Markos Lemma had the same takeaway after talking with Dorsey.
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Many in Oromia want it to be Mr Lemma, the country's most popular politician.
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Lemma said Walter ran back to his date's car, drove off and called 911.
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This could be a source of further complication: Mr. Lemma isn't a member of Parliament.
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Under Lemma Megersa, its charismatic new leader, it has rebranded itself as a quasi-opposition party.
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Mr Abiy's second task is to enact the reforms he and Mr Lemma have long promised.
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"Ethiopians think this is shameful," Ms. Lemma said, even though they found it difficult to resist.
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Lemma said the pair were texting with Barnes under the guise of going to a party together.
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But under Lemma Megersa, its charismatic new leader, it has rebranded itself as a quasi-opposition party.
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Logically, there's no difference between a lemma and a theorem: they're both words for proven mathematical results.
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Some think he and Lemma Megersa, Oromia's popular president, turned a blind eye to attacks on non-Oromos.
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"Jake and Ian were having conversations about a potential burglary that had occurred a few days earlier," Lemma said.
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Youth activist Tariku Lemma said security forces dispersed protesters by firing guns and teargas and two people had been wounded.
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"There's a lot of hate speech and misinformation that's been showing up on social media," said Ice Addis' Markos Lemma.
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Under Lemma Megersa, its charismatic new leader, it has adopted many of the protesters' demands, including the release of political prisoners.
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On that topic, Ice Addis co-founder Markos Lemma suggested Dorsey provide founders advice on operating around and influencing tech regulation.
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After taking over the OPDO's leadership in 2016, "Team Lemma", as the reformers are known, rebranded the party as a quasi-opposition.
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Founded in 2011, IceAddis's mission is to develop Ethiopia's IT ecosystem, co-founder and CEO Markos Lemma told me during a tour.
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Lemma said investigators believe Bilotta was the primary assailant, and that McClurg was tasked with grabbing Barnes in case he tried to flee.
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In a recent speech Lemma Mergersa, the regional president, said his government had resettled more than half a million Oromos around the city.
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Lemma said it was unclear why Barnes was evicted from the home and that no police report was made on the alleged burglary.
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His background may have made him more palatable to hardliners in the EPRDF than Mr Lemma, who was once a more likely prime minister.
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"It is the most bizarre and disgraceful act that one can imagine," Seminole County Sheriff Dennis Lemma said at a press conference earlier this week.
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Lemma Teshome, the 24 year-old son of a farmer in Goticha whose land is being expropriated this year, worked for three years at a soap factory.
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"The TPLF formed the rest of the parties -- they don't have an autonomous existence," says Tsedale Lemma, editor-in-chief of the Addis Standard, an independent newspaper.
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To end the succession battle, the choice is clear: The new reformist leaders of the Oromo People's Democratic Organization, led by Lemma Megersa, enjoy substantial public support.
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"That really aggravated Jake, and Jake and Ian had made plans to try to get him lured back over," Seminole County Sheriff Dennis Lemma told reporters on Tuesday.
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"[Dorsey] said the main reason [he was in Ethiopia and Africa] was to listen and to learn what's going on in the region," said Ice Addis' Markos Lemma .
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As the roommate walked into the house, "Ian had the knife in his hand and Jake was in the process of placing the body inside plastic garbage bags," Lemma said.
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Afwerki accepted the gift of a horse, a shield, and a spear from President of Ethiopia's Oromia region, Lemma Megerssa, according to Prime Minister Abiy's chief of staff, Fitsum Arega.
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"The family's canine that was in the house led firefighters to the two children who were inside," Seminole County sheriff's office chief deputy Dennis Lemma told WFTV 9, who covered the story.
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Lemma Megersa, the prime minister's closest ally and president of Oromia, Ethiopia's most populous region, is a board member of Assemblies of God, the church which hosted Nigusie in Addis Ababa in October.
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"It's frustrating to see that for all Abiy's intentions to bring about changes in politics, that is not translating into the economic sector," said Tsedale Lemma, the editor of the Addis Standard news website.
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Once Barnes arrived, Bilotta allegedly met him at the front door with a seven-inch chef's knife with an "aggressive blade" and got him inside the house and stabbed him multiple times, Lemma said.
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He visited Nigeria, Ghana, South Africa and Ethiopia and met with leaders at Nigeria's CcHub (Bosun Tijani), Ethiopia's Ice Addis (Markos Lemma) and did some meetings with fintech founders in Lagos (Paga's Tayo Oviosu).
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Sheriff Lemma said the case reminded authorities of the 2004 murder of six people and a dog who were bludgeoned to death with baseball bats and stabbed in Deltona, Florida, in a dispute over an Xbox.
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Abiy has spoken of the importance to democracy of a vibrant press, but state media still dominate, says Tsedale Lemma, the editor of Addis Standard, a feisty local which suspended print operations in 2016 citing censorship.
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Tsedale Lemma, editor and founder of the Addis Standard monthly, told Reuters that printers had refused to publish the magazine unless an authority set up to oversee the implementation of the new regulations gave them permission.
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But if you think your new result is interesting or important, you call it a theorem; if it's a result you feel obligated to prove, to get to the interesting or important stuff, you call it a lemma.
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Everywhere they go, Mr. Lemma and his entourage receive a hero's welcome, on a par with that received by the just-released opposition leaders — itself a significant change for a party whose support is often either bought or coerced.
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For all the likelihood Dorsey's pending move could be motivated by Square and Bitcoin, three of the founders interviewed by TechCrunch — Bosun Tijani, Ken Njoroge and Markos Lemma — underscored the rise of Twitter in Africa's civic and political spheres.
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But as Tsedale Lemma, the editor-in-chief of monthly news magazine Addis Standard, tweeted, the person who succeeds Desalegn — and the political party they represent — is less important than their capacity to regain the trust of a nation that has grown apathetic.
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Examples of proofs by diagram chasing include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.
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The 1970 film, Zorns Lemma, is named after the lemma. This lemma was referenced on The Simpsons in the episode "Bart's New Friend".
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In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages. The pumping lemma can be used to construct a proof by contradiction that a specific language is not context-free. Conversely, the pumping lemma does not suffice to guarantee that a language is context-free; there are other necessary conditions, such as Ogden's lemma, or the Interchange lemma.
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The triangle removal lemma was extended to general subgraphs by Erdős, Frankl, and Rödl in 1986. The proof is analogous to the proof of the triangle removal lemma, and uses a generalization of the triangle counting lemma, the graph counting lemma.
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Fertile spikelets have ciliated, curved and filiform pedicels. Margins of lemma are ciliate. The lemma itself though is long and have obtuse apex. Fertile lemma is chartaceous and is long and wide.
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It fertile spikelets are lanceolate and are . They carry one fertile floret which have a hairy floret callus which is over lemma. Fertile lemma is oblong and is of the same size as a spikelet, membranous and keelless. Lemma itself have an asperulous surface and dentate apex with the main lemma having awns which are over the lemma and are geniculated and are long.
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This is proved in an analogous manner to the case above, using Lemma 2 instead of Lemma 3.
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In mathematics, the Teichmüller–Tukey lemma (sometimes named just Tukey's lemma), named after John Tukey and Oswald Teichmüller, is a lemma that states that every nonempty collection of finite character has a maximal element with respect to inclusion. Over Zermelo–Fraenkel set theory, the Teichmüller–Tukey lemma is equivalent to the axiom of choice, and therefore to the well-ordering theorem, Zorn's lemma, and the Hausdorff maximal principle.
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In abstract algebra, Krull's separation lemma is a lemma in ring theory. It was proved by Wolfgang Krull in 1928.
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Its lemma have a toothed apex which is also truncate and awned. The fertile lemma is long and is both membranous and oblong. The species also have an elliptic and hyaline palea which is long of lemma.
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Margins of lemma are ciliate. The lemma itself though is long hairs and have acute apex. Fertile lemma is chartaceous, lanceolate and is long. Palea is long, have ciliolated keels which are 2-veined, and asperulous surface.
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In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in as the first lemma in section 12, and in more general form in as lemma 2. In 2004, Massera's original lemma for single variable functions was extended to the multivariable case, and the resulting lemma was used to prove the stability of switched dynamical systems, where a common Lyapunov function describes the stability of multiple modes and switching signals.
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Rokhlin lemma belongs to the group mathematical statements such as Zorn's lemma in set theory and Schwarz lemma in complex analysis which are traditionally called lemmas despite the fact that their roles in their respective fields are fundamental.
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The handshaking lemma is also used in proofs of Sperner's lemma and of the piecewise linear case of the mountain climbing problem.
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The above is known as the Levi lemma for strings; the lemma can occur in a more general form in graph theory and in monoid theory; for example, there is a more general Levi lemma for traces originally due to Christine Duboc. Several proofs of Levi's Lemma for traces can be found in The Book of Traces. A monoid in which Levi's lemma holds is said to have the equidivisibility property. The free monoid of strings and string concatenation has this property (by Levi's lemma for strings), but by itself equidivisibility is not enough to guarantee that a monoid is free.
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Riesz's lemma (after Frigyes Riesz) is a lemma in functional analysis. It specifies (often easy to check) conditions that guarantee that a subspace in a normed vector space is dense. The lemma may also be called the Riesz lemma or Riesz inequality. It can be seen as a substitute for orthogonality when one is not in an inner product space.
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The spikelets are also elliptic, are long, and have 2 fertile florets which are diminished at the apex. Lemma is chartaceous, lanceolated, and is long and wide. Its lemma have an obtuse apex while the fertile lemma itself is chartaceous, elliptic, keelless, and is long. It is also 7-9 veined while the surface of the lemma is villous with ciliated margins.
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The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz.. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem.
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In the theory of formal languages, Ogden's lemma (named after William F. Ogden) is a generalization of the pumping lemma for context-free languages.
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Abelian categories are the most general setting for homological algebra. All of the constructions used in that field are relevant, such as exact sequences, and especially short exact sequences, and derived functors. Important theorems that apply in all abelian categories include the five lemma (and the short five lemma as a special case), as well as the snake lemma (and the nine lemma as a special case).
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The other features are different though; Lower glume is long, while the upper one is long. Its lemma have scaberulous surface with the fertile lemma being chartaceous, keelless, lanceolate and long by . Lemma have ciliated margins, dentated apex, and the same surface as the glumes. Palea have ciliolated keels, is hairy, and is 2-veined with the surface that is identical to the chaffs and lemma.
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The lemma is generalized by (and usually used in the proof of) the Tietze extension theorem. The lemma is named after the mathematician Pavel Samuilovich Urysohn.
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Thus, by Euclid's lemma in , it divides one of the contents, and therefore one of the polynomials. If is not , it is a primitive polynomial (because it is irreducible). Then Euclid's lemma in results immediately from Euclid's lemma in , where is the field of fractions of .
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The notion of exact sequence is meaningful in Grp, and some results from the theory of abelian categories, such as the nine lemma, the five lemma, and their consequences hold true in Grp. The snake lemma however is not true in Grp. Grp is a regular category.
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The flowers have glassy lemma and leathery palea about 3.5 mm long, with the awn of the upper lemma 15 mm long and twisted at the base.
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William Burnside stated and proved this lemma, attributing it to , in his 1897 book on finite groups. But, even prior to Frobenius, the formula was known to Cauchy in 1845. In fact, the lemma was apparently so well known that Burnside simply omitted to attribute it to Cauchy. Consequently, this lemma is sometimes referred to as the lemma that is not Burnside's (see also Stigler's law of eponymy).
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In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: For example, if , , , then , and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In fact, . Inherently, if the premise of the lemma does not hold, i.e., is a composite number, its consequent may be either true or false.
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In mathematics, especially homological algebra and other applications of abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams. The five lemma is not only valid for abelian categories but also works in the category of groups, for example. The five lemma can be thought of as a combination of two other theorems, the four lemmas, which are dual to each other.
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To see where the snake lemma gets its name, expand the diagram above as follows: :File:Snake lemma complete.svg and then note that the exact sequence that is the conclusion of the lemma can be drawn on this expanded diagram in the reversed "S" shape of a slithering snake.
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In mathematics, Ky Fan's lemma (KFL) is a combinatorial lemma about labellings of triangulations. It is a generalization of Tucker's lemma. It was proved by Ky Fan in 1952. In this example, where n = 2, there is no 2-dimensional alternating simplex (since the labels are only 1,2).
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New York: Dover Publ., 1970. 184-89. Print. The glumes are found to be unequal, and are either longer or shorter than the lemma. The lemma is obtuse to acuminate or awned, while the membranous lemma is narrow, acute, mucronate, or awned, and usually pilose at the base.
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The species' lemma of fertile floret elliptic to oblong and is long. Lemma is also obtuse or subacute, 7-nerved, hairless and scaberulous. The species' anthers are long.
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Gowers's construction for the lower bound of Szemerédi's regularity lemma first introduced a weaker version of this lemma, restricted to bipartite graphs, in order to prove Szemerédi's theorem,. and in he proved the full lemma.. Extensions of the regularity method to hypergraphs were obtained by Rödl and his collaborators... and Gowers... János Komlós, Gábor Sárközy and Endre Szemerédi later (in 1997) proved in the blow-up lemma that the regular pairs in Szemerédi regularity lemma behave like complete bipartite graphs under the correct conditions. The lemma allowed for deeper exploration into the nature of embeddings of large sparse graphs into dense graphs. The first constructive version was provided by Alon, Duke, Lefmann, Rödl and Yuster.
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In elementary number theory, the lifting-the-exponent (LTE) lemma provides several formulas for computing the p-adic valuation u_p of special forms of integers. The lemma is named as such because it describes the steps necessary to "lift" the exponent of p in such expressions. It is related to Hensel's lemma.
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In probability theory, Hoeffding's lemma is an inequality that bounds the moment-generating function of any bounded random variable. It is named after the Finnish-American mathematical statistician Wassily Hoeffding. The proof of Hoeffding's lemma uses Taylor's theorem and Jensen's inequality. Hoeffding's lemma is itself used in the proof of McDiarmid's inequality.
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Newman's lemma states that if an abstract rewriting system A is strongly normalizing and is weakly confluent, then A is confluent. The result enables to further generalize the critical pair lemma.
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The Moschovakis coding lemma is a lemma from descriptive set theory involving sets of real numbers under the axiom of determinacy (the principle — incompatible with choice — that every two-player integer game is determined). The lemma was developed and named after the mathematician Yiannis N. Moschovakis. The lemma may be expressed generally as follows: :Let be a non- selfdual pointclass closed under real quantification and , and a -well-founded relation on of rank . Let be such that .
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In mathematics, Kronecker's lemma (see, e.g., ) is a result about the relationship between convergence of infinite sums and convergence of sequences. The lemma is often used in the proofs of theorems concerning sums of independent random variables such as the strong Law of large numbers. The lemma is named after the German mathematician Leopold Kronecker.
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The process of determining the lemma for a given word is called lemmatisation. The lemma can be viewed as the chief of the principal parts, although lemmatisation is at least partly arbitrary.
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This proof does not rely on Fatou's lemma. However, we do explain how that lemma might be used. For those not interested in independent proof, the intermediate results below may be skipped.
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Sisay Lemma during the Vienna City Marathon 2015 at km 10 (Opera) Running in Frankfurt. Sisay Lemma Kasaye (born 12 December 1990) is an Ethiopian long- distance runner. Lemma began his running career at the age of 17 and initially competed barefoot due to a lack of running shoes. In 2012, he won the Maratona d’Italia.
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They have fertile spikelets that are pediceled, the pedicels of which are long. Lemma is chartaceous, lanceolated, and is long and wide. Its lemma have an obtuse apex while the fertile lemma itself is chartaceous, keelless, oblong and is long. The species also carry 2–3 sterile florets which are barren, cuneate, clumped and are long.
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Stallings' proof of Grushko Theorem follows from the following lemma.
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The correspondence theorem (also known as the lattice theorem) is sometimes called the third or fourth isomorphism theorem. The Zassenhaus lemma (also known as the butterfly lemma) is sometimes called the fourth isomorphism theorem.
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He is known for Mautner's Lemma and Mautner's Phenomenon in the representation theory of Lie groups. Mautner's work on the lemma and the phenomenon was done in connection with the ergodic theory of geodesic flows.
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Komlós, G. N. Sárközy, E. Szemerédi: Blow-up Lemma, "Combinatorica", 17 (1), 1997, pp. 109-123J. Komlós, G. N. Sárközy, E. Szemerédi: An algorithmic version of the Blow-up Lemma, "Random Structures and Algorithms", 12, 1998, pp. 297-312 in which, together with János Komlós and Endre Szemerédi he proved that the regular pairs in Szemerédi regularity lemma behave like complete bipartite graphs under the correct conditions. The lemma allowed for deeper exploration into the nature of embeddings of large sparse graphs into dense graphs.
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In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem.See Boolos and Jeffrey (2002, sec. 15) and Mendelson (1997, Prop.
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They have fertile spikelets that are pediceled, the pedicels of which are ciliate, curved, filiform, and hairy. Lemma is chartaceous, lanceolated, and is long and wide. Its lemma have either erose or obtuse apex while the fertile lemma itself is chartaceous, keelless, oblong and is long. The species also carry 2–3 sterile florets which are barren, cuneate, clumped and are long.
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Lemma itself have a dentate apex with the main lemma having awns which are over the lemma and are sized . The species also have glumes which are lanceolate, membranous, and have acuminate apexes with the upper glume being of the same size as a spikelet. Rhachilla is long and pilose. Flowers have two lodicules and two stigmas along with and three stamens.
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In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function. Section 15. Urysohn's lemma is commonly used to construct continuous functions with various properties on normal spaces. It is widely applicable since all metric spaces and all compact Hausdorff spaces are normal.
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Goursat's lemma, named after the French mathematician Édouard Goursat, is an algebraic theorem about subgroups of the direct product of two groups. It can be stated more generally in a Goursat variety (and consequently it also holds in any Maltsev variety), from which one recovers a more general version of Zassenhaus' butterfly lemma. In this form, Goursat's theorem also implies the snake lemma.
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In mathematics, Heegner's lemma is a lemma used by Kurt Heegner in his paper on the class number problem. His lemma states that if :y^2=a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 is a curve over a field with a4 not a square, then it has a solution if it has a solution in an extension of odd degree.
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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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One consequence of the lemma is the Krull intersection theorem. The result is also used to prove the exactness property of completion . The lemma also plays a key role in the study of ℓ-adic sheaves.
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In mathematics, the ping-pong lemma, or table-tennis lemma, is any of several mathematical statements that ensure that several elements in a group acting on a set freely generates a free subgroup of that group.
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Above we showed how to prove the Borsuk–Ulam theorem from Tucker's lemma. The converse is also true: it is possible to prove Tucker's lemma from the Borsuk–Ulam theorem. Therefore, these two theorems are equivalent.
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While he was a graduate student at University of Chicago, he discovered Schanuel's lemma, an essential lemma in homological algebra. Schanuel received his Ph.D. in mathematics from Columbia University in 1963, under the supervision of Serge Lang.
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Shephard's lemma gives a relationship between expenditure (or cost) functions and Hicksian demand. The lemma can be re-expressed as Roy's identity, which gives a relationship between an indirect utility function and a corresponding Marshallian demand function.
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There is a similar lemma about finite and infinite trees and cycles.
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Advanced mathematical proofs like Siegel's lemma build upon this more general concept.
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In mathematics, informal logic and argument mapping, a lemma (plural lemmas or lemmata) is a generally minor, proven proposition which is used as a stepping stone to a larger result. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove, however, a lemma can also turn out to be more important than originally thought. The word "lemma" derives from the Ancient Greek λῆμμα ("anything which is received", such as a gift, profit, or a bribe).
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In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by removing a small number of edges. The special case in which the subgraph is a triangle is known as the triangle removal lemma. The graph removal lemma can be used to prove Roth's theorem on 3-term arithmetic progressions, and a generalization of it, the hypergraph removal lemma, can be used to prove Szemerédi's theorem. It also has applications to property testing.
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For this reason, Sperner's lemma can also be used in root-finding algorithms and fair division algorithms; see Simmons–Su protocols. Sperner's lemma is one of the key ingredients of the proof of Monsky's theorem, that a square cannot be cut into an odd number of equal-area triangles. Sperner's lemma can be used to find a competitive equilibrium in an exchange economy, although there are more efficient ways to find it. Fifty years after first publishing it, Sperner presented a survey on the development, influence and applications of his combinatorial lemma.
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In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular problems. Halberstam & Richert write: Diamond & Halberstam attribute the terminology Fundamental Lemma to Jonas Kubilius.
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Both the upper and lower glumes are keelless, membranous, have asperulous surfaces and acute apexes. The other features are different though; Lower glume is elliptic and is long, while the upper one is lanceolate and is long. Its lemma have scaberulous surface with the fertile lemma being chartaceous, keelless, lanceolate and long by . Lemma have ciliated margins, dentated apex, and hairs which are long.
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The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz. The result is often called the Steinitz–Mac Lane exchange lemma, also recognizing the generalization . by Saunders Mac Lane of Steinitz's lemma to matroids. .
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In mathematics, the Artin-Rees lemma is a basic result about modules over a Noetherian ring, along with results such as the Hilbert basis theorem. It was proved in the 1950s in independent works by the mathematicians Emil Artin and David Rees; Here: Lemma 1 Here: Sect.7, Lemma 7.2, p.10 a special case was known to Oscar Zariski prior to their work.
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The name "entropy compression" was given to this method in a blog posting by Terence Tao. and has since been used for it by other researchers.... Moser's original version of the algorithmic Lovász local lemma, using this method, achieved weaker bounds than the original Lovász local lemma, which was originally formulated as an existence theorem without a constructive method for finding the object whose existence it proves. Later, Moser and Gábor Tardos used the same method to prove a version of the algorithmic Lovász local lemma that matches the bounds of the original lemma.. Since the discovery of the entropy compression method, it has also been used to achieve stronger bounds for some problems than would be given by the Lovász local lemma. For example, for the problem of acyclic edge coloring of graphs with maximum degree Δ, it was first shown using the local lemma that there always exists a coloring with 64Δ colors, and later using a stronger version of the local lemma this was improved to 9.62Δ.
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A lemma is the primary form of a word—the one that would appear in a dictionary. The Spanish infinitive tener ("to have") is a lemma, while tiene ("has")—which is a conjugation of tener—is a word form.
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They carry 1 fertile floret which is callus and glabrous. Florets have lanceolated lemma which is long and wide. It is also chartaceous and way thinner above and where margins are. Lemma hairs long while it apex is obtuse.
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The Riemann–Lebesgue lemma can be used to prove the validity of asymptotic approximations for integrals. Rigorous treatments of the method of steepest descent and the method of stationary phase, amongst others, are based on the Riemann–Lebesgue lemma.
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Willard, p. 120]; others allow it to share this honor with Urysohn's lemma.
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The spikelets consist of a single awnless floret with a 3-nerved lemma.
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Daniel Lemma was contacted by Josef Fares to work on the movie's score.
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The lower sterile floret of the lemma is ovate and is 1 length of a spikelet which is also emarginate, membranous and mucronate. The fertile lemma is coriaceous, keelless, oblong, shiny and is long with involute margins and acute apex.
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Fertile spikelets are pediceled, the pedicels of which are curved, ciliate, hairy, and filiform. Florets are diminished at the apex. Its lemma have ciliated margins that have a hairy middle. It fertile lemma is chartaceous, lanceolate, and is long by wide.
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The Hilbert–Bernays provability conditions, combined with the diagonal lemma, allow proving both of Gödel's incompleteness theorems shortly. Indeed the main effort of Godel's proofs lied in showing that these conditions (or equivalent ones) and the diagonal lemma hold for Peano arithmetics; once these are established the proof can be easily formalized. Using the diagonal lemma, there is a formula \rho such that T \Vdash \rho \leftrightarrow eg Prov(\\#(\rho)).
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Finsler's lemma is a mathematical result named after Paul Finsler. It states equivalent ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. Since it is equivalent to another lemmas used in optimization and control theory, such as Yakubovich's S-lemma, Finsler's lemma has been given many proofs and has been widely used, particularly in results related to robust optimization and linear matrix inequalities.
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In convex geometry, Gordan's lemma states that the semigroup of integral points in the dual cone of a rational convex polyhedral cone is finitely generated. In algebraic geometry, the prime spectrum of the semigroup algebra of such a semigroup is, by definition, an affine toric variety; thus, the lemma says an affine toric variety is indeed an algebraic variety. The lemma is named after the German mathematician Paul Gordan (1837–1912).
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Ogden's lemma can also be used to prove the inherent ambiguity of some languages.
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The following is an immediate corollary of the Schur lemma for the Ricci tensor.
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Two other characterizations of squares modulo a prime are Euler's criterion and Zolotarev's lemma.
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The proof of the β function lemma makes use of the Chinese remainder theorem.
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The palea is over half the length of the lemma. The anthers are long.
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A lot of political observers made Lemma Megersa (the ODP Chairman) and Abiy Ahmed the front- runners to become the Leader of the ruling coalition and eventually Prime Minister of Ethiopia. Despite being the clear favourite for the general public, Lemma Megersa was not a member of the national parliament, a requirement to become Prime Minister as required by the Ethiopian constitution. Therefore, Lemma Megersa was excluded from the leadership race. On 22 February 2018, Lemma Megersa's party, ODP, called for an emergency executive committee meeting and replaced him as Chairman of ODP with Abiy Ahmed, who was a Member of Parliament.
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The forking lemma was later generalized by Mihir Bellare and Gregory Neven.Mihir Bellare and Gregory Neven, "Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma", Proceedings of the 13th Association for Computing Machinery (ACM) Conference on Computer and Communications Security (CCS), Alexandria, Virginia, 2006, pp. 390-399. The forking lemma has been used and further generalized to prove the security of a variety of digital signature schemes and other random-oracle based cryptographic constructions. Ali Bagherzandi, Jung Hee Cheon, Stanislaw Jarecki: Multisignatures secure under the discrete logarithm assumption and a generalized forking lemma.
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In the early 1960s minimalist artist Carl Andre described to Frampton the Dedekind cut, which partitions a totally ordered set into two subsets, one of whose elements are all less than those of the other, and can be used to construct the real numbers. He became interested in the relationship between set theory and film while working on his ongoing project Magellan. Frampton titled Zorns Lemma after Zorn's lemma (also known as the Kuratowski–Zorn lemma), a proposition of set theory formulated by mathematician Max Zorn in 1935. Zorn's lemma describes partially ordered sets where every totally ordered subset has an upper bound.
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Florets are diminished at the apex. Its lemma is obtuse and lobed while fertile lemma is herbaceous, keelless, obovate, and long. Both low and upper glumes are oblong, scarious, yellow in colour, but are different in size. Also, both glumes have acute apexes.
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Noam Ta-ShmaNoam Ta-Shma (2015); A simple proof of the Isolation Lemma, in eccc gives an isolation lemma with slightly stronger parameters, and gives non-trivial results even when the size of the weight domain is smaller than the number of variables.
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Each spikelet is long; the lemma is long with an awn attached around the middle.
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Furthermore, the concept of pole and polar is revealed as a lemma in Book VII.
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This lemma was introduced by Yegor Ivanovich Zolotarev in an 1872 proof of quadratic reciprocity.
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Many equivalent statements of Hensel's lemma exist. Arguably the most common statement is the following.
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In algebra, Gauss's lemma,Article 42 of Carl Friedrich Gauss's Disquisitiones Arithmeticae (1801) named after Carl Friedrich Gauss, is a statement about polynomials over the integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization property similar to the fundamental theorem of arithmetic). Gauss's lemma underlies all the theory of factorization and greatest common divisors of such polynomials. Gauss's lemma asserts that the product of two primitive polynomials is primitive (a polynomial with integer coefficients is primitive if it has 1 as a greatest common divisor of its coefficients). A corollary of Gauss's lemma, sometimes also called Gauss's lemma, is that a primitive polynomial is irreducible over the integers if and only if it is irreducible over the rational numbers.
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In mathematics, the Rokhlin lemma, or Kakutani–Rokhlin lemma is an important result in ergodic theory. It states that an aperiodic measure preserving dynamical system can be decomposed to an arbitrary high tower of measurable sets and a remainder of arbitrarily small measure. It was proven by Vladimir Abramovich Rokhlin and independently by Shizuo Kakutani. The lemma is used extensively in ergodic theory, for example in Ornstein theory and has many generalizations.
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Zorn's lemma is equivalent (in ZF) to three main results: # Hausdorff maximal principle # Axiom of choice # Well- ordering theorem. A well-known joke alluding to this equivalency (which may defy human intuition) is attributed to Jerry Bona: "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?". Zorn's lemma is also equivalent to the strong completeness theorem of first-order logic.J.L. Bell & A.B. Slomson (1969).
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In graph theory, the hypergraph removal lemma states that when a hypergraph contains few copies of a given sub-hypergraph, then all of the copies can be eliminated by removing a small number of hyperedges. It is a generalization of the graph removal lemma. The special case in which the graph is a tetrahedron is known as the tetrahedron removal lemma. It was first proved by Gowers and, independently, by Nagle, Rödl, Schacht and Skokan.
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Lemma 2. For any positive integers n and m, and any 0 ≤ x ≤ 1, :T_m(T_n(x)) = T_{mn}(x). In other words, Tmn(x) is the composition of Tn(x) and Tm(x). Proof. The proof of this lemma is not difficult, but we need to be slightly careful with the endpoint x = 1. For this point the lemma is clearly true, since :T_m(T_n(1)) = T_m(1) = 1 = T_{mn}(1).
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At the same time, , so the Zeckendorf representation of does not contain . As a result, can be represented as the sum of and the Zeckendorf representation of . The second part of Zeckendorf's theorem (uniqueness) requires the following lemma: :Lemma: The sum of any non-empty set of distinct, non-consecutive Fibonacci numbers whose largest member is is strictly less than the next larger Fibonacci number . The lemma can be proven by induction on .
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Palermo (2) 27 (1909) pp. 247–271.F.P. Cantelli, "Sulla probabilità come limite della frequenza", Atti Accad. Naz. Lincei 26:1 (1917) pp.39–45. A related result, sometimes called the second Borel–Cantelli lemma, is a partial converse of the first Borel–Cantelli lemma.
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However, Bantu is a linguistic classification (see the Bantu lemma as well as the lemma on "Bantu people – the latter says: Bantu people are the speakers of Bantu languages"). As the Tutsi speak the same Bantu language as the Hutu, they are Bantu (speaking) people.
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Bromus hordeaceus is closely related to and difficult to distinguish from Bromus racemosus. The only obvious distinguishing characteristic is the level of lemma nerve protrusion; the lemma nerves are raised and conspicuous in B. hordeaceus while they are smooth and obscure in B. racemosus.
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Then is the set of elements greater than or equal to , and , showing that is indeed a member of the completion., Lemma 11.8, p. 444; , Lemma 3.9(i), p. 166. It is straightforward to verify that the mapping from to is an order- embedding.
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Generalizations of the Farkas' lemma are about the solvability theorem for convex inequalities, i.e., infinite system of linear inequalities. Farkas' lemma belongs to a class of statements called "theorems of the alternative": a theorem stating that exactly one of two systems has a solution.
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Under natural assumptions, the centers of polygons which satisfy Archimedes' Lemma are precisely the points of its Euler line. In other words, the only "well-behaved" centers which satisfy Archimedes' Lemma are the affine combinations of the circumcenter of mass and center of mass.
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The lemma itself have an acute apex while the main lemma have an awn that is long. The palea have two veins while the flowers have three stamens and hairy apex on the ovary. The fruits are caryopses with an additional pericarp and linear hilum.
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In the following subsections we discuss versions of Itô's lemma for different types of stochastic processes.
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Let A1, A2,..., Ak be a sequence of events such that each event occurs with probability at most p and such that each event is independent of all the other events except for at most d of them. > Lemma I (Lovász and Erdős 1973; published 1975) If :4 p d \le 1 then there > is a nonzero probability that none of the events occurs. > Lemma II (Lovász 1977; published by Joel Spencer) If :e p (d+1) \le 1, where > e = 2.718... is the base of natural logarithms, then there is a nonzero > probability that none of the events occurs. Lemma II today is usually referred to as "Lovász local lemma".
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Fertile spikelets are pediceled, the pedicels of which are filiform, oblong and are long. Fertile lemma is chartaceous, keelless, ovate, pallid, is long and 7-veined. It surface is asperulous, while it margins are ciliated and hairy on the bottom. The apex of the lemma is obtuse.
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The species' lemma have scaberulous surface and have emarginated apex as well. Its fertile lemma is chartaceous and lanceolated that is long and wide. Its palea have ciliolated keels, is long and have puberulous surface with hairy back. Flowers are fleshy, oblong, truncate and are long.
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Its lemma have scabrous surface and obtuse apex while the fertile lemma is chartaceous, elliptic, keelless and is by . Its palea have ciliolated keels and smooth surface. Flowers are long, fleshy, oblong and truncate. They also grow together, have 2 lodicules and 3 anthers which are long.
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Its lemma have prominent lateral veins with papillose surface and acute apex. Fertile lemma is chartaceous, keelless lanceolate, and is long by wide. Its palea have dentated apex and papillose surface. The species also carry 2–3 sterile florets which are barren, cuneate, clumped and are long.
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Florets are diminished at the apex. Its lemma have pilose surface and obtuse apex with fertile lemma being chartaceous, ovate, keelless, and is long. Both the lower and upper glumes are long, are keelless, oblong, and 5–7 -veined with obtuse apexes. Palea is 2-veined.
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Hilbert's lemma was proposed at the end of the 19th century by mathematician David Hilbert. The lemma describes a property of the principal curvatures of surfaces. It may be used to prove Liebmann's theorem that a compact surface with constant Gaussian curvature must be a sphere..
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This proof, due to Euler, uses induction to prove the theorem for all integers . The base step, that , is trivial. Next, we must show that if the theorem is true for , then it is also true for . For this inductive step, we need the following lemma. Lemma.
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In discrete geometry, many types of incidence graph are necessarily biclique-free. As a simple example, the graph of incidences between a finite set of points and lines in the Euclidean plane necessarily has no subgraph.. See in particular Lemma 3.1 and the remarks following the lemma.
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Both the upper and lower glumes are keelless and membranous while the other features are different; Lower glume is obovate, long and have an erosed apex while the upper one is cuneate, long and have obtuse apex. The species' lemma have ciliated margins that are hairy in the middle. The lemma also have an acute apex and have chartaceous and lanceolated fertile lemma that is long and wide. Its palea have ciliolated keels, is long and have scaberulous surface.
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The assertion that the Wadge lemma holds for sets in Γ is the semilinear ordering principle for Γ or SLO(Γ). Any defines a linear order on the equivalence classes modulo complements. Wadge's lemma can be applied locally to any pointclass Γ, for example the Borel sets, Δ1n sets, Σ1n sets, or Π1n sets. It follows from determinacy of differences of sets in Γ. Since Borel determinacy is proved in ZFC, ZFC implies Wadge's lemma for Borel sets.
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It is often useful to repeat zero times, which removes v and x from the string. This process of "pumping up" additional copies of v and x is what gives the pumping lemma its name. Finite languages (which are regular and hence context-free) obey the pumping lemma trivially by having p equal to the maximum string length in L plus one. As there are no strings of this length the pumping lemma is not violated.
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The appearance of this odd number is explained by a still more general result, known as the handshaking lemma: any graph has an even number of vertices of odd degree. Finally, the even number of odd vertices is naturally explained by the degree sum formula. Sperner's lemma is a more advanced application of the same strategy. The lemma states that a certain kind of coloring on a triangulation of a simplex has a subsimplex that contains every color.
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Pajor's formulation of the Sauer–Shelah lemma: for every finite family of sets (green) there is another family of equally many sets (blue outlines) such that each set in the second family is shattered by the first family In combinatorial mathematics and extremal set theory, the Sauer–Shelah lemma states that every family of sets with small VC dimension consists of a small number of sets. It is named after Norbert Sauer and Saharon Shelah, who published it independently of each other in 1972... The same result was also published slightly earlier and again independently, by Vladimir Vapnik and Alexey Chervonenkis, after whom the VC dimension is named.. In his paper containing the lemma, Shelah gives credit also to Micha Perles, and for this reason the lemma has also been called the Perles–Sauer–Shelah lemma.. Buzaglo et al. call this lemma "one of the most fundamental results on VC-dimension", and it has applications in many areas. Sauer's motivation was in the combinatorics of set systems, while Shelah's was in model theory and that of Vapnik and Chervonenkis was in statistics.
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Bernard Wick, Spencer M. Kase 49\. Luke H. Hite 49\. John Thomas 50\. William A. Lemma 50\.
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The lemma or citation form of a Korean verb is the form that ends in ta da.
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An alternative "abstract nonsense" proof of the splitting lemma may be formulated entirely in category theoretic terms.
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In Dijkstra A. B. & Janssens F. J. G. (red) Om de kwaliteit van het onderwijs. Boom: Lemma.
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The awn of the lemma barely exceeds its truncate lobes. The grass flowers from August to October.
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In mathematics, Weyl's lemma, named after Hermann Weyl, states that every weak solution of Laplace's equation is a smooth solution. This contrasts with the wave equation, for example, which has weak solutions that are not smooth solutions. Weyl's lemma is a special case of elliptic or hypoelliptic regularity.
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Its lemma have ciliated margins and truncate apex while the fertile lemma is chartaceous, keelless, obovate and is . Its palea is long while the rhachilla internodes are long. Flowers are long, fleshy, oblong and truncate. They also grow together, have 2 lodicules and 3 anthers which are long.
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Fertile lemma is long and is also chartaceous, elliptic and keelless with scaberulous surface. Lemma itself is muticous with acute apex. Flowers have a hairy ovary and three stamens that are long. The fruits are caryopses with an additional pericarp, which just like flowers is hairy as well.
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Both the upper and lower glumes are keelless, membranous and oblong with acute apexes. The size is different though; Lower glume is while the upper one is long. Its lemma have an acute apex with the fertile lemma being chartaceous, keelless, ovate and long. Its palea is 2-veined.
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Fertile spikelets are pediceled and have rhachilla stems that are long. Florets are diminished at the apex. Its lemma have scaberulous surface and emarginated apex with fertile lemma being chartaceous elliptic, keelless, and long. Both the lower and upper glumes are elliptic, keelless, membranous, and have acute apexes.
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This result follows immediately from the above lemma, and it is also called sometimes the Bramble–Hilbert lemma, for example by Ciarlet.Philippe G. Ciarlet. The finite element method for elliptic problems, volume 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002.
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One of the first reforms Lemma tried to undertake was to prevent the interference of the federal police in the state affairs of Oromia region. He called for respect of the constitution and let the region exercise its constitutional power. In this regard, Lemma managed to limit and prevent the interference of the military in regional demonstrations, and regulating investments within Oromia Regional State. Lemma also took measures on investment projects that were operating in violation of rules or not benefiting the region.
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Daniel Lemma, 2011 Daniel Lemma (born 1972 in Ethiopia) is a Swedish-based musician/singer-songwriter. His music is firmly connected to an American tradition of roots music, with visible ties to early blues and gospel. He has referred to singers such as Lead Belly and Pops Staples as being very influential to him- but also artists such as Chuck Berry, James Brown and Bob Dylan. Daniel Lemma was born in Addis Abeba, Ethiopia, but came to Sweden as an infant.
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Common tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma.
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Frampton 2009, p. 198. The final section of Zorns Lemma was shot in 1970.Frampton 1976, p. 76.
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The hypergraph removal lemma can be used to prove, for instance, Szemerédi's theorem, and multi- dimensional Szemerédi's theorem.
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This fact can be understood as an instance of the Yoneda lemma applied to the category of matrices.
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Rec (w',s) can recover w and Ext(w,x) can reproduce R . The following lemma formalizes this.
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Szemerédi's regularity lemma can be interpreted as saying that the space of all graphs is totally bounded (and hence precompact) in a suitable metric (the cut distance). Limits in this metric can be represented by graphons; another version of the regularity lemma simply states that the space of graphons is compact.
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The linear span of a set is dense in the closed linear span. Moreover, as stated in the lemma below, the closed linear span is indeed the closure of the linear span. Closed linear spans are important when dealing with closed linear subspaces (which are themselves highly important, see Riesz's lemma).
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The spikelets themselves are ovate and are long while the rachilla internodes are long. Fertile spikelets are pediceled, the pedicels of which are filiform and puberulous. The florets are diminished at the apex. Its fertile lemma is elliptic, scarious and is long while lemma itself is keelless with dentate apex.
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In mathematics, the Ellis–Numakura lemma states that if S is a non-empty semigroup with a topology such that S is compact and the product is semi- continuous, then S has an idempotent element p, (that is, with pp = p). The lemma is named after Robert Ellis and Katsui Numakura.
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Lemma is lanceolated as well and is long. Fruits are about long are in diameter and obovoid as well.
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The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH.
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The lemma has three veins and hairy margins. The glumes are persistent after fruiting. It spreads with elongated rhizomes.
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Calabi–Eckmann manifolds, Eckmann–Hilton duality, the Eckmann–Hilton argument, and the Eckmann–Shapiro lemma are named after Eckmann.
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Liberman's lemma is a theorem used in studying intrinsic geometry of convex surface. It is named after Joseph Liberman.
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A generalized version of the lemma holds for a sequence of equal angles at a single vertex, surrounded on both sides by a larger angle. For such a sequence, the number of mountain and valley folds bounding any of these angles must either be equal, or differ by one., Lemma 12.2.8, p. 205.
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Fertile spikelets are pediceled, the pedicels of which are hairy, pubescent, filiform and are long. Florets are diminished at the apex. Its lemma have asperulous surface with fertile lemma being herbaceous, lanceolate, keelless and long. Both the lower and upper glumes are keelless, scarious, are long, are grey coloured and have acuminated apexes.
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The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology. Homomorphisms constructed with its help are generally called connecting homomorphisms.
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Note that the proof of the graph removal lemma does not easily extend to induced subgraphs because given a regular partition of the vertex set of G, it now becomes unclear whether to add or remove all the edges between irregular pairs. This issue must be remedied using the strong regularity lemma.
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The lemma itself have one awn which is long and palea which is long and is as hyaline as fertile lemma. The glumes are no different in size then the spikelet. They both are lanceolate, membranous, have no lateral veins and have acute apexes. Flowers are membranous too and have two lodicules.
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The spikelets are made out of 4–5 fertile florets which are oblong and long. Fertile spikelets are pediceled, the pedicels of which are filiform. Florets are diminished at the apex and are bisexual. Its lemma have rugulose surface and obtuse apex while fertile lemma is being coriaceous, elliptic, keelless, and is long.
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Stronger isolation lemmas have been introduced in the literature to fit different needs in various settings. For example, the isolation lemma of has similar guarantees as that of Mulmuley et al., but it uses fewer random bits. In the context of the exponential time hypothesis, prove an isolation lemma for k-CNF formulas.
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Fertile spikelets are pediceled, the pedicels of which are filiform and are long. Florets are diminished at the apex. Its lemma have scabrous surface and acute apex with fertile lemma is being chartaceous, elliptic, keelless, and is long. Both the lower and upper glumes are elliptic, keelless, membranous, and have acute apexes.
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Fertile lemma is long and is also glaucous, ovate, and is as chartaceous and keelless as the glumes. The main lemma is carrying one awn that is long and also have an acuminated apex. Flowers have three stamens while the fruits are ellipsoid and have caryopses with an additional pericarp. Hilum is linear.
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The glumes are chartaceous, lanceolate, and keelless. They also have acute apexes, while only the upper glume is sized . Fertile lemma is long and is also chartaceous, lanceolate, keelless, and are of the same colour as leaf blades. The main lemma have an acuminate apex and carries one awn that is long.
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The glumes are chartaceous and keelless, have acute apexes, with only difference is in size. The upper one is long while the other one is . Fertile lemma is long and is also chartaceous, lanceolate, keelless, and purple in colour. Lemma itself is muticous with acuminate apex, scaberulous surface and carries one awn.
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This is proved in a manner similar to the argument of Lemma 2 (or by simply taking the Hermitian conjugate).
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Schur's lemma admits generalisations to Lie groups and Lie algebras, the most common of which is due to Jacques Dixmier.
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Both versions reduce to Sperner's lemma when m=1, or when all m labelings are identical. See for similar generalizations.
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The original proof given by Roth used Fourier analytic methods. Later on another proof was given using Szemerédi's regularity lemma.
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There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a theorem – a step in the direction of proof – or a short theorem appearing at an intermediate stage in a proof.
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Generalizations of Gauss's lemma can be used to compute higher power residue symbols. In his second monograph on biquadratic reciprocity, Gauss used a fourth-power lemma to derive the formula for the biquadratic character of in , the ring of Gaussian integers. Subsequently, Eisenstein used third- and fourth-power versions to prove cubic and quartic reciprocity.
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The spikelets themselves are made out of 2–3 fertile florets are oblong and are long. Fertile spikelets are pediceled, the pedicels of which are ciliate, flexuous, hairy and are long. Florets are diminished at the apex. Its lemma have scabrous surface and emarginated apex with fertile lemma being coriaceous, keelless, oblong, and long.
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Their other features are different though; Lower glume is oblong and is long while the upper one is elliptic and is long. The species' lemma have an obtuse apex and asperulous surface. Fertile lemma is herbaceous, lanceolate, is long and is light green in colour. Its palea have ciliolated keels and is 2-veined.
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In mathematics -- specifically, in measure theory -- Malliavin's absolute continuity lemma is a result due to the French mathematician Paul Malliavin that plays a foundational rôle in the regularity (smoothness) theorems of the Malliavin calculus. Malliavin's lemma gives a sufficient condition for a finite Borel measure to be absolutely continuous with respect to Lebesgue measure.
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70–79; , pp. 50–51. A construction based on the moment curve can be used to prove a lemma of Gale, according to which, for any positive integers k and d, it is possible to place 2k + d points on a d-dimensional sphere in such a way that every open hemisphere contains at least k points. This lemma, in turn, can be used to calculate the chromatic number of the Kneser graphs, a problem first solved in a different way by László Lovász., Section 3.5, Gale's Lemma and Schrijver's Theorem, pp. 64–67.
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In mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the Eckmann–Shapiro lemma, relates extensions of modules over one ring to extensions over another, especially the group ring of a group and of a subgroup. It thus relates the group cohomology with respect to a group to the cohomology with respect to a subgroup. Shapiro's lemma is named after Arnold Shapiro, who proved it in 1961;. however, Beno Eckmann had discovered it earlier, in 1953..
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In theoretical computer science, the term isolation lemma (or isolating lemma) refers to randomized algorithms that reduce the number of solutions to a problem to one, should a solution exist. This is achieved by constructing random constraints such that, with non-negligible probability, exactly one solution satisfies these additional constraints if the solution space is not empty. Isolation lemmas have important applications in computer science, such as the Valiant–Vazirani theorem and Toda's theorem in computational complexity theory. The first isolation lemma was introduced by , albeit not under that name.
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In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half-plane model. The Schwarz–Pick lemma states that every holomorphic function from the unit disk U to itself, or from the upper half-plane H to itself, will not increase the Poincaré distance between points. The unit disk U with the Poincaré metric has negative Gaussian curvature −1. In 1938, Lars Ahlfors generalised the lemma to maps from the unit disk to other negatively curved surfaces: Theorem (Schwarz–Ahlfors–Pick).
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Joseph Liberman (1917 in Henichesk – August 1941 in ) was a Soviet mathematician, a student of Aleksandrov, best known for Liberman's lemma.
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Fodor's lemma also holds for Thomas Jech's notion of stationary sets as well as for the general notion of stationary set.
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In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century.E. Borel, "Les probabilités dénombrables et leurs applications arithmetiques" Rend. Circ. Mat.
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In algebra, Quillen's lemma states that an endomorphism of a simple module over the enveloping algebra of a finite-dimensional Lie algebra over a field k is algebraic over k. In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable. Quillen's original short proof uses generic flatness.
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The closer the approximation is to zero or one, the more helpful the approximation is in linear cryptanalysis. However, in practice, the binary variables are not independent, as is assumed in the derivation of the piling- up lemma. This consideration has to be kept in mind when applying the lemma; it is not an automatic cryptanalysis formula.
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All of the above proofs use the axiom of choice (AC) in some way. For instance, the third proof uses that every filter is contained in an ultrafilter (i.e., a maximal filter), and this is seen by invoking Zorn's lemma. Zorn's lemma is also used to prove Kelley's theorem, that every net has a universal subnet.
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One of the reasons for this enormous growth in bounds is that many of the positive results for property testing of graphs are established using the Szemerédi regularity lemma, which also has tower-type bounds in its conclusions. The connection of property testing to the Szemerédi regularity lemma and related graph removal lemmas is elaborated on below.
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In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is less celebrated than stronger theorems, such as the Riemann mapping theorem, which it helps to prove. It is, however, one of the simplest results capturing the rigidity of holomorphic functions.
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The lemma tips are fused into the "crown", a short membrane that surrounds the base of the lemma. The rim of the crown usually has hairs. Many species form both cross-pollinating and self- pollinating florets in the terminal panicle. The self-pollinating florets have 1–3 small anthers; the cross-pollinating florets have 3 longer anthers.
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Another related statement, also known as Fodor's lemma (or Pressing-Down-lemma), is the following: For every non-special tree T and regressive mapping f:T\rightarrow T (that is, f(t), with respect to the order on T, for every t\in T), there is a non-special subtree S\subset T on which f is constant.
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An infinite graph that does not obey the handshaking lemma The handshaking lemma does not apply to infinite graphs, even when they have only a finite number of odd-degree vertices. For instance, an infinite path graph with one endpoint has only a single odd-degree vertex rather than having an even number of such vertices.
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In mathematics, Osgood's lemma, introduced by , is a proposition in complex analysis. It states that a continuous function of several complex variables that is holomorphic in each variable separately is holomorphic. The assumption that the function is continuous can be dropped, but that form of the lemma is much harder to prove and is known as Hartogs' theorem.
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The Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is less celebrated than stronger theorems, such as the Riemann mapping theorem, which it helps to prove. It is however one of the simplest results capturing the rigidity of holomorphic functions.
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The lemma itself have an asperulous surface and acute apex while the main lemma have an awn that is long. The palea have two veins and scaberulous keels. Flowers have three stamens and hairy ovary while the fruits are caryopses with an additional pericarp and linear hilum. Both flowers and fruits have hairy apexes as well.
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The glumes are membranous and keelless with scabrous veins. The upper one is long and is lanceolate while the other one is ovate and is long. Fertile lemma is long, is lanceolate just like the upper glume, and is both glaucous, keelless, and membranous as well. Lemma itself have scaberulous surface and muticous with dentated apex.
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In theoretical computer science, Arden's rule, also known as Arden's lemma, is a mathematical statement about a certain form of language equations.
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Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma.
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The letters and images in Zorns Lemma are sets whose order is discovered during the course of the film.Sitney 2002, pp. 369.
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The Lemma Senbet fund pays a 5% distribution to the UMD Deans Office each year. In 2017, this distribution amounted to $37,729.
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In mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma. It states that for the following commutative diagram (in any abelian category, or in the category of groups), if the rows are short exact sequences, and if g and h are isomorphisms, then f is an isomorphism as well. Image:Short_5_lemma.svg It follows immediately from the five lemma. The essence of the lemma can be summarized as follows: if you have a homomorphism f from an object B to an object B′, and this homomorphism induces an isomorphism from a subobject A of B to a subobject A′ of B′ and also an isomorphism from the factor object B/A to B′/A′, then f itself is an isomorphism.
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The convex hull of any finite set of points on the moment curve is a cyclic polytope.; , p. 101; , Lemma 5.4.2, p. 97.
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In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson-Mostowski collapse, is a theorem of set theory introduced by and .
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In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations.
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The proof of the snake lemma is taught by Jill Clayburgh's character at the very beginning of the 1980 film It's My Turn.
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Several versions of the lemma are in use. Basic versions are easy to formulate and prove. More powerful versions are used when needed.
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One can also use the Lindström–Gessel–Viennot lemma to prove the Cauchy–Binet formula, and in particular the multiplicativity of the determinant.
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In the form stated here, the splitting lemma does not hold in the full category of groups, which is not an abelian category.
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Yoshiki Kinoshita stated in 1996 that the term "Yoneda lemma" was coined by Saunders Mac Lane following an interview he had with Yoneda.
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The Poincaré metric is distance-decreasing on harmonic functions. This is an extension of the Schwarz lemma, called the Schwarz–Ahlfors–Pick theorem.
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In morphology and lexicography, a lemma (plural lemmas or lemmata) is the canonical form, dictionary form, or citation form of a set of words (headword). In English, for example, run, runs, ran and running are forms of the same lexeme, with run as the lemma by which they are indexed. Lexeme, in this context, refers to the set of all the forms that have the same meaning, and lemma refers to the particular form that is chosen by convention to represent the lexeme. Lemmas have special significance in highly inflected languages such as Arabic, Turkish and Russian.
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In probability theory, the Doob–Dynkin lemma, named after Joseph L. Doob and Eugene Dynkin, characterizes the situation when one random variable is a function of another by the inclusion of the \sigma-algebras generated by the random variables. The usual statement of the lemma is formulated in terms of one random variable being measurable with respect to the \sigma-algebra generated by the other. The lemma plays an important role in the conditional expectation in probability theory, where it allows replacement of the conditioning on a random variable by conditioning on the \sigma-algebra that is generated by the random variable.
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In mathematics, particularly in set theory, Fodor's lemma states the following: If \kappa is a regular, uncountable cardinal, S is a stationary subset of \kappa, and f:S\rightarrow\kappa is regressive (that is, f(\alpha)<\alpha for any \alpha\in S, \alpha eq 0) then there is some \gamma and some stationary S_0\subseteq S such that f(\alpha)=\gamma for any \alpha\in S_0. In modern parlance, the nonstationary ideal is normal. The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956. It is sometimes also called "The Pressing Down Lemma".
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Sometimes one wants to prove the existence of a mathematical object (which can be viewed as a maximal element in some poset). One could try proving the existence of such an object by assuming there is no maximal element and using transfinite induction and the assumptions of the situation to get a contradiction. Zorn's lemma tidies up the conditions a situation needs to satisfy in order for such an argument to work. Therefore Zorn's lemma enables mathematicians to not have to repeat the transfinite induction argument by hand each time, but just check the conditions of Zorn's lemma.
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Review by W.J. Trjitzinsky: The work was developed into a textbook in 1961 which was used in Moscow State University and many other Russian universities for several decades.U.W. Hochstrasser review: In 1959 he published a paper containing a lemma about implicit functions designed for use in optimal control theory which is named after him (Filippov's lemma).A.F. Filippov (1959) "On certain questions in the theory of optimal control", Journal of the Society for Industrial and Applied Mathematics Control, Series A, 1:76–84E.J. McShane & R.B. Warfield Jr. (1967) On Filippov's Implicit Functions Lemma, Proceedings of the American Mathematical SocietyS.
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In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. The map used for the embedding is at least Lipschitz, and can even be taken to be an orthogonal projection. The lemma has uses in compressed sensing, manifold learning, dimensionality reduction, and graph embedding.
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Grammatical encoding is the process of selecting the appropriate syntactic word or lemma. The selected lemma then activates the appropriate syntactic frame for the conceptualized message. Morpho-phonological encoding is the process of breaking words down into syllables to be produced in overt speech. Syllabification is dependent on the preceding and proceeding words, for instance: I-com-pre-hend vs.
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Both spikelets and lower glumes are long. The upper glume is emarginated, lanceolated, membranous, is long and 1.2 length of the top fertile lemma. Lemma is elliptic and have hairs which are in length, while it margins are pilose. The bottom of the upper glume is scabrous while the lower glume bottom is either asperulous or smooth with a rough top.
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Both the upper and lower glumes are elliptic, keelless, membranous and have acute apexes. Their size and veines are different though; Lower glume is long with the leaf veins being 3–5 while the upper one is long and is 5–9 veined. The species' lemma have scabrous surface and emarginated apex. Its fertile lemma is coriaceous and is long.
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This would mean that is an embedded non- compact Lie subgroup of the compact group . This is impossible with the subspace topology on since all embedded Lie subgroups of a Lie group are closed If were closed, it would be compact, Lemma A.17 (c). Closed subsets of compact sets are compact. and then would be compact, Lemma A.17 (a).
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He also introduced the Gowers norms, a tool in arithmetic combinatorics, and provided the basic techniques for analysing them. This work was further developed by Ben Green and Terence Tao, leading to the Green–Tao theorem. In 2003, Gowers established a regularity lemma for hypergraphs, analogous to the Szemerédi regularity lemma for graphs. In 2005, he introduced the notion of a quasirandom group.
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Neyman & Pearson collaborated on a different, but related, problem – selecting among competing hypotheses based on the experimental evidence alone. Of their joint papers, the most cited was from 1933. The famous result of that paper is the Neyman–Pearson lemma. The lemma says that a ratio of probabilities is an excellent criterion for selecting a hypothesis (with the threshold for comparison being arbitrary).
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Jalla! Jalla! (which in turn rendered Lemma a Grammis nomination for best song, the romantic "If I Used to Love You"). Morning Train, the album containing that single, went gold and served as a breakthrough to a much wider audience. Daniel Lemma has released three albums for Warner Music: Morning Train (2001), Meeting at the Building (2003) and Dreamers and Fools (2005).
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The many properties that characterize ultrafilters are also often useful. They are used to, for example, construct the Stone–Čech compactification. The use of ultrafilters generally requires that the ultrafilter lemma be assumed. But in the many fields where the axiom of choice (or the Hahn-Banach theorem) is assumed, the ultrafilter lemma necessarily holds and doesn't require an addition assumption.
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In mathematics, Ribet's lemma gives conditions for a subgroup of a product of groups to be the whole product group. It was introduced by .
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This lemma shows that for a complex number a, the fiber f−1(a) is a discrete (and therefore countable) set, unless f ≡ a.
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In mathematics, Watson's lemma, proved by G. N. Watson (1918, p. 133), has significant application within the theory on the asymptotic behavior of integrals.
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She made several conferences in punk clubs, universities and schools with special education – the lemma was "It's not a problem to be a girl".
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Retrieved on 2013-01-26.Sampaolo, Diego (2012-09-15). Lemma dominates in Carpi, Soi takes Trento 10K. IAAF. Retrieved on 2013-01-26.
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Dually, each right Euclidean relation is right quasi- reflexive, and each right unique and right quasi-reflexive relation is right Euclidean. Lemma 44-46.
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In mathematics, the Aubin–Lions lemma (or theorem) is the result in the theory of Sobolev spaces of Banach space-valued functions, which provides a compactness criterion that is useful in the study of nonlinear evolutionary partial differential equations. Typically, to prove the existence of solutions one first constructs approximate solutions (for example, by a Galerkin method or by mollification of the equation), then uses the compactness lemma to show that there is a convergent subsequence of approximate solutions whose limit is a solution. The result is named after the French mathematicians Jean-Pierre Aubin and Jacques-Louis Lions. In the original proof by Aubin, the spaces X0 and X1 in the statement of the lemma were assumed to be reflexive, but this assumption was removed by Simon, so the result is also referred to as the Aubin–Lions–Simon lemma.
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In mathematics, Schreier's lemma is a theorem in group theory used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup.
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The spikelets are very slender and loosely overlapping in two rows each side of the spikelet axis. Each lemma is tipped with a short awn.
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University of Chicago Press, Chicago. to distinguish it from Say's law. Some economic theoristsFlorenzano, M. 1987. On an extension of the Gale–Nikaido–Debreu lemma.
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The lower floret has a three awned lemma. B. radicosa may hybridize with Bouteloua repens and Bouteloua williamsii, which could contribute to its apparent diversity.
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Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family. It is one of the central results in extremal set theory. It is named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name "Sperner's lemma" also refers to an unrelated result on coloring triangulations.
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In a dictionary, the lemma "go" represents the inflected forms "go", "goes", "going", "went", and "gone". The relationship between an inflected form and its lemma is usually denoted by an angle bracket, e.g., "went" < "go". Of course, the disadvantage of such simplifications is the inability to look up a declined or conjugated form of the word, but some dictionaries, like Webster's Dictionary, list "went".
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In the following example, the lexical entry is associated with a lemma clergyman and two inflected forms clergyman and clergymen. The language coding is set for the whole lexical resource. The language value is set for the whole lexicon as shown in the following UML instance diagram. Image:LMFMorphoClergymanInflected.svg The elements Lexical Resource, Global Information, Lexicon, Lexical Entry, Lemma, and Word Form define the structure of the lexicon.
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Lemma is chartaceous, lanceolated, and is long and wide. Lemma hairs are long with erose, emarginate or obtuse apex. The bottom of both upper and lower glumes are asperulous but the apexes are different; Lower one is erose, obtuse, or sometimes acute, while the upper one is only acute. The lower glume is ovate and is 5-7 veined while the upper glume is only 5-veined.
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Its lemma have a dentate apex while its surface is scaberulous. Fertile lemma is long and wide. Both the lower and upper glumes are keelless, obovate and purple in colour, but have different size, apexes and surfaces. The lower glume is long with asperulous surface and erosed apex, while the upper glume is long and have a puberulous surface, and erosed as well as obtuse apex.
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The Riemann–Lebesgue lemma states that the integral of a function like the above is small. The integral will approach zero as the number of oscillations increases. In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, states that the Fourier transform or Laplace transform of an L1 function vanishes at infinity. It is of importance in harmonic analysis and asymptotic analysis.
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The species' spikelets are long and are both elliptic and solitary with pedicelled fertile spikelets and one fertile floret which have a hairy callus. The glumes are long and are lanceolate, membranous and have one keel. They also have scaberulous veins and acute apexes. It have a hairy and long rhachilla and elliptic long and keelless fertile lemma while the lemma itself have a dentated apex.
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Spikelets are lanceolate, solitary, are long, and have fertile spikelets that are pediceled. The main lemma have an awn that is subapical and is long. It is also have a dentate apex with lanceolated fertile lemma that is wide and is of the same length as the awn. The species also carry 3–4 sterile florets which are barren, lanceolate, clumped and are long.
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Charles Chapman Pugh (born 1940) is an American mathematician who researches dynamical systems. Pugh received his PhD under Philip Hartman of Johns Hopkins University in 1965, with the dissertation The Closing Lemma for Dimensions Two and Three. He has since been a professor, now emeritus, at the University of California, Berkeley. In 1967 he published a closing lemma named after him in the theory of dynamical systems.
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In mathematics, Dickson's lemma states that every set of n-tuples of natural numbers has finitely many minimal elements. This simple fact from combinatorics has become attributed to the American algebraist L. E. Dickson, who used it in order to prove a result in number theory about perfect numbers. However, the lemma was certainly known earlier, for example to Paul Gordan in his research on invariant theory..
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The lemma is called "diagonal" because it bears some resemblance to Cantor's diagonal argument.See, for example, Gaifman (2006). The terms "diagonal lemma" or "fixed point" do not appear in Kurt Gödel's 1931 article or in Alfred Tarski's 1936 article. Rudolf Carnap (1934) was the first to prove the general self-referential lemmaKurt Gödel, Collected Works, Volume I: Publications 1929–1936, Oxford University Press, 1986, p. 339.
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Spikelets are oblong and solitary with pedicelled fertile spikelets that carry 3–5 fertile florets. The glumes are chartaceous, lanceolate, and keelless, have acute apexes, with only difference is in size. The upper one is long while the other one is . Fertile lemma is long and have the same visual appearance as the glumes while the lemma itself have scaberulous surface and acute apex.
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For example, f(x)=x^2 is a superadditive function for nonnegative real numbers because the square of (x+y) is always greater than or equal to the square of x plus the square of y, for nonnegative real numbers x and y. The analogue of Fekete's lemma holds for subadditive functions as well. There are extensions of Fekete's lemma that do not require the definition of superadditivity above to hold for all m and n. There are also results that allow one to deduce the rate of convergence to the limit whose existence is stated in Fekete's lemma if some kind of both superadditivity and subadditivity is present.
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In their book Geometric Folding Algorithms, Erik Demaine and Joe O'Rourke credit the lemma to publications of Toshikazu Kawasaki in 1989, and Jacques Justin in 1994.
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As of 2011, The Jepson Manual includes Nassella within Stipa.Stipa pulchra. The Jepson Manual. Nasella is characterized by strongly overlapping lemma margins and reduced, veinless paleas.
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A variant of Sperner's lemma on a cube (instead of a simplex) was proved by Harold W. Kuhn. It is related to the Poincaré–Miranda theorem.
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In 2000 Susan Frelich Appleton, J.D., was installed as the inaugural Lemma Barkeloo and Phoebe Couzins Professor of Law at the Washington University school of law.
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Since founding in 2006, even after annual distributions the Lemma Senbet Fund has grown 18-fold from $50,000 to $911,032 (fiscal year ended March 31, 2017).
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In 2000 Susan Frelich Appleton, J.D., was installed as the inaugural Lemma Barkeloo and Phoebe Couzins Professor of Law at the Washington University School of Law.
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Then Tucker's lemma states that T contains a complementary edge - an edge (a 1-simplex) whose vertices are labelled by the same number but with opposite signs.
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1 -- 29 The Proper Iteration Lemma is proved by a fairly straightforward induction on \kappa, and the Fundamental Theorem of Proper Forcing follows by taking \alpha=0.
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Bourbaki's Théorie des Ensembles of 1939 refers to a similar maximal principle as "le théorème de Zorn".. The name "Kuratowski–Zorn lemma" prevails in Poland and Russia.
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In the limit where we allow arbitrarily large ordinals, we recover the proof of the full Zorn's lemma using the axiom of choice in the preceding section.
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The stem is the part of the word that never changes even when morphologically inflected; a lemma is the base form of the word. For example, from "produced", the lemma is "produce", but the stem is "produc-". This is because there are words such as production. and producing In linguistic analysis, the stem is defined more generally as the analyzed base form from which all inflected forms can be formed.
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Itô's lemma can also be applied to general -dimensional semimartingales, which need not be continuous. In general, a semimartingale is a càdlàg process, and an additional term needs to be added to the formula to ensure that the jumps of the process are correctly given by Itô's lemma. For any cadlag process , the left limit in is denoted by , which is a left- continuous process. The jumps are written as .
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Such morphemes that cannot occur on their own in this way are usually referred to as bound morphemes. In computational linguistics, the term "stem" is used for the part of the word that never changes, even morphologically, when inflected, and a lemma is the base form of the word. For example, given the word "produced", its lemma (linguistics) is "produce", but the stem is "produc" because of the inflected form "producing".
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Max August Zorn (; June 6, 1906 – March 9, 1993) was a German mathematician. He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a method used in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, ordered sets and the like. Zorn's lemma was first postulated by Kazimierz Kuratowski in 1922, and then independently by Zorn in 1935.
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It follows immediately from the lemma that g(x) < g(bk) for x in (ak,bk). Since g is continuous, we must also have g(ak) ≤ g(bk). If ak ≠ a or a ∉ S, then ak ∉ S, so g(ak) ≥ g(bk), for otherwise ak ∈ S. Thus, g(ak) = g(bk) in these cases. Finally, if ak = a ∈ S, the lemma tells us that g(a) < g(bk).
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In mathematics, and more specifically in ring theory, Krull's theorem, named after Wolfgang Krull, asserts that a nonzero ringIn this article, rings have a 1. has at least one maximal ideal. The theorem was proved in 1929 by Krull, who used transfinite induction. The theorem admits a simple proof using Zorn's lemma, and in fact is equivalent to Zorn's lemma, which in turn is equivalent to the axiom of choice.
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In this example, where n=2, the red 1-simplex has vertices which are labelled by the same number with opposite signs. Tucker's lemma states that for such a triangulation at least one such 1-simplex must exist. In mathematics, Tucker's lemma is a combinatorial analog of the Borsuk-Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed n-dimensional ball B_n.
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Lemma Megersa was born in East Wollega Sibu Sire Aanaa of Oromia Region. He completed his secondary education at General Tadesse Biru Secondary School. He received a bachelor's degree from Addis Ababa University in Political Science and International Relations, and later graduated with a master's degree in International Relations from the same university. Lemma served as speaker of Caffee, the Oromia regional parliament, before becoming regional president in October 2016.
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Below the florets are two glumes, one long and the other long. The fertile floret has a lemma (bract) long, with three short awns (bristles) at the tip, and the sterile floret has a lemma about long with three awns about long. If pollinated, the fertile floret produces an oblong-elliptic brown seed long. When the seed is mature, the whole spikelet detaches, except for the two glumes, which remain.
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The sterile florets are also present in a number of 2-3, and are barren, cuneate, and clumped. Both the upper and lower glumes are keelless, membranous, oblong and have acute apexes. Their size is different though; Lower glume is long, while the upper one is long. Its lemma have scaberulous surface with the fertile lemma being chartaceous, keelless, oblong, ovate and of the same size as the upper glume.
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The glumes are dissimilar and are keelless and membranous, with other features being different; Lower glume is obovate, long with an obtuses apex, while the upper one is lanceolate, long and have an acute apex. Lemma have ciliated margins, scaberulous surface, acute apex with the hairs being long. It fertile lemma is chartaceous, elliptic and is long by wide. The species' palea have ciliolated keels, smooth surface and dentated apex.
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The sterile florets are 2-3 in number and are long, barren, oblong and clumped. Both the upper and lower glumes are keelless, membranous, oblong and are purple coloured. Other features are different though; Lower glume is long with an acute apex while the upper one is long with an obtuse apex. Its lemma have smooth surface and an obtuse apex while the fertile lemma is chartaceous, elliptic, keelless, and long.
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Farkas' lemma is a solvability theorem for a finite system of linear inequalities in mathematics. It was originally proven by the Hungarian mathematician Gyula Farkas. Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively, mathematical programming). It is used amongst other things in the proof of the Karush–Kuhn–Tucker theorem in nonlinear programming.
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Zorns Lemma premiered at the Philharmonic Hall for the 1970 New York Film Festival. It was the first experimental feature film to be screened there. J. Hoberman wrote that it "drove the audience mad", and Howard Thompson observed that "never, at least so far during the Film Festival, have so many Philharmonic Hall viewers slithered outside for a cigarette." Nevertheless, the sale of Zorns Lemma was a financial success for Frampton.
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The racetrack principle can be used to prove a lemma necessary to show that the exponential function grows faster than any power function. The lemma required is that : e^{x}>x for all real x. This is obvious for x<0 but the racetrack principle is required for x>0. To see how it is used we consider the functions : f(x)=e^{x} and : g(x)=x+1.
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The glumes are chartaceous, linear and keelless while the apexes and size are different. The upper glume is long and have an acuminate apex while the lower glume apex is acute with absent lateral veins. Fertile lemma is long and is also chartaceous, lanceolate, and keelless just like the glumes while the colour of it is dark green. Lemma itself have smooth surface, eciliate margins, and acuminate apex.
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The proof uses Euclid's lemma (Elements VII, 30): If a prime divides the product of two integers and , then must divide at least one of those integers and .
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Its fertile lemma is ovate, keelless, membranous and is long. The floret callus is hairy with rhachilla internodes being pilose. The flowers have three stamens which are long.
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In mathematics, more specifically group theory, the three subgroups lemma is a result concerning commutators. It is a consequence of the Philip Hall and Ernst Witt's eponymous identity.
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In number theory, more specifically in p-adic analysis, Krasner's lemma is a basic result relating the topology of a complete non-archimedean field to its algebraic extensions.
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It turns out that this problem is very similar to the problem of finding the most powerful statistical test, and so the Neyman–Pearson lemma can be used.
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Lemma was educated at Addis Ababa University College and at Johns Hopkins University, USA, where he obtained his D.Sc. in 1964. His dissertation was on sandfly-borne leishmaniasis.
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The linear palea is typically enclosed by the folded lemma. The anthers are long. The caryopsis is lanceolate in shape. The grass flowers from July into early October.
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The first core model was Kurt Gödel's constructible universe L. Ronald Jensen proved the covering lemma for L in the 1970s under the assumption of the non-existence of zero sharp, establishing that L is the "core model below zero sharp". The work of Solovay isolated another core model L[U], for U an ultrafilter on a measurable cardinal (and its associated "sharp", zero dagger). Together with Tony Dodd, Jensen constructed the Dodd–Jensen core model ("the core model below a measurable cardinal") and proved the covering lemma for it and a generalized covering lemma for L[U]. Mitchell used coherent sequences of measures to develop core models containing multiple or higher-order measurables.
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Third proof: "Corresponding to each computing machine M we construct a formula Un(M) and we show that, if there is a general method for determining whether Un(M) is provable, then there is a general method for determining whether M ever prints 0" (Undecidable, p. 145). The third proof requires the use of formal logic to prove a first lemma, followed by a brief word-proof of the second: :"Lemma 1: If S1 [symbol "0"] appears on the tape in some complete configuration of M, then Un(M) is provable" (Undecidable, p. 147) :"Lemma 2: [The converse] If Un(M) is provable then S1 [symbol "0"] appears on the tape in some complete configuration of M" (Undecidable, p.
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Shephard's lemma is a major result in microeconomics having applications in the theory of the firm and in consumer choice. The lemma states that if indifference curves of the expenditure or cost function are convex, then the cost minimizing point of a given good (i) with price p_i is unique. The idea is that a consumer will buy a unique ideal amount of each item to minimize the price for obtaining a certain level of utility given the price of goods in the market. The lemma is named after Ronald Shephard who gave a proof using the distance formula in his book Theory of Cost and Production Functions (Princeton University Press, 1953).
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Lemma: for k>1, p>2 (Z/pkZ) such polynomial defines a permutation if and only if a \equiv 0 \pmod p and b ot \equiv 0 \pmod p.
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It pedicels are oblong and are 0.5 mm long while its lemma is long and is both apical and geniculate. The column of lemma's awn is hispidulous and twisted.
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Eisenbud, Theorem 14.4 Generic freeness is proved using Grothendieck's technique of dévissage. See Noether's normalization lemma#Illustrative application : generic freeness for a proof of a version of generic freeness.
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Lemma: A number n is k-hyperperfect (including k=1) if and only if for some k, δk-j(n) = -δk+j(n) for at least one j > 0.
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Models and Ultraproducts. North Holland Publishing Company. In this sense, we see how Zorn's lemma can be seen as a powerful tool, especially in the sense of unified mathematics.
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It is similar to Elymus hystrix, with which it sometimes hybridizes. It can be distinguished from Elymus hystrix by its curving lemma awns, generally larger glumes, and nodding spikes.
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Absolutely the same arguments can be applied to the case of primitive matrices; we just need to mention the following simple lemma, which clarifies the properties of primitive matrices.
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The original proof of the switching lemma involves an argument with conditional probabilities. Arguably simpler proofs have been subsequently given by and . For an introduction, see Chapter 14 in .
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The converse of Schur's lemma is not true in general. For example, the Z-module Q is not simple, but its endomorphism ring is isomorphic to the field Q.
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Based on the Vedic Word Concordance, the institute currently compiles a Dictionary of Vedic Interpretation, of which the first volume, running up to the lemma Agni, has been completed.
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For similar reasons, the cutwidth is at most the pathwidth times the maximum degree of the vertices in a given graph., Lemma 1, p. 99; , Theorem 49, p. 24.
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Note that, as is often the case with probabilistic arguments, this theorem is nonconstructive and gives no method of determining an explicit element of the probability space in which no event occurs. However, algorithmic versions of the local lemma with stronger preconditions are also known (Beck 1991; Czumaj and Scheideler 2000). More recently, a constructive version of the local lemma was given by Robin Moser and Gábor Tardos requiring no stronger preconditions.
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When phonology is taken into account, the definition of the unchangeable part of the word is not useful, as can be seen in the phonological forms of the words in the preceding example: "produced" vs. "production" . Some lexemes have several stems but one lemma. For instance the verb "to go" (the lemma) has the stems "go" and "went" due to suppletion: the past tense was co-opted from a different verb, "to wend".
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Löwenheim's paper was actually concerned with the more general Peirce-Schröder calculus of relatives (relation algebra with quantifiers). He also used the now antiquated notations of Ernst Schröder. For a summary of the paper in English and using modern notations see . According to the received historical view, Löwenheim's proof was faulty because it implicitly used Kőnig's lemma without proving it, although the lemma was not yet a published result at the time.
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Zassenhaus proved this lemma specifically to give the most direct proof of the Schreier refinement theorem. The 'butterfly' becomes apparent when trying to draw the Hasse diagram of the various groups involved. Zassenhaus' lemma for groups can be derived from a more general result known as Goursat's theorem stated in a Goursat variety (of which groups are an instance); however the group-specific modular law also needs to be used in the derivation.
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The American historian of mathematics, David Eugene Smith, mentions that Saccheri "used the same lemma as the one of Tusi, even lettering the figure in precisely the same way and using the lemma for the same purpose". He further says that "Tusi distinctly states that it is due to Omar Khayyam, and from the text, it seems clear that the latter was his inspirer."Smith, David (1935). "Euclid, Omar Khayyam and Saccheri," Scripta Mathematica.
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In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field. More precisely, Abhyankar's lemma states that if A, B, C are local fields such that A and B are finite extensions of C, with ramification indices a and b, and B is tamely ramified over C and b divides a, then the compositum AB is an unramified extension of A.
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Legesse Wolde-Yohannes is an Ethiopian horticultural scientist. He cooperated with Aklilu Lemma on the discovery and research on how to use the plant endod as a means of preventing the parasitic disease bilharzia. He was awarded the Right Livelihood Award in 1989, jointly with Lemma. Bilharzia, or schistosomiasis, is a debilitating and eventually fatal illness, which afflicts more than 200 million people in 74 countries of Africa, Asia and Latin America.
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Pascal's original note has no proof, but there are various modern proofs of the theorem. It is sufficient to prove the theorem when the conic is a circle, because any (non-degenerate) conic can be reduced to a circle by a projective transformation. This was realised by Pascal, whose first lemma states the theorem for a circle. His second lemma states that what is true in one plane remains true upon projection to another plane.
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Although this is not an exceptionally strong lower bound, random restrictions have become an essential tool in complexity. In a similar vein to this proof, the exponent 3/2 in the main lemma has been increased through careful analysis to 1.63 by Paterson and Zwick (1993) and then to 2 by Håstad (1998). Additionally, Håstad's Switching lemma (1987) applied the same technique to the much richer model of constant depth Boolean circuits.
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Lemma Barkeloo (1840–1870, aka Lemma Barkaloo) was the first woman in America to attend law school. She began attending Washington University in 1869, after having been refused admission to the Law School at Columbia. However, she never finished her course work or graduated. In 1870 she was admitted to the Missouri bar and became the first woman to try a case in an American court; she died a few months later from typhoid fever.
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Around the floret are a lemma and palea, each about long, though the palea is sometimes longer than the lemma. Prairie dropseed is a fine-textured grass with long, narrow leaves that arch outward, forming attractive, round tufts. The leaves range in color from a rich green hue in summer to a golden rust color in the fall. Foliage is resilient enough to resist flattening by snow, so it provides year-round interest.
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This can be prove by the lemma we present above. So we an get the irreducibility of the Markov Chain based on simple swaps for the 1-dimension Ising model.
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It was later noticed that this lemma provides a direct proof of the Brouwer fixed- point theorem without explicit use of homology. Sperner's students included Kurt Leichtweiss and Gerhard Ringel.
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Zorn's lemma can be stated as: Variants of this formulation are sometimes used, such as requiring that the set P and the chains be non-empty. See the discussion below.
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Models and Ultraproducts. North Holland Publishing Company. Chapter 5, Theorem 4.3, page 103. Moreover, Zorn's lemma (or one of its equivalent forms) implies some major results in other mathematical areas.
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The lanceolate to somewhat ovate inflorescence is long. The glumes are long. The lemma is long, occasionally with a straight awn measuring between . The palea is either absent or vestigial.
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In mathematics, Auerbach's lemma, named after Herman Auerbach, is a theorem in functional analysis which asserts that a certain property of Euclidean spaces holds for general finite-dimensional normed vector spaces.
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In particular, no theory extending ZF can prove either the completeness or compactness theorems over arbitrary (possibly uncountable) languages without also proving the ultrafilter lemma on a set of same cardinality.
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6–8; Edwards, pp. 39–40. However, since Euler himself had proved the lemma necessary to complete the proof in other work, he is generally credited with the first proof.Aczel, p.
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But then is not covered by . Note, that in the last step we implicitly used the axiom of choice (which is actually equivalent to Zorn's lemma) to ensure the existence of .
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While Sperner's lemma can be used to find a CE, it is very inefficient computationally. There are much more efficient methods, which are usually based on convex programming or linear programming.
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The formula can be generalized to non-continuous semimartingales by adding a pure jump term to ensure that the jumps of the left and right hand sides agree (see Itô's lemma).
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In the mathematics of paper folding, the big-little-big lemma is a necessary condition for a crease pattern with specified mountain folds and valley folds to be able to be folded flat. It differs from Kawasaki's theorem, which characterizes the flat-foldable crease patterns in which a mountain-valley assignment has not yet been made. Together with Maekawa's theorem on the total number of folds of each type, the big-little-big lemma is one of the two main conditions used to characterize the flat-foldability of mountain-valley assignments for crease patterns that meet the conditions of Kawasaki's theorem. Mathematical origami expert Tom Hull calls the big-little-big lemma "one of the most basic rules" for flat foldability of crease patterns.
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Pugh An Improved Closing Lemma and a General Density Theorem, American Journal of Mathematics, Band 89, 1967, S.1010–1021, "Closing Lemma" by Christian Bonatti in Scholarpedia The lemma states: Let f be a diffeomorphism of a compact manifold with a nonwandering point x.Wandering points were introduced by George Birkhoff to describe dissipative systems (with chaotic behavior). In the case of a dynamical system given by a map f, a point wanders if it has a neighborhood U which is disjoint to all of the iterations of the map on it: f^n(U) \cap U = \varnothing.\, Then there is (in the space of diffeomorphisms, equipped with the C^1 topology) in a neighborhood of f a diffeomorphism g for which x is a periodic point.
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The Hausdorff maximal principle is an early statement similar to Zorn's lemma. Kazimierz Kuratowski proved in 1922 a version of the lemma close to its modern formulation (it applies to sets ordered by inclusion and closed under unions of well-ordered chains). Essentially the same formulation (weakened by using arbitrary chains, not just well-ordered) was independently given by Max Zorn in 1935, who proposed it as a new axiom of set theory replacing the well- ordering theorem, exhibited some of its applications in algebra, and promised to show its equivalence with the axiom of choice in another paper, which never appeared. The name "Zorn's lemma" appears to be due to John Tukey, who used it in his book Convergence and Uniformity in Topology in 1940.
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Let \Gamma be a group acting by homeomorphisms on a compact metrizable space Mwith at least three points, and let \gamma\in\Gamma. Then it is known (Lemma 3.1 in or Lemma 6.2 in B. H. Bowditch, Treelike structures arising from continua and convergence groups. Memoirs of the American Mathematical Society 139 (1999), no. 662.) that exactly one of the following occurs: (1) The element \gamma has finite order in \Gamma ; in this case \gamma is called elliptic.
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The third member may be absent or it may be represented by the lemma, according to different botanical interpretations. The perianth interpretation of palea is supported by the expression of MADS-box genes in this organ during development, as is the case in sepals of eudicot plants.Prasad, K, et al. (2005) OsMADS1, a rice MADS-box factor, controls differentiation of specific cell types in the lemma and palea and is an early- acting regulator of inner floral organs.
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Chomsky and Miller (1957) used the pumping lemma: they guess a part v of an input string uvw and try to build a corresponding cycle into the automaton to be learned; using membership queries they ask, for appropriate k, which of the strings uw, uvvw, uvvvw, ..., uvkw also belongs to the language to be learned, thereby refining the structure of their automaton. In 1959, Solomonoff generalized this approach to context-free languages, which also obey a pumping lemma.
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The Vitali covering lemma is vital to the proof of this theorem; its role lies in proving the estimate for the Hardy–Littlewood maximal function. The theorem also holds if balls are replaced, in the definition of the derivative, by families of sets with diameter tending to zero satisfying the Lebesgue's regularity condition, defined above as family of sets with bounded eccentricity. This follows since the same substitution can be made in the statement of the Vitali covering lemma.
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In mathematics, the Morse–Palais lemma is a result in the calculus of variations and theory of Hilbert spaces. Roughly speaking, it states that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable change of coordinates. The Morse–Palais lemma was originally proved in the finite-dimensional case by the American mathematician Marston Morse, using the Gram–Schmidt orthogonalization process. This result plays a crucial role in Morse theory.
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Kőnig's 1927 publication Kőnig's lemma or Kőnig's infinity lemma is a theorem in graph theory due to the Hungarian mathematician Dénes Kőnig who published it in 1927. as explained in It gives a sufficient condition for an infinite graph to have an infinitely long path. The computability aspects of this theorem have been thoroughly investigated by researchers in mathematical logic, especially in computability theory. This theorem also has important roles in constructive mathematics and proof theory.
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Let R be a commutative ring with identity 1. The following is Nakayama's lemma, as stated in : Statement 1: Let I be an ideal in R, and M a finitely-generated module over R. If IM = M, then there exists an r ∈ R with r ≡ 1 (mod I), such that rM = 0\. This is proven below. The following corollary is also known as Nakayama's lemma, and it is in this form that it most often appears.
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Lemma: Hein, INL In Belgium, this personification of Death is now commonly called Pietje de Dood "Little Pete, the Death." As with other Dutch names, it can also refer to the Devil.
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In Euclidean geometry, the trillium theorem – (from , literally 'lemma about trident', , literally 'theorem of trillium' or 'theorem of trefoil') is a statement about properties of inscribed and circumscribed circles and their relations.
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The term lemma is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result, rather than as a useful statement in-and-of itself.
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The Seminole County Sheriff's Office is the law enforcement agency for unincorporated areas of Seminole County, Florida, USA. The current sheriff is Dennis M. Lemma, who took office on January 3, 2017.
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In complex analysis, Jordan's lemma is a result frequently used in conjunction with the residue theorem to evaluate contour integrals and improper integrals. It is named after the French mathematician Camille Jordan.
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In mathematics, Hadamard's lemma, named after Jacques Hadamard, is essentially a first-order form of Taylor's theorem, in which we can express a smooth, real-valued function exactly in a convenient manner.
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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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He has made a number of discoveries in combinatorics and computer science, including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter theorem.
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The above lemma contradicts the fact that after some finite number of rounds in an execution of A, one process entered the elected state and other processes entered the non-elected state.
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The Hungarian Academy of Science elected him corresponding member May 6, 1898. He made a contribution to linear algebra with Farkas' lemma, which is named after him for his derivation of it.
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Zorn's lemma, also known as the Kuratowski–Zorn lemma, after mathematicians Max Zorn and Kazimierz Kuratowski, is a proposition of set theory. It states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered subset) necessarily contains at least one maximal element. Proved by Kuratowski in 1922 and independently by Zorn in 1935, this lemma occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that in a ring with identity every proper ideal is contained in a maximal ideal and that every field has an algebraic closure. Zorn's lemma is equivalent to the well-ordering theorem and also to the axiom of choice, in the sense that any one of the three, together with the Zermelo–Fraenkel axioms of set theory, is sufficient to prove the other two.
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Benci, G. Cerami, Existence of positive solutions of the equation −Δu+a(x)u=u(N+2)/(N−2) in RN, J. Funct. Anal. 88 (1990), no. 1, 90–117.(Lemma 2.5),S.
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Its spikelets are elliptic and are long. Fertile spikelets are pediceled, the pedicels of which are curved, filiform and are long. Florets are diminished. Its lemma have long hairs and have villous surface.
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The quadrivium was taught after the preparatory work of the trivium and would lead to the degree of Master of Arts. Gilman, Daniel Coit, et al. (1905). New International Encyclopedia. Lemma "Arts, Liberal".
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Fertile spikelets have hairy, pubescent, curved and filiformed pedicels. Florets are diminished with callus being pubescent as well. The species have a smooth rachilla. Its lemma have long hairs and have villous surface.
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See Gödel's Collected Works, Vol. 1, Oxford University Press, 1986, p. 363, fn 23. The diagonal lemma is closely related to Kleene's recursion theorem in computability theory, and their respective proofs are similar.
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The main lemma carries an awn that is long and also have a palea with two veins. Flowers have three stamens while the fruits are caryopses with an additional pericarp and linear hilum.
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Without the assumption that A is Noetherian, the statement of the Artin-Tate lemma is no longer true. Indeed, for any non-Noetherian ring A we can define an A-algebra structure on C = A\oplus A by declaring (a,x)(b,y) = (ab,bx+ay). Then for any ideal I \subset A which is not finitely generated, B = A \oplus I \subset C is not of finite type over A, but all conditions as in the lemma are satisfied.
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In mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. This lemma is an intermediate step, of independent interest, in the proof of the Vitali covering theorem. The covering theorem is credited to the Italian mathematician Giuseppe Vitali.. The theorem states that it is possible to cover, up to a Lebesgue-negligible set, a given subset E of Rd by a disjoint family extracted from a Vitali covering of E.
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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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To prove Berge's lemma, we first need another lemma. Take a graph G and let M and M′ be two matchings in G. Let G′ be the resultant graph from taking the symmetric difference of M and M′; i.e. (M - M′) ∪ (M′ \- M). G′ will consist of connected components that are one of the following: # An isolated vertex. # An even cycle whose edges alternate between M and M′. # A path whose edges alternate between M and M′, with distinct endpoints.
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In mathematics, in particular in computational algebra, the Berlekamp- Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus. As a consequence of Gauss's lemma, this amounts to solving the problem also over the rationals. The algorithm starts by finding factorizations over suitable finite fields using Hensel's lemma to lift the solution from modulo a prime p to a convenient power of p. After this the right factors are found as a subset of these.
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A sketch of the proof of Zorn's lemma follows, assuming the axiom of choice. Suppose the lemma is false. Then there exists a partially ordered set, or poset, P such that every totally ordered subset has an upper bound, and that for every element in P there is another element bigger than it. For every totally ordered subset T we may then define a bigger element b(T), because T has an upper bound, and that upper bound has a bigger element.
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In mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwall–Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a differential form and an integral form. For the latter there are several variants. Grönwall's inequality is an important tool to obtain various estimates in the theory of ordinary and stochastic differential equations.
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In -adic analysis, the standard method to show a polynomial equation in one variable has a -adic root is Hensel's lemma, which uses the recursion from Newton's method on the -adic numbers. Because of the more stable behavior of addition and multiplication in the -adic numbers compared to the real numbers (specifically, the unit ball in the -adics is a ring), convergence in Hensel's lemma can be guaranteed under much simpler hypotheses than in the classical Newton's method on the real line.
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Let be a vector space, be a linearly independent set of elements of , and be a generating set. One has to prove that the cardinality of is not larger than that of . If is finite, this results from the Steinitz exchange lemma. (Indeed, the Steinitz exchange lemma implies every finite subset of has cardinality not larger than that of , hence is finite with cardinality not larger than that of .) If is finite, a proof based on matrix theory is also possible.
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Consider the following commutative diagram in any abelian category (such as the category of abelian groups or the category of vector spaces over a given field) or in the category of groups. file:5 lemma.svg The five lemma states that, if the rows are exact, m and p are isomorphisms, l is an epimorphism, and q is a monomorphism, then n is also an isomorphism. The two four-lemmas state: (1) If the rows in the commutative diagram file:4 lemma right.
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In algebra, the Artin–Tate lemma, named after Emil Artin and John Tate, states: :Let A be a commutative Noetherian ring and B \sub C commutative algebras over A. If C is of finite type over A and if C is finite over B, then B is of finite type over A. (Here, "of finite type" means "finitely generated algebra" and "finite" means "finitely generated module".) The lemma was introduced by E. Artin and J. Tate in 1951E Artin, J.T Tate, "A note on finite ring extensions," J. Math. Soc Japan, Volume 3, 1951, pp. 74–77 to give a proof of Hilbert's Nullstellensatz. The lemma is similar to the Eakin–Nagata theorem, which says: if C is finite over B and C is a Noetherian ring, then B is a Noetherian ring.
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The pumping lemma for context-free languages (called just "the pumping lemma" for the rest of this article) describes a property that all context-free languages are guaranteed to have. The property is a property of all strings in the language that are of length at least p, where p is a constant—called the pumping length—that varies between context-free languages. Say s is a string of length at least p that is in the language. The pumping lemma states that s can be split into five substrings, s = uvwxy, where vx is non-empty and the length of vwx is at most p, such that repeating v and x the same number of times (n) in s produces a string that is still in the language.
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Starr first published the Shapley–Folkman lemma on the existence of quasi-equilibria in economies with non-convexities. In addition to publications in economic journals, he wrote the textbook General Equilibrium Theory: An Introduction.
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An ideal m is maximal if and only if R / m is a field. Except for the zero ring, any ring (with identity) possesses at least one maximal ideal; this follows from Zorn's lemma.
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The florets are long and are elliptic. Flowers have 3 anthers which are in length. Glumes are thinner than fertile lemma with the lower one being of which is one length of upper one.
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Cleft Tongue: The Language of Psychic Structures. New-York and London: Karnac Books. (Translated from Hebrew with back cover text by Professor Alessandra Lemma, Unit Director, Psychological Therapies Development Unit, Tavistock Center). 161 pp.
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A more general form of this result is called the Pumping lemma for regular languages, which can be used to show that broad classes of languages cannot be recognized by a finite state machine.
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In mathematics, particularly homological algebra, the zig-zag lemma asserts the existence of a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category.
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Two key contributions made by Alan Frieze are: (1) polynomial time algorithm for approximating the volume of convex bodies (2) algorithmic version for Szemerédi regularity lemma Both these algorithms will be described briefly here.
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Finally, given two solutions such that , one deduces that . As and are coprime, Euclid's lemma shows that divides , and thus that there exists an integer such that and . Therefore, and , which completes the proof.
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Precisely, one has: :Nakayama's lemma: Let U be a finitely generated right module over a (unital) ring R. If U is a non-zero module, then U·J(R) is a proper submodule of U.
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Lemma itself is muticous with acuminate apex. Flowers have a hairy ovary and three stamens that are long. The fruits are caryopses with an additional pericarp that is ellipsoid, while the hilum is linear.
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Slepian's lemma was first proven by Slepian in 1962, and has since been used in reliability theory, extreme value theory and areas of pure probability. It has also been re-proven in several different forms.
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Visualization of the lemma in \R^1. On the top: a collection of balls; the green balls are the disjoint subcollection. On the bottom: the subcollection with three times the radius covers all the balls.
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In mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates, originally used by Robin Moser to prove an algorithmic version of the Lovász local lemma...
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A confluent and terminating ARS is called convergent. In a convergent ARS, every object has a unique normal form. Theorem (Newman's Lemma): A terminating ARS is confluent if and only if it is locally confluent.
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Its palea have ciliolated keels and is of the same length as fertile lemma. Flowers are fleshy, glabrous and truncate. They also grow together and are long with 2 lodicules. The 3 anthers are long.
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In addition to studying Riemann surfaces, Keen has worked in hyperbolic geometry, Kleinian groups and Fuchsian groups, complex analysis, and hyperbolic dynamics. In the field of hyperbolic geometry, she is known for the Collar lemma.
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The panicles have filiform and pubescent pedicels. The spikelets are solitary while it florets are diminished at the apex. Its fertile lemma is chartaceous, lanceolate and is long. The glumes are different from each other.
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University of Chicago Press, Chicago. ; Ch. II.B "The table-Tennis Lemma (Klein's criterion) and examples of free products"; pp. 25-41. Bridson&Haefliger;Martin R. Bridson, and André Haefliger. Metric spaces of non-positive curvature.
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In 1839, was published Fergola's manuscript entitled Teorica de miracoli esposta con metodo dimostrativo in which Fergola tried to demonstrate the possibility of the miracles in a mathematical way: proposition, demonstration, theorem, lemma, scolium, i.e.
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In algebraic geometry, Chow's moving lemma, proved by , states: given algebraic cycles Y, Z on a nonsingular quasi-projective variety X, there is another algebraic cycle Z' on X such that Z' is rationally equivalent to Z and Y and Z' intersect properly. The lemma is one of key ingredients in developing the intersection theory, as it is used to show the uniqueness of the theory. Even if Z is an effective cycle, it is not, in general, possible to choose the cycle Z' to be effective.
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The likelihood-ratio test is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent. In the case of comparing two models each of which has no unknown parameters, use of the likelihood-ratio test can be justified by the Neyman–Pearson lemma. The lemma demonstrates that the test has the highest power among all competitors.
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The edges between parts behave in a "random-like" fashion. Szemerédi's regularity lemma is one of the most powerful tools in extremal graph theory, particularly in the study of large dense graphs. It states that the vertices of every large enough graph can be partitioned into a bounded number of parts so that the edges between different parts behave almost randomly. According to the lemma, no matter how large a graph is, we can approximate it with the edge densities between a bounded number of parts.
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In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset. The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over ZF (Zermelo–Fraenkel set theory without the axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33).
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A simple proof is based on the beautiful Cycle Lemma of Dvoretzky and Motzkin. Call a ballot sequence dominating if A is strictly ahead of B throughout the counting of the votes. The Cycle Lemma asserts that any sequence of p A's and q B's, where p> q, has precisely p-q dominating cyclic permutations. To see this, just arrange the given sequence of p+q A's and B's in a circle and repeatedly remove adjacent pairs AB until only p-q A's remain.
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Mac Lane also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda. Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influential A Survey of Modern Algebra, coauthored in 1941 with Garrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. His Categories for the Working Mathematician remains the definitive introduction to category theory.
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This is systematically used (explicitly or implicitly) in all implemented algorithms (see Polynomial greatest common divisor and Factorization of polynomials). Gauss's lemma, and all its consequences that do not involve the existence of a complete factorization remain true over any GCD domain (an integral domain over which greatest common divisors exist). In particular, a polynomial ring over a GCD domain is also a GCD domain. If one calls primitive a polynomial such that the coefficients generate the unit ideal, Gauss's lemma is true over every commutative ring.
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The Neyman–Pearson lemma is quite useful in electronics engineering, namely in the design and use of radar systems, digital communication systems, and in signal processing systems. In radar systems, the Neyman–Pearson lemma is used in first setting the rate of missed detections to a desired (low) level, and then minimizing the rate of false alarms, or vice versa. Neither false alarms nor missed detections can be set at arbitrarily low rates, including zero. All of the above goes also for many systems in signal processing.
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By contrast, neither a maximum nor a minimum exists for S. Zorn's lemma states that every partially ordered set for which every totally ordered subset has an upper bound contains at least one maximal element. This lemma is equivalent to the well-ordering theorem and the axiom of choice and implies major results in other mathematical areas like the Hahn–Banach theorem, the Kirszbraun theorem, Tychonoff's theorem, the existence of a Hamel basis for every vector space, and the existence of an algebraic closure for every field.
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By the local lemma, there is a positive probability that none of the bad events occur, meaning that our set contains no pair of adjacent points. This implies that a set satisfying our conditions must exist.
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The lemmas have hyaline margins broad. The apex is bifid and the cleft is deep. The awns are long, arising below the lemma. The paleas are shorter than the lemmas, with glabrous backs and ciliate keels.
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B. G. Teubner, Leipzig und Berlin 1912, S. 98-132Friedrich von Schrötter et al. (ed.): Wörterbuch der Münzkunde. 2. unveränderte Auflage. de Gruyter, Berlin 1970, Reprint 2012, (Nachdruck der Originalausgabe von 1930), Lemma "Begräbnis- oder Sterbemünzen".
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It is also long and wide with the branches being scaberulous. Spikelets are cuneate and are . They carry one fertile floret which have a bearded floret callus. Fertile lemma is keelless, membranous, oblong and is long.
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In 1798 Kleuker became professor of theology at the University of Kiel.Kamelott ist eine Gewebe in Leinwandbindung: Wollkammgarn in der Kette und Baumwolle im Schuss. (DTV-Lexikon: Lemma Kamelott. Munic 2006.)Werner Schütz: Johann Friedrich Kleuker.
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The fertile lemma is herbaceous, keelless, oblong and long. Its palea have ciliolated keels and is 2-veined. Flowers have 3 anthers that are long while the fruits are caryopsis and have additional pericarp as well.
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The fertile lemma is chartaceous, elliptic, keelless, and is long. The species' palea have ciliolated keels and is 2-veined. Flowers are fleshy, oblong and truncate. They also grow together, have 2 lodicules and 3 anthers.
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Fertile spikelets have hairy, pubescent, curved and filiformed pedicels. Florets are diminished with callus being pubescent as well. The species have a smooth rachilla. Its lemma have ribbed lateral veins, long hairs and have acute apex.
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In statistics, the Neyman–Pearson lemma was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933. It shows that the likelihood-ratio test is the most powerful test, among all possible statistical tests.
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An earlier formulation of Zorn's lemma is Hausdorff's maximum principle which states that every totally ordered subset of a given partially ordered set is contained in a maximal totally ordered subset of that partially ordered set.
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On the basis of the model’s analytical framework, five important perspectives of quality of education can be distinguished.Dijkstra, A. B., & Janssens, F. J. G. (2012). Om de kwaliteit van het onderwijs: kwaliteitsbepaling en kwaliteitsbevordering. Boom: Lemma.
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In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints with limited dependence. Given a finite set of bad events {A1, ..., An} in a probability space with limited dependence amongst the Ais and with specific bounds on their respective probabilities, the Lovász local lemma proves that with non-zero probability all of these events can be avoided. However, the lemma is non-constructive in that it does not provide any insight on how to avoid the bad events. If the events {A1, ..., An} are determined by a finite collection of mutually independent random variables, a simple Las Vegas algorithm with expected polynomial runtime proposed by Robin Moser and Gábor Tardos can compute an assignment to the random variables such that all events are avoided.
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In mathematics, more specifically abstract algebra and commutative algebra, Nakayama's lemma -- also known as the Krull–Azumaya theorem -- governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field. It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring. The lemma is named after the Japanese mathematician Tadashi Nakayama and introduced in its present form in , although it was first discovered in the special case of ideals in a commutative ring by Wolfgang Krull and then in general by Goro Azumaya (1951).
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In cryptanalysis, the piling-up lemma is a principle used in linear cryptanalysis to construct linear approximation to the action of block ciphers. It was introduced by Mitsuru Matsui (1993) as an analytical tool for linear cryptanalysis.
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The flowering culms are tall. The inflorescence is an open panicle with solitary spikelets on narrow pedicels. Each spikelet has between two and six florets. The glumes have pointed tips and are narrower than the fertile lemma.
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E-HRM is not same as HRIS (Human resource information system) which refers to ICT systems used within HR departments.Ruël, H. J. M., Bondarouk, T., & Looise, J. C. (2004). E-HRM: Innovation or irritation. Utrecht: Lemma Publishers.
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Euclid's lemma applies to . That is, if divides , and is coprime with , then is divides . Here, coprime means that the monic greatest common divisor is . Proof: By hypothesis and Bézout's identity, there are , , and such that and .
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Lemma 1. For any n ≥ 2, the function Tn(x) has exactly n fixed points. Proof. There are 3 fixed points in the illustration above, and the same sort of geometrical argument applies for any n ≥ 2.
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His teachings and writings strongly influenced an entire generation of Israeli philosophers and linguists, including Asa Kasher and Avishai Margalit. In 1953, he founded a pioneering algebraic-computational linguistic group, and in 1961 he contributed to the proof of the pumping lemma for context-free languages (sometimes called the Bar-Hillel lemma). Bar-Hillel helped found the Hebrew University's department of Philosophy of Science. From 1966 to 1969 Bar-Hillel presided over the Division for Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science.
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A spikelet consists of two (or sometimes fewer) bracts at the base, called glumes, followed by one or more florets. A floret consists of the flower surrounded by two bracts, one external—the lemma—and one internal—the palea. The perianth is reduced to two scales, called lodicules, that expand and contract to spread the lemma and palea; these are generally interpreted to be modified sepals. The flowers are usually hermaphroditic—maize being an important exception—and mainly anemophilous or wind-pollinated, although insects occasionally play a role.
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As in the previous editions particular attention was given to fixed expressions and idioms, elucidated and grouped in a set fashion at the end of a lemma. HAT3 was the first Afrikaans dictionary in which the compiler tried to give a proper explanation of the modus operandi and the theoretical principles on which a dictionary is based. Still lacking was a schematic representation of the various components of a lemma, something which could be of great help to the user. This was rectified in HAT4 and even more so in HAT5.
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In mathematics, the Schwartz–Zippel lemma (also called the DeMillo-Lipton- Schwartz–Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determining whether a given multivariate polynomial is the 0-polynomial (or identically equal to 0). It was discovered independently by Jack Schwartz, Richard Zippel, and Richard DeMillo and Richard J. Lipton, although DeMillo and Lipton's version was shown a year prior to Schwartz and Zippel's result. The finite field version of this bound was proved by Øystein Ore in 1922.
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The S-procedure or S-lemma is a mathematical result that gives conditions under which a particular quadratic inequality is a consequence of another quadratic inequality. The S-procedure was developed independently in a number of different contextsFrank Uhlig, A recurring theorem about pairs of quadratic forms and extensions: a survey, Linear Algebra and its Applications, Volume 25, 1979, pages 219–237.Imre Pólik and Tamás Terlaky, A Survey of the S-Lemma, SIAM Review, Volume 49, 2007, Pages 371–418. and has applications in control theory, linear algebra and mathematical optimization.
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In mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which is equivalent to it. Sperner's lemma states that every Sperner coloring (described below) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors. The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms.
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In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects A' and A to resolutions of extensions of A' by A. It says that if an object A is an extension of A' by A, then a resolution of A can be built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of A' and A. The name of the lemma comes from the shape of the diagram illustrating the lemma's hypothesis.
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Kőnig's lemma may be considered to be a choice principle; the first proof above illustrates the relationship between the lemma and the axiom of dependent choice. At each step of the induction, a vertex with a particular property must be selected. Although it is proved that at least one appropriate vertex exists, if there is more than one suitable vertex there may be no canonical choice. In fact, the full strength of the axiom of dependent choice is not needed; as described below, the axiom of countable choice suffices.
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In particular, when the branching at each node is done on a finite subset of an arbitrary set not assumed to be countable, the form of Kőnig's lemma that says "Every infinite finitely branching tree has an infinite path" is equivalent to the principle that every countable set of finite sets has a choice function, that is to say, the axiom of countable choice for finite sets., p. 273; compare , Exercise IX.2.18. This form of the axiom of choice (and hence of Kőnig's lemma) is not provable in ZF set theory.
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In mathematics - more specifically, in functional analysis and numerical analysis - Stechkin's lemma is a result about the ℓq norm of the tail of a sequence, when the whole sequence is known to have finite ℓp norm. Here, the term "tail" means those terms in the sequence that are not among the N largest terms, for an arbitrary natural number N. Stechkin's lemma is often useful when analysing best-N-term approximations to functions in a given basis of a function space. The result was originally proved by Stechkin in the case q = 2.
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They grow in a cluster of 2 and are subequal. Glumes are shorter than a spikelet and thinner than fertile lemma. The lower glume is ovate and have a pubescent surface. Its apex is acute and 1 awned.
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Both leaf-sheaths and leaf-blades have glabrous surface. The panicle is linear, spiciform, secund and is long. Spikelets are cuneate, solitary, are long and have fertile spikelets that are pediceled. Its lemma have hairs that are long.
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Lemma have an acute apex, with palea being 2-veined. Flowers are fleshy, oblong and truncate. They also grow together, have 2 lodicules and 3 anthers. The fruits have caryopsis, are long with additional pericarp and linear hilum.
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The Neyman–Pearson lemma is applied to the construction of analysis-specific likelihood-ratios, used to e.g. test for signatures of new physics against the nominal Standard Model prediction in proton-proton collision datasets collected at the LHC.
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In mathematics, the Lindström–Gessel–Viennot lemma provides a way to count the number of tuples of non-intersecting lattice paths. It was proved by Gessel–Viennot in 1985, based on previous work of Lindström published in 1973.
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Let X be non-empty, F ⊆ 2X, F having the finite intersection property. Then there exists an U ultrafilter (in 2X) such that F ⊆ U. See details and proof in .. This result is known as the ultrafilter lemma.
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Pierre Joseph Louis Fatou (28 February 1878 – 09 August 1929) was a French mathematician and astronomer. He is known for major contributions to several branches of analysis. The Fatou lemma and the Fatou set are named after him.
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This is a joke: although the three are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive, and Zorn's lemma to be too complex for any intuition.
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The lemma was proved by Bramble and Hilbert J. H. Bramble and S. R. Hilbert. Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal., 7:112–124, 1970.
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The fixed-point lemma for normal functions is a basic result in axiomatic set theory stating that any normal function has arbitrarily large fixed points (Levy 1979: p. 117). It was first proved by Oswald Veblen in 1908.
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The function f : Ord → Ord, f(α) = ωα is normal (see initial ordinal). Thus, there exists an ordinal θ such that θ = ωθ. In fact, the lemma shows that there is a closed, unbounded class of such θ.
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Beyond its original application to conformal mapping, the circle packing theorem and the ring lemma play key roles in a proof by Keszegh, Pach, and Pálvölgyi that planar graphs of bounded degree can be drawn with bounded slope number.
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In mathematics, especially in singularity theory the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point.
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For instance, the Lens space L(4,1) contains an incompressible Klein bottle that is not π1-injective. However, if S is two-sided, the loop theorem implies Kneser's lemma, that if S is incompressible, then it is π1-injective.
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In probability theory, Kelly's lemma states that for a stationary continuous time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process. The theorem is named after Frank Kelly.
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Schanuel's lemma is the following statement: If 0 -> K -> P -> M -> 0 and 0 -> K' -> P ' -> M -> 0 are short exact sequences of R-modules and P and P ' are projective, then K ⊕ P ' is isomorphic to K ' ⊕ P.
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The awns are straight or curved and are long. The palea is as long or longer than the lemma and its tip slightly projects at maturity. The anthers are long. The caryopses are thick and strongly inrolled when mature.
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For any integers and and for any prime , . The lemma is a case of the freshman's dream. Leaving the proof for later on, we proceed with the induction. Proof. Assume kp ≡ k (mod p), and consider (k+1)p.
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Even though Lüroth's theorem is often thought as a non elementary result, several elementary short proofs have been discovered for long. These simple proofs use only the basics of field theory and Gauss's lemma for primitive polynomials (see e.g.).
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The Lemma Senbet Fund is a student managed investments fund offered as a limited-enrollment year-round experiential learning course to top tier undergraduate students from the Robert H. Smith School of Business at the University of Maryland (UMD).
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The fund, named for Lemma Wolde Senbet, the William E. Mayer Chair Professor of Finance at the Smith School of the University of Maryland, was founded in 2006 with initial capital of US$50,000 from the school's endowment fund.
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It is not possible to prove a variant of the regularity lemma in which all pairs of partition sets are regular. Some graphs, such as the half graphs, require many pairs of partitions (but a small fraction of all pairs) to be irregular. It is a common variant in the definition of an \varepsilon-regular partition to require that the vertex sets all have the same size, while collecting the leftover vertices in an "error"-set V_0 whose size is at most an \varepsilon-fraction of the size of the vertex set of G. A stronger variation of the regularity lemma was proven by Alon, Fischer, Krivelevich, and Szegedy while proving the induced graph removal lemma. This works with a sequence of \varepsilon instead of just one, and shows that there exists a partition with an extremely regular refinement, where the refinement doesn't have too large of an energy increment.
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In ergodic theory, Kac's lemma, demonstrated by mathematician Mark Kac in 1947, states that in a measure space the orbit of almost all the points contained in a set A of such space, whose measure is \mu(A), return to A within an average time inversely proportional to \mu(A). The lemma extends what is stated by Poincaré recurrence theorem, in which it is shown that the points return in A infinite times. Since the phase space of a dynamical system with n variables and bounded, i.e. with the n variables all having a minimum and a maximum, is, for the Liouville theorem, a measure space, the lemma implies that given a configuration of the system (point of space) the average return period close to this configuration (in the neighbourhood of the point) is inversely proportional to the considered size of volume surrounding the configuration.
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In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in Cn, the function –log d(z) is plurisubharmonic, where d is the distance to the boundary. This property shows that the domain is pseudoconvex.
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PPA (standing for "Polynomial time Parity Argument") is the class of problems whose solution is guaranteed by the handshaking lemma: any undirected graph with an odd degree vertex must have another odd degree vertex. It contains the subclasses PWPP and PPAD.
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Limits can be difficult to compute. There exist limit expressions whose modulus of convergence is undecidable. In recursion theory, the limit lemma proves that it is possible to encode undecidable problems using limits.Recursively enumerable sets and degrees, Soare, Robert I.
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The lower glume by itself is elliptic just like lemma, with an erose apex. The species palea is elliptic too, is long and have 2 veines. Paleas keels are ciliated and adorned. Flowers are fleshy, oblong, truncate, and grow together.
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They also have 2 fertile florets which are diminished at the apex. Lemma have ribbed literal veins with rugulose and scaberulous bottom. Palea is ciliolate and have scaberulous keels. Rhachilla is extended while sterile florets are barren, cuneate and are clumped.
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Fertile lemma is chartaceous, ovate, is long and keelless. Sterile floret is barren, ovate, and is clumped. Both the lower and upper glumes are keelless, oblong, are long, and have obtuse apexes. Palea have eciliate keels and is 2-veined.
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Standish Hayes O'Grady. Reprint of the 1892 ed. New York, Lemma Pub. Corp., 1970 Cape Clear Island south west of County Cork is regarded as his birthplace and it is said that a church was built by him on the island.
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The hairs are long while the fertile lemma is chartaceous, lanceolate, and is long by wide. Its palea have ciliolated keels and emarginated apex. It is also oblanceolate, long and is 2 veined. Flowers are fleshy, oblong, truncate and are long.
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The hairs are long while the fertile lemma is chartaceous, lanceolate, and is long by wide. Its palea have ciliolated keels and emarginated apex. It is also oblanceolate, long and is 2 veined. Flowers are fleshy, oblong, truncate and are long.
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There is basically only one pattern for verb endings, with predictable variations dependent on the phonological context. The lemma or citation form is always the third person singular indefinite present. This usually has a ∅ suffix, e.g. kér ("ask", "have a request").
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The theorem then follows from the lemma. Theorem (Alphonse Antonio de Sarasa 1649) As area measured against the asymptote increases in arithmetic progression, the projections upon the asymptote increase in geometric sequence. Thus the areas form logarithms of the asymptote index.
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They carry 2 fertile florets which are oblong and long. Fertile spikelets are pediceled, the pedicels of which are curved, ciliate and filiform. Florets are diminished at the apex. Its lemma is pubescent and have hairy veins with asperulous surface.
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The upper glume though is oblong and is long by wide. Both first and second florets are bisexual but the second one is hairless. The species lemma is lanceolate, and is long by wide. It palea is long and about wide.
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Wilfrid Norman Bailey (born 5 September 1893 Consett, Durham; died 23 October 1961, Eastbourne) was a mathematician who introduced Bailey's lemma and Bailey pairs into the theory of basic hypergeometric series. Bailey chains and Bailey transforms are named after him.
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In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. The summation by parts formula is sometimes called Abel's lemma or Abel transformation.
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Modern versions of the ping-pong lemma can be found in many books such as Lyndon&Schupp;,Roger C. Lyndon and Paul E. Schupp. Combinatorial Group Theory. Springer-Verlag, New York, 2001. "Classics in Mathematics" series, reprint of the 1977 edition.
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In reverse mathematics, Brouwer's theorem can be proved in the system WKL0, and conversely over the base system RCA0 Brouwer's theorem for a square implies the weak König's lemma, so this gives a precise description of the strength of Brouwer's theorem.
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Lemma itself is muticous with acute apex and scaberulous surface. Flowers have a hairy ovary and three stamens that are long. The fruits are caryopses with an additional pericarp, which just like flowers is hairy as well. Hilum is linear.
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In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive (possibly small) probability that none of the events will occur. The Lovász local lemma allows one to relax the independence condition slightly: As long as the events are "mostly" independent from one another and aren't individually too likely, then there will still be a positive probability that none of them occurs. It is most commonly used in the probabilistic method, in particular to give existence proofs. There are several different versions of the lemma.
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For Korean, -da is attached to the stem. In Irish, words are highly inflected by case (genitive, nominative, dative and vocative) and by their place within a sentence because of initial mutations. The noun cainteoir, the lemma for the noun meaning "speaker", has a variety of forms: chainteoir, gcainteoir, cainteora, chainteora, cainteoirí, chainteoirí and gcainteoirí. Some phrases are cited in a sort of lemma: Carthago delenda est (literally, "Carthage must be destroyed") is a common way of citing Cato, but what he said was nearer to censeo Carthaginem esse delendam ("I hold Carthage to be in need of destruction").
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In mathematics, Itô's lemma is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black–Scholes equation for option values.
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In the mathematical subject of geometric group theory, the Švarc–Milnor lemma (sometimes also called Milnor–Švarc lemma, with both variants also sometimes spelling Švarc as Schwarz) is a statement which says that a group G, equipped with a "nice" discrete isometric action on a metric space X, is quasi- isometric to X. This result goes back, in different form, before the notion of quasi-isometry was formally introduced, to the work of Albert S. Schwarz (1955)A. S. Švarc, A volume invariant of coverings , Doklady Akademii Nauk SSSR, vol. 105, 1955, pp. 32–34. and John Milnor (1968).
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In homological algebra, Whitehead's lemmas (named after J. H. C. Whitehead) represent a series of statements regarding representation theory of finite- dimensional, semisimple Lie algebras in characteristic zero. Historically, they are regarded as leading to the discovery of Lie algebra cohomology. One usually makes the distinction between Whitehead's first and second lemma for the corresponding statements about first and second order cohomology, respectively, but there are similar statements pertaining to Lie algebra cohomology in arbitrary orders which are also attributed to Whitehead. The first Whitehead lemma is an important step toward the proof of Weyl's theorem on complete reducibility.
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Subsequently, Frieze and Kannan gave a different version and extended it to hypergraphs. They later produced a different construction due to Alan Frieze and Ravi Kannan that uses singular values of matrices. One can find more efficient non- deterministic algorithms, as formally detailed in Terence Tao's blog and implicitly mentioned in various papers. An inequality of Terence Tao extends the Szemerédi regularity lemma, by revisiting it from the perspective of probability theory and information theory instead of graph theory.. Terence Tao has also provided a proof of the lemma based on spectral theory, using the adjacency matrices of graphs.
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The covering lemma can be used as intermediate step in the proof of the following basic form of the Vitali covering theorem. Actually, a little more is needed, namely the precised form of the covering lemma obtained in the "proof of the infinite version". :Theorem. For every subset E of Rd and every Vitali cover of E by a collection F of closed balls, there exists a disjoint subcollection G which covers E up to a Lebesgue-negligible set. Without loss of generality, one can assume that all balls in F are nondegenerate and have radius ≤ 1\.
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For example, let A be an algorithm for breaking a digital signature scheme in the random oracle model. Then x would be the public parameters (including the public key) A is attacking, and hi would be the output of the random oracle on its ith distinct input. The forking lemma is of use when it would be possible, given two different random signatures of the same message, to solve some underlying hard problem. An adversary that forges once, however, gives rise to one that forges twice on the same message with non-negligible probability through the forking lemma.
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In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. It was conjectured by in the course of developing the Langlands program. The fundamental lemma was proved by Gérard Laumon and Ngô Bảo Châu in the case of unitary groups and then by for general reductive groups, building on a series of important reductions made by Jean- Loup Waldspurger to the case of Lie algebras. Time magazine placed Ngô's proof on the list of the "Top 10 scientific discoveries of 2009".
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The third section contains a seemingly single shot of a couple walking across a snowy meadow. The sound is of six women reading one word at a time from Theory of Light. One interpretation of Zorns Lemma was that it was a comment on life's stages, the morality of the Bay State Primer being childhood, the sets of numbers representing maturing and interaction with the world, and the third part representing old age and death. After Zorns Lemma, he made the Hapax Legomena films, a series of seven films of which (nostalgia) is the most well known.
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There are 4–40 florets, which break above the glumes, and, in maturity, between the florets. The lemmas are prominently 5-nerved (referring to a strand of vascular and supporting tissue in a leaf or similar structure); these end in prominent teeth that are 1/3 to 1/2 or more the length of the lemma. Each individual tooth is flanked on either side of the strong central nerve by an additional weaker nerve, which extends about halfway to the base of the lemma. The palea (scales) are well-developed, and have 2 nerves; there are no lodicules.
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When R is a power of a small positive integer b, can be computed by Hensel's lemma: The inverse of N modulo b is computed by a naive algorithm (for instance, if then the inverse is 1), and Hensel's lemma is used repeatedly to find the inverse modulo higher and higher powers of b, stopping when the inverse modulo R is known; is the negation of this inverse. The constants and can be generated as and as . The fundamental operation is to compute REDC of a product. When standalone REDC is needed, it can be computed as REDC of a product with .
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Samuel Assefa is an Ethiopian academic and diplomat who served as the Ambassador of Ethiopia to the United States from 11 May 2006 and ended it on 19 November 2009. Samuel Assefa is the son of Assefa Lemma, the Ethiopian ambassador to Germany; Assefa Lemma held that position from 1961 to 1964 and again from 1970 to 1974. Samuel earned his bachelor's degree in philosophy and economics from Swarthmore College, and his doctorate in political science from Princeton University, where he afterwards taught. Prior to becoming ambassador to the United States, Samuel Assefa served as vice president of Addis Ababa University.
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If the graph is countable, the vertices are well-ordered and one can canonically choose the smallest suitable vertex. In this case, Kőnig's lemma is provable in second-order arithmetic with arithmetical comprehension, and, a fortiori, in ZF set theory (without choice). Kőnig's lemma is essentially the restriction of the axiom of dependent choice to entire relations R such that for each x there are only finitely many z such that xRz. Although the axiom of choice is, in general, stronger than the principle of dependent choice, this restriction of dependent choice is equivalent to a restriction of the axiom of choice.
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An endod research and application network has also been established, linking five African countries, and the plant is being grown and used for experimental control of schistosomiasis. Before his death in 1997, Lemma and colleagues established the Endod Foundation to serve as an umbrella for all endod-related work. Following collaboration with Lemma, the University of Toledo, USA, was granted a US patent on an endod-based molluscicide intended to control the zebra mussels which have recently invaded American lakes and caused extensive damage to water supplies. This has opened a major new hope for marketing and exporting endod as a cash crop.
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Because the exterior derivative has the property that , it can be used as the differential (coboundary) to define de Rham cohomology on a manifold. The -th de Rham cohomology (group) is the vector space of closed -forms modulo the exact -forms; as noted in the previous section, the Poincaré lemma states that these vector spaces are trivial for a contractible region, for . For smooth manifolds, integration of forms gives a natural homomorphism from the de Rham cohomology to the singular cohomology over . The theorem of de Rham shows that this map is actually an isomorphism, a far-reaching generalization of the Poincaré lemma.
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In mathematics, Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear map of the disk which is an embedding and is identical to the original on the boundary of the disk. This theorem was thought to be proven by , but found a gap in the proof. The status of Dehn's lemma remained in doubt until using work by Johansson (1938) proved it using his "tower construction". He also generalized the theorem to the loop theorem and sphere theorem.
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The five lemma is often applied to long exact sequences: when computing homology or cohomology of a given object, one typically employs a simpler subobject whose homology/cohomology is known, and arrives at a long exact sequence which involves the unknown homology groups of the original object. This alone is often not sufficient to determine the unknown homology groups, but if one can compare the original object and sub object to well- understood ones via morphisms, then a morphism between the respective long exact sequences is induced, and the five lemma can then be used to determine the unknown homology groups.
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Start with n=1. For every instance of the problem of length n fix oracle answers (see lemma below) to fix the instance output. Next, provide the instance outputs for queries consisting of the instance followed by kn-length string, and then treat output for queries of length ≤(k+1)n as fixed, and proceed with instances of length n+1. Lemma: Given a problem (specifically, an oracle machine code and time constraint) in relativized ENP, for every partially constructed oracle and input of length n, the output can be fixed by specifying 2O(n) oracle answers.
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A different proof using Zorn's lemma was given by Lajos Pósa, and also in the 1951 Ph.D. thesis of Gabriel Andrew Dirac. If is an infinite graph in which every finite subgraph is -colorable, then by Zorn's lemma it is a subgraph of a maximal graph with the same property (one to which no more edges may be added without causing some finite subgraph to require more than colors). The binary relation of nonadjacency in is an equivalence relation, and its equivalence classes provide a -coloring of . However, this proof is more difficult to generalize than the compactness proof.
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In mathematics, the Calderón–Zygmund lemma is a fundamental result in Fourier analysis, harmonic analysis, and singular integrals. It is named for the mathematicians Alberto Calderón and Antoni Zygmund. Given an integrable function , where denotes Euclidean space and denotes the complex numbers, the lemma gives a precise way of partitioning into two sets: one where is essentially small; the other a countable collection of cubes where is essentially large, but where some control of the function is retained. This leads to the associated Calderón–Zygmund decomposition of , wherein is written as the sum of "good" and "bad" functions, using the above sets.
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Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem. The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics. When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak König's lemma, with the equivalence provable in RCA0 (a second- order variant of Peano arithmetic restricted to induction over Σ01 formulas). Weak König's lemma is provable in ZF, the system of Zermelo–Fraenkel set theory without axiom of choice, and thus the completeness and compactness theorems for countable languages are provable in ZF. However the situation is different when the language is of arbitrary large cardinality since then, though the completeness and compactness theorems remain provably equivalent to each other in ZF, they are also provably equivalent to a weak form of the axiom of choice known as the ultrafilter lemma.
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Michael J. Steele. "Probability theory and combinatorial optimization". SIAM, Philadelphia (1997). . Besides, analogues of Fekete's lemma have been proved for subadditive real maps (with additional assumptions) from finite subsets of an amenable group Theorem 6.1 , and further, of a cancellative left-amenable semigroup.
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When mature the spikelets (2.5–3 mm long ) fall entirely. The upper glume has five nerves. The lower lemma (similar to the upper glume), has seven nerves and is sterile. The fertile florets are elliptic to lanceolate, with nerves which are obscure.
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Key to Umbria Biography. Among his colleagues at the studio of Valeri were Alessandro Vertami, Domenico Belimi, Guglielmo Mangiarelli, Tito Moretti, Annibale Mariani, Lemma Rossi-Scotti, and Pasquale Frenguelli.Storia della pittura in Perugia e delle arti (1895) By Angelo Lupattelli, page 97-98.
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In Riemannian geometry, Schur's lemma is a result that says, heuristically, whenever certain curvatures are pointwise constant then they are forced to be globally constant. The proof is essentially a one-step calculation, which has only one input: the second Bianchi identity.
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It palea is long and have 2 veines. The palea keels are ciliolate while it surface is scaberulous. Apical florets are in length and are barren, sterile and have a cuneated clump. Glumes are thinner than fertile lemma and could exceed florets apex.
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Each inflorescence bears 30-80 spikelets. The glumes are hairless, with lower glumes being long and upper glumes long. The lemma is hairy at the base, is long, and three awned. It is similar to Bouteloua barbata, but bears only a single spike.
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The lemma itself have ciliated margins with acute apex. Lower glume is obovate and is long while the upper is lanceolate and is long. Palea is long and is 2-veined. It sterile florets are barren, cuneate, and grow in a clump.
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Kobayashi (1998), Theorem 3.7.12. If a complex manifold X has a Hermitian metric with holomorphic sectional curvature bounded above by a negative constant, then X is Kobayashi hyperbolic.Kobayashi (2005), section III.2. In dimension 1, this is called the Ahlfors–Schwarz lemma.
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He received his degrees from Tokyo University and Osaka University and held permanent positions at Osaka University and Nagoya University. He had visiting positions at Princeton University, Illinois University, and Hamburg University. Nakayama's lemma, Nakayama algebras, and Nakayama's conjecture are named after him.
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It exists precisely when a is coprime to n, because in that case and by Bézout's lemma there are integers x and y satisfying . Notice that the equation implies that x is coprime to n, so the multiplicative inverse belongs to the group.
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Formation of the transgressives bears similarities to the transgressives of other Slavic languages. The transgressive can be formed from a perfective or an imperfective infinitive verb lemma. The imperfective transgressive can be in the present or past tense. The perfective transgressive is in the past.
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Pineland three-awn (A. stricta) flowers Aristida is a very nearly cosmopolitan genus of plants in the grass family.Linnaeus, Carl von. 1753. Species Plantarum 1: 82 in LatinTropicos, Aristida L Aristida is distinguished by having three awns (bristles) on each lemma of each floret.
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Solimini, A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 319–337.(Theorem 1), or by ad-hoc monikers such as vanishing lemma or inverse embedding.
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It has panicles which are long and wide. Its pedicels are in length while the leaf blades are long and wide. Both the upper and lower glumes are shiny, lanceolate, and membranous. The lemma have a dorsal awn and dentate apex with obscure lateral veins.
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A version of Fitting's lemma is often used in the representation theory of groups. This is in fact a special case of the version above, since every K-linear representation of a group G can be viewed as a module over the group algebra KG.
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The main branches have 1–6 fertile spikelets which are located on lower branches which are also scaberulous. Spikelets do ascend and have pedicelled fertile spikelets. Pedicels are long and are straight. The fertile floret lemma is both chartaceous and elliptic and is long.
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Consider g(x) = ax^2+bx+c for the ring Z/pkZ. Lemma: for k=1 (i.e. Z/pZ) such polynomial defines a permutation only in the case a=0 and b not equal to zero. So the polynomial is not quadratic, but linear.
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More precisely, for no such set A there exists x in M such that A = R−1[x]. So M satisfies the axiom of regularity (it is "internally" well- founded) but it is not well-founded and the collapse lemma does not apply to it.
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Following Uzawa's theorem, many mathematical economists consider proving existence a deeper result than proving the two Fundamental Theorems. Another method of proof of existence, global analysis, uses Sard's lemma and the Baire category theorem; this method was pioneered by Gérard Debreu and Stephen Smale.
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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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Paul B. Henze, Layers of Time (New York: Palgrave, 2000), pp. 254f. In 1961, it numbered nine battalions; in 1969 some 7,000 men. In 1974, the Commander was Major-General Tafessa Lemma. The Kebur Zabagna was disbanded after the Derg consolidated their hold on Ethiopia.
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Several variants of the Dialectica interpretation have been proposed since. Most notably the Diller- Nahm variant (to avoid the contraction problem) and Kohlenbach's monotone and Ferreira-Oliva bounded interpretations (to interpret weak König's lemma). Comprehensive treatments of the interpretation can be found at , and .
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It also has a pilose and scaberulous surface. Fertile lemma is chartaceous, elliptic and is long. Sterile floret is long and is also barren, cuneate, and is clumped. Lower glumes are obovate and are long while the upper glumes are lanceolate and are long.
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The spikelets are long while the rhachilla is prolonged. The glumes are scaberulous and lanceolate while the lemma is only a half of its length. Its awns are and are located closer to the lemmas middle. The large inflorescence is a rich brown colour.
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A nonlinear system has the universal stabilizability property if every forward-complete solution of a system can be globally stabilized. By the use of Finsler's lemma, it is possible to derive a sufficient condition for universal stabilizability in terms of a differential linear matrix inequality.
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Applying this lemma to the Stone–Čech compactification βN of the natural numbers shows that there are idempotent elements in βN. The product on βN is not continuous, but is only semi-continuous (right or left, depending on the preferred construction, but never both).
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It spikelets are elliptic and are long. The glumes are purple in colour with pale green florets that have 2-3 fertile florets. The stem itself is with its lemma being elliptic and long. It is also herbaceous, granular- scaberulous and is 5–7-veined.
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The panicles have curved, filiform and pubescent pedicels which are hairy above. The spikelets are orbicular, solitary, and are long. They are comprised out of 1 fertile floret which is diminished at the apex. Its lemma have ciliate margins and scabrous surface with obtuse apex.
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Then e is the bias of the bitstream. If two uncorrelated bit streams with bias e are exclusive-or-ed together, then the bias of the result will be 2e2. This may be repeated with more bit streams (see also the Piling-up lemma).
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A -form is called closed if ; closed forms are the kernel of . is called exact if for some -form ; exact forms are the image of . Because , every exact form is closed. The Poincaré lemma states that in a contractible region, the converse is true.
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For x in X, the set C_x of all points y such that y \equiv_c x is called the connected component of x.Willard, Definition 26.11, p.194 The Lemma implies that C_x is the unique maximal connected subset of X containing x.Willard, Problem 26B, pp.
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In mathematics, Spijker's lemma is a result in the theory of rational mappings of the Riemann sphere. It states that the image of a circle under a complex rational map with numerator and denominator having degree at most n has length at most 2nπ.
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Spikelets within the inflorescence (flower cluster) are generally arranged on spicate racemes in pairs. A fertile, unstalked spikelet is subtended by a sterile, stalked spikelet. In species where awns are present they are found on the fertile, unstalked spikelet as an extension of the lemma.
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Proof: The definition of projection function Pr can be extended such that in the second argument it can accept a finite word. For some set of states S, finite word w, and symbol a, let Pr(S,aw) = Pr(Pr(S,a),w) and Pr(S,ε) = S. Let w ∈ L(A) and ρ=q0,q1,... be an accepting run of A on w. First, we will prove following useful lemma. ;Lemma 1 :There is an index n such that qn ∈ F and, for all m ≥ n there exist a k > m, such that Pr({ qn },w(n,k)) = Pr({ qm },w(m,k)).
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One application for the half graph occurs in the Szemerédi regularity lemma, which states that the vertices of any graph can be partitioned into a constant number of subsets of equal size, such that most pairs of subsets are regular (the edges connecting the pair behave in certain ways like a random graph of some particular density). If the half graph is partitioned in this way into k subsets, the number of irregular pairs will be at least proportional to k. Therefore, it is not possible to strengthen the regularity lemma to show the existence of a partition for which all pairs are regular.
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In mathematics, in the field of functional analysis, the Cotlar–Stein almost orthogonality lemma is named after mathematicians Mischa Cotlar and Elias Stein. It may be used to obtain information on the operator norm on an operator, acting from one Hilbert space into another when the operator can be decomposed into almost orthogonal pieces. The original version of this lemma (for self-adjoint and mutually commuting operators) was proved by Mischa Cotlar in 1955 and allowed him to conclude that the Hilbert transform is a continuous linear operator in L^2 without using the Fourier transform. A more general version was proved by Elias Stein.
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Lemmatisation (or lemmatization) in linguistics is the process of grouping together the inflected forms of a word so they can be analysed as a single item, identified by the word's lemma, or dictionary form.Collins English Dictionary, entry for "lemmatise" In computational linguistics, lemmatisation is the algorithmic process of determining the lemma of a word based on its intended meaning. Unlike stemming, lemmatisation depends on correctly identifying the intended part of speech and meaning of a word in a sentence, as well as within the larger context surrounding that sentence, such as neighboring sentences or even an entire document. As a result, developing efficient lemmatisation algorithms is an open area of research.
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In the foundations of mathematics, a covering lemma is used to prove that the non-existence of certain large cardinals leads to the existence of a canonical inner model, called the core model, that is, in a sense, maximal and approximates the structure of the von Neumann universe V. A covering lemma asserts that under some particular anti-large cardinal assumption, the core model exists and is maximal in a sense that depends on the chosen large cardinal. The first such result was proved by Ronald Jensen for the constructible universe assuming 0# does not exist, which is now known as Jensen's covering theorem.
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Using the submodular property of the capacity function c, one has : c(X) + c(Y) ≥ c(X ∩ Y) + c(X ∪ Y). Then it can be shown that the minimum s-t cut in G' is also a minimum s-t cut in G for any s, t ∈ X. To show that for all (P, Q) ∈ ET, w(P,Q) = λpq for some p ∈ P, q ∈ Q throughout the algorithm, one makes use of the following Lemma, : For any i, j, k in VG, λik ≥ min(λij, λjk). The Lemma can be used again repeatedly to show that the output T satisfies the properties of a Gomory–Hu Tree.
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Endre Szemerédi has published over 200 scientific articles in the fields of discrete mathematics, theoretical computer science, arithmetic combinatorics and discrete geometry. He is best known for his proof from 1975 of an old conjecture of Paul Erdős and Pál Turán: if a sequence of natural numbers has positive upper density then it contains arbitrarily long arithmetic progressions. This is now known as Szemerédi's theorem. One of the lemmas introduced in his proof is now known as the Szemerédi regularity lemma, which has become an important lemma in combinatorics, being used for instance in property testing for graphs and in the theory of graph limits.
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Present therapies for bilharzia, and molluscicides to kill the snail-carriers of the disease, are far too expensive for the communities that need them. In 1964 a young Ethiopian doctor, Aklilu Lemma, discovered that suds from the fruit of a common African plant, the endod or soapberry, which African women have used as soap for centuries, act as a potent molluscicide. To follow up this discovery, Lemma in 1966 established the Institute of Pathobiology in Addis Ababa University, and for the next 10 years he directed a team to carry out systematic research on endod. He was joined in this work in 1974 by Legesse Wolde-Yohannes.
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This simple proof is also based on the Dyck words interpretation of the Catalan numbers but uses the beautiful Cycle Lemma of Dvoretzky and Motzkin. Call a sequence of X's and Y's dominating if, reading from left to right, the imbalance is always positive, that is, the number of X's is always strictly greater than the number of Y's. The Cycle Lemma asserts that any sequence of m X's and n Y's, where m> n, has precisely m-n dominating cyclic permutations. To see this, just arrange the given sequence of m+n X's and Y's in a circle and repeatedly remove adjacent pairs XY until only m-n X's remain.
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In particular if is finitely generated, then all its bases are finite and have the same number of elements. While the proof of the existence of a basis for any vector space in the general case requires Zorn's lemma and is in fact equivalent to the axiom of choice, the uniqueness of the cardinality of the basis requires only the ultrafilter lemma,Howard, P., Rubin, J.: "Consequences of the axiom of choice" - Mathematical Surveys and Monographs, vol 59 (1998) . which is strictly weaker (the proof given below, however, assumes trichotomy, i.e., that all cardinal numbers are comparable, a statement which is also equivalent to the axiom of choice).
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The subspecies can be mistaken for Bromus lepidus in its similar lemma form and characteristics. It grows in meadows and grasslands. Bromus hordeaceus subsp. thominei, the lesser soft brome, occurs in West Europe and the western United States, in California and the Pacific coast of Canada.
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Lemma is chartaceous, elliptic, and is long. It is also shiny and keelless but have 3 veines. The lemmas apex is obtuse just like glumes, with palea being 2-veined, lanceolated, and in length. Flowers are fleshy, oblong, truncate and grow side by side, with 3 anthers.
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Nearly all of the important theorems in the traditional theory of the Lebesgue integral, such as Lebesgue's dominated convergence theorem, the Riesz–Fischer theorem, Fatou's lemma, and Fubini's theorem may also readily be proved using this construction. Its properties are identical to the traditional Lebesgue integral.
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It has an open, linear, and secund panicle which is long. The main panicle branches are indistinct and almost racemose. The spikelets are cuneate, solitary, and have fertile spikelets that are pediceled. It has an acute apex with a chartaceous fertile lemma with hairs that are long.
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Non-trivial semidirect products do not arise in abelian categories, such as the category of modules. In this case, the splitting lemma shows that every semidirect product is a direct product. Thus the existence of semidirect products reflects a failure of the category to be abelian.
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The usual proof involves another lemma called Bézout's identity. This states that if and are relatively prime integers (i.e. they share no common divisors other than 1 and -1) there exist integers and such that : rx+sy = 1. Let and be relatively prime, and assume that .
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Originally intending to represent each letter of the alphabet with multiple words, Friedrich ultimately used a 26-segment structure that moves in reverse alphabetical order.Sitney 2008, pp. 309–310. Zorns Lemma received three critics' votes in the 2012 Sight & Sound polls of the world's greatest films.
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They are also pediceled, the pedicels of which are long with spikelerts themselves being oblong and long. Fertile lemma is chartaceous, elliptic, keelless and is long. It margins are ciliated while it apex is obtuse. Sterile florets are barren, clumped, cuneate, and grow 2–3 in number.
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This is a resolution, i.e. an exact complex of sheaves by the Poincaré lemma. The cohomology of X with values in \R can thus be computed as the cohomology of the complex of globally defined differential forms: :H^i(X,\R) = H^i(C^\bullet_X(X)).
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The quadrivium followed the preparatory work of the trivium, consisting of grammar, logic, and rhetoric. In turn, the quadrivium was considered the foundation for the study of philosophy (sometimes called the "liberal art par excellence")Gilman, Daniel Coit, et al. (1905). New International Encyclopedia. Lemma "Arts, Liberal".
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A homonymic pun may also be polysemic, in which the words must be homonymic and also possess related meanings, a condition that is often subjective. However, lexicographers define polysemes as listed under a single dictionary lemma (a unique numbered meaning) while homonyms are treated in separate lemmata.
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Lemma Schauenburg/Schaumburg. In: Klaus-Joachim Lorenzen-Schmidt, Ortwin Pelc (Hrsg.): Schleswig-Holstein Lexikon. 2. Aufl., Wachholtz, Neumünster, 2006. Holstein was occupied by Denmark after the Battle of Stellau (1201), but was reconquered by the Count of Schauenburg and his allies in the Battle of Bornhöved (1227).
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Gebru was married three times. Her third husband, Aseffa Lemma, was appointed ambassador to Germany in 1968. She followed him to Bonn as an educational attache. The outbreak of the Ethiopian Civil War in 1974 caused him to seek exile there, but she returned to Ethiopia.
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Lemma Schauenburg/Schaumburg. In: Klaus-Joachim Lorenzen-Schmidt, Ortwin Pelc (Hrsg.): Schleswig-Holstein Lexikon. 2. Aufl., Wachholtz, Neumünster, 2006. In a battle with Denmark, however, Adolf III became prisoner of the king Valdemar II, to whom he had to give Holstein in exchange for his freedom.
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When just 21, Zassenhaus was studying composition series in group theory. He proved his butterfly lemma that provides a refinement of two normal chains to isomorphic central chains. Inspired by Artin, Zassenhaus wrote a textbook Lehrbuch der Gruppentheorie that was later translated as Theory of Groups.
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Now apply Zorn's lemma: the possible extensions of are partially ordered by extension of each other, so there is a maximal extension . By the codimension-1 result, if is not defined on all of , then it can be further extended. Thus must be defined everywhere, as claimed.
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In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power 1 - \beta among all possible tests of a given size α. For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
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The lemma states that, under certain conditions, an event will have probability of either zero or one. Accordingly, it is the best-known of a class of similar theorems, known as zero-one laws. Other examples include Kolmogorov's zero–one law and the Hewitt–Savage zero–one law.
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The spikelets also have one basal sterile florets and one fertile florets while its rhachilla is not extended. They are in length and are lanceolate. The glume is shorter than a spikelet and thinner than fertile lemma. It lower glume is ovate with its awn being in length.
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In mathematics, Mazur's lemma is a result in the theory of Banach spaces. It shows that any weakly convergent sequence in a Banach space has a sequence of convex combinations of its members that converges strongly to the same limit, and is used in the proof of Tonelli's theorem.
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In mathematics -- specifically, in large deviations theory -- the tilted large deviation principle is a result that allows one to generate a new large deviation principle from an old one by "tilting", i.e. integration against an exponential functional. It can be seen as an alternative formulation of Varadhan's lemma.
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The residue field of R is defined as :k = R / m. Any R-module M yields a k-vector space given by M / mM. Nakayama's lemma shows this passage is preserving important information: a finitely generated module M is zero if and only if M / mM is zero.
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José Luis Massera (Genoa, Italy, June 8, 1915 – Montevideo, September 9, 2002).. was a Uruguayan mathematician who researched the stability of differential equations. Massera's lemma is named after him. He published over 40 papers during 1940–1970. A militant Communist, he was a political prisoner during 1975–1984.
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The converse of Jensen's covering theorem is also true: if 0# exists then the countable set of all cardinals less than ℵω cannot be covered by a constructible set of cardinality less than ℵω. In his book Proper Forcing, Shelah proved a strong form of Jensen's covering lemma.
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Diplopogon is a genus of Australian plants in the grass family. It was first described in 1810 by Robert Brown. it contains only a singles species, Diplopogon setaceus, found in southwestern Australia. It is similar to the genus Amphipogon, the only difference being the awns of the lemma.
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Lemma margins are ciliate and hairy on the bottom with obtuse apex. It has 2-veined palea with ciliolated keels. The sterile florets are barren, oblong, grow in clump of 2–3, and are long. The lower glume is ovate, is long and is longer than upper glume.
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In mathematics, Wiener's lemma is a well-known identity which relates the asymptotic behaviour of the Fourier coefficients of a Borel measure on the circle to its atomic part. This result admits an analogous statement for measures on the real line. It was first discovered by Norbert Wiener.
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Because 2 is a prime number, it must also divide p, by Euclid's lemma. So p = 2r, for some integer r. But then, :2q^2 = (2r)^2 = 4r^2, :q^2 = 2r^2, which shows that 2 must divide q as well. So q = 2s for some integer s.
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A co-premise is a premise in reasoning and informal logic which is not the main supporting reason for a contention or a lemma, but is logically necessary to ensure the validity of an argument. One premise by itself, or a group of co-premises can form a reason.
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In mathematics, the Schur orthogonality relations, which is proven by Issai Schur through Schur's lemma, express a central fact about representations of finite groups. They admit a generalization to the case of compact groups in general, and in particular compact Lie groups, such as the rotation group SO(3).
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74-87, in J. McEvoy & M. Dunne (eds), The Irish Contribution to European Scholastic Thought (Dublin: Four Courts Press, 2009). See also James McEvoy, "Flowers from Ancient Gardens: The Lemma 'Amicitia' in the Manipulus florum of Thomas of Ireland", chp. 4, p. 60-73 in the same volume.
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The levels and sublevels are themselves Σ1 uniformly definable (i.e. the definition of Jα, n in Jβ does not depend on β), and have a uniform Σ1 well-ordering. Finally, the levels of the Jensen hierarchy satisfy a condensation lemma much like the levels of Gödel's original hierarchy.
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In mathematics, especially in the area of algebra known as module theory, Schanuel's lemma, named after Stephen Schanuel, allows one to compare how far modules depart from being projective. It is useful in defining the Heller operator in the stable category, and in giving elementary descriptions of dimension shifting.
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There are some fairly simply stated yet hard problems in infinite tree theory. Examples of this are the Kurepa conjecture and the Suslin conjecture. Both of these problems are known to be independent of Zermelo–Fraenkel set theory. Kőnig's lemma states that every ω-tree has an infinite branch.
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As head of the ODP Secretariat from October 2017, Abiy crossed over religious and ethnic divides to facilitate the formation of a new alliance between Oromo and the Amhara groups, both making up two thirds of the 100 million Ethiopian population. In early 2018, many political observers considered Abiy and Lemma Megersa as the most popular politicians within the Oromo community, as well as other Ethiopian communities. This came after several years of unrest in Ethiopia. But despite this favourable rating for Abiy Ahmed and Lemma Megersa, young people from the Oromia region called for immediate action without delays to bring fundamental change and freedom to Oromia Region and Ethiopia – otherwise more unrest was to be expected.
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Total RNA extractions from the whole flower, lemma, palea, lodicule, pistil, anther, and mature pollen grains of the wild type plants took place in order to discover where RMD is specifically expressed in the plant as a whole. Using RT-qPCR (reverse transcription quantitative PCR), it was evident that there were different amounts of RMD transcripts within each part of the plant. And then it was evident where RMD was present in each part of the plant using RT-PCR (reverse transcription PCR) and using UBIQUITIN as a control. These two methods demonstrated that there was an abundant presence of the RMD transcripts in the lemma, pistil, anther, and mature pollen grains.
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A weakened form of Zorn's lemma can be proven from ZF + DC (Zermelo–Fraenkel set theory with the axiom of choice replaced by the axiom of dependent choice). Zorn's lemma can be expressed straightforwardly by observing that the set having no maximal element would be equivalent to stating that the set's ordering relation would be entire, which would allow us to apply the axiom of dependent choice to construct a countable chain. As a result, any partially ordered set with exclusively finite chains must have a maximal element. More generally, strengthening the axiom of dependent choice to higher ordinals allows us to generalize the statement in the previous paragraph to higher cardinalities.
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This result is known as Euclid's lemma. Specifically, if a prime number divides L, then it must divide at least one factor of L. Conversely, if a number w is coprime to each of a series of numbers a1, a2, ..., an, then w is also coprime to their product, a1 × a2 × ... × an. Euclid's lemma suffices to prove that every number has a unique factorization into prime numbers. To see this, assume the contrary, that there are two independent factorizations of L into m and n prime factors, respectively : Since each prime p divides L by assumption, it must also divide one of the q factors; since each q is prime as well, it must be that p = q.
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In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number , then this root corresponds to a unique root of the same equation modulo any higher power of , which can be found by iteratively "lifting" the solution modulo successive powers of . More generally it is used as a generic name for analogues for complete commutative rings (including p-adic fields in particular) of Newton's method for solving equations. Since p-adic analysis is in some ways simpler than real analysis, there are relatively neat criteria guaranteeing a root of a polynomial.
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University of Chicago Press, Chicago, IL, 2000. ; p. 87 because of its importance for the subject. Occasionally the name "fundamental observation in geometric group theory" is now used for this statement, instead of calling it the Švarc–Milnor lemma; see, for example, Theorem 8.2 in the book of Farb and Margalit.
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Several minor variations of the statement of the lemma exist in the literature (see the Notes section below). Here we follow the version given in the book of Bridson and Haefliger (see Proposition 8.19 on p. 140 there).M. R. Bridson and A. Haefliger, Metric spaces of non-positive curvature.
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Itô (right) with Issei Shiraishi in 1935. Shiraishi later became a mathematician. Itô pioneered the theory of stochastic integration and stochastic differential equations, now known as Itô calculus. Its basic concept is the Itô integral, and among the most important results is a change of variable formula known as Itô's lemma.
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The few remaining men of the 128th Illinois were consolidated into a detachment under command of First Lieutenants W. A. Lemma, William M. Cooper, and Assistant Surgeon George W. French and reassigned to 9th Illinois Volunteer Infantry Regiment (3 Years).Adjutant General's Report, Special Order, April 1, 1863, Cario, Ill.
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In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma, named after Malo Hautus, can prove to be a powerful tool. This result appeared first in and. Today it can be found in most textbooks on control theory.
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The reduction provided by the forking lemma is not a tight reduction. Pointcheval and Stern proposed security arguments for Digital Signatures and Blind Signature using Forking Lemma.David Pointcheval and Jacques Stern, "Security Arguments for Digital Signatures and Blind Signatures," JOURNAL OF CRYPTOLOGY, Volume 13, pp 361-- 396, 2000. Available on Internet.
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Orcuttia is a genus of grass in the family Poaceae. Plants grow up to tall, usually with many stems emerging from the base of the plant, and forming a tuft. The spikelets (groups of flowers) are several-flowered, with reduced upper florets. The lemma tips have between two and five teeth.
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The species have culms which are erect and are both tall and wide. It spikelets are long and are yellowish green in colour. The panicle is long and open, while the ligule is long and is truncate. Plants' lemma is long and is pilose, with hairs being long near the awn.
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The apex of the lemma is emarginated with the hairs being of in length. The lower glume is membranous, ovate, is long and is longer than the upper glume. The upper glume is oblong and is long. Both glumes are emarginated, are asperulous on the bottom and have no keels.
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The ontology structure (i.e., data model) is similar to Wordnet structure. Each concept in the ontology is given a unique concept identifier (URI), informally described by a gloss, and lexicalized by one or more of synonymous lemma terms. Each term-concept pair is called a sense, and is given a SenseID.
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In 2007, a recording entitled Zoro Gettem (Reunion) was released on the Nahom Records label; the CD, recorded in Washington, D.C. in September 2006, features four of the Orchestra's former members (Charles Sutton, Getamesay Abbebe, Melaku Gelaw, and Tesfaye Lemma) performing repertoire they had performed together in the late 1960s.
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Spikelets are long and are both elliptic and solitary. They also carry both a pediceled fertile spikelet and one fertile floret which have a hairless callus. The glumes are long, lanceolate, membranous and have acute apexes. Fertile lemma is of the same size as glumes and is both elliptic and hyaline.
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This information is often exploited in contour integration. In the field of Nevanlinna Theory, an important lemma states that the proximity function of a logarithmic derivative is small with respect to the Nevanlinna Characteristic of the original function, for instance m(r,h'/h) = S(r,h) = o(T(r,h)).
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However, it turns out there are languages that cannot be decided by push-down automaton either. The result is similar to that for regular expressions, and won't be detailed here. There exists a Pumping lemma for context-free languages. An example of such a language is the set of prime numbers.
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Accessed 28 April 2009. The most familiar federal enterprise architecture is the enterprise architecture of the Federal government of the United States, the U.S. "Federal Enterprise Architecture" (FEA) and the corresponding U.S. "Federal Enterprise Architecture Framework" (FEAF). This lemma will focus on this particular enterprise architecture and enterprise architecture framework.
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If one wishes to count free polyominoes instead, then one may check for symmetries after creating each n-omino. However, it is fasterRedelmeier, section 4 to generate symmetric polyominoes separately (by a variation of this method)Redelmeier, section 6 and so determine the number of free polyominoes by Burnside's lemma.
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He was given the Taft Professorship in 1999. His research falls within the branch of mathematics known as Complex Analysis. His research interests include structure of hyperbolic metric, Riemann surfaces, and geometric Schwarz-Pick lemma. In 2001, Minda won the University of Cincinnati's Dolly Cohen Award for Excellence in Teaching,.
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Shamir was one of the discoverers of the pumping lemma for context-free languages. He did research in partial differential equations, automata theory, random graphs, computational learning theory, and computational linguistics. He was (with Michael O. Rabin) one of the founders of the computer science program at the Hebrew University.
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In mathematics, Varadhan's lemma is a result from large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic φ(Zε) of a family of random variables Zε as ε becomes small in terms of a rate function for the variables.
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Other bishops of Castulo were at later Visigoth councils down to the tenth Council of Toledo in 656. Thereafter, Castulo is replaced as bishopric by the Diocese of Baeza. Enrique Flórez,España Sagrada, volume VII, Madrid 1751, pages 134–160A. Lambert, lemma Beacia, in Dictionnaire d'Histoire et de Géographie ecclésiastiques, vol.
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Isabelle features locales which are modules that structure large proofs. A locale fixes types, constants, and assumptions within a specified scope so that they do not have to be repeated for every lemma. Isar ("intelligible semi-automated reasoning") is Isabelle's formal proof language. It is inspired by the Mizar system.
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Each spikelet holds one to two seeds, and in some cases three, that are reddish-brown in colour and reach maturity in mid-summer which is when the spikelets shatter. These seeds adhere to the lemma and palea of the glume, so that removing the seeds from the joints is difficult.
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It has lanceolate shaped glumes that are in length with the upper portion being obtuse and the lower part acute to acuminate. The linear to elliptic lemma is purple or brown in colour with even darker margins and in length. The divergent flattened awns have a length of up to .
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The glabrous glumes at the base of the spikelets gradually taper to a point, averaging from in length. The glumes have a single vein and are unequal in length. The lemma, excluding the awns, is approximately long. The delicate lateral awns are in length and can be erect or spreading.
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We need a lemma: Suppose [c,d) ⊂ S, but d ∉ S. Then g(c) < g(d). To prove this, suppose g(c) ≥ g(d). Then g achieves its maximum on [c,d] at some point z < d. Since z ∈ S, there is a y in (z,b] with g(z) < g(y).
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In 2008, Ngô Bảo Châu proved the "fundamental lemma", which was originally conjectured by Langlands and Shelstad in 1983 and being required in the proof of some important conjectures in the Langlands program.Ngô Bảo Châu, "Le lemme fondamental pour les algèbres de Lie", Publications Mathématiques de l'IHES, t. 111 (2010), 1–169.
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1, 1--52. Lemma 4.6). Moreover, the Douady space of X (that is, the moduli of deformations of a subvariety X\subset M, M fixed) is compact and in Fujiki class C.A. Fujiki, On the Douady space of a compact complex space in the category C. Nagoya Math. J. 85 (1982), 189--211.
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Its spikelets are solitary, lanceolate, and are long. They have pedicelled fertile spikelets which are long, filiformed, and have the same features as the branches. The spikelets also carry fertile one which have a long rhachilla which is pilosed. It callus is hairy with its hairs being long, barely reaching the lemma.
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Unlike the Hilbert function, the Hilbert–Samuel function is not additive on an exact sequence. However, it is still reasonably close to being additive, as a consequence of the Artin–Rees lemma. We denote by P_{I, M} the Hilbert-Samuel polynomial; i.e., it coincides with the Hilbert–Samuel function for large integers.
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Fertile lemma is chartaceous and elliptic and is long. Palea is 2 veined and have scaberulous keels as well. Sterile florets are barren, cuneated, and grow in a clump. Both upper and lower glumes are oblong, scarious and keelless, but the lower one is in length while the upper one is long.
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Phytologia 83 (1): 312-330. The determining characteristic between the two is the presence of divergent awns, or hair-like projections that extend off a larger structure, such as the lemma or floret. These two subspecies have been known to hybridize.Daubenmire RF (1939) The taxonomy and ecology of Agopyron spicatum and A. inerme.
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Using this lemma it is simple to solve the puzzle in two questions. Rabern and Rabern (2008) use a similar trick (tempering the liar's paradox) to solve the original puzzle in just two questions. Uzquiano (2010) uses these techniques to provide a two question solution to the amended puzzle.Rabern, Brian and Rabern, Landon.
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32 (1991–1992)(Leiden, 1993), p. 122, note 8 This bird- sign is used only as a phonogram in order to spell the name of the god (H.te Velde, in: Lexikon der Aegyptologie II, lemma: Geb). An alternative ancient name for this goose species was trp meaning similarly 'walk like a drunk', 'stumbler'.
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The only contemporaneous language in which the phoneme survives is Arabic, as the letter Ghayn. The Ancient Greek lemma was coined before the absorption was finalised and so the original pronunciation of Puġ‘mayyaton was preserved as Pugmalíōn. Pygmalion's name was also sometimes written without the Ayin at all, resulting in "𐤐𐤌𐤉𐤉𐤕𐤍" or Pumayyaton.
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The glumes are up to three-quarters the length of the spikelet; their outer surface is finely ribbed with longitudinal veins. There is no awn, the lemma is oblong and has five nerves and the palea is a similar shape with two nerve and a few fine hairs. The three anthers are yellow.
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The panicle is long and is inflorescenced, lanceolate, open and reddish-purple in colour. It have solitary spikelets which carry one fertile floret which have a pubescent callus. The spikelets themselves are elliptic, are long and carry filiformed pedicels. The species carry an oblong fertile lemma which is long and is keelless.
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Linear approximations for S-boxes then must be combined with the cipher's other actions, such as permutation and key mixing, to arrive at linear approximations for the entire cipher. The piling-up lemma is a useful tool for this combination step. There are also techniques for iteratively improving linear approximations (Matsui 1994).
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88, pp. 85-139 was influential for the Chicago School of hard analysis. The Calderón-Zygmund decomposition lemma, invented to prove the weak-type continuity of singular integrals of integrable functions, became a standard tool in analysis and probability theory. The Calderón-Zygmund Seminar at the University of Chicago ran for decades.
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In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of monotonic functions. It can be proven by using Fatou's lemma and the properties of null sets.Jones, Frank (2001), Lebesgue Integration on Euclidean Space, Jones and Bartlett publishers, pp. 527–529.
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Zorns Lemma is a 1970 American structural experimental film by Hollis Frampton. Originally starting as a series of photographs, the non-narrative film is structured around a 24-letter Latin alphabet. It remains, along with Michael Snow's Wavelength and Tony Conrad's The Flicker, one of the best known examples of structural filmmaking.
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It also have hairs that are long while fertile lemma is chartaceous, elliptic, keelless, and is long by wide. Both low and upper glumes are membranous and have an obtuse apexes, but are different in size. Also, both glumes have acute apexes. Low glume is long, while the upper one is long.
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The main branches are appressed and carry oblong and solitary spikelets that are long. They are comprised out of 3–6 fertile florets which are diminished at the apex. It sterile florets are barren, oblong, growing in a clump and are long. The species' fertile lemma is chartaceous, keelless, oblong and is long.
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In mathematics, a Henselian ring (or Hensel ring) is a local ring in which Hensel's lemma holds. They were introduced by , who named them after Kurt Hensel. Azumaya originally allowed Henselian rings to be non-commutative, but most authors now restrict them to be commutative. Some standard references for Hensel rings are , , and .
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If we count the words as they appear in language, even if they are repeated, the words are called tokens. If we count all the words but not counting the repetition of a word, the words are called types. A lemma is the head word and some of its reduced and inflected forms.
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250–270 containing the proof of a famous result now known as the Tits alternative. The result states that a finitely generated linear group is either virtually solvable or contains a free subgroup of rank two. The ping-pong lemma and its variations are widely used in geometric topology and geometric group theory.
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Pures Appl., 82 (2003), p. 253-274 notably by introducing a new idea, that of non-linear Korn inequalities on a surface, another notion that he essentially created and developed with his collaborators.Ciarlet, P.G.; Gratie, L.; Mardare C., « A nonlinear Korn inequality on a surface », J. Math. Pures Appl., 85 (2006), p. 2-16 Functional analysis: Philippe Ciarlet established weak forms of Poincaré's lemma and conditions of compatibility of Saint Venant, in Sobolev's spaces with negative exponents; he established that there are deep relationships between Jacques-Louis Lions' lemma, Nečas's inequality, Rham's theorem, and Bogovskii's theorem, which provide new methods to establish these results.Amrouche, C.; Ciarlet, P.G.; Mardare, C., « On a lemma of Jacques- Louis Lions and its relation to other fundamental results », J. Math. Pures Appl., 104 (2015), p. 207-226 Intrinsic methods in linearized elasticity: Philippe Ciarlet has developed a new field, that of the mathematical justification of "intrinsic" methods in linearized elasticity, where the linearized metric tensor and the linearized tensor of curvature change are the new, and only, unknowns:Ciarlet, P.G.; Ciarlet, JR., P., « Direct computation of stresses in planar linearized elasticity », Math. Models Methods Appl. Sci.
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An infinite sequence of circles can be constructed, containing rings for each n that exactly meet the bound of the ring lemma, showing that it is tight. The construction allows halfplanes to be considered as degenerate circles with infinite radius, and includes additional tangencies between the circles beyond those required in the statement of the lemma. It begins by sandwiching the unit circle between two parallel halfplanes; in the geometry of circles, these are considered to be tangent to each other at the point at infinity. Each successive circle after these first two is tangent to the central unit circle and to the two most recently added circles; see the illustration for the first six circles (including the two halfplanes) constructed in this way.
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However, a different notion of compactness altogether had also slowly emerged at the end of the 19th century from the study of the continuum, which was seen as fundamental for the rigorous formulation of analysis. In 1870, Eduard Heine showed that a continuous function defined on a closed and bounded interval was in fact uniformly continuous. In the course of the proof, he made use of a lemma that from any countable cover of the interval by smaller open intervals, it was possible to select a finite number of these that also covered it. The significance of this lemma was recognized by Émile Borel (1895), and it was generalized to arbitrary collections of intervals by Pierre Cousin (1895) and Henri Lebesgue (1904).
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Any counting formula involving vertices and faces that is valid for all planar graphs may be transformed by planar duality into an equivalent formula in which the roles of the vertices and faces have been swapped. Euler's formula, which is self-dual, is one example. Another given by Harary involves the handshaking lemma, according to which the sum of the degrees of the vertices of any graph equals twice the number of edges. In its dual form, this lemma states that in a plane graph, the sum of the numbers of sides of the faces of the graph equals twice the number of edges.. The medial graph of a plane graph is isomorphic to the medial graph of its dual.
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In axiomatic set theory, the Rasiowa–Sikorski lemma (named after Helena Rasiowa and Roman Sikorski) is one of the most fundamental facts used in the technique of forcing. In the area of forcing, a subset E of a poset (P, ≤) is called dense in P if for any p ∈ P there is e ∈ E with e ≤ p. If D is a family of dense subsets of P, then a filter F in P is called D-generic if :F ∩ E ≠ ∅ for all E ∈ D. Now we can state the Rasiowa–Sikorski lemma: :Let (P, ≤) be a poset and p ∈ P. If D is a countable family of dense subsets of P then there exists a D-generic filter F in P such that p ∈ F.
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As well as behaving well under graph minors, tree-depth has close connections to the theory of induced subgraphs of a graph. Within the class of graphs that have tree-depth at most d (for any fixed integer d), the relation of being an induced subgraph forms a well-quasi-ordering., Lemma 6.13, p. 137. The basic idea of the proof that this relation is a well-quasi-ordering is to use induction on d; the forests of height d may be interpreted as sequences of forests of height d − 1 (formed by deleting the roots of the trees in the height-d forest) and Higman's lemma can be used together with the induction hypothesis to show that these sequences are well-quasi-ordered.
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In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows restating of definitions or properties of morphisms (such as monomorphism or product) given by a universal property in more familiar terms, by stating their relation to elements. Some very general theorems, such as Yoneda's lemma and the Mitchell embedding theorem, are of great utility for this, by allowing one to work in a context where these translations are valid. This approach to category theory, in particular the use of the Yoneda lemma in this way, is due to Grothendieck, and is often called the method of the functor of points.
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The above proof uses Zorn's lemma, which is equivalent to the axiom of choice. It is now known (see below) that the ultrafilter lemma (or equivalently, the Boolean prime ideal theorem), which is slightly weaker than the axiom of choice, is actually strong enough. The Hahn–Banach theorem is equivalent to the following: :(∗): On every Boolean algebra there exists a "probability charge", that is: a nonconstant finitely additive map from into . (The Boolean prime ideal theorem is equivalent to the statement that there are always nonconstant probability charges which take only the values 0 and 1.) In Zermelo–Fraenkel set theory, one can show that the Hahn–Banach theorem is enough to derive the existence of a non-Lebesgue measurable set.
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The first n circles of this construction form a ring, whose minimum radius can be calculated by Descartes' theorem to be the same as the radius specified in the ring lemma. This construction can be perturbed to a ring of n finite circles, without additional tangencies, whose minimum radius is arbitrarily close to this bound.
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The proof of Lüroth's theorem can be derived easily from the theory of rational curves, using the geometric genus.. This method is non-elementary, but several short proofs using only the basics of field theory have long been known. Many of these simple proofs use Gauss's lemma on primitive polynomials as a main step.E.g. see .
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The awns of lower glumes are purple, are in length and are 3-5 veined. The lower lemma is herbaceous and have 5-9 veins while the upper one is 5 veined with an awn that is . The species apex have a stout that is long. Flowers and fruits grow from July to November.
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The glumes are firmer than fertile lemma and are elliptic, membranous, with acute apexes and asperulous surfaces. The flowers have two lodicules and two stigmas. They also have three stamens which are long with it fruits being caryopsis and fusiformed with an additional pericarp. The fruits also have a farinosed endosperm and punctiform hilum.
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A free monoid is equidivisible: if the equation mn = pq holds, then there exists an s such that either m = ps, sn = q (example see image) or ms = p, n = sq.Sakarovitch (2009) p.26 This result is also known as Levi's lemma. A monoid is free if and only if it is graded and equidivisible.
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Almost all integrable systems of classical mechanics can be obtained as particular cases of the Hitchin system (or its meromorphic generalization or in a singular limit). The Hitchin fibration is the map from the moduli space of Hitchin pairs to characteristic polynomials. used Hitchin fibrations over finite fields in his proof of the fundamental lemma.
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Yoshiharu Kohayakawa, in 2017. Yoshiharu Kohayakawa (Japanese: 小早川美晴; born 1963) is a Japanese-Brazilian mathematician working on discrete mathematics and probability theory.Brazilian Academy of Sciences – Yoshiharu Kohayakawa He is known for his work on Szemerédi's regularity lemma, which he extended to sparser graphs.László Lovász – Large Networks and Graph Limits, p.
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In fact, when used within information retrieval systems, stemming improves query recall accuracy, or true positive rate, when compared to lemmatisation. Nonetheless, stemming reduces precision, or true negative rate, for such systems. For instance: #The word "better" has "good" as its lemma. This link is missed by stemming, as it requires a dictionary look-up.
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Spikelets are oblong, solitary, and are long with pedicelled fertile ones. Sterile spikelets grow in pairs and carry 2–3 fertile florets. Both upper and lower glumes are long and are also ovate, membranous, glaucous, with a single keel and vein, and with acuminated and muticous apexes. Fertile lemma is ovate, membranous, and is long.
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She won the Maratona di Sant'Antonio in 2005 and won the Italian Marathon in 2012 at age 39. She underwent a liver operation in 2011 and was pleased to return to good form with her run of 2:35:08 hours.Sampaolo, Diego (2012-10-15). Lemma dominates in Carpi, Soi takes Trento 10K . IAAF.
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In morphology and lexicography, a lemma is the canonical form of a set of words. In English, for example, run, runs, ran and running are forms of the same lexeme, so we can select one of them, ex. run, to represent all the forms. Lexical databases such as Unitex use this kind of representation.
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Fertile lemma is chartaceous, lanceolate and is long. Sterile floret is also barren, cuneate, and is clumped. Both the lower and upper glumes are keelless, lanceolate, and have attenuate apexes, but have different surfaces. The upper glume is long with pilose surface, while the lower glumes is long and is puberulous on the bottom.
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They are covered in soft pubescence and are plump with a broadly ovate (i.e. egg-shaped) to broadly oblong shape. Each contains 5 to 11 flowers and they slowly break up beneath each lemma once mature. The glumes, or sterile husks at the base of each spikelet, are unequal in morphology and persist after maturity.
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Copernicus used what is now known as the Urdi lemma and the Tusi couple in the same planetary models as found in Arabic sources. Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn al-Shatir (d. c. 1375) of Damascus.
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In the category of sets, the inverse limit of any inverse system of non-empty finite sets is non-empty. This may be seen as a generalization of Kőnig's lemma and can be proved with Tychonoff's theorem, viewing the finite sets as compact discrete spaces, and then using the finite intersection property characterization of compactness.
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Rather than directly construct such a subsimplex, it is more convenient to prove that there exists an odd number of such subsimplices through an induction argument. A stronger statement of the lemma then explains why this number is odd: it naturally breaks down as when one considers the two possible orientations of a simplex.
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He has also released three albums on his own label Dextra Music: Somebody on Your Side (2007), Rebound (2009) and Telescope (2012). He has also made music for various films and theatre-projects. Lemma has, in cooperation with Pär Klang, written and performed the official song, "Changing the World", of the World Scout Jamboree 2011.
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Like distinct-degree factorization algorithm, Rabin's algorithm is based on the Lemma stated above. Distinct- degree factorization algorithm tests every d not greater than half the degree of the input polynomial. Rabin's algorithm takes advantage that the factors are not needed for considering fewer d. Otherwise, it is similar to distinct- degree factorization algorithm.
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Mischa Cotlar (1913, Sarny, Ukraine – January 16, 2007, Buenos Aires, Argentina) was a mathematician who started his scientific career in Uruguay and worked most of his life on it in Argentina and Venezuela. His contributions to mathematics are in the fields of harmonic analysis, ergodic theory and spectral theory. He introduced the Cotlar–Stein lemma.
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If is correctly extended we obtain a linear representation of the extended group, which induces the original projective representation when pushed back down to . The solution is always a central extension. From Schur's lemma, it follows that the irreducible representations of central extensions of , and the irreducible projective representations of , are essentially the same objects.
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A completion is any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar to localization, and together they are among the most basic tools in analysing commutative rings. Complete commutative rings have simpler structure than the general ones and Hensel's lemma applies to them.
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The inflorescence is a loose, open array of wavy, hairlike branches bearing rows of spikelets. Each spikelet is a flat fruit with a rough, bristly lemma without an awn, and no glumes. Some of the spikelet branches develop within the sheaths of the leaves and are cleistogamous. This grass is sometimes used for erosion control and restoring wetlands.
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Multilingual dictionaries vary in how they deal with this issue: the Langenscheidt dictionary of German does not list ging (< gehen), but the Cassell does. Lemmas or word stems are used often in corpus linguistics for determining word frequency. In that usage, the specific definition of "lemma" is flexible depending on the task it is being used for.
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If y ≤ d, then g would not reach its maximum on [c,d] at z. Thus, y ∈ (d,b], and g(d) ≤ g(z) < g(y). This means that d ∈ S, which is a contradiction, thus establishing the lemma. The set E is open, so it is composed of a countable union of disjoint intervals (ak,bk).
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For any base, while rational numbers can be simply normal in a particular base, every normal number is irrational. The concept of a normal number was introduced by . Using the Borel–Cantelli lemma, he proved that almost all real numbers are normal, establishing the existence of normal numbers. showed that it is possible to specify a particular such number.
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The branching points will correspond to the choice points in the program. Since there are always only finitely many alternatives at each choice point, the branching factor of the tree is always finite. That is, the tree is finitary. Now Kőnig's lemma says that if every branch of a finitary tree is finite, then so is the tree itself.
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5 pp. , says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman–Morrison–Woodbury formula or just Woodbury formula. However, the identity appeared in several papers before the Woodbury report.
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Stephenson has implemented algorithms for circle packing and used them to construct the many illustrations of the book, giving to much of this work the flavor of experimental mathematics, although it is also mathematically rigorous. Unsolved problems are listed throughout the book, which also includes nine appendices on related topics such as the ring lemma and Doyle spirals.
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An example is: ::Q: What's yellow and equivalent to the Axiom of Choice? ::A: Zorn's lemon. This joke is so esoteric that most outsiders could not even confidently guess to which group it might be funny, let alone why. In fact, it is a mathematics joke, a pun on the name of a famous result, Zorn's Lemma.
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Therefore,Pr({ qnp },w(np,k)) = ∅. Contradiction. In any run, A' can only once make a non-deterministic choice that is when it chooses to take a Δ2 transition and rest of the execution of A' is deterministic. Let n be such that it satisfies lemma 1. We make A' to take Δ2 transition at nth step.
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For example, chatters has the inflectional root or lemma chatter, but the lexical root chat. Inflectional roots are often called stems, and a root in the stricter sense may be thought of as a monomorphemic stem. The traditional definition allows roots to be either free morphemes or bound morphemes. Root morphemes are essential for affixation and compounds.
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The main panicle branches are indistinct and almost racemose. Spikelets are solitary with fertile spikelets being pedicelled, pedicels of which are filiform and puberulous. They also have 2 fertile florets which are diminished at the apex and which are also cuneated and are long. Glumes are reaching the apex of florets and are thinner than lemma.
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They also have 2 fertile florets which are diminished at the apex and which are also elliptic and are long. The callus of the floret is pubescent and also has scaberulous rhachilla. The fertile lemma is chartaceous, oblong, is long and wide. Sterile florets are barren and grow in a clump, which is also cuneated and is in length.
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Spikelets are solitary with fertile spikelets being pedicelled, pedicels of which are ciliated, curved, filiform, scabrous and hairy on top. The spikelets are elliptic, are long, and have 2 fertile florets which are diminished at the apex. Floret callus is pubescent. The upper glume is lanceolated and is long and 0.9 length of the top fertile lemma.
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The species is perennial and tufted, with wiry culms that are long and in diameter. Its lemma is elliptic and oblong, lowest one of which is long. Low glume is ovate and is long while the upper glume is lanceolate and is long. The species spikelets are ovate to oblong, are purple in colour and are .
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The spikelets carry 2–3 sterile florets which are cuneate, clumped, and long. Both the upper and lower glumes are elliptic, keelless, membranous, and have an acute apex. The lower glume is long while the upper one is long. Just like the lower glume, the fertile lemma is elliptic, keelless, and is 4–8 mm long.
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Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity. It made its first appearance in Carl Friedrich Gauss's third proof (1808) of quadratic reciprocity and he proved it again in his fifth proof (1818).
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John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician best known for development of the Fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term 'bit'.
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Your task is to determine the identities of A, B, and C by asking yes-no questions; each question must be put to exactly one god. The gods understand English and will answer in English. Note that this puzzle is trivially solved with three questions. Furthermore, to solve the puzzle in two questions, the following lemma is proved.
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The species' rhachilla is scaberulous while callus is pubescent. Both the upper and lower glumes are keelless and membranous. Their other features are different though; Lower glume is obovate, long with an obtuse apex, while the upper one is lanceolate, long, and have an acute apex. The species' lemma have ciliated and hairy margins with obtuse apex.
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The species' also have 2–3 sterile florets which are long, barren, cuneate, and clumped. Both the upper and lower glumes are keelless, membranous, oblong and have obtuse apexes. The size is different though; Lower glume is long, while the upper one is long. Its lemma have pilose surface, obtuse apex and either white or yellow coloured hairs.
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The Evangelical College's first headmaster was Sven Rubenson. The Animal Health Assistants Training School was established in Bishoftu in 1963, with financial support by the United Nations Special Fund. The artist Lemma Tesefa Kesime was born (1956) in Bishoftu. He studied at the Art School 1972-1974 and received his M.A. from the Soviet Union in 1983.
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One of his most notable students was economist Ronald Shephard, famous for his derivation of Shephard's lemma. Shephard's 1953 Cost and Production Functions expands Evans' theoretical work on costs functions. He also restates Evans' classical dynamic monopoly problem, better incorporating expectations and price changes. Other notable students include Francis W. Dresch, Kenneth May, and Edward A. Davis.
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He also proved the possibility of singular detection, a perhaps unintuitive result. He is also known for Slepian's lemma in probability theory (1962), and for discovering a fundamental result in distributed source coding called Slepian–Wolf coding with Jack Keil Wolf (1973). He later joined the University of Hawaii. His father was Joseph Slepian, also a scientist.
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The signature of the intersection form is an important invariant. A 4-manifold bounds a 5-manifold if and only if it has zero signature. Van der Blij's lemma implies that a spin 4-manifold has signature a multiple of eight. In fact, Rokhlin's theorem implies that a smooth compact spin 4-manifold has signature a multiple of 16.
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In mathematics, Ihara's lemma, introduced by and named by , states that the kernel of the sum of the two p-degeneracy maps from J0(N)×J0(N) to J0(Np) is Eisenstein whenever the prime p does not divide N. Here J0(N) is the Jacobian of the compactification of the modular curve of Γ0(N).
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For this reason, Gauss's result is sometimes known as the Eureka theorem.. The full polygonal number theorem was not resolved until it was finally proven by Cauchy in 1813. The proof of is based on the following lemma due to Cauchy: For odd positive integers and such that and we can find nonnegative integers , , , and such that and .
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XL, fasc. I, pp. 141-144: «Il rischio di considerare indifferenziatamente come sinonimi termini che lo sono soltanto in determinate accezioni si evita del tutto consultando il DOSC (= Il Devoto-Oli dei sinonimi e contrari), che distingue in modo chiaro i diversi significati di un lemma, illustrando ciascuno di essi con una definizione e con un esempio.
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A strongly continuous semigroup T is called eventually compact if there exists a t0 > 0 such that T(t0) is a compact operator (equivalentlyEngel and Nagel Lemma II.4.22 if T(t) is a compact operator for all t ≥ t0) . The semigroup is called immediately compact if T(t) is a compact operator for all t > 0\.
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This is a consequence of Yoneda's lemma. Taking F(X) to be the singular cohomology group Hi(X,A) with coefficients in a given abelian group A, for fixed i > 0; then the representing space for F is the Eilenberg–MacLane space K(A, i). This gives a means of showing the existence of Eilenberg-MacLane spaces.
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It sterile lemma though is truncate. The glumes are all keelless but are different in size and texture. Lower glume is obovate and is long and 7-11 veined, while the upper one is lanceolate and is long and 5-7 veined. Lower glume also have an acute apex while the upper one have an obtuse one.
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In the case of linear invariant systems, this is known as positive real transfer functions, and a fundamental tool is the so-called Kalman–Yakubovich–Popov lemma which relates the state space and the frequency domain properties of positive real systems. Dissipative systems are still an active field of research in systems and control, due to their important applications.
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That intertwiner is then unique up to a multiplicative factor (a non-zero scalar from ). These properties hold when the image of is a simple algebra, with centre (by what is called Schur's Lemma: see simple module). As a consequence, in important cases the construction of an intertwiner is enough to show the representations are effectively the same..
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By Borel's lemma, there is a diffeomorphism defined in a neighbourhood of the unit circle, t = 0, for which the formal expression f(θ,t) is the Taylor series expansion in the t variable. It follows that, after composing with this diffeomorphism, the extension of the metric obtained by reflecting in the line t = 0 is smooth.
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The Jacobson radical of a ring has numerous internal characterizations, including a few definitions that successfully extend the notion to rings without unity. The radical of a module extends the definition of the Jacobson radical to include modules. The Jacobson radical plays a prominent role in many ring and module theoretic results, such as Nakayama's lemma.
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This theorem is equivalent to Urysohn's lemma (which is also equivalent to the normality of the space) and is widely applicable, since all metric spaces and all compact Hausdorff spaces are normal. It can be generalized by replacing R with RJ for some indexing set J, any retract of RJ, or any normal absolute retract whatsoever.
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For example, the coordinate vectors , , to , form a basis of , called the standard basis, since any vector can be uniquely expressed as a linear combination of these vectors: :. The corresponding coordinates , , , are just the Cartesian coordinates of the vector. Every vector space has a basis. This follows from Zorn's lemma, an equivalent formulation of the Axiom of Choice.
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Harley, T. (2005) The Psychology of Language. Hove; New York: Psychology Press: 359 Some recent work has challenged this model, suggesting for example that there is no lemma stage, and that syntactic information is retrieved in the semantic and phonological stages.Caramazza, A. (1997) How many levels of processing are there in lexical access? Cognitive Neuropsychology, 14, 177-208.
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Vladimir Andreevich Yakubovich (October 21, 1926 in Novosibirsk - August 17, 2012 in the Gdov region) was a notable Russian control theorist and head of the Department of Theoretical Cybernetics at Saint Petersburg State University (formerly Leningrad University). In 1996 he received the IEEE Control Systems Award for his contributions to control theory, including the Kalman–Yakubovich–Popov lemma.
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Then Nakayama's lemma says that M has a minimal generating set whose cardinality is \dim_k M / mM = \dim_k M \otimes_R k. If M is flat, then this minimal generating set is linearly independent (so M is free). See also: minimal resolution. A more refined information is obtained if one considers the relations between the generators; cf.
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Spikelets are oblong, solitary, long, and carry pedicelled fertile spikelets whose florets have a diminished apex. The glumes are chartaceous, lanceolate and keelless. Their size and apexes are different though; the upper one is obovate and is long with an obtuse apex, while the lower one has an acute apex. Fertile lemma is chartaceous, lanceolate, keelless, and is long.
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Spikelets are oblong and solitary with pedicelled fertile spikelets that carry 3–5 fertile florets. The glumes are chartaceous and keelless, have acute apexes, with only difference is in size. The upper one is lanceolate and is long while the other one is linear and is . Fertile lemma is long and are elliptic, coriaceous and keelless.
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Spikelets are elliptic, solitary, long, and carry fertile ones which have 2–3 fertile florets that are diminished at the apex. The glumes are chartaceous, lanceolate, keelless, with acuminate apexes, with only difference is in size. The upper one is long while the other one is long. Fertile lemma is long and is also chartaceous, ovate and keelless.
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The forking lemma is any of a number of related lemmas in cryptography research. The lemma states that if an adversary (typically a probabilistic Turing machine), on inputs drawn from some distribution, produces an output that has some property with non-negligible probability, then with non- negligible probability, if the adversary is re-run on new inputs but with the same random tape, its second output will also have the property. This concept was first used by David Pointcheval and Jacques Stern in "Security proofs for signature schemes," published in the proceedings of Eurocrypt 1996.Ernest Brickell, David Pointcheval, Serge Vaudenay, and Moti Yung, "Design Validations for Discrete Logarithm Based Signature Schemes", Third International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2000, Melbourne, Australia, January 18-20, 2000, pp. 276-292.
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As with HAT4 each editor assumed special responsibility for particular aspects of the dictionary as a whole: expanding the etymologies, improving the lemma layout, expanding the abbreviations and moving them to a special section at the back of the book, adding a section of geographical names with their derivatives, refining the labels further, sourcing additional suitable citations, and compiling a complete usage guide for the front matter. In addition more “foreign” yet common words were included and, with circumspection, words from varieties other than standard Afrikaans. HAT5 is the first edition of which the lemma selection was based on a representative, comprehensive and balanced electronic corpus. Odendal would have retired from the editorial team after the completion of the fourth edition of the HAT, but for various reasons stayed on till HAT5 was completed.
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In mathematics, in the theory of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating (or strongly normalizing) abstract rewriting system (ARS), that is, one in which there are no infinite reduction sequences, is confluent if it is locally confluent. In fact a terminating ARS is confluent precisely when it is locally confluent.Franz Baader, Tobias Nipkow, (1998) Term Rewriting and All That, Cambridge University Press Equivalently, for every binary relation with no decreasing infinite chains and satisfying a weak version of the diamond property, there is a unique minimal element in every connected component of the relation considered as a graph. Today, this is seen as a purely combinatorial result based on well-foundedness due to a proof of Gérard Huet in 1980.
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The acyclicity of G is an essential assumption in the Lindström–Gessel–Viennot lemma; it guarantees (in reasonable situations) that the sums e(a, b) are well-defined, and it advects into the proof (if G is not acyclic, then f might transform a self-intersection of a path into an intersection of two distinct paths, which breaks the argument that f is an involution). Nevertheless, Kelli Talaska's 2012 paper establishes a formula generalizing the lemma to arbitrary digraphs. The sums e(a, b) are replaced by formal power series, and the sum over nonintersecting path tuples now becomes a sum over collections of nonintersecting and non-self-intersecting paths and cycles, divided by a sum over collections of nonintersecting cycles. The reader is referred to Talaska's paper for details.
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Their isolation lemma chooses a random number of random hyperplanes, and has the property that, with non-negligible probability, the intersection of any fixed non-empty solution space with the chosen hyperplanes contains exactly one element. This suffices to show the Valiant–Vazirani theorem: there exists a randomized polynomial-time reduction from the satisfiability problem for Boolean formulas to the problem of detecting whether a Boolean formula has a unique solution. introduced an isolation lemma of a slightly different kind: Here every coordinate of the solution space gets assigned a random weight in a certain range of integers, and the property is that, with non-negligible probability, there is exactly one element in the solution space that has minimum weight. This can be used to obtain a randomized parallel algorithm for the maximum matching problem.
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The simplest and most frequently used is the symmetric version given below. A weaker version was proved in 1975 by László Lovász and Paul Erdős in the article Problems and results on 3-chromatic hypergraphs and some related questions. For other versions, see . In 2020, Moser and Gábor Tardos received the Gödel Prize for their algorithmic version of the Lovász Local Lemma.
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This is an infinitesimal version of the fact that the annualized return is less than the average return, with the difference proportional to the variance. See geometric moments of the log-normal distribution for further discussion. The same factor of appears in the d1 and d2 auxiliary variables of the Black–Scholes formula, and can be interpreted as a consequence of Itô's lemma.
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Weyl's lemma follows from more general results concerning the regularity properties of elliptic or hypoelliptic operators.Lars Hörmander, The Analysis of Linear Partial Differential Operators I, 2nd ed., Springer-Verlag (1990), p.110 A linear partial differential operator P with smooth coefficients is hypoelliptic if the singular support of P u is equal to the singular support of u for every distribution u.
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Core models are constructed by transfinite recursion from small fragments of the core model called mice. An important ingredient of the construction is the comparison lemma that allows giving a wellordering of the relevant mice. At the level of strong cardinals and above, one constructs an intermediate countably certified core model Kc, and then, if possible, extracts K from Kc.
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The Complex Morphological Search system developed by us in 2015-2016 allows to perform searches in the Corpus by different combinations of such parameters as word form, lemma, morphological (grammatical) tags set, beginning of the word, middle part, end of the word, and the distance between searched words. The maximum length of the search query is five tokens + accordingly four distances between them.
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A conference honoring James H. Bramble, Texas A&M; University, May 2–3, 2008. He has received honorary doctorate from the Chalmers University of Technology.James H. Bramble , citation for honorary doctorate, Chalmers University of Technology He is known for his fundamental contributions in the development of the finite element methods, including the Bramble–Hilbert lemma,J. H. Bramble and S. R. Hilbert.
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A version of the ring lemma with a weaker bound was first proven by Burton Rodin and Dennis Sullivan as part of their proof of William Thurston's conjecture that circle packings can be used to approximate conformal maps. Lowell Hansen gave a recurrence relation for the tightest possible lower bound, and Dov Aharonov found a closed-form expression for the same bound.
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Proceedings of the Eighth Workshop on Innovative Use of NLP for Building Educational Applications. 2013. Various linguistic feature types have been applied for this task. These include syntactic features such as constituent parses, grammatical dependencies and part-of-speech tags. Surface level lexical features such as character, word and lemma n-grams have also been found to be quite useful for this task.
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In mathematics, cocompact embeddings are embeddings of normed vector spaces possessing a certain property similar to but weaker than compactness. Cocompactness has been in use in mathematical analysis since the 1980s, without being referred to by any name E. Lieb, On the lowest eigenvalue of the Laplacian for the intersection of two domains. Invent. Math. 74 (1983), 441–448.(Lemma 6),V.
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Consider the following commutative diagram in any abelian category (such as the category of abelian groups or the category of vector spaces over a given field) or in the category of groups. image:FiveLemma.png The five lemma states that, if the rows are exact, m and p are isomorphisms, l is an epimorphism, and q is a monomorphism, then n is also an isomorphism.
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There is one requirement for this to be a functor, namely that the derivative of a composite must be the composite of the derivatives. This is exactly the formula . There are also chain rules in stochastic calculus. One of these, Itō's lemma, expresses the composite of an Itō process (or more generally a semimartingale) dXt with a twice-differentiable function f.
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In the Jacobson density theorem, the right -module is simultaneously viewed as a left -module where , in the natural way: . It can be verified that this is indeed a left module structure on .Incidentally it is also a bimodule structure. As noted before, Schur's lemma proves is a division ring if is simple, and so is a vector space over .
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A lemma is a group of lexemes generated by inflectional morphology. Lemmas are represented in dictionaries by headwords which list the citation forms and any irregular forms, since these must be learned to use the words correctly. Lexemes derived from a word by derivational morphology are considered new lemmas. The lexicon is also organized according to open and closed categories.
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The above map to has a section: we can view as the subgroup of that are diagonal with in the upper left corner and on the rest of the diagonal. Therefore is a semi-direct product of with . The unitary group is not abelian for . The center of is the set of scalar matrices with ; this follows from Schur's lemma.
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As stated above, Busch's theorem prevents a free lunch: there can be no information gain without disturbance. However, the tradeoff between information gain and disturbance has been characterized by many authors, including Fuchs and Peres; Fuchs; Fuchs and Jacobs; and Banaszek. Recently the information- gain–disturbance tradeoff relation has been examined in the context of what is called the "gentle-measurement lemma".
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William Buhmann Johnson (born December 5, 1944) is an American mathematician, one of the namesakes of the Johnson–Lindenstrauss lemma. He is Distinguished Professor and A.G. & M.E. Owen Chair of Mathematics at Texas A&M; University. His research specialties include the theory of Banach spaces, nonlinear functional analysis, and probability theory.Faculty directory listing, Texas A&M; Mathematics, retrieved 2013-01-26.
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Thus any 3-SAT instance with m clauses and n variables may be converted into an equisatisfiable one-in-three 3-SAT instance with 5m clauses and n+6m variables.(Schaefer, 1978), p.222, Lemma 3.5 Another reduction involves only four fresh variables and three clauses: R(¬x,a,b) ∧ R(b,y,c) ∧ R(c,d,¬z), see picture (right).
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Suda, Tetralogia The modern form "Diogenes Laertius" is much rarer, used by Stephanus of Byzantium,Stephanus of Byzantium, Druidai and in a lemma to the Greek Anthology.Lemma to Anthologia Palatina, vii. 95 He is also referred to as "Laertes"Eustathius, on Iliad, M. 153 or simply "Diogenes".Stephanus of Byzantium, Enetoi The origin of the name "Laertius" is also uncertain.
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In 1974 the Commander was Major-General Tafessa Lemma. The Kebur Zabagna was disbanded after the Derg consolidated their hold on Ethiopia. The first permanent military band in the country to be established the Imperial Bodyguard Ban in 1929 under the direction of Swiss conductor Andre Nicod. Notable members of the Imperial Bodyguard Band included Tilahun Gessesse and Mahmoud Ahmed.
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By definition, a Hilbert space is separable provided it contains a dense countable subset. Along with Zorn's lemma, this means a Hilbert space is separable if and only if it admits a countable orthonormal basis. All infinite-dimensional separable Hilbert spaces are therefore isometrically isomorphic to . In the past, Hilbert spaces were often required to be separable as part of the definition.
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The Ross–Fahroo methods are founded on the Ross–Fahroo lemma; they can be applied to optimal control problems governed by differential equations, differential-algebraic equations, differential inclusions, and differentially-flat systems. They can also be applied to infinite-horizon optimal control problems by a simple domain transformation technique. The Ross–Fahroo pseudospectral methods also form the foundations for the Bellman pseudospectral method.
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He published solutions to the first and second Cousin problems, and work on domains of holomorphy, in the period 1936-1940\. These were later taken up by Henri Cartan and his school, playing a basic role in the development of sheaf theory. Oka continued to work in the field, and proved Oka's coherence theorem in 1950. Oka's lemma is also named after him.
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The Fitting lemma, named after the mathematician Hans Fitting, is a basic statement in abstract algebra. Suppose M is a module over some ring. If M is indecomposable and has finite length, then every endomorphism of M is either an automorphism or nilpotent. As an immediate consequence, we see that the endomorphism ring of every finite-length indecomposable module is local.
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Blades up to 30 cm long, inrolled or folded. Ligules up to 2mm long, firm with tiny hairs on their margins and backs. Flowering spikelets are broadly ovate to lanceolate, 2–6 flowered, green or purplish, often viviparous. P. constantina and P. fawcettiae can be identified from P. gunnii due to the features of the lemma and the prickliness of the leaves.
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In many languages, words appear in several inflected forms. For example, in English, the verb 'to walk' may appear as 'walk', 'walked', 'walks' or 'walking'. The base form, 'walk', that one might look up in a dictionary, is called the lemma for the word. The association of the base form with a part of speech is often called a lexeme of the word.
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Its peduncle is long while the main branches are appressed and are . It have solitary spikelets which carry one fertile floret and have a pubescent callus. The spikelets themselves are elliptic, are long and carry filiformed pedicels which are long and scabrous as well. The species carry an ovate fertile lemma which is long and is keelless with dentate apex.
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It is also have an acute apex with the fertile lemma itself being chartaceous, elliptic, keelless, and is long. The species also carry 2–3 sterile florets which are barren, cuneate, clumped and are long. Both the upper and lower glumes are oblong, keelless, and are membranous. Their size is different though; lower one is long while the upper one is long.
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Papias set forth his principles in a preface to his dictionary and contributes new features to lexicography. He marks vowel length in the word entry when ambiguous, and notes the gender and declension or conjugation, recognizing that the lemma may be insufficient for grammatical usage.Sharpe, "Vocabulary, Word Formation, and Lexicography," p. 96. He does not, however, distinguish between Classical and Vulgar Latin forms.
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The Schwarz–Ahlfors–Pick theorem provides an analogous theorem for hyperbolic manifolds. De Branges' theorem, formerly known as the Bieberbach Conjecture, is an important extension of the lemma, giving restrictions on the higher derivatives of f at 0 in case f is injective; that is, univalent. The Koebe 1/4 theorem provides a related estimate in the case that f is univalent.
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False smut does not replace all or part of the kernel with a mass of black spores, rather sori form erupting through the palea and lemma forming a ball of mycelia, the outermost layers are spore- producing.Webster, R. K. and Gunnell, P. S. 1992. Compendium of rice diseases. American Phytopathological Society, St. Paul, MN Infected rice kernels are always destroyed by the disease.
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If, for every Weakly Pareto Efficient utility-profile u, the set A(u) is a singleton (i.e, there are no two WPE allocations such that all agents are indifferent between them), then PEEF allocations exist. The proof uses the Knaster–Kuratowski–Mazurkiewicz lemma. Note: The conditions in Theorem 1 and in Theorem 2 are independent - none of them implies the other.
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For example, in the case of , , , composite number 10 divides , but 10 divides neither 4 nor 15. This property is the key in the proof of the fundamental theorem of arithmetic. It is used to define prime elements, a generalization of prime numbers to arbitrary commutative rings. Euclid's Lemma shows that in the integers irreducible elements are also prime elements.
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The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen. It is sometimes known as the Hewitt–Savage law for symmetric events. It is named after Edwin Hewitt and Leonard Jimmie Savage.
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Goursat's lemma for groups can be stated as follows. :Let G, G' be groups, and let H be a subgroup of G\times G' such that the two projections p_1: H\rightarrow G and p_2: H\rightarrow G' are surjective (i.e., H is a subdirect product of G and G'). Let N be the kernel of p_2 and N' the kernel of p_1.
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The inner automorphisms form a normal subgroup of Aut(G), denoted by Inn(G); this is called Goursat's lemma. The other automorphisms are called outer automorphisms. The quotient group is usually denoted by Out(G); the non-trivial elements are the cosets that contain the outer automorphisms. The same definition holds in any unital ring or algebra where a is any invertible element.
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One-dimensional case example In one dimension, Sperner's Lemma can be regarded as a discrete version of the intermediate value theorem. In this case, it essentially says that if a discrete function takes only the values 0 and 1, begins at the value 0 and ends at the value 1, then it must switch values an odd number of times.
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Graham's Hierarchy of Disagreement In reasoning and argument mapping, a counterargument is an objection to an objection. A counterargument can be used to rebut an objection to a premise, a main contention or a lemma. Synonyms of counterargument may include rebuttal, reply, counterstatement, counterreason, comeback and response. The attempt to rebut an argument may involve generating a counterargument or finding a counterexample.
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The condition for a nonzero number mod p to be a quadratic non-residue is to be an odd power of a primitive root. The lemma therefore comes down to saying that i is odd when j is odd, which is true a fortiori, and j is odd when i is odd, which is true because p − 1 is even (p is odd).
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In linguistic morphology, an uninflected word is a word that has no morphological markers (inflection) such as affixes, ablate, consonant gradation, etc., indicating declension or conjugation. If a word has an uninflected form, this is usually the form used as the lemma for the word.Glasgow.com In English and many other languages, uninflected words include prepositions, interjections, and conjunctions, often called invariable words.
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Carpha alpina was first described by Robert Brown after he sailed to Tasmania aboard the Lady Nelson in 1803. It has some resemblance to the grasses of the Rytidosperma genus, however, the flat grey-green or red-green leaves, combined with the lack of lemma and palea on the flowers, and the distinctive stipitate nut; differentiate it from those species.
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Jean-Loup Waldspurger (born 1953) is a French mathematician working on the Langlands program and related areas. He proved Waldspurger's theorem, the Waldspurger formula, and the local Gan–Gross–Prasad conjecture for orthogonal groups. He played a role in the proof of the fundamental lemma, reducing the conjecture to a version for Lie algebras. This formulation was ultimately proven by Ngô Bảo Châu.
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The language of squares is not regular, nor is it context-free, due to the pumping lemma. However, pattern matching with an unbounded number of backreferences, as supported by numerous modern tools, is still context sensitive. Theorem 3 (p.9) The general problem of matching any number of backreferences is NP-complete, growing exponentially by the number of backref groups used.
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The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. It is said that commutative diagrams play the role in category theory that equations play in algebra (see ).
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The Bolzano–Weierstrass theorem is named after mathematicians Bernard Bolzano and Karl Weierstrass. It was actually first proved by Bolzano in 1817 as a lemma in the proof of the intermediate value theorem. Some fifty years later the result was identified as significant in its own right, and proved again by Weierstrass. It has since become an essential theorem of analysis.
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Panicum hillmannii is a perennial grass that resembles the related P. capillare (hairy panic) in habitat and appearance. It is distinguished by slightly stiffer panicles, firmer foliage, the rachilla shortly developed between the upper and lower glumes, the sterile floret which has the palea developed; and larger darker fertile lemma (up to 2mm long) with a prominent crescent-shaped scar at its base.
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The theorem states that given any field F, an algebraic extension field E of F and an isomorphism \phi mapping F onto a field F' then \phi can be extended to an isomorphism \tau mapping E onto an algebraic extension E' of F' (a subfield of the algebraic closure of F'). The proof of the isomorphism extension theorem depends on Zorn's lemma.
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Without loss of generality, suppose . Then by the lemma, the sum of is strictly less than and so is strictly less than , whereas the sum of is clearly at least . This contradicts the fact that and have the same sum, and we can conclude that either or must be empty. Now assume (again without loss of generality) that is empty.
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Lindenstrauss was born into an Israeli-Jewish family with German Jewish origins. He was also born into a mathematical family, the son of the mathematician Joram Lindenstrauss, the namesake of the Johnson–Lindenstrauss lemma, and computer scientist Naomi Lindenstrauss, both professors at the Hebrew University. His sister Ayelet Lindenstrauss is also a mathematician. He attended the Hebrew University Secondary School.
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A heuristic principle known as Bloch's Principle (made precise by Zalcman's lemma) states that properties that imply that an entire function is constant correspond to properties that ensure that a family of holomorphic functions is normal. For example, the first version of Montel's theorem stated above is the analog of Liouville's theorem, while the second version corresponds to Picard's theorem.
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In particular, if the representation is faithful. On the other hand, given a well-understood group acting on a complicated object, this simplifies the study of the object in question. For example, if G is finite, it is known that V above decomposes into irreducible parts. These parts in turn are much more easily manageable than the whole V (via Schur's lemma).
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For any particular E, the probability that x is missed while y is larger than its median is very small, and the Sauer–Shelah lemma (applied to x\cup y) shows that only a small number of distinct events E need to be considered, so by the union bound, with nonzero probability, x is an ε-net. In turn, ε-nets and ε-approximations, and the likelihood that a random sample of large enough cardinality has these properties, have important applications in machine learning, in the area of probably approximately correct learning.. In computational geometry, they have been applied to range searching, derandomization,. and approximation algorithms... use generalizations of the Sauer–Shelah lemma to prove results in graph theory such as that the number of strong orientations of a given graph is sandwiched between its numbers of connected and 2-edge-connected subgraphs.
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Following his doctorate, Lemma returned to his home country, Ethiopia, where he obtained a position at the then Haile Selassie I University. He founded the Institute of Pathobiology, now known as the Aklilu Lemma Institute of Pathobiology, and taught there until 1976, when he left it for a job in the United Nations. He served the UN in many capacities as a scientist, became the Deputy Director of UNICEF's International Child Development Centre, now known as UNICEF's Innocenti Research Centre and finally obtained a position in his alma mater, Johns Hopkins University. He made his most important scientific discovery very early in his career, in 1964, when he discovered a natural treatment to schistosomiasis, also known as snail fever disease or bilharzia, a debilitating disease caused by the parasitic worm Schistosoma, which is spread by freshwater snails.
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A lemma of Brian White shows that the minimum area double bubble must be a surface of revolution. For, if not, it would be possible to find two orthogonal planes that bisect both volumes, replace surfaces in two of the four quadrants by the reflections of the surfaces in the other quadrants, and then smooth the singularities at the reflection planes, reducing the total area. Based on this lemma, Michael Hutchings was able to restrict the possible shapes of non-standard optimal double bubbles, to consist of layers of toroidal tubes.. Additionally, Hutchings showed that the number of toroids in a non-standard but minimizing double bubble could be bounded by a function of the two volumes. In particular, for two equal volumes, the only possible nonstandard double bubble consists of a single central bubble with a single toroid around its equator.
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It follows that → is confluent if and only if is locally confluent. A rewriting system may be locally confluent without being (globally) confluent. Examples are shown in picture 3 and 4. However, Newman's lemma states that if a locally confluent rewriting system has no infinite reduction sequences (in which case it is said to be terminating or strongly normalizing), then it is globally confluent.
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A complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b such that ::a ∨ b = 1 and a ∧ b = 0. In general an element may have more than one complement. However, in a (bounded) distributive lattice every element will have at most one complement.Grätzer (1971), Lemma I.6.1, p. 47.
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The lemma concerns the angles made by consecutive pairs of creases at a single vertex of the crease pattern. It states that if any one of these angles is a local minimum (that is, smaller than the two angles on either side of it), then exactly one of the two creases bounding the angle must be a mountain fold and exactly one must be a valley fold.
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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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In fact, every semiorder is a quasitransitive relation, since it is a transitive one. Moreover, adding to a given semiorder all its pairs of incomparable items keeps the resulting relation a quasitransitive one. Here: Lemma 20, p.27. Since Luce modelled indifference between x and y as "neither xRy nor yRx", while Sen modelled it as "both xRy and yRx", Sen's remark on p.
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Spinrad also pointed out that Moreau published several mathematical papers. In particular introduced Moreau's necklace-counting function, and described a variation of this that he credited to Moreau. pointed out a counterexample to a lemma used by Adrien-Marie Legendre in his attempt to prove Dirichlet's theorem on arithmetic progressions. describes Moreau's analysis of the mathematical game "red and black" invented by Arnous de Rivière.
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Conversely, if S is defined by (1), then xax is an inverse for a, since a(xax)a = axa(xa) = axa = a and (xax)a(xax) = x(axa)(xax) = xa(xax) = x(axa)x = xax.Clifford and Preston 1961 : Lemma 1.14. The set of inverses (in the above sense) of an element a in an arbitrary semigroup S is denoted by V(a).Howie 1995 : p. 52.
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We now describe Schur's lemma as it is usually stated in the context of representations of Lie groups and Lie algebras. There are three parts to the result. Theorem 4.29 First, suppose that V_1 and V_2 are irreducible representations of a Lie group or Lie algebra over any field and that \phi:V_1\rightarrow V_2 is an intertwining map. Then \phi is either zero or an isomorphism.
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Ben is married, but a relationship develops with Kate. He takes her to Yankee Stadium for an old-timers' day ceremony, and eventually, they have an affair. When they part, Kate goes back to Chicago and breaks up with Homer, not knowing what the future holds. The first scene shows Kate Gunzinger in a lecture giving a correct proof of the snake lemma from homological algebra.
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In mathematics, Laplace's principle is a basic theorem in large deviations theory which is similar to Varadhan's lemma. It gives an asymptotic expression for the Lebesgue integral of exp(−θφ(x)) over a fixed set A as θ becomes large. Such expressions can be used, for example, in statistical mechanics to determining the limiting behaviour of a system as the temperature tends to absolute zero.
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Hollis William Frampton, Jr. (March 11, 1936 – March 30, 1984) was an American avant-garde filmmaker, photographer, writer, theoretician, and pioneer of digital art. He was best known for his innovative and non-linear structural films that defined the movement, including Lemon (1969), Zorns Lemma (1970) and (nostalgia) (1971), as well as his anthology book, Circles of Confusion: Film, Photography, Video: Texts, 1968-1980 (1983).
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Papakyriakopoulos is best known for his proofs of Dehn's lemma, the loop theorem, and the sphere theorem, three foundational results for the study of 3-manifolds. In honor of this work, he was awarded the first Oswald Veblen Prize in Geometry in 1964. From the early 1960s on, he mostly worked on the Poincaré conjecture. Bernard Maskit produced counter examples about his proof three times.
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The Zassenhaus lemma gives an isomorphism between certain combinations of quotients and products in the lattice of subgroups. In general, there is no restriction on the shape of the lattice of subgroups, in the sense that every lattice is isomorphic to a sublattice of the subgroup lattice of some group. Furthermore, every finite lattice is isomorphic to a sublattice of the subgroup lattice of some finite group .
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If R is Noetherian, and U is finitely generated, then U is a Noetherian module over R, and the conclusion is satisfied. Somewhat remarkable is that the weaker assumption, namely that U is finitely generated as an R-module (and no finiteness assumption on R), is sufficient to guarantee the conclusion. This is essentially the statement of Nakayama's lemma. Precisely, one has the following.
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Sperner's lemma, from 1928, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes. Abh. Math. Sem. Hamburg VI (1928) 265–272. It was proven by Sperner to provide an alternate proof of a theorem of Lebesgue characterizing dimensionality of Euclidean spaces.
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Géza Fodor Géza Fodor (6 May 1927 in Szeged - 28 September 1977 in Szeged) was a Hungarian mathematician, working in set theory. He proved Fodor's lemma on stationary sets, one of the most important, and most used results in set theory. He was a professor at the Bolyai Institute of Mathematics at the Szeged University. He was vice-president, then president of the Szeged University.
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Copernicus cited his system in the De revolutionibus while discussing theories of the order of the inferior planets. Some historians maintain that the thought of the Maragheh observatory, in particular the mathematical devices known as the Urdi lemma and the Tusi couple, influenced Renaissance-era European astronomy and thus Copernicus.A. I. Sabra (1998). Copernicus used such devices in the same planetary models as found in Arabic sources.
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In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma.
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Zorn's lemma can be used to show that every nontrivial ring R with unity contains a maximal ideal. In the terminology above, the set P consists of all (two-sided) ideals in R except R itself. Since R is non- trivial, the set P contains the trivial ideal {0}, and therefore P is non- empty. This set P is partially ordered by set inclusion.
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Suppose C is any category and A, T are two objects of C. A T-valued point of A is simply an arrow p \colon T \to A. The set of all T-valued points of A varies functorially with T, giving rise to the "functor of points" of A; according to the Yoneda lemma, this completely determines A as an object of C.
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It hairs are long while fertile lemma is being chartaceous, elliptic, keelless, and is long. The glumes are all keelless but are different in size and texture. Lower glume is obovate and is long and 7-9 veined, while the upper one is lanceolate and is long and 5 veined. Lower glume also have an emarginated apex while the upper one have an obtuse one.
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Pigres (), a native of Halicarnassus, either the brother or the son of the celebrated Artemisia, satrap of Caria. He is spoken of by the Suda as the author of the Margites and the Batrachomyomachia.Suda π 1551. The author of the lemma "Pigres", however, makes the mistake of conflating this Artemisia, the advisor of Xerxes in the Histories of Herodotus, with another Artemisia, the wife of Mausolus.
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By the three > subgroups lemma (or equivalently, by the Hall-Witt identity), it follows > that [G, Z2] = G, G], Z2] = [G, G, Z2] = {1}. Therefore, Z2 ⊆ Z1 = Z(G), and > the center of the quotient group G ⁄ Z(G) is the trivial group. As a consequence, all higher centers (that is, higher terms in the upper central series) of a perfect group equal the center.
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The neighbourhood swept out has similar properties to balls in Euclidean space, namely any two points in it are joined by a unique geodesic. This property is called "geodesic convexity" and the coordinates are called "normal coordinates". The explicit calculation of normal coordinates can be accomplished by considering the differential equation satisfied by geodesics. The convexity properties are consequences of Gauss's lemma and its generalisations.
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Yiannis Nicholas Moschovakis (; born January 18, 1938) is a set theorist, descriptive set theorist, and recursion (computability) theorist, at UCLA. His book Descriptive Set Theory (North-Holland) is the primary reference for the subject. He is especially associated with the development of the effective, or lightface, version of descriptive set theory, and he is known for the Moschovakis coding lemma that is named after him.
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Addis Standard is an Ethiopian monthly social, economic and political news magazine published and distributed by Jakenn Publishing Plc, and was established in February 2011. The magazine has an independent political stance. Tsedale Lemma was the editor-in-chief of the magazine which is headquartered in Addis Ababa. The magazines is distributed in Ghana, Burundi and South Sudan in addition to its native country, Ethiopia.
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Consider an anonymous ring R with size n>1. Assume there exists an algorithm "A" to solve leader election in this anonymous ring R. :Lemma: after round k of the admissible execution of A in R, all the processes have the same states. Proof. prove by induction on k. Base case: k=0: all the processes are in the initial state, so all the processes are identical.
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In Euclidean spaces, random projections are elucidated using the Johnson–Lindenstrauss lemma. Johnson, W. and Lindenstrauss, J. (1984) Extensions of Lipschitz mappings into a Hilbert space, in Contemporary Mathematics. American Mathematical Society, vol. 26, pp. 189–206. The TopSig techniqueGeva, S. & De Vries, C.M. (2011) TopSig: Topology Preserving Document Signatures, In Proceedings of Conference on Information and Knowledge Management 2011, 24-28 October 2011, Glasgow, Scotland.
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Plant toxins from Phytolacca are being explored as a means to control zebra mussels.Harold H. Lee, Lemma Aklilu, and Harriett J. Bennett, 1992, The use of Endod (Phytolacca dodecandra) to Control the Zebra Mussels (Dreissena polymorpha), Chapter 37, pp. 643-656, in Zebra Mussels Biology, Impacts, and Control, Thomas F. Nalepa & Don W. Schloesser, Eds., Boca Raton, FL:CRC Press, , see , accessed 5 May 2015.
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A corpus manager (corpus browser or corpus query system) is a tool for multilingual corpus analysis, which allows effective searching in corpora. A corpus manager usually represents a complex tool that allows one to perform searches for language forms or sequences. It may provide information about the context or allow the user to search by positional attributes, such as lemma, tag, etc. These are called concordances.
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Pugh's closing lemma means, for example, that any chaotic set in a bounded continuous dynamical system corresponds to a periodic orbit in a different but closely related dynamical system. As such, an open set of conditions on a bounded continuous dynamical system that rules out periodic behaviour also implies that the system cannot behave chaotically; this is the basis of some autonomous convergence theorems.
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The proportionality factor in the definition of Ross' time constant is dependent upon the magnitude of the disturbance on the plant and the specifications for feedback control. When there are no disturbances, Ross' -lemma shows that the open-loop optimal solution is the same as the closed-loop one. In the presence of disturbances, the proportionality factor can be written in terms of the Lambert W-function.
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Reciprocity is also a basic lemma that is used to prove other theorems about electromagnetic systems, such as the symmetry of the impedance matrix and scattering matrix, symmetries of Green's functions for use in boundary-element and transfer-matrix computational methods, as well as orthogonality properties of harmonic modes in waveguide systems (as an alternative to proving those properties directly from the symmetries of the eigen-operators).
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Shelstad has been a key player in the development of the theory of endoscopy which is part of Langlands program. She co-conjectured the fundamental lemma with Robert Langlands in 1984. After over 20 years, this conjecture was solved by Ngô Bảo Châu in 2009, thus opening up a wealth of consequences. In 1999, Shelstad developed a theory of twisted endoscopy with Robert Kottwitz.
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Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used. Important results of Itô calculus include the integration by parts formula and Itô's lemma, which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms.
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Strategy pair (G, G) risk dominates (H, H) if the product of the deviation losses is highest for (G, G) (Harsanyi and Selten, 1988, Lemma 5.4.4). In other words, if the following inequality holds: . If the inequality is strict then (G, G) strictly risk dominates (H, H).(That is, players have more incentive to deviate). If the game is symmetric, so if A = a, B = b, etc.
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In statistics, Pyrrho's lemma is the result that if one adds just one extra variable as a regressor from a suitable set to a linear regression model, one can get any desired outcome in terms of the coefficients (signs and sizes), as well as predictions, the R-squared, the t-statistics, prediction- and confidence-intervals. The argument for the coefficients was advanced by Herman Wold and Lars JuréenWold, Herman and L. Juréen (1953) Demand Analysis: A Study in Econometrics, John Wiley & Sons (2nd Ed) but named, extended to include the other statistics and explained more fully by Theo Dijkstra. Dijkstra named it after the sceptic philosopher Pyrrho and concludes his article by noting that this lemma provides "some ground for a wide-spread scepticism concerning products of extensive datamining". One can only prove that a model 'works' by testing it on data different from the data that gave it birth.
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In 2013, he was fifth in the Tiberias Marathon, won the Orlen Warsaw Marathon and finished fourth at the Eindhoven Marathon. In 2015, he was fifth at the Dubai Marathon in January in 2:07:06, won the Vienna City Marathon IAAF: Lemma and Neuenschwander take the honours at the Vienna City Marathon. April 12, 2015 in April in 2:07:31 and the Frankfurt Marathon in October where he ran a personal best of 2:06:26.Frankfurt Marathon: Arne Gabius bricht deutschen Rekord mit 2:08:33 Stunden, Äthiopier Sisay Lemma und Gulume Tollesa siegen in Frankfurt October 25, 2015 In 2016 he improved his best to 2:05:16 at the Dubai Marathon where he finished fourth. In 2017 he was third at the Dubai Marathon in January and fourth at the Chicago Marathon in October but did not finish the Boston Marathon in April.
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As p is a unit, its inverse used in a rotation will move p to U[1,1], resulting in a, b, c being all properly placed. The lemma refers to sufficient conditions for the existence of h. One application of cross ratio defines the projective harmonic conjugate of a triple a, b, c, as the element x satisfying (x, a, b, c) = −1. Such a quadruple is a harmonic tetrad.
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It requires a set that contains the union of any chain of subsets to have one chain not contained in any other, called the maximal element. He illustrated the principle with applications in ring theory and field extensions. Zorn's lemma is an alternative expression of the axiom of choice, and thus a subject of interest in axiomatic set theory. In 1936 he moved to UCLA and remained until 1946.
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The magnitude, shape, periodicity and frequency of the TLM will depend on many factors such as the type of light source, the electrical mains-supply frequency, the driver or ballast technologySee root causes of flicker in Fluorescent lamp lemma. and type of light regulation technology applied (e.g. pulse-width modulation). These TLM properties may vary over time due to aging effects, component failure or end-of-life behavior.
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In other words, a relatively complemented lattice is characterized by the property that for every element a in an interval [c, d] there is an element b such that ::a ∨ b = d and a ∧ b = c. Such an element b is called a complement of a relative to the interval. A distributive lattice is complemented if and only if it is bounded and relatively complemented.Grätzer (1971), Lemma I.6.2, p. 48.
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It can be used as part of a linear time algorithm that tests whether a folding pattern with a single vertex can be folded flat, by repeatedly looking for sequences of angles that obey the lemma and pinching them off, until either getting stuck or reducing the input to two equal angles bounded by two creases of the same type as each other., Theorem 12.2.9 and Corollary 12.2.10, p. 207.
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Suppose, to the contrary, there is an integer that has two distinct prime factorizations. Let n be the least such integer and write n = p1 p2 ... pj = q1 q2 ... qk, where each pi and qi is prime. (Note j and k are both at least 2.) We see p1 divides q1 q2 ... qk, so p1 divides some qi by Euclid's lemma. Without loss of generality, say p1 divides q1.
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Nuprl was first released in 1984, and was first described in detail in the book Implementing Mathematics with the Nuprl Proof Development System, published in 1986. Nuprl 2 was the first Unix version. Nuprl 3 provided machine proof for mathematical problems related to Girard's paradox and Higman's lemma. Nuprl 4, the first version developed for the World Wide Web, was used to verify cache coherency protocols and other computer systems.
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Thus this shows that Lmax spans V. Hence Lmax is linearly independent and spans V. It is thus a basis of V, and this proves that every vector space has a basis. This proof relies on Zorn's lemma, which is equivalent to the axiom of choice. Conversely, it has been proved that if every vector space has a basis, then the axiom of choice is true.Blass, Andreas (1984).
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The Ministry of National Defense of Ethiopia is a cabinet-level office in charge of defense related matters of the Federal Democratic Republic of Ethiopia. It oversees the Ethiopian National Defense Force and Ethiopian Defense Industry. The current minister is Lemma Megersa. This institution can trace its origins back to the Ministry of War, which Emperor Menelik II established in 1907, and made Fitawrari Habte Giyorgis Minister over it.
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As of July 2012, the MML included 1150 articles written by 241 authors.The MML Query search engine In aggregate, these contain more than 10,000 formal definitions of mathematical objects and about 52,000 theorems proved on these objects. More than 180 named mathematical facts have so benefited from formal codification. Some examples are the Hahn–Banach theorem, Kőnig's lemma, Brouwer fixed point theorem, Gödel's completeness theorem and Jordan curve theorem.
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Lemma Megersa Wako (; born 26 July 1970) is an Ethiopian politician who served as the Ministry of Defense of Ethiopia 18 April 2019 to 18 August 2020 and was the President of the Oromia regional state of Ethiopia and Deputy Chairman of the ruling party in the region, Oromo Democratic Party. Since the Ethiopian People’s Revolutionary Democratic Front (EPRDF) has been renamed the Prosperity Party, Megersa has been independent.
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There is a relationship between the one-line and the canonical cycle notation. Consider the permutation (\,2\,)(\,3\,1\,), in canonical cycle notation, if we erase its cycle parentheses, we obtain the permutation (2, 3, 1) in one-line notation. Foata's transition lemma establishes the nature of this correspondence as a bijection on the set of n-permutations (to itself). Richard P. Stanley calls this correspondence the fundamental bijection.
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Suppose contrary then there exists an index m such that, for all i ≥ m, Li≠Ri. Let j > m such that qj+n ∈ F therefore qj+n ∈ Rj. By lemma 1, there exist k > j such that Lk = Pr({ qn },w(n,k+n)) = Pr({ qj+n },w(j+n,k+n)) ⊆ Rk. So, Lk=Rk. A contradiction has been derived. Hence, ρ' is an accepting run and w ∈ L(A').
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Radio Lemma (FM 102,7 MHz, since 1996) broadcasts news, radioshows and various Russian and European-American songs. Vladivostok FM (FM 106,4 MHz, was launched in 2008) broadcasts local news and popular music (Top 40). The State broadcasting company "Vladivostok" broadcasts local news and music programs from 7 to 9, from 12 to 14 and from 18 to 19 on weekdays on the frequency of Radio Rossii (Radio of Russia).
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Both of these naturalities follow from the naturality of the sequence provided by the snake lemma. Conversely, the following characterization of derived functors holds: given a family of functors Ri: A → B, satisfying the above, i.e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, Ri(I)=0 for every positive i, then these functors are the right derived functors of R0.
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His work in and on the converse to Lyapunov's criterion is also influential, and contain the well known Massera's lemma. His textbook is also heavily cited. After military intervention in Uruguay in 1973, Massera was arrested on October 22, 1975 in Montevideo and was held in solitary confinement for nearly a year. During this time he was subjected to repeated torture resulting in injuries including a fractured pelvis.
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In 1984 Furst, Saxe, and Sipser showed that calculating the parity of an input cannot be decided by any AC0 circuits, even with non-uniformity. It follows that AC0 is not equal to NC1, because a family of circuits in the latter class can compute parity. More precise bounds follow from switching lemma. Using them, it has been shown that there is an oracle separation between the polynomial hierarchy and PSPACE.
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The system involved both custom software and custom hardware. In the late 1960s the company developed a system called SAM (Semi-Automated Mathematics) for proving mathematical theories without human intervention. A theorem proved by the system, "SAM's lemma", was "widely hailed as the first contribution of automated reasoning systems to mathematics." The SAM series was one of the first interactive theorem provers and had an influence on subsequent theorem provers.
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When the invariant manifolds W^s(f,p) and W^u(f,q), possibly with p=q, intersect but there is no homoclinic/heteroclinic connection, a different structure is formed by the two manifolds, sometimes referred to as the homoclinic/heteroclinic tangle. The figure has a conceptual drawing illustrating their complicated structure. The theoretical result supporting the drawing is the lambda-lemma. Homoclinic tangles are always accompanied by a Smale horseshoe.
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The Schreier–Sims algorithm is an algorithm in computational group theory, named after the mathematicians Otto Schreier and Charles Sims. This algorithm can find the order of a finite permutation group, test membership (is a given permutation contained in a group?), and many other tasks in polynomial time. It was introduced by Sims in 1970, based on Schreier's subgroup lemma. The timing was subsequently improved by Donald Knuth in 1991.
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He introduced the box plot in his 1977 book, "Exploratory Data Analysis". Tukey's range test, the Tukey lambda distribution, Tukey's test of additivity, Tukey's lemma, and the Tukey window all bear his name. He is also the creator of several little-known methods such as the trimean and median- median line, an easier alternative to linear regression. In 1974, he developed, with Jerome H. Friedman, the concept of the projection pursuit.
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In 1962, he was appointed Associate Professor in the Faculty of Science at Gakushuin University, and was promoted in 1966 to the rank of Professor. He became a professor of Theoretical Foundation of Information Science in 1972. After retiring from the University of Tokyo in 1990, he moved to Tokyo Denki University. The Yoneda lemma in category theory and the Yoneda product in homological algebra are named after him.
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At the other extreme, the open unit ball in Cn has a complete Kähler metric with holomorphic sectional curvature equal to −1. (With this metric, the ball is also called complex hyperbolic space.) The holomorphic sectional curvature is closely tied to the properties of X as a complex manifold. For example, every Hermitian manifold X with holomorphic sectional curvature bounded above by a negative constant is Kobayashi hyperbolic.Zheng (2000), Lemma 9.14.
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A smooth real-valued function ρ on a complex manifold is called strictly plurisubharmonic if the real closed (1,1)-form : \omega = \frac i2 \partial \bar\partial \rho is positive, that is, a Kähler form. Here \partial, \bar\partial are the Dolbeault operators. The function ρ is called a Kähler potential for ω. Conversely, by the complex version of the Poincaré lemma, every Kähler metric can locally be described in this way.
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Now one has to check that d is well- defined (i.e., d(x) only depends on x and not on the choice of y), that it is a homomorphism, and that the resulting long sequence is indeed exact. One may routinely verify the exactness by diagram chasing (see the proof of Lemma 9.1 in ). Once that is done, the theorem is proven for abelian groups or modules over a ring.
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In 1951, alongside Lev Kaluznin, he proved the Krasner-Kaloujnine universal embedding theorem, which states that every extension of one group by another is isomorphic to a subgroup of the wreath product. A well-known Krasner's theorem, everywhere known as Krasner's lemma, relies the topological structure and the algebraic structure of vector spaces over local fields. In 1958 he received the Prix Paul Doistau–Émile Blutet of the Académie des Sciences.
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366, Lemma 7.1Jacobson (2009), p. 142 and 147 These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin. The conditions themselves can be stated in an abstract form, so that they make sense for any partially ordered set. This point of view is useful in abstract algebraic dimension theory due to Gabriel and Rentschler.
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If the determinant of A and the inverse of A have already been computed, the matrix determinant lemma allows rapid calculation of the determinant of , where u and v are column vectors. Since the definition of the determinant does not need divisions, a question arises: do fast algorithms exist that do not need divisions? This is especially interesting for matrices over rings. Indeed, algorithms with run- time proportional to n4 exist.
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Zorns Lemma emerged from Word Pictures, a photography project that Frampton made from 1962 to 1963. For Word Pictures, Frampton shot over 2000 black-and-white 35mm photographs of environmental words, seeking to explore the illusions of photography as a medium. However, he had difficulty devising a form in which to present the photographs. During this period, Frampton became less active as a photographer and first started to experiment with filmmaking.
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This article is supplemental for “Convergence of random variables” and provides proofs for selected results. Several results will be established using the portmanteau lemma: A sequence {Xn} converges in distribution to X if and only if any of the following conditions are met: 1. E[f(Xn)] → E[f(X)] for all bounded, continuous functions f; 2. E[f(Xn)] → E[f(X)] for all bounded, Lipschitz functions f; 3.
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In mathematics, Mautner's lemma in representation theory states that if G is a topological group and π a unitary representation of G on a Hilbert space H, then for any x in G, which has conjugates :yxy−1 converging to the identity element e, for a net of elements y, then any vector v of H invariant under all the π(y) is also invariant under π(x).
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While "malakas" is a strictly masculine noun, a female form of the word exists, malako (), but is a recent coinage and not as widely used, whereas malakismeni () seems to be rather more vintage, but also more common, though its meaning is slightly different.Cf. the lemma "μαλάκω" and references for "μαλακισμένη" on slang.gr. Retrieved 2016-01-17. In everyday speech, the word malakas is often used as a synonym of idiot.
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The complex numbers also cannot be turned into an ordered field, as −1 is a square (of the imaginary number i) and would thus be positive. Also, the p-adic numbers cannot be ordered, since according to Hensel's lemma Q2 contains a square root of −7, thus 12+12+12+22+()2=0, and Qp (p > 2) contains a square root of 1−p, thus (p−1)⋅12+()2=0.
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Naturally, if U is a Noetherian module, this holds. If R is Noetherian, and U is finitely generated, then U is a Noetherian module over R, and the conclusion is satisfied. Somewhat remarkable is that the weaker assumption, namely that U is finitely generated as an R-module (and no finiteness assumption on R), is sufficient to guarantee the conclusion. This is essentially the statement of Nakayama's lemma.
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Gromov showed that if the scaling possibility is broken by only considering Riemannian manifolds of a fixed diameter, then a closed manifold admitting such a Riemannian metric with sectional curvatures sufficiently close to zero must be finitely covered by a nilmanifold. The proof works by replaying the proofs of the Bieberbach theorem and Margulis lemma. Gromov's proof was given a careful exposition by Peter Buser and Hermann Karcher.Hermann Karcher.
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A poset is chain-complete if and only if it is a pointed dcpo. However, this equivalence requires the axiom of choice. Zorn's lemma states that, if a poset has an upper bound for every chain, then it has a maximal element. Thus, it applies to chain-complete posets, but is more general in that it allows chains that have upper bounds but do not have least upper bounds.
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Among them was a left thighbone, specimen GSM 109560. In 1859, Owen named the genus Scelidosaurus in an entry about palaeontology in the Encyclopædia Britannica.Owen, R., 1859, "Palaeontology", In: Encyclopædia Britannica Edition 8, Volume 17, p. 150 The lemma text contained a diagnosis, implicating that the genus was validly named and was not a nomen nudum, despite the fact that the definition was vague and no specimens were identified.
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Alexander's Lemma: Up to isotopy, there is a unique (piecewise linear) embedding of the two-sphere into the three-sphere. (In higher dimensions this is known as the Schoenflies theorem. In dimension two this is the Jordan curve theorem.) This may be restated as follows: the genus zero splitting of S^3 is unique. Waldhausen's Theorem: Every splitting of S^3 is obtained by stabilizing the unique splitting of genus zero.
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Suppose now that M is a closed orientable three-manifold. Reidemeister–Singer Theorem: For any pair of splittings H_1 and H_2 in M there is a third splitting H in M which is a stabilization of both. Haken's Lemma: Suppose that S_1 is an essential two-sphere in M and H is a Heegaard splitting. Then there is an essential two-sphere S_2 in M meeting H in a single curve.
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The lemma establishes an important property for solving the problem. By employing an inductive proof, one can arrive at a formula for f(n) in terms of f(n − 1). Proof In the figure the dark lines are connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8). This figure illustrates the inductive step from n = 4 to n = 5 with the dashed lines.
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Foxtail barley is distinguished from cultivated barley (Hordeum vulgare L.) and Meadow barley (Hordeum brachyantherum) by lemma awn length. H. brachyantherum has awn lengths of ; Foxtail barley has lengths of ; and cultivated barley of in length. Once foxtail barley is established, it becomes extremely difficult to eradicate. Its extensive root systems and aggressive habit, as well as its ability to tolerate saline soils make it a resilient competitor.
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One reason for the importance of reductive groups comes from representation theory. Every irreducible representation of a unipotent group is trivial. More generally, for any linear algebraic group G written as an extension :1\to U\to G\to R\to 1 with U unipotent and R reductive, every irreducible representation of G factors through R.Milne (2017), Lemma 19.16. This focuses attention on the representation theory of reductive groups.
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Since the exterior derivative of a closed form is zero, β is not unique, but can be modified by the addition of any closed form of degree one less than that of α. Because , every exact form is necessarily closed. The question of whether every closed form is exact depends on the topology of the domain of interest. On a contractible domain, every closed form is exact by the Poincaré lemma.
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It makes no real sense to ask whether a 0-form (smooth function) is exact, since d increases degree by 1; but the clues from topology suggest that only the zero function should be called "exact". The cohomology classes are identified with locally constant functions. Using contracting homotopies similar to the one used in the proof of the Poincaré lemma, it can be shown that de Rham cohomology is homotopy-invariant.
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American Journal of Mathematics, vol. 55 (1933), pp. 261-267. The main result of the paper on van Kampen diagrams, now known as the van Kampen lemma can be deduced from the Seifert–van Kampen theorem by applying the latter to the presentation complex of a group. However, van Kampen did not notice it at the time and this fact was only made explicit much later (see, e.g.
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However, polynomially convex sets do not behave as nicely as convex sets. Kallin studied conditions under which unions of convex balls are polynomially convex, and found an example of three disjoint cubical cylinders whose union is not polynomially convex.. As part of her work on polynomial convexity, she proved a result now known as Kallin's lemma, giving conditions under which the union of two polynomially convex sets remains itself polynomially convex...
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The lemma can be proven by observing that each vertex in G′ can be incident to at most 2 edges: one from M and one from M′. Graphs where every vertex has degree less than or equal to 2 must consist of either isolated vertices, cycles, and paths. Furthermore, each path and cycle in G′ must alternate between M and M′. In order for a cycle to do this, it must have an equal number of edges from M and M′, and therefore be of even length. Let us now prove the contrapositive of Berge's lemma: G has a matching larger than M if and only if G has an augmenting path. Clearly, an augmenting path P of G can be used to produce a matching M′ that is larger than M — just take M′ to be the symmetric difference of P and M (M′ contains exactly those edges of G that appear in exactly one of P and M). Hence, the reverse direction follows.
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It is not possible for sk to equal s∞ for any finite k: as showed, there exists a constant α such that sk ≤ s∞(1 − α/k). Therefore, if the exponential time hypothesis is true, there must be infinitely many values of k for which sk differs from sk + 1. An important tool in this area is the sparsification lemma of , which shows that, for any ε > 0, any k-CNF formula can be replaced by O(2εn) simpler k-CNF formulas in which each variable appears only a constant number of times, and therefore in which the number of clauses is linear. The sparsification lemma is proven by repeatedly finding large sets of clauses that have a nonempty common intersection in a given formula, and replacing the formula by two simpler formulas, one of which has each of these clauses replaced by their common intersection and the other of which has the intersection removed from each clause.
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The trees within a graph may be partially ordered by their subgraph relation, and any infinite chain in this partial order has an upper bound (the union of the trees in the chain). Zorn's lemma, one of many equivalent statements to the axiom of choice, requires that a partial order in which all chains are upper bounded have a maximal element; in the partial order on the trees of the graph, this maximal element must be a spanning tree. Therefore, if Zorn's lemma is assumed, every infinite connected graph has a spanning tree.. In the other direction, given a family of sets, it is possible to construct an infinite graph such that every spanning tree of the graph corresponds to a choice function of the family of sets. Therefore, if every infinite connected graph has a spanning tree, then the axiom of choice is true.. See in particular Theorem 2.1, pp. 192–193.
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Flower spike Digitaria insularis is a tufted perennial bunchgrass with very short, swollen rhizomes. The stems reach a height of 80–130 cm and are erect, branched from the lower and middle nodes, swollen bases, with woolly bracts, glabrous internodes and nodes. Sheaths papillose - pilose in their majority, ligule 4–6 mm long, blades linear, 20–50 cm long and 10–20 mm wide. Inflorescence 20–35 cm long, numerous clusters, 10–15 cm long, solitary triquetrous rachis of clusters, 0.4-0.7 mm wide, scabrous; spikelets lanceolate, 4.2-4.6 mm long, paired, caudate, densely covered with trichomes up to 6 mm long, brown or whitish, ranging up to 5 mm from the apex of the spikelet; lower glume triangular to ovate, to 0.6 mm long, enervate, membranous; upper glume 3.5-4.5 mm long, acute, 3-5 nerved, ciliated; inferior lemma as long as spikelet, acuminate, 7-nerved, covered with silky hairs, upper lemma 3.2-3.6 mm long, acuminate, dark brown; anthers 1-1.2 mm long.
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One of the theorems proved by Ramsey in his 1928 paper On a Problem of Formal Logic now bears his name (Ramsey's theorem). While this theorem is the work Ramsey is probably best remembered for, he only proved it in passing, as a minor lemma along the way to his true goal in the paper, solving a special case of the decision problem for first-order logic, namely the decidability of what is now called the Bernays–Schönfinkel–Ramsey class of first-order logic, as well as a characterisation of the spectrum of sentences in this fragment of logic. Alonzo Church would go on to show that the general case of the decision problem for first-order logic is unsolvable (see Church's theorem). A great amount of later work in mathematics was fruitfully developed out of the ostensibly minor lemma, which turned out to be an important early result in combinatorics, supporting the idea that within some sufficiently large systems, however disordered, there must be some order.
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All wild wheats are hulled: they have tough glumes (husks) that tightly enclose the grains. Each package of glumes, lemma and palaea, and grain(s) is known as a spikelet. At maturity the rachis (central stalk of the cereal ear) disarticulates, allowing the spikelets to disperse. The first domesticated wheats, einkorn and emmer, were hulled like their wild ancestors, but with rachises that (while not entirely tough) did not disarticulate at maturity.
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A polynomial ring over a field is a unique factorization domain. The same is true for a polynomial ring over a unique factorization domain. To prove this, it suffices to consider the univariate case, as the general case may be deduced by a recurrence on the number of indeterminates. The unique factorization property is a direct consequence of Euclid's lemma: If an irreducible element divides a product, then it divides one of the factors.
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In the field of computational linguistics, a morphological dictionary is a linguistic resource that contains correspondences between surface form and lexical forms of words. Surface forms of words are those found in any text. The corresponding lexical form of a surface form is the lemma followed by grammatical information (for example the part of speech, gender and number). In English give, gives, giving, gave and given are surface forms of the verb give.
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A factorial language L is one where if a word is in L, then all factors of that word are also in L. In combinatorics on words, a common problem is to determine the number A(n) of length-n words in a factorial language. Clearly A(m+n) \leq A(m)A(n), so \log A(n) is subadditive, and hence Fekete's lemma can be used to estimate the growth of A(n).
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This is where word selection would occur, a person would choose which words they wish to express. The next, or middle level, the lemma-stratum, contains information about the syntactic functions of individual words including tense and function. This level functions to maintain syntax and place words correctly into sentence structure that makes sense to the speaker. The lowest and final level is the form stratum which, similarly to the Dell Model, contains syllabic information.
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Hiltgunt Zassenhaus was born in Hamburg to Julius H. and Margret Ziegler Zassenhaus. Her father was a historian and school principal who lost his job when the Nazi regime came to power in 1933. Her brothers were the mathematician Hans (known for the butterfly lemma and the Zassenhaus group), and physicians Günther and Willfried. Following a bicycling holiday in Denmark in 1933, she decided to study philology, specializing in the Scandinavian languages.
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The technique, which culminates in Lemma 7.10 on p.218 of Imrich and Klavžar, consists of applying an algorithm of to list all 4-cycles in the graph G, forming an undirected graph having as its vertices the edges of G and having as its edges the opposite sides of a 4-cycle, and using the connected components of this derived graph to form hypercube coordinates. An equivalent algorithm is , Algorithm H, p. 69.
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In an interview with Robert Gardner he stated a discomfort with that term because it was too broad and didn't accurately reflect the nature of his work. Autumnal Equinox (1974) was shot inside a meat-packing plant, and shot using 30 mm film that contained bovine jelly. His most significant work is arguably Zorns Lemma (1970), a film which drastically altered perceptions towards experimental film at the time. It is formed in three different sections.
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In Zorns Lemma, the concept is reversed. It starts off with a twenty four letter alphabet (I/J and U/V are considered one letter), each letter shown for one second of screentime and then looping. The second cycle replaces each letter with a word that starts with each letter. Gradually the word stills are replaced by an active film shot, such as washing hands or peeling a tangerine until there are only moving images.
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The proof runs as follows: since D is countable, one can enumerate the dense subsets of P as D1, D2, …. By assumption, there exists p ∈ P. Then by density, there exists p1 ≤ p with p1 ∈ D1. Repeating, one gets … ≤ p2 ≤ p1 ≤ p with pi ∈ Di. Then G = { q ∈ P: ∃ i, q ≥ pi} is a D-generic filter. The Rasiowa–Sikorski lemma can be viewed as an equivalent to a weaker form of Martin's axiom.
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The Polish mathematician Jan Mikusinski has made an alternative and more natural formulation of Daniell integration by using the notion of absolutely convergent series. His formulation works for the Bochner integral (the Lebesgue integral for mappings taking values in Banach spaces). Mikusinski's lemma allows one to define the integral without mentioning null sets. He also proved the change of variables theorem for multiple Bochner integrals and Fubini's theorem for Bochner integrals using Daniell integration.
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For example, in Latin, a highly fusional language, the word amo ("I love") is marked by suffix -o for indicative mood, active voice, first person, singular, present tense. Analytic languages tend to have a relatively limited number of markers. Markers should be distinguished from the linguistic concept of markedness. An unmarked form is the basic "neutral" form of a word, typically used as its dictionary lemma, such as—in English—for nouns the singular (e.g.
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In graph theory, Berge's lemma states that a matching M in a graph G is maximum (contains the largest possible number of edges) if and only if there is no augmenting path (a path that starts and ends on free (unmatched) vertices, and alternates between edges in and not in the matching) with M. It was proven by French mathematician Claude Berge in 1957 (though already observed by Petersen in 1891 and Kőnig in 1931).
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Members of the genus grow as tall, wetland grasses, growing to 1–2 m tall; the genus includes both annual and perennial species. Oryza is situated in tribe Oryzeae, which is characterized morphologically by its single-flowered spikelets whose glumes are almost completely suppressed. In Oryza, two sterile lemma simulate glumes. The tribe Oryzeae is in subfamily Ehrhartoideae, a group of Poaceae tribes with certain features of internal leaf anatomy in common.
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That is, it is a product of a generic Yt with an open subset of the t-plane. X, therefore, can be understood if one understands how hyperplane sections are identified across the slits and at the singular points. Away from the singular points, the identification can be described inductively. At the singular points, the Morse lemma implies that there is a choice of coordinate system for X of a particularly simple form.
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While L^p to L^p bounds can be derived immediately from the L^1 to weak L^1 estimate by a clever change of variables, Marcinkiewicz interpolation is a more intuitive approach. Since the Hardy–Littlewood Maximal Function is trivially bounded from L^\infty to L^\infty, strong boundedness for all p>1 follows immediately from the weak (1,1) estimate and interpolation. The weak (1,1) estimate can be obtained from the Vitali covering lemma.
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The English "Pygmalion" comes from the Ancient Greek "Πυγμαλίων" Pugmalíōn. The Greek lemma in turn mostly likely comes from the Phoenician "𐤐𐤏𐤌𐤉𐤕𐤍", transliterated as p‘mytn. Ancient Semitic languages contained a distinct voiced velar fricative (/ɣ/ sound) which was denoted by a letter called Ayin. However, that letter more commonly denoted another phoneme, the voiced pharyngeal fricative (/ʕ/), and over time, the latter pronunciation gradually absorbed /ɣ/ until it was no longer preserved.
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Also in 1907, he described the construction of a new homology sphere. In 1908 he believed that he had found a proof of the Poincaré conjecture, but Tietze found an error. In 1910 Dehn published a paper on three-dimensional topology in which he introduced Dehn surgery and used it to construct homology spheres. He also stated Dehn's lemma, but an error was found in his proof by Hellmuth Kneser in 1929.
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The origin of her name is believed by Robert S. P. Beekes to be Pre-Greek and related to pēnelops (πηνέλοψ) or pēnelōps (πηνέλωψ), glossed by Hesychius as "some kind of bird"Γλῶσσαι. (today arbitrarily identified with the Eurasian wigeon, to which Linnaeus gave the binomial Anas penelope), where -elōps (-έλωψ) is a common Pre-Greek suffix for predatory animals;Zeno.org lemma relating πηνέλωψ (gen. πηνέλοπος) and <χην(ά)λοπες>· ὄρνεα (predators) ποιά.
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In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. Likewise, the mathematical literature sometimes refers to the fundamental lemma of a field.
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The utility of the β function comes from the following result, which is the purpose of the β function in Gödel's incompleteness proof (Gödel 1931). This result is explained in more detail than in Gödel's proof in (Mendelson 1997:186) and (Smith 2013:113-118). : β function lemma. For any sequence of natural numbers (k0, k1, …, kn), there are natural numbers b and c such that, for every i ≤ n, β(b, c, i) = ki.
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Pavel Urysohn Pavel Samuilovich Urysohn () (February 3, 1898 – August 17, 1924) was a Soviet mathematician who is best known for his contributions in dimension theory, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of which are fundamental results in topology. His name is also commemorated in the terms Urysohn universal space, Fréchet–Urysohn space, Menger–Urysohn dimension and Urysohn integral equation. He and Pavel Alexandrov formulated the modern definition of compactness in 1923.
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The part of the spikelet that bears the florets is called the rachilla. A spikelet consists of two (or sometimes fewer) bracts at the base, called glumes, followed by one or more florets. A floret consists of the flower surrounded by two bracts, one external—the lemma—and one internal—the palea. The flowers are usually hermaphroditic—maize being an important exception—and mainly anemophilous or wind-pollinated, although insects occasionally play a role.
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In the case that A or D is singular, substituting a generalized inverse for the inverses on M/A and M/D yields the generalized Schur complement. The Schur complement is named after Issai Schur who used it to prove Schur's lemma, although it had been used previously. Emilie Virginia Haynsworth was the first to call it the Schur complement.Haynsworth, E. V., "On the Schur Complement", Basel Mathematical Notes, #BNB 20, 17 pages, June 1968.
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So c=c(ap+bq)=cap+aeq=a(cp+eq). The unique factorization property results from Euclid's lemma. In the case of integers, this is the fundamental theorem of arithmetic. In the case of , it may be stated as: every non-constant polynomial can be expressed in a unique way as the product of a constant, and one or several irreducible monic polynomials; this decomposition is unique up to the order of the factors.
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In 1961, Zalcman graduated from Southwest High School in Kansas City, Missouri. In the theory of normal families, Zalcman's Lemma, which he used as part of his treatment of Bloch's principle, is named after him. Other eponymous honors are Zalcman domains, which play a role in the classification of Riemann surfaces, and Zalcman functions in complex dynamics. In the theory of partial differential equations, the Pizzetti-Zalcman formula is named after him.
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In mathematics, the Weinstein–Aronszajn identity states that if A and B are matrices of size and respectively (either or both of which may be infinite) then, provided AB is of trace class (and hence, so is BA), :\det(I_m + AB) = \det(I_n + BA), where I_k is the identity matrix. It is closely related to the Matrix determinant lemma and its generalization. It is the determinant analogue of the Woodbury matrix identity for matrix inverses.
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Examples were the Ochsenweg in Schleswig-Holstein which had toll stations at Königsau and Rendsburg, Neumünster, Bramstedt and Ulzburg,Klaus-Joachim Lorenzen-Schmidt, Ortwin Pelc (ed.): Das neue Schleswig-Holstein Lexikon. Wachholtz, Neumünster, 2006, Lemma Zoll. as well as the Gabler Road with the Karlsfried Castle as its toll station. Another form of road tax was Liniengeld, which had to be paid when entering the city of Vienna from the beginning of the 18th century.
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Examples were the Ochsenweg in Schleswig-Holstein which had toll stations at Königsau and Rendsburg, Neumünster, Bramstedt and Ulzburg,Klaus- Joachim Lorenzen-Schmidt, Ortwin Pelc (ed.): Das neue Schleswig-Holstein Lexikon. Wachholtz, Neumünster, 2006, Lemma Zoll. as well as the Gabler Road with the Karlsfried Castle as its toll station. Another form of road tax was Liniengeld, which had to be paid when entering the city of Vienna from the beginning of the 18th century.
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3, 437–443. The Futaki invariant and Mabuchi energy are fundamental in understanding obstructions to the existence of Kähler metrics which are Einstein or which have constant scalar curvature. A year later, by use of the -lemma, Mabuchi considered a natural Riemannian metric on a Kähler class, which allowed him to define length, geodesics, and curvature; the sectional curvature of Mabuchi's metric is nonpositive. Along geodesics in the Kähler class, the Mabuchi energy is convex.
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In mathematics, the Yoneda lemma is arguably the most important result in category theory. It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms). It allows the embedding of any category into a category of functors (contravariant set-valued functors) defined on that category.
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Lemma If there are n points on the circle and add one more point is added, n lines can be drawn from the new point to previously existing points. Two cases are possible. In the first case (a), the new line passes through a point where two or more old lines (between previously existing points) cross. In the second case (b), the new line crosses each of the old lines in a different point.
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Angluin defines a pattern to be "a string of constant symbols from Σ and variable symbols from a disjoint set". The language of such a pattern is the set of all its nonempty ground instances i.e. all strings resulting from consistent replacement of its variable symbols by nonempty strings of constant symbols.The language of a pattern with at least two occurrences of the same variable is not regular due to the pumping lemma.
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In that case, Jensen's covering lemma holds: :For every uncountable set x of ordinals there is a constructible y such that x ⊂ y and y has the same cardinality as x. This deep result is due to Ronald Jensen. Using forcing it is easy to see that the condition that x is uncountable cannot be removed. For example, consider Namba forcing, that preserves \omega_1 and collapses \omega_2 to an ordinal of cofinality \omega.
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The ping- pong argument goes back to late 19th century and is commonly attributed to Felix Klein who used it to study subgroups of Kleinian groups, that is, of discrete groups of isometries of the hyperbolic 3-space or, equivalently Möbius transformations of the Riemann sphere. The ping-pong lemma was a key tool used by Jacques Tits in his 1972 paperJ. Tits. Free subgroups in linear groups. Journal of Algebra, vol. 20 (1972), pp.
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Moreover, the Hahn–Banach theorem implies the Banach–Tarski paradox. For separable Banach spaces, D. K. Brown and S. G. Simpson proved that the Hahn–Banach theorem follows from WKL0, a weak subsystem of second-order arithmetic that takes a form of Kőnig's lemma restricted to binary trees as an axiom. In fact, they prove that under a weak set of assumptions, the two are equivalent, an example of reverse mathematics. Source of citation.
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Spikelets are oblong and solitary with pedicelled fertile spikelets that carry some fertile florets that are diminished at the apex. The glumes are chartaceous, keelless, have acute apexes, with only difference is in size. The upper one is ovate and is long while the other one is lanceolate and have no size what so ever. Fertile lemma is long and is chartaceous, keelless, and oblong as well with either green or purple colouring.
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There are 11 points on the circle sharing a color with a (including a itself), each of which is involved with 2 pairs. This means there are 21 pairs other than (a, b) which include the same color as a, and the same holds true for b. The worst that can happen is that these two sets are disjoint, so we can take d = 42 in the lemma. This gives : e p (d+1) \approx 0.966<1.
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The American National Corpus (ANC) is a text corpus of American English containing 22 million words of written and spoken data produced since 1990. Currently, the ANC includes a range of genres, including emerging genres such as email, tweets, and web data that are not included in earlier corpora such as the British National Corpus. It is annotated for part of speech and lemma, shallow parse, and named entities. The ANC is available from the Linguistic Data Consortium.
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But it is sufficient for the system to be confluent and normalizing for a unique normal to exist for every element, as seen in example 1. Theorem (Newman's Lemma): A terminating ARS is confluent if and only if it is locally confluent. The original 1942 proof of this result by Newman was rather complicated. It wasn't until 1980 that Huet published a much simpler proof exploiting the fact that when \rightarrow is terminating we can apply well-founded induction.
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In many sources the Švarc–Milnor lemma is stated under a slightly more restrictive assumption that the space X be a geodesic metric space (rather that a length space), and most applications concern this context. Sometimes a properly discontinuous cocompact isometric action of a group G on a proper geodesic metric space X is called a geometric action.I. Kapovich, and N. Benakli, Boundaries of hyperbolic groups. Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp.
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Any field has an algebraic closure, which is moreover unique up to (non-unique) isomorphism. It is commonly referred to as the algebraic closure and denoted . For example, the algebraic closure of is called the field of algebraic numbers. The field is usually rather implicit since its construction requires the ultrafilter lemma, a set-theoretic axiom that is weaker than the axiom of choice.. Mathoverflow post In this regard, the algebraic closure of , is exceptionally simple.
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Vinzenz Bronzin (1908) produced very early results, also. Itô's lemma (Kiyosi Itô, 1944) provides the underlying mathematics, and remains fundamental in quantitative finance.) As mentioned, it can be shown that the two models are consistent; then, as is to be expected, "classical" financial economics is thus unified. Here, the Black Scholes equation can alternatively be derived from the CAPM, and the price obtained from the Black–Scholes model is thus consistent with the expected return from the CAPM.
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The result originated in Euclid's Elements, where solids are called equal if the same holds for their faces. This version of the result was proved by Cauchy in 1813 based on earlier work by Lagrange. An error in Cauchy's proof of the main lemma was corrected by Ernst Steinitz, Isaac Jacob Schoenberg, and Aleksandr Danilovich Aleksandrov. The corrected proof of Cauchy is so short and elegant, that it is considered to be one of the Proofs from THE BOOK.
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When pseudospectral methods are applied to discretize optimal control problems, the implications of the Ross–Fahroo lemma appear in the form of the discrete covectors seemingly being discretized by the transpose of the differentiation matrix. When the covector mapping principle is applied, it reveals the proper transformation for the adjoints. Application of the transformation generates the Ross–Fahroo pseudospectral methods.A. M. Hawkins, Constrained Trajectory Optimization of a Soft Lunar Landing From a Parking Orbit, S.M. Thesis, Dept.
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When they reach two and a half years their speech production becomes increasingly complex, particularly in its semantic structure. With a more detailed semantic network the infant learns to express a wider range of meanings, helping the infant develop a complex conceptual system of lemmas. Around the age of four or five the child lemmas have a wide range of diversity, this helps them select the right lemma needed to produce correct speech. Reading to infants enhances their lexicon.
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Much of his work concerns the Geometry of Numbers, Hausdorff Measures, Analytic Sets, Geometry and Topology of Banach Spaces, Selection Theorems and Finite Dimensionsl Convex Geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky-Rogers lemma and the Dvoretzky-Rogers theorem, both with Aryeh Dvoretzky. He constructed a counterexample to a conjecture related to the Busemann–Petty problem. In the geometry of numbers, the Rogers bound is a bound for dense packings of spheres.
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So the Poincaré lemma for 1-forms holds with this additional conditions of compact support. A similar statement is true for 2-forms; but, since there is some choices for the solution, a little more care has to be taken in making those choices. In fact if Ω has compact support on and if furthermore , then with ω a 1-form of compact support on . Indeed, Ω must have support in some smaller rectangle with and .
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This map is closed, continuous (by the pasting lemma), and surjective and therefore is a perfect map (the other condition is trivially satisfied). However, p is not open, for the image of under p is which is not open relative to (the range of p). Note that this map is a quotient map and the quotient operation is 'gluing' two intervals together. 8\. Notice how, to preserve properties such as local connectedness, second countability, local compactness etc.
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As Ethiopia produces more power than it consumes, it has become a regional power exporter. In 2015, it sells electricity to Kenya, Sudan and Djibouti and has future contracts for power sales to Tanzania, Rwanda, South Sudan and Yemen.Ethiopia to Export Renewable Energy, Reuters, Bethelhem Lemma, 14 May 2015 The Eastern African Power Pool will expand transmission lines to make this possible. Exports to Egypt and Sudan are possible after the completion of the Grand Ethiopian Renaissance Dam.
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All foxtails have a hardened tip, sometimes called a "callus", and retrorse barbs, pointing away from the tip of the callus. Wild barleys have clusters of three spikelets, and the callus is the portion of the rachis to which they attach. In other grasses, such as needlegrass and brome grasses, the foxtail consists of a single spikelet, with the callus being the hardened lemma tip. Retrorse barbs can be found on the callus, the lemmas, and the awns.
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For the forward direction, let M′ be a matching in G larger than M. Consider D, the symmetric difference of M and M′. Observe that D consists of paths and even cycles (as observed by the earlier lemma). Since M′ is larger than M, D contains a component that has more edges from M′ than M. Such a component is a path in G that starts and ends with an edge from M′, so it is an augmenting path.
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Adolf Lindenbaum (12 June 1904 – August 1941), was a Polish-Jewish logician and mathematician best known for Lindenbaum's lemma and Lindenbaum algebras. He was born and brought up in Warsaw. He earned a Ph.D. in 1928 under Wacław Sierpiński and habilitated at the University of Warsaw in 1934. He published works on mathematical logic, set theory, cardinal and ordinal arithmetic, the axiom of choice, the continuum hypothesis, theory of functions, measure theory, point-set topology, geometry and real analysis.
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Therefore, the circles 1 and 2 intersect – a contradiction.See also Lemma 3.1 in A highly symmetrical realization of the kissing number 12 in three dimensions is by aligning the centers of outer spheres with vertices of a regular icosahedron. This leaves slightly more than 0.1 of the radius between two nearby spheres. In three dimensions, the kissing number is 12, but the correct value was much more difficult to establish than in dimensions one and two.
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Suppose we create, for each agent, k copies with identical preferences. Let X be an allocation in the original economy. Let Xk be an allocation in the k-replicated economy where all copies of the same agent receive the same bundle as the original agent in X. The allocation X is called sigma-optimal if for every k, the allocation Xk is Pareto-optimal. Lemma: An allocation is sigma-optimal, if-and-only-if it is a competitive equilibrium.
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It is now believed to be an intractable computational problem to find a Brouwer fixed point or equivalently a Sperner coloring, even in the plane, in the general case. The problem is PPAD-complete, a complexity class invented by Christos Papadimitriou. According to the Soviet Mathematical Encyclopaedia (ed. I.M. Vinogradov), a related 1929 theorem (of Knaster, Borsuk and Mazurkiewicz) had also become known as the Sperner lemma – this point is discussed in the English translation (ed.
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The perianth is reduced to two scales, called lodicules, that expand and contract to spread the lemma and palea; these are generally interpreted to be modified sepals. This complex structure can be seen in the image on the right, portraying a wheat (Triticum aestivum) spikelet. The fruit of grasses is a caryopsis, in which the seed coat is fused to the fruit wall. A tiller is a leafy shoot other than the first shoot produced from the seed.
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Egon Sharpe Pearson (11 August 1895 – 12 June 1980) was one of three children and, like his father Karl Pearson, a leading British statistician. He was educated at Winchester College and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal Biometrika. Pearson is best known for development of the Neyman–Pearson lemma of statistical hypothesis testing. He was elected a Fellow of the Econometric Society in 1948.
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Aho(o)i, ahoy and ehoi are rather uncommon in Dutch and are not included in numerous specialist dictionaries. This could be due to the prevalence of the similar and shorter exclamation hoi. The sources for earlier uses of the term are lacking, because ahoi did not get its own lemma in the Woordenboek der Nederlandsche Taal (WNT), even though this comprehensive dictionary includes interjections. In addition later editions of the WNT from recent decades lack this entry.
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To prove the result Lang took two algebraically independent functions from , say, and , and then created an auxiliary function . Using Siegel's lemma, he then showed that one could assume vanished to a high order at the . Thus a high-order derivative of takes a value of small size at one such s, "size" here referring to an algebraic property of a number. Using the maximum modulus principle, Lang also found a separate estimate for absolute values of derivatives of .
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A branch through a tree T is an infinite sequence of elements of X, each of whose finite prefixes belongs to T. The set of all branches through T is denoted [T] and called the body of the tree T. A tree that has no branches is called wellfounded; a tree with at least one branch is illfounded. By Kőnig's lemma, a tree on a finite set with an infinite number of sequences must necessarily be illfounded.
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If S is a stationary set and C is a club set, then their intersection S \cap C is also stationary. This is because if D is any club set, then C \cap D is a club set, thus (S \cap C) \cap D = S \cap (C \cap D) is non empty. Therefore, (S \cap C) must be stationary. See also: Fodor's lemma The restriction to uncountable cofinality is in order to avoid trivialities: Suppose \kappa has countable cofinality.
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The Ethiopian National Defense Force (ENDF) is the military of Ethiopia. Civil direction of the military is carried out through the Ministry of Defense, which oversees the ground forces, air force, as well as the Defense Industry Sector. The current minister of defense is Lemma Megersa. The size of the ENDF has fluctuated significantly since the end of the Ethiopia-Eritrea war in 2000. In 2002 the Ethiopian Defense Forces had a strength of approximately 400,000 troops.
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This is known as the Heine–Borel theorem. Note that compactness depends only on the topology, while boundedness depends on the metric. Lebesgue's number lemma states that for every open cover of a compact metric space M, there exists a "Lebesgue number" \delta such that every subset of M of diameter r<\delta is contained in some member of the cover. Every compact metric space is second countable, and is a continuous image of the Cantor set.
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If the leading terms of fi and fj share no variables in common, then Sij will always reduce to 0 (if we use only fi and fj for reduction), so we needn't calculate it at all. The algorithm terminates because it is consistently increasing the size of the monomial ideal generated by the leading terms of our set F, and Dickson's lemma (or the Hilbert basis theorem) guarantees that any such ascending chain must eventually become constant.
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Let E\supseteq F be a field extension. An element \alpha\in E is separable over if it is algebraic over , and its minimal polynomial is separable (the minimal polynomial of an element is necessarily irreducible). If \alpha,\beta\in E are separable over , then \alpha+\beta, \alpha\beta and 1/\alpha are separable over F. Thus the set of all elements in separable over forms a subfield of , called the separable closure of in .Isaacs, Lemma 19.15, p.
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Director Peter Greenaway has cited the film as an influence on his work, based on its illustration of how to "structure a film without necessarily using narrative". Greenaway's 1973 short film H Is for House presents long lists of words beginning with the letter h, and his later feature films The Draughtsman's Contract and A Zed & Two Noughts feature children reciting abecedaries.Pascoe 1997. Su Friedrich adapted the structure of Zorns Lemma for her 1990 film Sink or Swim.
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In probability theory, the reversed compound agent theorem (RCAT) is a set of sufficient conditions for a stochastic process expressed in any formalism to have a product form stationary distribution (assuming that the process is stationary). The theorem shows that product form solutions in Jackson's theorem, the BCMP theorem and G-networks are based on the same fundamental mechanisms. The theorem identifies a reversed process using Kelly's lemma, from which the stationary distribution can be computed.
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Spikelets on each raceme are in pairs; one spikelet is fertile and sessile, and the other is sterile and pedicelled. Sessile spikelets are 4–6 mm long and contain two florets, one sterile and one fertile; the pair lack a rachilla extension between them. The awn of the upper lemma reaches up to 2 cm. Glumes are unalike; the lower glume is ovate with a ridged, convex surface, and the upper is thinner and boat- shaped.
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Prof George Neville Watson FRS HFRSE LLD (31 January 1886 – 2 February 1965) was an English mathematician, who applied complex analysis to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker's A Course of Modern Analysis (1902) produced the classic "Whittaker and Watson" text. In 1918 he proved a significant result known as Watson's lemma, that has many applications in the theory on the asymptotic behaviour of exponential integrals.
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Hall's second place was the first time that an American had finished in the top three of the London Marathon since 2006, when Deena Kastor won the race. Natasha Cockram won the prize for best British finisher, although she was outside the Olympic qualifying time. After the race, Kosgei called the 2020 London Marathon course "mundane". In the men's race, Shura Kitata won a sprint finish with Vincent Kipchumba and Sisay Lemma, who finished second and third respectively.
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In additive combinatorics, the Ruzsa triangle inequality, also known as the Ruzsa difference triangle inequality to differentiate it from some of its variants, bounds the size of the difference of two sets in terms of the sizes of both their differences with a third set. It was proven by Imre Ruzsa (1996), and is so named for its resemblance to the triangle inequality. It is an important lemma in the proof of the Plünnecke-Ruzsa inequality.
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Illustration of the squeeze theorem When a sequence lies between two other converging sequences with the same limit, it also converges to this limit. In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, the police theorem and sometimes the squeeze lemma, is a theorem regarding the limit of a function. In Italy, the theorem is also known as theorem of carabinieri. The squeeze theorem is used in calculus and mathematical analysis.
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The Valiant–Vazirani theorem is a theorem in computational complexity theory. It was proven by Leslie Valiant and Vijay Vazirani in their paper titled NP is as easy as detecting unique solutions published in 1986. The theorem states that if there is a polynomial time algorithm for Unambiguous-SAT, then NP=RP. The proof is based on the Mulmuley–Vazirani isolation lemma, which was subsequently used for a number of important applications in theoretical computer science.
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He found that berries from the endod plant, which is commonly used to make soap and shampoos in many parts of Africa, is a potent, inexpensive and safe molluscicide, to prevent the spread of the parasitic worm. This discovery made the plant an object of scientific research in many parts of the world. Lemma himself was at the forefront of this research. His work acquired an international reputation, which in turn led to various awards, including honorary doctorate degrees.
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Otto Albin Frostman (3 January 1907 - 29 December 1977) was a Swedish mathematician, known for his work in potential theory and complex analysis. Frostman earned his Ph.D. in 1935 at Lund University under the Hungarian-born mathematician Marcel Riesz, the younger brother of F. Riesz. In potential theory, Frostman's lemma is named after him. He supervised the 1971 Stockholm University Ph.D. thesis of Bernt Lindström, which initiated the "Stockholm School" of topological combinatorics (combining simplicial homology and enumerative combinatorics).
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At least one Finnish verb lacks the first infinitive (dictionary/lemma) form. In Finnish, "kutian helposti" ("I'm sensitive to tickling") can be said, but for the verb "kutian" (here conjugated in singular first person, present tense) there is no non-conjugated form. Hypothetically, the first infinitive could be "kudita", but this form is not actually used. Additionally, the negative verb (ei, et, en, emme...) has neither an infinitive form nor a 1st person singular imperative form.
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R is a GCD domain if and only if finite intersections of its principal ideals are principal. In particular, (a) \cap (b) = (c), where c is the LCM of a and b. For a polynomial in X over a GCD domain, one can define its content as the GCD of all its coefficients. Then the content of a product of polynomials is the product of their contents, as expressed by Gauss's lemma, which is valid over GCD domains.
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The same year, the Smith School launched the Lemma Senbet Fund student-run investment management fund for undergraduate Finance students starting with an initial capital infusion of $50,000. In 2009, Smith added another Master of Science (MS) business degree with a concentration in Finance. In the 2000s, most major universities began to add web-based ("online") courses to their curriculum. In 2013, the Smith School created its first online degree program, which culminates in an MBA.
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1410–1413, August 2004 The Ross–Fahroo lemma and the Ross–Fahroo pseudospectral method are named after her. In 2010, she received (jointly with Ross), the AIAA Mechanics and Control of Flight Award for fundamental contributions to flight mechanics. In 2019, she was named a Fellow of the Society for Industrial and Applied Mathematics "for outstanding scientific leadership while managing AFOSR and DARPA programs in dynamics and control and computational mathematics and fundamental research accomplishments in computational optimal control".
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In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that a smooth mapping f\colon M \rightarrow N where M and N are smooth manifolds such that f is # a surjective submersion, and # a proper map, (in particular, this condition is always satisfied if M is compact), is a locally trivial fibration. This is a foundational result in differential topology, and exists in many further variants. It is due to Charles Ehresmann.
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Evidently both relations are reflexive and symmetric. Moreover, if x and y are contained in a connected (respectively, path connected) subset A and y and z are connected in a connected (respectively, path connected) subset B, then the Lemma implies that A \cup B is a connected (respectively, path connected) subset containing x, y and z. Thus each relation is an equivalence relation, and defines a partition of X into equivalence classes. We consider these two partitions in turn.
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See Lemma 12 of Richard W. Hamming invented Hamming codes in 1950 as a way of automatically correcting errors introduced by punched card readers. In his original paper, Hamming elaborated his general idea, but specifically focused on the Hamming(7,4) code which adds three parity bits to four bits of data. In mathematical terms, Hamming codes are a class of binary linear codes. For each integer there is a code with block length and message length .
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Lemma- Let H be a subgraph of G formed by including each edge of G independently with probability p and let F be the minimum spanning forest of H. The expected number of F-light edges in G is at most n/p where n is the number of vertices in G To prove the lemma examine the edges of G as they are being added to H. The number of F-light edges in G is independent of the order in which the edges of H are selected since the minimum spanning forest of H is the same for all selection orders. For the sake of the proof consider selecting edges for H by taking the edges of G one at a time in order of edge weight from lightest to heaviest. Let e be the current edge being considered. If the endpoints of e are in two disconnected components of H then e is the lightest edge connecting those components and if it is added to H it will be in F by the cut property.
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In mathematics, the Schreier refinement theorem of group theory states that any two subnormal series of subgroups of a given group have equivalent refinements, where two series are equivalent if there is a bijection between their factor groups that sends each factor group to an isomorphic one. The theorem is named after the Austrian mathematician Otto Schreier who proved it in 1928. It provides an elegant proof of the Jordan–Hölder theorem. It is often proved using the Zassenhaus lemma.
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So the Lemma is proven. Now if D_n is refutable for some n, it follows that φ is refutable. On the other hand, suppose that D_n is not refutable for any n. Then for each n there is some way of assigning truth values to the distinct subpropositions E_h (ordered by their first appearance in D_n; "distinct" here means either distinct predicates, or distinct bound variables) in B_k , such that D_n will be true when each proposition is evaluated in this fashion.
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We will prove that the algorithm never computes incorrect shortest path lengths. : Lemma: Whenever the queue is checked for emptiness, any vertex currently capable of causing relaxation is in the queue. : Proof: We want to show that if dist[w] > dist[u]+wt(u,w) for any two vertices u and w at the time the condition is checked,u is in the queue. We do so by induction on the number of iterations of the loop that have already occurred.
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The important fact is: In Mumford's red book, the theorem is proved by means of Noether's normalization lemma. For an algebraic approach where the generic freeness plays a main role and the notion of "universally catenary ring" is a key in the proof, see Eisenbud, Ch. 14 of "Commutative algebra with a view toward algebraic geometry." In fact, the proof there shows that if f is flat, then the dimension equality in 2. of the theorem holds in general (not just generically).
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A paper of George Lusztig and David Kazhdan pointed out that orbital integrals could be interpreted as counting points on certain algebraic varieties over finite fields. Further, the integrals in question can be computed in a way that depends only on the residue field of F; and the issue can be reduced to the Lie algebra version of the orbital integrals. Then the problem was restated in terms of the Springer fiber of algebraic groups.The Fundamental Lemma for Unitary Groups , at p. 12.
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The expander mixing lemma can be used to upper bound the size of an independent set within a graph. In particular, the size of an independent set in an (n, d, \lambda)-graph is at most \lambda n/d. This is proved by letting T=S in the statement above and using the fact that e(S,S)=0. An additional consequence is that, if G is an (n, d, \lambda)-graph, then its chromatic number \chi(G) is at least d/\lambda.
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Tip of the tongue (TOT) studies refer to studies when higher order characteristics of words such as the meaning, concept, or its syntactic category are retrieved from memory. These characteristics are called the lexeme of a word. Tip of tongue studies have shown that a word’s lemma may be responsible for eliciting a taste sensation, not its phonologic sound or spelling. Further TOT studies determined the possibility that during TOT states, lexemes could be partially activated to yield phoneme-triggered tastes.
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The spikelets have 1-2 fertile florets which are diminished at the apex while the sterile florets are barren, cuneate, and clumped with both its rhachilla and its floret callus being pubescent. Both the upper and lower glumes are keelless, membranous and are of the same size as spikelets. Their other features are different; Lower glume is elliptic with an acute apex while the upper one is lanceolate, and have obtuse apex. The species' lemma have ciliated and hairy margins with obtuse apex.
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If G is a regular graph of degree d whose edge connectivity is at least d − 1, and G has an even number of vertices, then it has a perfect matching. More strongly, every edge of G belongs to at least one perfect matching. The condition on the number of vertices can be omitted from this result when the degree is odd, because in that case (by the handshaking lemma) the number of vertices is always even., Theorem 4, p. 285.
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The theorem is a direct corollary of the following lemma: Suppose that the nth ray makes an angle \gamma_n with the normal to the baseline. If \gamma_n is parameterized according to the equation, \tan \gamma_n = \sinh\theta_n, then values of \theta_n = a + nb, where a and b are real constants, define a sequence of rays that satisfy the condition of equal incircles, and furthermore any sequence of rays satisfying the condition can be produced by suitable choice of the constants a and b.
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At this time, Copernicus anticipated that he could reconcile the motion of the Earth with the perceived motions of the planets easily, with fewer motions than were necessary in the Alfonsine Tables, the version of the Ptolemaic system current at the time. In particular, the heliocentric Copernican model made use of the Urdi Lemma developed in the 13th century by Mu'ayyad al-Din al-'Urdi, the first of the Maragha astronomers to develop a non-Ptolemaic model of planetary motion.Saliba (1979).
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Danielson collaborated with Cornelius Lanczos to write the paper, Some Improvements in Practical Fourier Analysis and their Application to X-ray Scattering from Liquids (1942). The Danielson-Lanczos lemma, which appears in this paper, is the basis of the Cooley–Tukey FFT algorithm, an efficient algorithm for computing the discrete Fourier transform.Danielson, G. C., and C. Lanczos, "Some improvements in practical Fourier analysis and their application to X-ray scattering from liquids," J. Franklin Inst. 233, 365–380 and 435–452 (1942).
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Howard Eves: "An Introduction to the History of Mathematics", page 405, Saunders College Publishing, 1990. () ;Hironaka's example : Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds discovered by Heisuke Hironaka. ;Itô calculus : Developed by Kiyosi Itô throughout the 20th century, Itô calculus extends calculus to stochastic processes such as Brownian motion (Wiener process). Its basic concept is the Itô integral, and among the most important results is a change of variable formula known as Itô's lemma.
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Muco- inositol is typically phosphorylated (becoming muco-inositol phosphate) in the process of being attached to a lipid of the outer lemma of the sensory neurons of taste. The final chemical is phosphatidyl muco-inositol (PtdIns). PtdIns occurs in a specialized area of the cilia of the sensory neurons where it exists in a liquid crystalline form. In this form, it is the sensory receptor of the sensory neuron forming the initial element of the sodium ion sensitive channel of gustation.
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It is modeled by an infinite ray, but violates Euler's handshaking lemma for finite graphs. However, it follows from the negative solution to the Entscheidungsproblem (by Alonzo Church and Alan Turing in the 1930s) that satisfiability of first-order sentences for graphs that are not constrained to be finite remains undecidable. It is also undecidable to distinguish between the first-order sentences that are true for all graphs and the ones that are true of finite graphs but false for some infinite graphs.
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Also it follows that if two subsets A and B are separated by a function then A and B are separated by neighbourhoods. A normal space is a topological space in which any two disjoint closed sets can be separated by neighbourhoods. Urysohn's lemma states that a topological space is normal if and only if any two disjoint closed sets can be separated by a continuous function. The sets A and B need not be precisely separated by f, i.e.
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As for the Wadge lemma, this holds for any pointclass Γ, assuming the axiom of determinacy. If we associate with each set A the collection of all sets strictly below A on the Wadge hierarchy, this forms a pointclass. Equivalently, for each ordinal α ≤ θ the collection Wα of sets that show up before stage α is a pointclass. Conversely, every pointclass is equal to some Wα. A pointclass is said to be self-dual if it is closed under complementation.
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Diophantus himself refers to a work which consists of a collection of lemmas called The Porisms (or Porismata), but this book is entirely lost. Although The Porisms is lost, we know three lemmas contained there, since Diophantus refers to them in the Arithmetica. One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i.e. given any and , with , there exist , all positive and rational, such that :.
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The difference may seem subtle, but in many proofs that invoke Zorn's lemma one takes unions of some sort to produce an upper bound, and so the case of the empty chain may be overlooked; that is, the verification that all chains have upper bounds may have to deal with empty and non-empty chains separately. So many authors prefer to verify the non-emptiness of the set P rather than deal with the empty chain in the general argument.
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The original proof of the irrationality of the non-square natural numbers depends on Euclid's lemma. Many proofs of the irrationality of the square roots of non-square natural numbers implicitly assume the fundamental theorem of arithmetic, which was first proven by Carl Friedrich Gauss in his Disquisitiones Arithmeticae. This asserts that every integer has a unique factorization into primes. For any rational non-integer in lowest terms there must be a prime in the denominator which does not divide into the numerator.
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Many important logical ideas are explained in the book. For example, the difference between a counterexample to a lemma (a so-called 'local counterexample') and a counterexample to the specific conjecture under attack (a 'global counterexample' to the Euler characteristic, in this case) is discussed. Lakatos argues for a different kind of textbook, one that uses heuristic style. To the critics that say such a textbook would be too long, he replies: 'The answer to this pedestrian argument is: let us try.
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He goes on and gives further stages that might sometimes take place: 5. Proofs of other theorems are examined to see if the newly found lemma or the new proof-generated concept occurs in them: this concept may be found lying at cross-roads of different proofs, and thus emerge as of basic importance. 6. The hitherto accepted consequences of the original and now refuted conjecture are checked. 7. Counterexamples are turned into new examples - new fields of inquiry open up.
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Finsler's lemma can be used to give novel linear matrix inequality (LMI) characterizations to stability and control problems. The set of LMIs stemmed from this procedure yields less conservative results when applied to control problems where the system matrices has dependence on a parameter, such as robust control problems and control of linear-parameter varying systems. This approach has recently been called as S-variable approach and the LMIs stemming from this approach are known as SV-LMIs (also known as dilated LMIs).
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The Chernoff bound states that, when sampling many independent samples from a random variables in the range [−1, 1], with high probability the average of our samples is close to the expectation of the random variable. The expander walk sampling lemma, due to and , states that this also holds true when sampling from a walk on an expander graph. This is particularly useful in the theory of derandomization, since sampling according to an expander walk uses many fewer random bits than sampling independently.
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Vazirani's research career has been centered around the design of algorithms, together with work on computational complexity theory, cryptography, and algorithmic game theory. During the 1980s, he made seminal contributions to the classical maximum matching problem,Three of his papers on the subject from that time period have over 100 citations each, according to Google scholar: ; ; . and some key contributions to computational complexity theory, e.g., the isolation lemma, the Valiant-Vazirani theorem, and the equivalence between random generation and approximate counting.. See ; .
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If F(X) is a modal formula with only one propositional variable X, then a modal fixed point of F(X) is a sentence \Psi such that :\vdash \Psi \leftrightarrow F(\Box \Psi) We will assume the existence of such fixed points for every modal formula with one free variable. This is of course not an obvious thing to assume, but if we interpret \Box as provability in Peano Arithmetic, then the existence of modal fixed points follows from the diagonal lemma.
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The function giving the sum of a convergent series is linear, and it follows from the Hahn–Banach theorem that it may be extended to a summation method summing any series with bounded partial sums. This is called the Banach limit. This fact is not very useful in practice, since there are many such extensions, inconsistent with each other, and also since proving such operators exist requires invoking the axiom of choice or its equivalents, such as Zorn's lemma. They are therefore nonconstructive.
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The opening section of Zorns Lemma is 5 minutes long. In it a woman reads an abecedary of 24 couplets from The Bay State Primer, an eighteenth century book designed to teach children the alphabet. The film is entirely black during this section. A letter A stamped on tin foil, the first of 24 such letters shown at the beginning of the second section The film's main section is silent and lasts 45 minutes, broken into 2,700 one-second units.
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Ethiopian Degitu Azimeraw was scheduled to race, but withdrew after testing positive for COVID-19. The men's race featured Eliud Kipchoge, Mosinet Geremew, Mule Wasihun, Sisay Lemma, and Tamirat Tola, all of whom have personal best times under 2:05. Sondre Nordstad Moen, who broke the European one hour run record earlier in 2020, also competed. Briton Sir Mo Farah, who in September 2020 set the men's world record for the one hour run, acted as a pacemaker for the men's race.
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It is well known that a nonzero nonunit in a Noetherian integral domain factors into irreducibles. The proof of this relies on only (ACCP) not (ACC), so in any integral domain with (ACCP), an irreducible factorization exists. (In other words, any integral domains with (ACCP) are atomic. But the converse is false, as shown in .) Such a factorization may not be unique; the usual way to establish uniqueness of factorizations uses Euclid's lemma, which requires factors to be prime rather than just irreducible.
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Euclidean division is based on the following result, which is sometimes called Euclid's division lemma. Given two integers and , with , there exist unique integers and such that : and :, where denotes the absolute value of . In the above theorem, each of the four integers has a name of its own: is called the , is called the , is called the and is called the . The computation of the quotient and the remainder from the dividend and the divisor is called or — in case of ambiguity — .
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Now the switching lemma guarantees that after setting some variables randomly, we end up with a Boolean function that depends only on few variables, i.e., it can be computed by a decision tree of some small depth d. This allows us to write the restricted function as a small formula in disjunctive normal form. A formula in conjunctive normal form hit by a random restriction of the variables can therefore be "switched" to a small formula in disjunctive normal form.
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During these years he did research on the mathematics of finance theory and actuarial science as well as the probability theory for which he became famous. Cantelli's later work was all on probability and it is in this field where his name graces the Borel-Cantelli lemma and the Glivenko–Cantelli theorem. In 1916–1917 he contributed to the theory of stochastic convergence. In 1923 he resigned his actuarial position when he was appointed professor of actuarial mathematics at the University of Catania.
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Stephen R. Hilbert is an American mathematician best known as co-author of the Bramble–Hilbert lemma, which he published with James H. Bramble in 1970. Hilbert's area of specialty is numerical analysis. He has been a professor of mathematics at Ithaca College since 1968.An Introduction to Sobolev Spaces and Interpolation Spaces, Lecture Notes of the Unione Matematica Italiana, 2007, Volume 3, 53–57, Additionally, he taught mathematics at Cornell University as a visiting program professor during the 2003–2004 academic year.
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Noether's normalisation lemma is a theorem in commutative algebra. Given a field K and a finitely generated K-algebra A, the theorem says it is possible to find elements y1, y2, ..., ym in A that are algebraically independent over K such that A is finite (and hence integral) over B = K[y1,..., ym]. Thus the extension K ⊂ A can be written as a composite K ⊂ B ⊂ A where K ⊂ B is a purely transcendental extension and B ⊂ A is finite.Chapter 4 of Reid.
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Translation software between multiple languages usually apply bidirectional dictionaries. An MRD may be a dictionary with a proprietary structure that is queried by dedicated software (for example online via internet) or it can be a dictionary that has an open structure and is available for loading in computer databases and thus can be used via various software applications. Conventional dictionaries contain a lemma with various descriptions. A machine-readable dictionary may have additional capabilities and is therefore sometimes called a smart dictionary.
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Flag of Sardinia. It is similar to the traditional flag of Corsica. Location of Sardinia Sardinian nationalism or also Sardism (Sardismu in Sardinian, Sardismo in ItalianSardismo, lemma, Garzanti Linguistica.) is a social, cultural and political movement in Sardinia calling for the self-determination of the Sardinian people in a context of national devolution, further autonomy in Italy, or even outright independence from the latter. It also promotes the protection of the island's environment and the preservation of its cultural heritage.
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He joined The Black Soul Band while they were on tour in Addis Ababa in 1973. Alemayehu Eshete and Slim Jones were the main singers of the group and together with Tesfaye Lemma of Orchestra Ethiopia, they traveled to various parts of Ethiopia. Towards mid-1974, Woldemariam and some other members of Black Soul Band joined the Venus Club. After working for a year or so at the Venus Club, Woldemariam replaced Zimbabwean Ibex Band guitar player Andrew Wilson at the Ras Hotel.
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Compared to lemma-based keyword grouping, SERP-based keyword clustering produces groups of keywords that might reveal no morphological matches, but will have matches in the search results. It allows search engine professionals getting a keyword structure close to what a search engine dictates. Soft and Hard type of keyword clustering and the general algorithm was introduced by the Russian SEO expert Alexey Chekushin in 2015. In the same year, he developed and introduced the automated tool that could cluster keywords.
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The long-term performance goal of the Lemma Senbet Fund is to outpace appreciation of the S&P; 500 Index on a risk- adjusted basis. Historically, the fund has adopted a top-down investment approach that is driven by Economic indicators, then Industry trends, and finally individual Company performance (EIC). Most asset instruments are long equity positions. Specific stock selections are based on a combination of fundamental analysis and technical analysis valuation techniques under the Growth at a Reasonable Price (GARP) model.
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He wrote a number of articles about the use of electricity for the 1911 edition of Encyclopædia Britannica for example the lemma on Electric lighting, and on the Telephone. He was also a keen publisher of electrical books, some of which were published as the “Manuals” series, such as Garcke's Manual of Electricity Supply, even after his death. In London Garcke was the City's expert on electrical applications, and chaired the Electrical Committee of the London Chamber of Commerce.Raphael Schapiro.
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Zurich, copy-left, 1997-2004. Another ongoing project is his subjective encyclopedia, a collection of comments, images and everyday poetry, each entry assigned to a distinct lemma. About 500 (of more than 1000) lemmata are available on a website. Stirnemann was awarded grants and distinctions from many different institutions, among them the Swiss Federal State, the canton and the city of Zurich, the canton Aargau, Pro Helvetia, the Cassinelli-Vogel-Stiftung, the Canada Council, and the Stanley Thomas Johnson Foundation.
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Then there exists a global coloring of all of with the property that every finite set has a finite superset on which and agree. In particular, if we choose a -coloring for every finite subgraph of an infinite graph , then there is a -coloring of in which each finite graph has a larger supergraph whose coloring agrees with the coloring of the whole graph.For this connection between Rado's lemma and the De Bruijn–Erdős theorem, see e.g. the discussion following Theorem A of .
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The lowest basal leaf sheaths are densely hairy, or very rarely smooth. The leaf blades are typically 5–60 cm long, 2–14 mm wide and may be either hairy or smooth. Each inflorescence typically has six or seven spicate branches, each of which carries numerous florets. These spikelets are usually 2–4 mm long, where the lower glume is as long as the spikelet and the upper glumes are where the lemma is situated (covered with 1 mm long hairs).
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Many other nations have adopted the French slogan of "liberty, equality, and fraternity" as an ideal. These words appear in the preamble to the Constitution of India, enforced in 1950. Since its founding, "Liberty, Equality and Brotherhood" has been the lemma of the Social Democratic Party of Denmark. In the United Kingdom the political party the Liberal Democrats refer to "the fundamental values of liberty, equality and community" in the preamble of the party's Federal Constitution, and this is printed on party membership cards.
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Stein's lemma,Ingersoll, J., Theory of Financial Decision Making, Rowman and Littlefield, 1987: 13-14. named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference -- in particular, to James–Stein estimation and empirical Bayes methods -- and its applications to portfolio choice theory. The theorem gives a formula for the covariance of one random variable with the value of a function of another, when the two random variables are jointly normally distributed.
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Suppose that R is an algebra over a field k and the vector space M = N is a simple module of R. Then Schur's lemma says that the endomorphism ring of the module M is a division algebra over the field k. If M is finite-dimensional, this division algebra is finite-dimensional. If k is the field of complex numbers, the only option is that this division algebra is the complex numbers. Thus the endomorphism ring of the module M is "as small as possible".
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On a Riemann surface the Poincaré lemma states that every closed 1-form or 2-form is locally exact. Thus if ω is a smooth 1-form with then in some open neighbourhood of a given point there is a smooth function f such that in that neighbourhood; and for any smooth 2-form Ω there is a smooth 1-form ω defined in some open neighbourhood of a given point such that in that neighbourhood. If is a closed 1-form on , then . If then and .
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A diagram used in the snake lemma, a basic result in homological algebra. Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. The development of homological algebra was closely intertwined with the emergence of category theory.
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In Itō's lemma, the derivative of the composite function depends not only on dXt and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way. This variant of the chain rule is not an example of a functor because the two functions being composed are of different types.
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The widespread distribution of E. caninus has led to sizable differences in morphology, isozyme, prolamine, and DNA levels. Morphological differences seen throughout E. caninus populations include: the number of florets per spikelet, the length of lemma awn, and the pubescence of leaves and their sheaths. Populations from China, Italy, Pakistan, and Russia were determined to have the lowest levels of intra-population variation among E. caninus morphologies. These lower levels may be due to selection factors, population bottlenecks, genetic drift, or a combination of the bunch.
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The vertices of the graph are the right cosets Hg = { hg : h in H } for g in G. The edges of the graph are of the form (Hg,Hgxi). The Cayley graph of the group G with {xi : i in I} is the Schreier coset graph for H = {1G} . A spanning tree of a Schreier coset graph corresponds to a Schreier transversal, as in Schreier's subgroup lemma . The book "Categories and Groupoids" listed below relates this to the theory of covering morphisms of groupoids.
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Diarrhoea and dysentery prevailed among the crew from Angier to Manila; after a fortnight there, cholera struck despite the overall cleanliness of the ship. Peacock lost seven crewmen, and many who did recover died later in the voyage of other diseases. No new case of cholera occurred after 2 November 1833 while Peacock was under way for Macao. Within two leagues of the Lemma or Ladrone islands, she took aboard a pilot after settling on a fee of thirteen dollars and a bottle of rum.
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As a student of Ferdinand Georg Frobenius, he worked on group representations (the subject with which he is most closely associated), but also in combinatorics and number theory and even theoretical physics. He is perhaps best known today for his result on the existence of the Schur decomposition and for his work on group representations (Schur's lemma). Schur published under the name of both I. Schur, and J. Schur, the latter especially in Journal für die reine und angewandte Mathematik. This has led to some confusion.
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The spikelets have 2 fertile florets which are diminished at the apex while the sterile florets are barren, lanceolate, clumped and are long. Its rhachilla have scaberulous internodes while the floret callus is glabrous. Both the upper and lower glumes are keelless, membranous, and have acute apexes but have different size and description; Lower glume is obovate and is long while upper one is elliptic and is long. The species' lemma have eciliated margins while its fertile one is chartaceous, elliptic, and is long by wide.
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From 1969 to 1984 he was secretary general of the Organisation for Economic Co-operation and Development (OECD). Van Lennep was instrumental in making the OECD a more effective forum for international cooperation.Encyclopædia Britannica, lemma In the 1970s he was named several times to be a candidate for a function in the government of the Netherlands, but he did not have political aspirations. After his career at the OECD he was appointed to be Minister of State from 1986 until his death in 1996.
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The spikelets have fertile florets that are diminished at the apex while the sterile florets are barren, clumped and orbicular. Both the upper and lower glumes are keelless, membranous, long, and light green in colour. They are also have acute apexes but are different in the amount of veins and other features; Lower glume is 1–3 veined and is ovate while the upper one is only 3–5 veined and is linear. Its lemma have scabrous and tuberculate surface with an obtuse apex.
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In mathematics, endoscopic groups of reductive algebraic groups were introduced by in his work on the stable trace formula. Roughly speaking, an endoscopic group H of G is a quasi-split group whose L-group is the connected component of the centralizer of a semisimple element of the L-group of G. In the stable trace formula, unstable orbital integrals on a group G correspond to stable orbital integrals on its endoscopic groups H. The relation between them is given by the fundamental lemma.
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The Johnson-Lindenstrauss lemma states that large sets of vectors in a high-dimensional space can be linearly mapped in a space of much lower (but still high) dimension n with approximate preservation of distances. One of the explanations of this effect is the exponentially high quasiorthogonal dimension of n-dimensional Euclidean space. There are exponentially large (in dimension n) sets of almost orthogonal vectors (with small value of inner products) in n–dimensional Euclidean space. This observation is useful in indexing of high-dimensional data.
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In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. The β function was introduced without the name in the proof of the first of Gödel's incompleteness theorems (Gödel 1931). The β function lemma given below is an essential step of that proof.
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A simple two- dimensional triangulation of the example figure, colored and named in accordance with the assumptions of Sperner's Lemma The graph derived from the example figure Here is an elaboration of the proof given previously, for a reader new to graph theory. This diagram numbers the colors of the vertices of the example given previously. The small triangles whose vertices all have different numbers are shaded in the graph. Each small triangle becomes a node in the new graph derived from the triangulation.
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A cut in a nonstandard model M is a nonempty subset C of M so that C is downward closed (x < y and y ∈ C ⇒ x ∈ C) and C is closed under successor. A proper cut is a cut that is a proper subset of M. Each nonstandard model has many proper cuts, including one that corresponds to the standard natural numbers. However, the induction scheme in Peano arithmetic prevents any proper cut from being definable. The overspill lemma, first proved by Abraham Robinson, formalizes this fact.
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Mengistu was born in Harar, to Aleqa Lemma Hailu and Wro Abebech Yilma. After undertaking traditional religious studies at the Tiqo Mekane Selassie church where his father was Aleqa (a title given to church leaders), he moved to the capital Addis Ababa due to the transfer of his father to the Qatchane Medhane'alem Church. There he was admitted to Kotebe Qedamawi Haile Selassie school. In 1948, Mengistu studied in London at the Regent Street Polytechnic before studying economics and political science at the London School of Economics.
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