planted in a 'T' configuration (for Trinity) with the letter's base at the statue of Bishop Brownell (built 1867).
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Channel capacity is the tightest upper bound on the rate of information that can be reliably transmitted over a communications channel. By the noisy-channel coding theorem, the channel capacity of a given channel is the limiting information rate (in units of information per unit time) that can be achieved with arbitrarily small error probability. Information theory, developed by Claude E. Shannon during World War II, defines the notion of channel capacity and provides a mathematical model by which one can compute it. The key result states that the capacity of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the maximization is with respect to the input distribution.
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In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size increases to infinity. Under stronger assumptions, the Berry–Esseen theorem, or Berry–Esseen inequality, gives a more quantitative result, because it also specifies the rate at which this convergence takes place by giving a bound on the maximal error of approximation between the normal distribution and the true distribution of the scaled sample mean. The approximation is measured by the Kolmogorov–Smirnov distance. In the case of independent samples, the convergence rate is , where is the sample size, and the constant is estimated in terms of the third absolute normalized moments.
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Graphical representation of the encoding process. The message being encoded here is "AABA" Range encoding conceptually encodes all the symbols of the message into one number, unlike Huffman coding which assigns each symbol a bit-pattern and concatenates all the bit-patterns together. Thus range encoding can achieve greater compression ratios than the one-bit-per-symbol lower bound on Huffman encoding and it does not suffer the inefficiencies that Huffman does when dealing with probabilities that are not exact powers of two. The central concept behind range encoding is this: given a large-enough range of integers, and a probability estimation for the symbols, the initial range can easily be divided into sub-ranges whose sizes are proportional to the probability of the symbol they represent.
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Structurally, the Torsäule rises in front of the mountain ridge which the high plateau of the Hochkönig massif and its plateau glacier bound on the eastern side and which opens like a rock arena in a semi-circle facing the column and looking towards the Salzach valley. The Torsäule rises, as the crow flies, roughly between the eastern top of the Schoberköpfe (2,666 and 2,708 m) and the Königs- and Bratschenköpfe (2,630 to 2,857 m). On the other side (north- facing) it drops down to the Eiskar, beyond which the Teufelskirche mountain and cave lie on the steep slopes of the Schoberköpfe. The elongated, rocky cirque on the south side, past the foot of which the path runs, has the name, rather common in Salzburg, of Ochsenkar.
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Unfortunately, the solar minima in this period coincided with volcanic eruptions, which have a cooling effect on the global temperature. Because the eruptions caused a larger and less well quantified decrease in radiative forcing than the reduced solar irradiance, it is questionable whether useful quantitative conclusions can be derived from the observed temperature variations. Observations of volcanic eruptions have also been used to try to estimate climate sensitivity, but as the aerosols from a single eruption last at most a couple of years in the atmosphere, the climate system can never come close to equilibrium, and there is less cooling than there would be if the aerosols stayed in the atmosphere for longer. Therefore, volcanic eruptions give information only about a lower bound on transient climate sensitivity.
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Theoretical support for the importance of this measure of network performance was developed in the PhD research of Clark Thomborson (formerly Clark Thompson). Thomborson proved that important algorithms for sorting, Fast Fourier transformation, and matrix-matrix multiplication become communication-limited—as opposed to CPU-limited or memory-limited—on computers with insufficient bisection width. F. Thomson Leighton's PhD research tightened Thomborson's loose bound on the bisection width of a computationally-important variant of the De Bruijn graph known as the shuffle-exchange graph. Based on Bill Dally's analysis of latency, average case throughput, and hot-spot throughput of m-ary n-cube networks for various m, It can be observed that low-dimensional networks, in comparison to high- dimensional networks (e.g.
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After her return to the United States, she taught in Baltimore for three years until a second scholarship, by the Baltimore Association for the Promotion of University Education of Women, permitted her to return to Bryn Mawr college to complete her Ph.D. under the direction of Charlotte Scott. Her dissertation, "On the Arrangement of the Real Branches of Plane Algebraic Curves," was published in 1906 by the American Journal of Mathematics. Her dissertation addressed the 16th of Hilbert's problems, for which Ragsdale formulated a conjecture that provided an upper bound on the number of topological circles of a certain type. Her result is called the Ragsdale conjecture; it was an open problem for 90 years until counterexamples were derived by Oleg Viro (1979) and Ilya Itenberg (1994).
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Their argument consists of finding an upper bound on the number of o-polynomials defined over GF(16) and then, by examining the possible automorphism groups of hyperovals in this plane, showing that if a hyperoval other than the known ones existed in this plane then the upper bound would be exceeded. provides a group-theoretic construction of the Lunelli-Sce hyperoval as the union of orbits of the group generated by the elations of PGU(3,4) considered as a subgroup of PGL(3,16). Also included in this paper is a discussion of some remarkable properties concerning the intersections of Lunelli-Sce hyperovals and hyperconics. In it is shown that the Lunelli-Sce hyperoval is the first non-trivial member of theSubiaco family (see also ).
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Meshulam's game is a game played on a graph G, that can be used to calculate a lower bound on the homological connectivity of the independence complex of G. The matching complex of a graph G, denoted M(G), is an abstract simplicial complex of the matchings in G. It is the independence complex of the line graph of G. The (m,n)-chessboard complex is the matching complex on the complete bipartite graph Km,n. It is the abstract simplicial complex of all sets of positions on an m-by-n chessboard, on which it is possible to put rooks without each of them threatening the other. The clique complex of G is the independence complex of the complement graph of G.
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Minimum vertex degree gives a trivial upper bound on edge- connectivity. That is, if a graph G = (V, E) is k-edge-connected then it is necessary that k ≤ δ(G), where δ(G) is the minimum degree of any vertex v ∈ V. Obviously, deleting all edges incident to a vertex, v, would then disconnect v from the graph. Edge connectivity is the dual concept to girth, the length of the shortest cycle in a graph, in the sense that the girth of a planar graph is the edge connectivity of its dual graph, and vice versa. These concepts are unified in matroid theory by the girth of a matroid, the size of the smallest dependent set in the matroid.
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A complete sparse ruler is called minimal if there is no complete sparse ruler of length L with m-1 marks. In other words, if any of the marks is removed one can no longer measure all of the distances, even if the marks could be rearranged. A complete sparse ruler is called maximal if there is no complete sparse ruler of length L+1 with m marks. A sparse ruler is called optimal if it is both minimal and maximal. Since the number of distinct pairs of marks is m(m-1)/2, this is an upper bound on the length L of any maximal sparse ruler with m marks. This upper bound can be achieved only for 2, 3 or 4 marks.
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Depending on the color depth, a pixel in the picture will occupy at least n/8 bytes, where n is the bit depth. For an uncompressed, packed within rows, bitmap, such as is stored in Microsoft DIB or BMP file format, or in uncompressed TIFF format, a lower bound on storage size for a n-bit-per-pixel (2n colors) bitmap, in bytes, can be calculated as: :size = width • height • n/8, where height and width are given in pixels. In the formula above, header size and color palette size, if any, are not included. Due to effects of row padding to align each row start to a storage unit boundary such as a word, additional bytes may be needed.
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Examples of games that are PSPACE-complete (when generalized so that they can be played on an n × n board) are the games Hex and Reversi the solitaire games Rush Hour, Mahjong, Atomix and Sokoban, and the mechanical computer Turing Tumble. Some other generalized games, such as chess, checkers (draughts), and Go are EXPTIME-complete because a game between two perfect players can be very long, so they are unlikely to be in PSPACE. But they will become PSPACE-complete if a polynomial bound on the number of moves is enforced. Note that the definition of PSPACE-completeness is based on asymptotic complexity: the time it takes to solve a problem of size n, in the limit as n grows without bound.
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A framing story is told in the first person by Darrell Standing, a university professor serving life imprisonment in San Quentin State Prison for murder. Prison officials try to break his spirit by means of a torture device called "the jacket," a canvas jacket which can be tightly laced so as to compress the whole body, inducing angina. Standing discovers how to withstand the torture by entering a kind of trance state, in which he walks among the stars and experiences portions of past lives. : I trod interstellar space, exalted by the knowledge that I was bound on vast adventure, where, at the end, I would find all the cosmic formulae and have made clear to me the ultimate secret of the universe.
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Saurashtra peninsula is bound on the south and south-west by the Arabian sea, on the north-west by the Gulf of Kutch and on the east by the Gulf of Khambhat. From the apex of these two gulfs, the Little Rann of Kutch and Khambhat, waste tracts half salt morass half sandy desert, stretch inland towards each other and complete the isolation of Kathiawar, except one narrow neck which connects it on the north-east with the mainland of Gujarat. The peninsula is sometimes referred to as Kathiawar after the Kathi Darbar, which once ruled most of the region. However, Saurashtra is not entirely synonymous with Kathiawar, since a small portion of the historical Saurashtra region extends beyond the Kathiawar peninsula.
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High responds that "the gods hold their sacred places and sanctuaries in such respect that they chose not to defile them with the wolf's blood, even though the prophecies foretold that he would be the death of Odin." As a consequence of his role in the death of the god Baldr, Loki (described as father of Fenrir) is bound on top of three stones with the internal organs of his son Narfi (which are turned into iron) in three places. There, venom drops onto his face periodically from a snake placed by the Skaði. Loki's wife Sigyn collects the venom into a bucket, but whenever she leaves to empty it, the drops reach Loki's face, and the pain he experiences causes convulsions, resulting in earthquakes.
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Dunbar's surveys of village and tribe sizes also appeared to approximate this predicted value, including 150 as the estimated size of a Neolithic farming village; 150 as the splitting point of Hutterite settlements; 200 as the upper bound on the number of academics in a discipline's sub-specialisation; 150 as the basic unit size of professional armies in Roman antiquity and in modern times since the 16th century; and notions of appropriate company size. Dunbar has argued that 150 would be the mean group size only for communities with a very high incentive to remain together. For a group of this size to remain cohesive, Dunbar speculated that as much as 42% of the group's time would have to be devoted to social grooming.
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The Owambo Basin is a sedimentary basin located on the Congo Craton in Southern Africa that extends from southern Angola into Namibia and includes the Etosha Pan. It is bound on the southern and western sides by the Damara Belt in Northern Namibia and by the Cubango River to the East. The northern boundary is scientifically disputed, but is currently mapped by most stratigraphers to include southern Angola with the boundary set at the Kunene River. The Owambo Basin is host to two famous regions: Tsumeb, a major Namibian city and site of a formerly active copper mine with exceptional mineralogical variability producing museum quality rare specimens, and Etosha National Park, the largest protected wildlife sanctuary in Namibia centered around Etosha Pan.
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Her research has focused on graph theory and discrete mathematics, specializing mainly in topological and chromatic graph theory and on visibility graphs; for overviews of this work see and . She has published over 75 research and expository papers in graph theory, many with Michael O. Albertson, formerly of Smith College. In one of their most cited works, Albertson and Hutchinson completed work of Gabriel Andrew Dirac related to the Heawood conjecture by proving that, on any surface other than the sphere or Klein bottle, the only graphs meeting Heawood's bound on the chromatic number of surface-embedded graphs are the complete graphs. She has also considered algorithmic aspects in these areas, for example, generalizing the planar separator theorem to surfaces.
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From the other direction, there has been considerable clarification of what constructive mathematics is—without the emergence of a 'master theory'. For example, according to Errett Bishop's definitions, the continuity of a function such as \sin(x) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a promise that can always be kept. Accordingly, Bishop rejects the standard idea of pointwise continuity, and proposed that continuity should be defined in terms of "local uniform continuity". One could get another explanation of existence theorem from type theory, in which a proof of an existential statement can come only from a term (which one can see as the computational content).
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Semi-transitive orientations provide a powerful tool to study word-representable graphs. A directed graph is semi-transitively oriented iff it is acyclic and for any directed path u1→u2→ ...→ut, t ≥ 2, either there is no edge from u1 to ut or all edges ui → uj exist for 1 ≤ i < j ≤ t. A key theorem in the theory of word-representable graphs states that a graph is word-representable iff it admits a semi-transitive orientation . As a corollary to the proof of the key theorem one obtain an upper bound on word-representants: Each non-complete word-representable graph G is 2(n − κ(G))-representable, where κ(G) is the size of a maximal clique in G .
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The section of the range north of Enoggera Creek (sometimes called the Enoggera side of the range) includes the Keperra Bushland, Enoggera Military Area and the Ashgrove Golf Club golf course. Most of the range south of Enoggera Creek (the Mt Coot-tha side) is covered by the protected area of Mt Coot-tha Reserve (or Mt Coot-tha Forest). The two sections of the range separate at Enoggera Reservoir and circle the crater shaped suburb of The Gap like the claws of a crab, leaving a narrow entrance via Waterworks Road from the east (this being ‘the gap’ from which the suburb got its name). The Enoggera side of the range is bound on the north by the upper end of the Kedron Brook catchment area which includes the tributary of Cedar Creek.
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A submissive woman bound on Saint Andrew's Cross (BDSM) In BDSM, servitude refers to performing personal tasks for their dominant partner, as part of their submissive role in a BDSM relationship. In domestic servitude roles, the submissive can receive pleasure and satisfaction from performing personal services for their dominant, such as serving as a butler, waitress, chauffeur, maid or housekeeper. In workplace BDSM, the submissive can somehow secretly contrive that a colleague, of the same or opposite gender to the submissive, unwittingly finds themselves with imagined or real work-related disciplinary power and/or status over the submissive. The created dominant may never realize they are bringing secret pleasure and satisfaction to the submissive, in the giving of orders or else in rebuking the submissive for supposed performance failings at the workplace, such as "laziness".
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HPET is a continuously running timer that counts upward, not a one-shot device that counts down to zero, causes one interrupt and then stops. Since HPET compares the actual timer value and the programmed target value on equality rather than "greater or equal", interrupts can be missed if the target time has already passed when the comparator value is written into the chip's register. In such a case, not only is the intended interrupt missed, but actually set far into the future (about 232 or 264 counts). In the presence of non-maskable interrupts (such as a System Management Interrupt (SMI)) that do not have a hard upper bound on their execution time, this race condition requires time-consuming re-checks of the timer after setup and is hard to avoid completely.
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Gibbs' phase rule, F=C-P+2, can be used to determine an upper bound on the number of phases that will form in an equilibrium system. In his 2004 paper, Cantor created a 20-component alloy containing 5 at% of Mn, Cr, Fe, Co, Ni, Cu, Ag, W, Mo, Nb, Al, Cd, Sn, Pb, Bi, Zn, Ge, Si, Sb, and Mg. At constant pressure, the phase rule would allow for up to 21 phases at equilibrium, but far fewer actually formed. The predominant phase was a face-centered cubic solid solution phase, containing mainly Fe, Ni, Cr, Co, and Mn. From that result, the FeCrMnNiCo alloy, which forms only a solid solution phase, was developed. The Hume-Rothery rules have historically been applied to determine whether a mixture will form a solid solution.
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Multiferroics have been used to address fundamental questions in cosmology and particle physics. In the first, the fact that an individual electron is an ideal multiferroic, with any electric dipole moment required by symmetry to adopt the same axis as its magnetic dipole moment, has been exploited to search for the electric dipole moment of the electron. Using the designed multiferroic material (Eu,Ba)TiO3, the change in net magnetic moment on switching of the ferroelectric polarisation in an applied electric field was monitored, allowing an upper bound on the possible value of the electron electric dipole moment to be extracted. This quantity is important because it reflects the amount of time-reversal (and hence CP) symmetry breaking in the universe, which imposes severe constraints on theories of elementary particle physics.
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The spectrum of the secondary star has not been determined, but, based on the mass, it may have a stellar classification of F5 III–V or G0 V. It is about four magnitudes fainter than the primary; hence the energy output from the system is dominated by the primary star. In a few million years, as the primary evolves toward a red giant, significant amounts of mass transfer to the secondary component is expected. The primary has been classified as a rapid rotator, with a projected rotational velocity of 73 km/s providing a lower bound on the azimuthal rotational velocity along the equator. It may also be a mildly Am star, which is a class of stars that show a peculiar spectrum with strong absorption lines from various elements and deficiencies in others.
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The county was formed in 1855 from parts of Stanstead, Shefford and Missisquoi counties. The county is located in the Eastern Townships, one of the 12 regions of Quebec. The county lies in the foothills of the Appalachian Mountains. Its eastern half is rolling countryside while its western half is part of the Richelieu River plains. The county is roughly an upside-down "L" shape, bound on the south by the Canada–US border (along 45° for 17.5 km from 72° 15′ W in Lake Memphremagog to 72° 41.5′ W), in the east by in part Lake Memphremagog and Stanstead County, in the north by Shefford County (45° 20′ N for 48 km from 72° 15′ W to 72° 52′ W) and in the west by Rouville and Missisquoi counties.
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Edelsbrunner and Welzl (1986) first studied the problem of constructing all k-sets of an input point set, or dually of constructing the k-level of an arrangement. The k-level version of their algorithm can be viewed as a plane sweep algorithm that constructs the level in left-to-right order. Viewed in terms of k-sets of point sets, their algorithm maintains a dynamic convex hull for the points on each side of a separating line, repeatedly finds a bitangent of these two hulls, and moves each of the two points of tangency to the opposite hull. Chan (1999) surveys subsequent results on this problem, and shows that it can be solved in time proportional to Dey's O(nk1/3) bound on the complexity of the k-level.
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If π is a partition of an amorphous set into finite subsets, then there must be exactly one integer n(π) such that π has infinitely many subsets of size n; for, if every size was used finitely many times, or if more than one size was used infinitely many times, this information could be used to coarsen the partition and split π into two infinite subsets. If an amorphous set has the additional property that, for every partition π, n(π) = 1, then it is called strictly amorphous or strongly amorphous, and if there is a finite upper bound on n(π) then the set is called bounded amorphous. It is consistent with ZF that amorphous sets exist and are all bounded, or that they exist and are all unbounded.
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The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices but has no complete bipartite subgraphs of a given size.. Reprint of 1978 Academic Press edition, . It belongs to the field of extremal graph theory, a branch of combinatorics, and is named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951.. As cited by . The Kővári–Sós–Turán theorem, named after Tamás Kővári, Vera T. Sós, and Pál Turán, provides an upper bound on the solution to the Zarankiewicz problem. When the forbidden complete bipartite subgraph has one side with at most three vertices, this bound has been proven to be within a constant factor of the correct answer.
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22, No. 12, IEEE Communications Magazine Ones-density is often controlled using precoding techniques such as run-length limited encoding, where the PCM code is expanded into a slightly longer code with a guaranteed bound on ones-density before modulation into the channel. In other cases, extra framing bits are added into the stream, which guarantees at least occasional symbol transitions. Another technique used to control ones-density is the use of a scrambler on the data, which will tend to turn the data stream into a stream that looks pseudo- random, but where the data can be recovered exactly by a complementary descrambler. In this case, long runs of zeroes or ones are still possible on the output, but are considered unlikely enough to allow reliable synchronization.
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This argument allows us to discuss specific features of the model that we may otherwise miss—for example, a bound on a specific increasing sequence cn can be expressed as realizing the type which uses countably many parameters. If the sequence is not definable, this fact about the structure cannot be described using the base language, so a weakly saturated structure may not bound the sequence, while an ω-saturated structure will. The reason we only require parameter sets that are strictly smaller than the model is trivial: without this restriction, no infinite model is saturated. Consider a model M, and the type Each finite subset of this type is realized in the (infinite) model M, so by compactness it is consistent with M, but is trivially not realized.
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The density of a channel, defined for every x within the channel, is the number of nets that appear on both the left and right of a vertical line at that x. The maximum density is a lower bound on the height of the channel. A "cyclic constraint" occurs when two pins occur in the same column (but with different orders) in at least two columns. In the example shown, nets 1 and 3 suffer from cyclic constraints. This can only be solved by "doglegs" as shown on net 1 of the example. Channel routers were one of the first forms of routers for integrated circuits,Feller, A. 1976. . In Proceedings of the 13th Conference on Design Automation (San Francisco, California, United States, June 28–30, 1976). DAC '76.
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Following the approach suggested by , Thomas Hales, then at the University of Michigan, determined that the maximum density of all arrangements could be found by minimizing a function with 150 variables. In 1992, assisted by his graduate student Samuel Ferguson, he embarked on a research program to systematically apply linear programming methods to find a lower bound on the value of this function for each one of a set of over 5,000 different configurations of spheres. If a lower bound (for the function value) could be found for every one of these configurations that was greater than the value of the function for the cubic close packing arrangement, then the Kepler conjecture would be proved. To find lower bounds for all cases involved solving about 100,000 linear programming problems.
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The hepatic lipase can either remain attached to the liver or can unbind from the liver endothelial cells and is free to enter the body's circulation system. When bound on the endothelial cells of the liver, it is often found bound to HSPG, heparan sulfate proteoglycans (HSPG), keeping HL inactive and unable to bind to HDL (high density lipoprotein) or IDL (intermediate density lipoprotein). When it is free in the bloodstream, however, it is found associated with HDL to maintain it inactive. This is because the triacylglycerides in HDL serve as a substrate, but the lipoprotein contains proteins around the triacylglycerides that can prevent the triacylglycerides from being broken down by HL. One of the principal functions of hepatic lipase is to convert intermediate-density lipoprotein (IDL) to low-density lipoprotein (LDL).
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He then proceeded to Paris where he studied medicine, receiving a doctorate for a thesis entitled Essai sur cette question d'économie médicale : Convient-il qu'un malade soit instruit de sa situation? Budan died in Paris on 6 October 1840. Budan explains in his book how, given a monic polynomial p(x), the coefficients of p(x+1) can be obtained by developing a Pascal-like triangle with first row the coefficients of p(x), rather than by expanding successive powers of x+1, as in Pascal's triangle proper, and then summing; thus, the method has the flavour of lattice path combinatorics. Taken together with Descartes' Rule of Signs, this leads to an upper bound on the number of the real roots a polynomial has inside an open interval.
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Clb5 and Clb6 are part of a regulatory network that initiates DNA replication during S-phase. Clb5 and Clb6 levels rise during G1 (earlier than other B-type cyclins) and stay high throughout S and M phases. During S-phase, Clb5 and Clb6 are simultaneously expressed with other genes encoding proteins required for individual DNA strand replication and separation. Clb5 and Clb6 differentially bind to Cdk1, and this activation directly promotes firing of the various origins of replication. Clb5, in particular, has unique hydrophobic section of amino acids that allows specific interactions with proteins in the pre-replication complex bound on the DNA and helps localize Clb5 to DNA replication origins. Clb5 and Clb6 also assist in spindle pole body duplication during S-phase, primarily when Clb3 and Clb4 are inactivated.
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Argentière is located near the head of the valley of Chamonix approximately from Chamonix town. It is connected by road with Switzerland by the pass over the Col des Montets, and the Col de la Forclaz to Martigny in the Rhône valley. The village also lies on the route of the incredibly scenic Mont Blanc Express railway which runs from St Gervais and Le Fayet through Chamonix, Argentiere and Vallorcine before crossing the Franco/Swiss border at Chatelard, passing through Finhaut before reaching the end of the line in Martigny. The Argentière glacier lies to the southeast of the village, and is bound on its northeast side by the Aiguille du Chardonnet, the Aiguille d'Argentière and the Tour Noir, and on its southwest by the Aiguille Verte, Les Droites and Les Courtes.
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For straight-line drawings of planar graphs with n vertices, the optimal worst-case bound on the area of a drawing is Θ(n2). The nested triangles graph requires this much area no matter how it is embedded, and several methods are known that can draw planar graphs with at most quadratic area... Binary trees, and trees of bounded degree more generally, have drawings with linear or near- linear area, depending on the drawing style...... Every outerplanar graph has a straight-line outerplanar drawing with area subquadratic in its number of vertices,.. If bends or crossings are allowed, then outerplanar graphs have drawings with near-linear area... However, drawing series-parallel graphs requires an area larger than n multiplied by a superpolylogarithmic factor, even if edges can be drawn as polylines..
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A matroid has branchwidth one if and only if every element is either a loop or a coloop, so the unique minimal forbidden minor is the uniform matroid U(2,3), the graphic matroid of the triangle graph. A matroid has branchwidth two if and only if it is the graphic matroid of a graph of branchwidth two, so its minimal forbidden minors are the graphic matroid of K4 and the non-graphic matroid U(2,4). The matroids of branchwidth three are not well-quasi-ordered without the additional assumption of representability over a finite field, but nevertheless the matroids with any finite bound on their branchwidth have finitely many minimal forbidden minors, all of which have a number of elements that is at most exponential in the branchwidth.; .
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This is a generalization of Descartes' rule of signs, because, for sufficiently large, there is no sign variation in the coefficients of , and all real roots are smaller than . Budan's may provide a real-root-isolation algorithm for a square-free polynomial (a polynomial without multiple root): from the coefficients of polynomial, one may compute an upper bound of the absolute values of the roots and a lower bound on the absolute values of the differences of two roots (see Properties of polynomial roots). Then, if one divides the interval into intervals of length less than , then every real root is contained in some interval, and no interval contains two roots. The isolating intervals are thus the intervals for which Budan's theorem asserts an odd number of roots.
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Proton decay is one of the key predictions of the various grand unified theories (GUTs) proposed in the 1970s, another major one being the existence of magnetic monopoles. Both concepts have been the focus of major experimental physics efforts since the early 1980s. To date, all attempts to observe these events have failed; however, these experiments have been able to establish lower bounds on the half-life of the proton. Currently the most precise results come from the Super-Kamiokande water Cherenkov radiation detector in Japan: a 2015 analysis placed a lower bound on the proton's half-life of years via positron decay, and similarly, a 2012 analysis gave a lower bound to the proton's half-life of years via antimuon decay, close to a supersymmetry (SUSY) prediction of 1034–1036 years.
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The District of Columbia government is considering redevelopment plans for the McMillan Sand Filtration Site which is no longer used for water treatment. McMillan Sand Filtration Site is a twenty-five acre decommissioned water treatment plant in northwest Washington, D.C., built as part of the historic McMillan Reservoir Park. It is bound on the north by Michigan Avenue, on the east by North Capitol Street, on the south by Channing Street and on the west by McMillan Drive; which runs along the edge of the reservoir, to which it was formerly attached. Two paved courts lined by regulator houses, tower-like sand bins, sand washers and the gated entrances to the underground filter cells provided a promenade for citizens taking the air in the park before it was fenced off in WWII.
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That is, every graph has either a small separator or a haven of high order.. If a graph G has a haven of order k, with for some integer h, then G must also have a complete graph Kh as a minor. In other words, the Hadwiger number of an n-vertex graph with a haven of order k is at least k2/3n−1/3. As a consequence, the Kh-minor-free graphs have treewidth less than h3/2n1/2 and separators of size less than h3/2n1/2. More generally an O() bound on treewidth and separator size holds for any nontrivial family of graphs that can be characterized by forbidden minors, because for any such family there is a constant h such that the family does not include Kh.
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Ephemeralization, a term coined by R. Buckminster Fuller in 1938, is the ability of technological advancement to do "more and more with less and less until eventually you can do everything with nothing," that is, an accelerating increase in the efficiency of achieving the same or more output (products, services, information, etc.) while requiring less input (effort, time, resources, etc.). Fuller's vision was that ephemeralization will result in ever-increasing standards of living for an ever-growing population despite finite resources. The concept has been embraced by those who argue against Malthusian philosophy.. The subsequently coined economics term "dematerialization" refers to essentially the same concept. Fuller uses Henry Ford's assembly line as an example of how ephemeralization can continuously lead to better products at lower cost with no upper bound on productivity.
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Some years ago, Essex County Council tried to improve safety on the route by filling in the middle of the road so the junction is no longer a roundabout, but the road layout still resembles one by not being straight. After the Fortune of War, the first of the Basildon exits appears immediately, for the A176 to Basildon town centre and hospital, and Billericay. After a couple of exits to Crays Hill, the next junction is over on for the A132 Basildon and Wickford exit. London bound there is an exit for the Mayflower Retail Park just past the A132, so traffic Southend bound needs to use the roundabout to head the other way briefly to the Mayflower exit. A127/A1015 looking London bound on Southend bound is the junction with the A1245 (old A130) and new A130 Chelmsford/Canvey Island exit.
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Over 40 species of mammals, 200 species of birds, 40 species of reptiles, 12 species of amphibians, 42 species of fishes, 39 species of odonates, 85 species of butterflies and 38 species of spiders have been found living in the sanctuary. The sanctuary is bound on the east and north by the huge Hirakud reservoir. It is one of the select few sanctuaries in the state supporting both terrestrial and aquatic biodiversity; which further attracts a significant number of migratory waterfowl during winter; and is also home to over 250 plant species, many of which have ethno-botanical and medicinal value. Debrigarh Wildlife Sanctuary is a Eco-sensitive Zone from both a ecological and environmental point of view and to prohibit industries or class of industries and their operations and processes in the said Eco-sensitive zone.
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Assuming no drawn games, determining a clear winner (and, incidentally, a clear loser) would require the same number of rounds as that of a knockout tournament, which is the binary logarithm of the number of players rounded up. Thus three rounds can handle eight players, four rounds can handle sixteen players and so on. If fewer than this minimum number of rounds are played, two or more players could finish the tournament with a perfect score, having won all their games but never having faced each other. Due to the fact that players should meet each other at most once and pairings are chosen dependent on the results, there is a natural upper bound on the number of rounds of a Swiss-system tournament, which is equal to half of the number of players rounded up.
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Each digit of the product depends only on a neighborhood of two digits in the given number: the digit in the same position and the digit one position to the right. More generally, multiplication or division of doubly infinite digit sequences in any radix , by a multiplier or divisor all of whose prime factors are also prime factors of , is an operation that forms a cellular automaton because it depends only on a bounded number of nearby digits, and is reversible because of the existence of multiplicative inverses., p. 1093. Multiplication by other values (for instance, multiplication of decimal numbers by three) remains reversible, but does not define a cellular automaton, because there is no fixed bound on the number of digits in the initial value that are needed to determine a single digit in the result.
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The gap-Hamming problem was originally proposed by Indyk and Woodruff, who initially proved a linear lower bound on the one-way communication complexity of the problem (where Alice is only allowed to receive data from Bob) and conjectured a linear lower bound in the general case. The question of the infinite-round case (in which Alice and Bob are allowed to exchange as many messages as desired) remained open until Chakrabarti and Regev proved, via an anti-concentration argument, that the general problem also has linear lower bound complexity, thus settling the original question completely. This result was followed by a series of other papers that sought to simplify or find new approaches to proving the desired lower bound, notably first by Vidick and later by Sherstov, and, recently, with an information-theoretic approach by Hadar, Liu, Polyanskiy, and Shayevitz.
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Each of these steps may be performed with simple trigonometric calculations, and as Collins and Stephenson argue, the system of radii converges rapidly to a unique fixed point for which all covering angles are exactly 2π. Once the system has converged, the circles may be placed one at a time, at each step using the positions and radii of two neighboring circles to determine the center of each successive circle. describes a similar iterative technique for finding simultaneous packings of a polyhedral graph and its dual, in which the dual circles are at right angles to the primal circles. He proves that the method takes time polynomial in the number of circles and in log 1/ε, where ε is a bound on the distance of the centers and radii of the computed packing from those in an optimal packing.
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A third variation of the problem, still unsolved, is Conway's dead fly problem. John Horton Conway recalled that, as a child, he slept in a room with wallpaper whose flower pattern resembled an array of dead flies, and that he would try to find convex regions that did not have a dead fly in them. In Conway's formulation, the question is whether there exists a Danzer set in which the points of the set (the dead flies) are separated at a bounded distance from each other. Such a set would necessarily also have an upper bound on the distance from each point of the plane to a dead fly (in order to touch all circles of unit area), so it would form a Delone set, a set with both lower and upper bounds on the spacing of the points.
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In the most general case, the input to counting sort consists of a collection of items, each of which has a non-negative integer key whose maximum value is at most . In some descriptions of counting sort, the input to be sorted is assumed to be more simply a sequence of integers itself, but this simplification does not accommodate many applications of counting sort. For instance, when used as a subroutine in radix sort, the keys for each call to counting sort are individual digits of larger item keys; it would not suffice to return only a sorted list of the key digits, separated from the items. In applications such as in radix sort, a bound on the maximum key value will be known in advance, and can be assumed to be part of the input to the algorithm.
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A graph is 1-planar if it has a drawing with at most one crossing per edge. Intuitively, this restriction makes it easier to cause this crossing to be at right angles, and the 4n − 10 bound on the number of edges of straight-line RAC drawings is close to the bounds of 4n − 8 on the number of edges in a 1-planar graph, and of 4n − 9 on the number of edges in a straight-line 1-planar graph. Every RAC drawing with 4n − 10 edges is 1-planar.. Additionally, every outer-1-planar graph (that is, a graph drawn with one crossing per edge with all vertices on the outer face of the drawing) has a RAC drawing.. However, there exist 1-planar graphs with 4n − 10 edges that do not have RAC drawings..
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The mappings : Xm -> Xn defined by projecting out certain coordinates and setting others as constants are all continuous. (B) For a projection : p: Xm -> Xn and an irreducible closed subset Y of Xm, p(Y) lies between its closure Z and Z \ Z′ where Z′ is a proper closed subset of Z. (This is quantifier elimination, at an abstract level.) (C) X is irreducible. (D) There is a uniform bound on the number of elements of a fiber in a projection of any closed set in Xm, other than the cases where the fiber is X. (E) A closed irreducible subset of Xm, of dimension r, when intersected with a diagonal subset in which s coordinates are set equal, has all components of dimension at least r − s + 1. The further condition required is called very ample (cf.
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On ceremonial occasions the Life Guards wear a scarlet tunic, a metal cuirass and a matching helmet with a white plume worn bound on the top into an 'onion' shape; the exceptions to this are the regiment's trumpeters, who wear a red plume, and farriers, who wear blue tunics and have a black plume. In addition, the Life Guards wear their chin strap below their lower lip, as opposed to the Blues and Royals who wear it under their chin. On service dress the Life Guards Officers and Warrant Officer Class Ones wear a red lanyard on the right shoulder, as well as a Sam Browne belt. The Life Guards, as part of the Household Division, does not use the Order of the Bath Star for its officer rank "pips", but rather the Order of the Garter Star.
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The number of edges in an n-vertex linkless graph is at most 4n − 10: maximal apex graphs with n > 4 have exactly this many edges, and proved a matching upper bound on the more general class of K6-minor-free graphs. observed that Sachs' question about the chromatic number would be resolved by a proof of Hadwiger's conjecture that any k-chromatic graph has as a minor a k-vertex complete graph. The proof by of the case k = 6 of Hadwiger's conjecture is sufficient to settle Sachs' question: the linkless graphs can be colored with at most five colors, as any 6-chromatic graph contains a K6 minor and is not linkless, and there exist linkless graphs such as K5 that require five colors. The snark theorem implies that every cubic linklessly embeddable graph is 3-edge-colorable.
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Step 1: Find a polynomial p such that, writing b(n) = a(n)/p(n), the ratio b(n)/b(n − 1) has the form q(n)/r(n) where q and r are polynomials and no q(n) has a nontrivial factor with r(n + j) for j = 0, 1, 2, ... . (This is always possible, whether or not the series is summable in closed form.) Step 2: Find a polynomial ƒ such that S(n) = q(n + 1)/p(n) ƒ(n) a(n). If the series is summable in closed form then clearly a rational function ƒ with this property exists; in fact it must always be a polynomial, and an upper bound on its degree can be found. Determining ƒ (or finding that there is no such ƒ) is then a matter of solving a system of linear equations.
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Given two compact oriented Riemannian manifolds, Mi, possibly with boundary: : dSWIF(M1, M2) = 0 iff there is an orientation preserving isometry from M1 to M2. If Mi converge in the Gromov–Hausdorff sense to a metric space Y then a subsequence of the Mi converge SWIF-ly to an integral current space contained in Y but not necessarily equal to Y. For example, the GH limit of a sequence of spheres with a long thin neck pinch is a pair of spheres with a line segment running between them while the SWIF limit is just the pair of spheres. The GH limit of a sequence of thinner and thinner tori is a circle but the flat limit is the 0 space. In the setting with nonnegative Ricci curvature and a uniform lower bound on volume, the GH and SWIF limits agree.
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Adding heat to a system increases its thermodynamic entropy because it increases the number of possible microscopic states of the system that are consistent with the measurable values of its macroscopic variables, making any complete state description longer. (See article: maximum entropy thermodynamics). Maxwell's demon can (hypothetically) reduce the thermodynamic entropy of a system by using information about the states of individual molecules; but, as Landauer (from 1961) and co-workers have shown, to function the demon himself must increase thermodynamic entropy in the process, by at least the amount of Shannon information he proposes to first acquire and store; and so the total thermodynamic entropy does not decrease (which resolves the paradox). Landauer's principle imposes a lower bound on the amount of heat a computer must generate to process a given amount of information, though modern computers are far less efficient.
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See Shannon number for details. to 1047), it is hard to rule out with mathematical certainty the possibility that the initial position allows either side to force a mate or a threefold repetition after relatively few moves, in which case the search tree might encompass only a very small subset of the set of possible positions. It has been mathematically proven that generalized chess (chess played with an arbitrarily large number of pieces on an arbitrarily large chessboard) is EXPTIME-complete, meaning that determining the winning side in an arbitrary position of generalized chess provably takes exponential time in the worst case; however, this theoretical result gives no lower bound on the amount of work required to solve ordinary 8x8 chess. Martin Gardner's Minichess, played on a 5×5 board with approximately 1018 possible board positions, has been solved; its game-theoretic value is 1/2 (i.e.
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In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into smaller pieces by removing a small number of vertices. Specifically, the removal of O(√n) vertices from an n-vertex graph (where the O invokes big O notation) can partition the graph into disjoint subgraphs each of which has at most 2n/3 vertices. A weaker form of the separator theorem with O(√n log n) vertices in the separator instead of O(√n) was originally proven by , and the form with the tight asymptotic bound on the separator size was first proven by . Since their work, the separator theorem has been reproven in several different ways, the constant in the O(√n) term of the theorem has been improved, and it has been extended to certain classes of nonplanar graphs.
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Papers by Gerard J. Foschini and Michael J. Gans, Foschini and Emre Telatar have shown that the channel capacity (a theoretical upper bound on system throughput) for a MIMO system is increased as the number of antennas is increased, proportional to the smaller of the number of transmit antennas and the number of receive antennas. This is known as the multiplexing gain and this basic finding in information theory is what led to a spurt of research in this area. Despite the simple propagation models used in the aforementioned seminal works, the multiplexing gain is a fundamental property that can be proved under almost any physical channel propagation model and with practical hardware that is prone to transceiver impairments. Papers by Dr. Fernando Rosas and Dr. Christian Oberli have shown that the entire MIMO SVD link can be approximated by the average of the SER of Nakagami-m channels.
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A tessellation of the plane is a partition of the plane into smaller regions called tiles. The zeroth corona of a tile is defined as the tile itself, and for k > 0 the kth corona is the set of tiles sharing a boundary point with the (k − 1)th corona. The Heesch number of a figure S is the maximum value k such that there exists a tiling of the plane, and tile t within that tiling, for which that all tiles in the zeroth through kth coronas of t are congruent to S. In some work on this problem this definition is modified to additionally require that the union of the zeroth through kth coronas of t is a simply connected region. If there is no upper bound on the number of layers by which a tile may be surrounded, its Heesch number is said to be infinite.
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In computational complexity theory, Yao's principle (also called Yao's minimax principle or Yao's lemma) states that the expected cost of a randomized algorithm on the worst-case input is no better than the expected cost for a worst-case probability distribution on the inputs of the deterministic algorithm that performs best against that distribution. Thus, to establish a lower bound on the performance of randomized algorithms, it suffices to find an appropriate distribution of difficult inputs, and to prove that no deterministic algorithm can perform well against that distribution. This principle is named after Andrew Yao, who first proposed it. Yao's principle may be interpreted in game theoretic terms, via a two-player zero-sum game in which one player, Alice, selects a deterministic algorithm, the other player, Bob, selects an input, and the payoff is the cost of the selected algorithm on the selected input.
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This relationship is conjectured to be valid not just for black holes, but also (since entropy is proportional to information) as an upper bound on the amount of information that can be contained in any volume of space, which has in turn spawned deeper reflections on the possible nature of reality.}} In June 2018, it was announced that Hawking's words, set to music by Greek composer Vangelis, would be beamed into space from a European space agency satellite dish in Spain with the aim of reaching the nearest black hole, 1A 0620-00. Hawking's final broadcast interview, about the detection of gravitational waves resulting from the collision of two neutron stars, occurred in October 2017. His final words to the world appeared posthumously, in April 2018, in the form of a Smithsonian TV Channel documentary entitled, Leaving Earth: Or How to Colonize a Planet.
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Several researchers have investigated algorithms for constructing the Dedekind–MacNeille completion of a finite partially ordered set. Because the Dedekind–MacNeille completion may be exponentially larger than the partial order it comes from,. it is necessary to measure the time bounds for such algorithms both in terms of the number of elements of the input partial order, but also in terms of the number of elements of its completion, and sometimes also in terms of additional measures of the complexity of the input and output. The format in which the output lattice is represented may also affect the running time of its construction algorithms; for instance, if it is represented as a logical matrix specifying the result of a comparison between each pair of lattice elements, the output size is and this will be a lower bound on the time for a construction algorithm.
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And Wendland has always been at the poor end of the scale. This has continued right up to the present day, with its unfortunate position as part of the old West Germany sticking out into the old East Germany, so that it was bound on three sides by an electric fence which was the barrier to the Communist East for most of the second half of the 20th century. Wendland has always somehow been passed by, right from the times of the early Christianisation, and even today it has no motorways, virtually no railways, very little industry, very little employment and a shrinking population. If it is known for anything today, it is known for its decades-long fight against the deposit of radioactive waste in Gorleben, a site chosen by the politicians of a generation ago precisely because so few people live there.
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Sun-tzu's original formulation: In number theory, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime. The earliest known statement of the theorem is by the Chinese mathematician Sun-tzu in the Sun-tzu Suan- ching in the 3rd century AD. The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain. It has been generalized to any commutative ring, with a formulation involving ideals.
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Site plan, circa 1983 The former Animal Research Institute is a complex of buildings, sheds and animal pens on a site in the Brisbane suburb of Yeerongpilly. Those structures considered of state-level heritage significance are: the Stock Experiment Station Main Building (1909), an associated Stable (1909), the purpose-built Animal Morgue (1934), and the Veterinary School Main Building and Hospital Block (1938-1940). The entire Institute site is bound on the north by King Arthur Terrace, to the east by Fairfield Road, on the south by the Tennyson Branch Railway line, and to the west by an easement shared with the Queensland Tennis Centre. Its entrance is on King Arthur Terrace on the north-eastern corner and the significant buildings are clustered on higher ground across the eastern half of the site with the remaining, lower area comprising many large, fenced yards of grass.
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The details of the Great Gulf changed somewhat among its various forms, but the ancient and Renaissance Ptolemaic accounts had it bound on the west by the Golden Chersonese and on the north and east by the ports of the Sinae, chief among which was Cattigara. Medieval Islamic cartographers followed al-Khwārizmī in having a strait southeast of the gulf communicating with the Sea of Darkness. Believing the circumference of the Earth to follow Ptolemy's reduced figures or even smaller ones, cartographers during the early phases of the Age of Discovery expanded the Gulf to form the Pacific Ocean west of South America, considered to represent a southeastern peninsula of Asia. Modern reconstructions agree in naming the Golden Chersonese a form of the Malay Peninsula but differ in their considerations of how much of the South China Sea to include within Ptolemy's reckoning of the Great Gulf.
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Under the kingdom of France, Anjou was practically identical with the diocese of Angers, bound on the north by Maine, on the east by Touraine, on the south by Poitou (Poitiers) and the Mauges, and the west by the countship of Nantes or the duchy of Brittany. Traditionally Anjou was divided into four natural regions: the Baugeois, the Haut-Anjou (or Segréen), the Mauges, and the Saumurois. It occupied the greater part of what is now the department of Maine-et-Loire. On the north, it further included Craon, Candé, Bazouges (Château-Gontier), Le Lude; on the east, it further added Château-la-Vallière and Bourgueil; while to the south, it lacked the towns of Montreuil-Bellay, Vihiers, Cholet, and Beaupréau, as well as the district lying to the west of the Ironne and Thouet on the left bank of the Loire, which formed the territory of the .
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Reassigned to the Military Sea Transportation Service (MSTS) on 30 March 1951, she would operate as United States Naval Ship (USNS) Enoree (T-AO-69) for the remainder of her operational service. Having reported to Commander, MSTS, for operational control and Commander, MSTS, Pacific, for administrative control, meanwhile, Enoree departed Pearl Harbor on 31 March 1951 for San Francisco, arriving there on 7 April 1951. Her departure thence delayed until 28 April 1951, the ship sailed for Balboa, Panama Canal Zone, on that date, and retransited the Panama Canal, Aruba-bound, on 8-9 May 1951. Over the remainder of the year 1951, Enoree picked up petroleum cargoes at Aruba; Marcus Hoo, Pennsylvania; Houston; Port Arthur; and Perth Amboy, New Jersey, delivering them to Norfolk; Melville, Rhode Island; Newport, Rhode Island; Savannah, Georgia; Boston, Massachusetts; Guantanamo Bay, Cuba; Roosevelt Roads, Puerto Rico; and Trinidad.
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Instead of upper bounding the number of vertices in a graph in terms of its maximum degree and its diameter, we can calculate via similar methods a lower bound on the number of vertices in terms of its minimum degree and its girth. Suppose G has minimum degree d and girth 2k+1. Choose arbitrarily a starting vertex v, and as before consider the breadth-first search tree rooted at v. This tree must have one vertex at level 0 (v itself), and at least d vertices at level 1. At level 2 (for k > 1), there must be at least d(d-1) vertices, because each vertex at level 1 has at least d-1 remaining adjacencies to fill, and no two vertices at level 1 can be adjacent to each other or to a shared vertex at level 2 because that would create a cycle shorter than the assumed girth.
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An obvious application of Euclidean minimum spanning trees is to find the cheapest network of wires or pipes to connect a set of places, assuming the links cost a fixed amount per unit length. However, while these give an absolute lower bound on the amount of connection needed, most such networks prefer a k-connected graph to a tree, so that failure of an any individual link will not split the network into parts. Another application of EMSTs is a constant-factor approximation algorithm for approximately solving the Euclidean traveling salesman problem, the version of the traveling salesman problem on a set of points in the plane with edges labelled by their length. This realistic variation of the problem can be solved within a factor of 2 by computing the EMST, doing a walk along its boundary which outlines the entire tree, and then removing all but one occurrence of each vertex from this walk.
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Fellow Passengers is a three-actor narrative theatre adaptation of Charles Dickens' 1843 novella A Christmas Carol, written by Greg Carter. The title is derived from a first-scene speech by Fred, the nephew of Ebenezer Scrooge, who says: "I have always thought of Christmas time, when it has come round... as a good time: a kind, forgiving, charitable, pleasant time: the only time I know of, in the long calendar of the year, when men and women seem by one consent to open their shut-up hearts freely, and to think of people below them as if they really were fellow passengers to the grave, and not another race of creatures bound on other journeys."Charles Dickens, A Christmas Carol (1843) Passengers opened at Strawberry Theatre Workshop in Seattle, Washington in December, 2004. The original director was Rhonda J Soikowski, and the acting ensemble was Todd Jefferson Moore, Gabriel Baron, and Marty Mukhalian.
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He took along his very extensive notes on Tibet, its culture and religion, and began work on his Relation, which in its latest manuscript was called "Historical Notices of Tibet" (Notizie Istoriche del Tibet) while still homeward bound on a French vessel. He landed in France in August 1727, and after a stay in that country, where he met with important cardinals and aristocrats and had an audience with King Louis XV, he arrived in Rome in January 1728. He took up residence in the Jesuit professed house, and his time was fully occupied in the legal proceedings at the Propaganda Fide between himself, representing the Jesuit order, and Fr. Felice di Montecchio, who fiercely prosecuted the Capuchin case; Desideri wrote three Defenses of the Jesuit position. On 29 November 1732, the Propaganda issued its final terse order on the matter, confirming the exclusive right of the Capuchins to the Tibet mission, and forbidding any further discussion on the subject.
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7 (Latin text): "Marcus Marius was dragged from a goat-pen and bound on orders of Sulla; after he was led across the Tiber to the tomb of the Lutatii, his eyes were gouged out, his body parts were cut off bit by bit or even broken, and he was slaughtered." Livy's account survives only in Periocha 88: "Sulla polluted (inquinavit) a most glorious victory by cruelty such as no man had ever shown before. He slaughtered 8,000 men, who had surrendered, in the Villa Publica; ...and had Marius, a man of senatorial rank, killed after having his legs and arms broken, his ears cut off and his eyes gouged out." Like the sacrificial pig at the Compitalia, he was paraded through the streets, past the very shrines at which his image had received honors,Cicero says, possibly but not necessarily with exaggeration, that Gratidianus' statues were in every neighborhood (De officiis 3.80); Gradel, Emperor worship and Roman religion, p.
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If no candidate were elected in the first round of voting, a progressively larger number of delegates would have been allowed to vote for the candidate of their choice. The voting rules on subsequent ballots were determined by individual states: most states released their delegates on the second round of voting, and only four states kept them bound on the third round and beyond. This table shows how many bound delegates each candidate had won before suspending his or her campaign; it does not show how many unbound delegates pledged their support to any candidate during the primaries, nor does it show the expected result of the vote at the national convention. Although a state is considered won by a candidate if a plurality of the state's delegates are bound, RNC Rule 40(b) required a candidate to demonstrate support from a majority of delegates in eight states to be eligible as the nominee.
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Returning to New York 9 June 1944, Farquhar trained in antisubmarine warfare at Bermuda with the hunter-killer group, then sailed on the Casablanca convoy route once more. Homeward bound, on 2 August she went to the rescue of who had been torpedoed while away from the group searching for a previously sighted target, and arrived in time to rescue 186 survivors. These she took into Argentia, Newfoundland, for medical attention and clothing, then on to Boston, Massachusetts, where they were landed. In September, she began patrols and convoy escort duty in the South Atlantic with the hunter-killer group. She voyaged from Bahia, Brazil, to Dakar, French West Africa, and Cape Town, Union of South Africa, and during a submarine hunt off the Cape Verde Islands on 30 September, made a contact against which she and her sisters operated 6 days, finally sighting a large oil slick, but no other evidence of a sunken submarine.
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The existence of an agreement between the parties is usually analysed through the rules of offer and acceptance.. This may be expressed as a clear indication ("offer") by one party (the "offeror") of a willingness to be bound on certain terms.. accompanied by a communication by the other party (the "offeree") to the offeror of an unqualified assent to that offer ("acceptance"). An offer indicates an intention by the offeror to be bound without further discussion or negotiation, on acceptance of the terms set out. The court will determine the offeror's intention objectively..Empirnall Holdings Pty Ltd v Machon Paull Partners Pty Ltd (1988) 14 NSWLR 52. It is distinguished from an "invitation to treat", which is a request to others to make offers to engage in negotiations with a contract in mind.Retailers have sometimes taken advantage of this distinction to engage in bait advertising (advertising goods at attractive prices but not in fact intending to sell in more than minimal quantities, if at all), but this is prohibited under section 35 of the Australian Consumer Law.
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A bucket queue can be used to maintain the vertices of an undirected graph, prioritized by their degrees, and repeatedly find and remove the vertex of minimum degree. This greedy algorithm can be used to calculate the degeneracy of a given graph. It takes linear time, with or without the optimization that maintains a lower bound on the minimum priority, because each vertex is found in time proportional to its degree and the sum of all vertex degrees is linear in the number of edges of the graph.. In Dijkstra's algorithm for shortest paths in positively-weighted directed graphs, a bucket queue can be used to obtain a time bound of , where is the number of vertices, is the number of edges, is the diameter of the network, and is the maximum (integer) link cost.. This variant of Dijkstra's algorithm is also known as Dial's algorithm, after Robert B. Dial, who published it in 1969. In this algorithm, the priorities will only span a range of width , so the modular optimization can be used to reduce the space to .
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Truemper observed that every grid graph is reducible by Δ-Y and Y-Δ transforms in this way, that this reducibility is preserved by graph minors, and that every planar graph is a minor of a grid graph.. This idea can be used to replace Steinitz's lemma that a reduction sequence exists, in a proof of Steinitz's theorem using induction in the same way. However, there exist graphs that require a nonlinear number of steps in any sequence of Δ-Y and Y-Δ transforms. More precisely, Ω(n3/2) steps are sometimes necessary, and the best known upper bound on the number of steps is even worse, O(n2).. An alternative form of induction proof is based on removing edges (and compressing out the degree-two vertices that might be performed by this removal) or contracting edges and forming a minor of the given planar graph. Any polyhedral graph can be reduced to K4 by a linear number of these operations, and again the operations can be reversed and the reversed operations performed geometrically, giving a polyhedral realization of the graph.
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A randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weakly random entropy source, together with a short, uniformly random seed, generates a highly random output that appears independent from the source and uniformly distributed. Examples of weakly random sources include radioactive decay or thermal noise; the only restriction on possible sources is that there is no way they can be fully controlled, calculated or predicted, and that a lower bound on their entropy rate can be established. For a given source, a randomness extractor can even be considered to be a true random number generator (TRNG); but there is no single extractor that has been proven to produce truly random output from any type of weakly random source. Sometimes the term "bias" is used to denote a weakly random source's departure from uniformity, and in older literature, some extractors are called unbiasing algorithms,David K. Gifford, Natural Random Numbers, MIT/LCS/TM-371, Massachusetts Institute of Technology, August 1988.
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In this framework, the -coordinate assignment again involves grouping elements of a partially ordered set (the vertices of the graph, with the reachability ordering on the vertex set) into layers (sets of vertices with the same -coordinate), which is the problem solved by the Coffman–Graham algorithm.. Although there exist alternative approaches than the Coffman–Graham algorithm to the layering step, these alternatives in general are either not able to incorporate a bound on the maximum width of a level or rely on complex integer programming procedures.. More abstractly, both of these problems can be formalized as a problem in which the input consists of a partially ordered set and an integer . The desired output is an assignment of integer level numbers to the elements of the partially ordered set such that, if is an ordered pair of related elements of the partial order, the number assigned to is smaller than the number assigned to , such that at most elements are assigned the same number as each other, and minimizing the difference between the smallest and the largest assigned numbers.
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In knot theory, the distortion of a knot is a knot invariant, the minimum stretch factor of any embedding of the knot as a space curve in Euclidean space. Undergraduate researcher John Pardon won the 2012 Morgan Prize for his research showing that there is no upper bound on the distortion of torus knots, solving a problem originally posed by Mikhail Gromov... In the study of the curve-shortening flow, in which each point of a curve in the Euclidean plane moves perpendicularly to the curve, with speed proportional to the local curvature, proved that the stretch factor of any simple closed smooth curve (with intrinsic distances measured by arc length) changes monotonically. More specifically, at each pair that forms a local maximum of the stretch factor, the stretch factor is strictly decreasing, except when the curve is a circle. This property was later used to simplify the proof of the Gage–Hamilton–Grayson theorem, according to which every simple closed smooth curve stays simple and smooth until it collapses to a point, converging in shape to a circle before doing so...
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On August 1, Kennedy stated that Carter was treating the delegates like robots and that the nominee might as well be chosen by mail order ballot if the convention wasn't open. Morley Winograd, who served as the chairman of the Commission on Presidential Nomination and Party Structure when the rule that all delegates are bound on the first ballot and now served as a Michigan delegate for Kennedy, criticized the roll call vote and the method of how the rule was passed citing the three minute debate time limit and that the commission was focused on more important issues at the time. On August 5, Senator Henry M. Jackson gave his support to an open convention and stated that Kennedy would have an easier time defeating Ronald Reagan. On August 6, Kennedy gave a speech in Washington, D.C. where he stated that he would not endorse Carter unless he accepts some of his economic policies and that he would give a speech in favor of his policies at the convention.
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The upper bound on Brayton cycle temperature for an MHD generator is not limited, so inherently an MHD generator has a higher potential capability for energy efficiency. The temperatures at which linear coal-fueled MHD generators can operate are limited by factors that include: (a) the combustion fuel, oxidizer, and oxidizer preheat temperature which limit the maximum temperature of the cycle; (b) the ability to protect the sidewalls and electrodes from melting; (c) the ability to protect the electrodes from electrochemical attack from the hot slag coating the walls combined with the high current or arcs that impinge on the electrodes as they carry off the direct current from the plasma; and (d) by the capability of the electrical insulators between each electrode. Coal-fired MHD plants with oxygen/air and high oxidant preheats would probably provide potassium seeded plasmas of about 4200°F, 10 atmospheres pressure, and begin expansion at Mach1.2. These plants would recover MHD exhaust heat for oxidant preheat, and for combined cycle steam generation.
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An algorithm is said to be fixed-parameter tractable if the number of elementary operations it performs has a bound of the form O(n^c)+f(k), where n is some measure of the input size (such as the number of vertices in a graph), k is a parameter describing the complexity of the input (such as the treewidth of the graph), c is a constant that does not depend on n or k, and f is a computable function. Given a time bound of this form, the klam value of the algorithm (or more properly of the time bound) is defined to be the largest value of k such that f(k) does not exceed "some reasonable absolute bound on the maximum number of steps of any computation". More precisely both and use the number 1020 as this bound, and this has been followed by later researchers. To prevent artificially improving the klam value of an algorithm by putting more of its complexity into the O(n^c) part of the time bound, also limit c to be at most three, valid for many known fixed-parameter tractable algorithms.
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Algorithms that recursively factorize the DFT into smaller operations other than DFTs include the Bruun and QFT algorithms. (The Rader–Brenner and QFT algorithms were proposed for power-of-two sizes, but it is possible that they could be adapted to general composite N. Bruun's algorithm applies to arbitrary even composite sizes.) Bruun's algorithm, in particular, is based on interpreting the FFT as a recursive factorization of the polynomial zN − 1, here into real-coefficient polynomials of the form zM − 1 and z2M + azM + 1\. Another polynomial viewpoint is exploited by the Winograd FFT algorithm, which factorizes zN − 1 into cyclotomic polynomials—these often have coefficients of 1, 0, or −1, and therefore require few (if any) multiplications, so Winograd can be used to obtain minimal-multiplication FFTs and is often used to find efficient algorithms for small factors. Indeed, Winograd showed that the DFT can be computed with only O(N) irrational multiplications, leading to a proven achievable lower bound on the number of multiplications for power-of-two sizes; unfortunately, this comes at the cost of many more additions, a tradeoff no longer favorable on modern processors with hardware multipliers.
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Lord Denning MR held that Fidelis was nevertheless bound on the contract to Panorama. Mr Bayne, as company secretary had implied actual authority by virtue of his position as Company Secretary to enter into such agreements. Times had changed since 1887 when Barnett v South London Tramways Co(1887) 18 QBD 815 held that company secretaries could not be assumed to have authority for anything. Secretaries are ‘certainly entitled to sign contracts connected with the administrative side of a company’s affairs, such as employing staff and ordering cars, and so forth.’ His judgment went as follows. Salmon LJ said the secretary ‘is the chief administrative officer of the company’ so he has ostensible authority with administrative matters. Nothing is more natural than ‘ordering cars so that its servants may go and meet foreign customers at airports, nothing to my mind, is more natural than that the company should hire those cars through its secretary.’ It might not be so with matters of commercial management of the company, for example, a contract for the sale or purchase of goods in which the company deals’ but that was not the case here.
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If r ≤ c (as in the illustration), then choosing a central column will give a separator S with r ≤ √n vertices, and similarly if c ≤ r then choosing a central row will give a separator with at most √n vertices. Thus, every grid graph has a separator S of size at most √n, the removal of which partitions it into two connected components, each of size at most n/2.. Instead of using a row or column of a grid graph, George partitions the graph into four pieces by using the union of a row and a column as a separator. The planar separator theorem states that a similar partition can be constructed in any planar graph. The case of arbitrary planar graphs differs from the case of grid graphs in that the separator has size O(√n) but may be larger than √n, the bound on the size of the two subsets A and B (in the most common versions of the theorem) is 2n/3 rather than n/2, and the two subsets A and B need not themselves form connected subgraphs.
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The planar k-level problem can be generalized to one of parametric optimization in a matroid: one is given a matroid in which each element is weighted by a linear function of a parameter λ, and must find the minimum weight basis of the matroid for each possible value of λ. If one graphs the weight functions as lines in a plane, the k-level of the arrangement of these lines graphs as a function of λ the weight of the largest element in an optimal basis in a uniform matroid, and Dey showed that his O(nk1/3) bound on the complexity of the k-level could be generalized to count the number of distinct optimal bases of any matroid with n elements and rank k. For instance, the same O(nk1/3) upper bound holds for counting the number of different minimum spanning trees formed in a graph with n edges and k vertices, when the edges have weights that vary linearly with a parameter λ. This parametric minimum spanning tree problem has been studied by various authors and can be used to solve other bicriterion spanning tree optimization problems.
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In 1973, David Slepian and Jack Keil Wolf proposed the information theoretical lossless compression bound on distributed compression of two correlated i.i.d. sources X and Y."Noiseless coding of correlated information sources" by D. Slepian and J. Wolf After that, this bound was extended to cases with more than two sources by Thomas M. Cover in 1975,"A proof of the data compression theorem of Slepian and Wolf for ergodic sources" by T. Cover while the theoretical results in the lossy compression case are presented by Aaron D. Wyner and Jacob Ziv in 1976."The rate-distortion function for source coding with side information at the decoder" by A. Wyner and J. Ziv Although the theorems on DSC were proposed on 1970s, it was after about 30 years that attempts were started for practical techniques, based on the idea that DSC is closely related to channel coding proposed in 1974 by Aaron D. Wyner."Recent results in Shannon theory" by A. D. Wyner The asymmetric DSC problem was addressed by S. S. Pradhan and K. Ramchandran in 1999, which focused on statistically dependent binary and Gaussian sources and used scalar and trellis coset constructions to solve the problem.
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Fogg's first cruise on convoy duty began with her departure from New York on 13 October 1943. She escorted unladen tankers to Aruba and Curaçao in the Netherlands West Indies, crossed to Algiers guarding loaded tankers, then returned by way of Curaçao and Trinidad to New York on 4 December 1943. Between 26 December 1943 and 20 August 1944, she made six escort voyages from New York to Londonderry Port, Northern Ireland, guarding the flow of men and material which made possible the invasion of Europe and the push across the continent which followed. The escort put to sea once more from New York on 12 September 1944, to escort a convoy through the English Channel to Cherbourg, France, then called at Portsmouth, England, before returning to New York on 9 October for a brief overhaul. After special training at Charleston, she sailed on 6 November to escort a slow towing convoy to England and back. Homeward bound, on 20 December, one of the LSTs in the convoy was torpedoed, and as Fogg began to search for the submarine, she, too, was torpedoed by commanded by Ernst Hechler.
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The ease of designing reversible block cellular automata, and of testing block cellular automata for reversibility, is in strong contrast to cellular automata with other non-block neighborhood structures, for which it is undecidable whether the automaton is reversible and for which the reverse dynamics may require much larger neighborhoods than the forward dynamics. Any reversible cellular automaton may be simulated by a reversible block cellular automaton with a larger number of states; however, because of the undecidability of reversibility for non-block cellular automata, there is no computable bound on the radius of the regions in the non-block automaton that correspond to blocks in the simulation, and the translation from a non-block rule to a block rule is also not computable.; Block cellular automata are also a convenient formalism in which to design rules that, in addition to reversibility, implement conservation laws such as the conservation of particle number, conservation of momentum, etc.. For instance, if the rule within each block preserves the number of live cells in the block, then the global evolution of the automaton will also preserve the same number. This property is useful in the applications of cellular automata to physical simulation.
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Justice Miller delivered the opinion of the court. He stated the facts as above recited and continued: Justice Miller went on to give an illustration from act of Congress prescribing rules of evidence in § 858 of the Revised Statutes, which read: Specifically the following sections of the Revised Statutes, in chapter XVII, on evidence: #SEC. 861. The mode of proof, in the trial of actions at common law, shall be by oral testimony and examination of witnesses in open court, except as hereinafter provided. #SEC. 863. The testimony of any witness may be taken in any civil cause, pending in a district or circuit court, by deposition de bene esse when the witness lives at a greater distance from the place of trial than one hundred miles, or is bound on a voyage to sea, or is about to go out of the United States, or out of the district in which the case is to be tried, and to a greater distance than one hundred miles from the place of trial, before the time of trial, or when he is ancient or infirm.
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To allow ships to receive messages and orders, the navy broadcast a continuous stream of information, originally in Morse code and later using radioteletype. Messages were included in this stream as needed and could be for individual ships, battle groups or the fleet as a whole. Each ship's radio room would monitor the broadcast and decode and forward those messages directed at her to the appropriate officer. The KW-37 was designed to automate this process. It consisted of two major components, the KWR-37 receive unit and the KWT-37 transmit unit. Each ship had a complement of KWR-37 receivers (usually at least two) that decrypted the fleet broadcast and fed the output to teleprinter machines. KWT-37's were typically located at shore facilities, where high power transmitters were located. The KWR-37 weighed 100 pounds (45 kg) and contained some 500 subminiature vacuum tubes, whose leads were soldered to printed circuit boards. Each flip-flop in the KW-37 required three tubes, placing an upper bound on the total number of stages in any shift registers used at 166. Squeezing so much logic in such a small and rugged package was quite a feat in the 1950s.
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Karaite Jews do not wear tefillin in any form. According to Karaites, the Biblical passages cited for this practice are metaphorical, and mean to "remember the Torah always and treasure it". This is because the commandment in scripture is "And these words, which I command thee this day, shall be upon thy heart"... "And thou shalt bind them for a sign upon thy hand, and they shall be for forehead ornaments between thine eyes". (Deuteronomy 6:5,9) Since words cannot be on one's heart, or bound on one's hand, the entire passage is understood metaphorically. Furthermore, the same expressions ("And thou shalt bind them for a sign upon thy hand" as well as "and they shall be as frontal ornaments between thine eyes") are used in Exodus 13:9 in reference to the commandments of Ḥagh HaMaṣṣot, in Exodus 13:16 in reference to the ritual of redeeming the first born, in Deuteronomy 6:8 in reference to the ‘Aseret HaDevarim (the Ten Utterances, usually mistranslated as "the Ten Commandments"), and in Deuteronomy 11:18 in reference to all the words of the Torah, indicating that, from a Karaite perspective, they must be metaphorical in nature (because one could never ritually "write" and "bind" upon their hearts themselves).
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