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searching for Analytic proof 30 found (41 total)

Non-analytic smooth function (2,056 words) [view diff] no match in snippet view article find links to article

In mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One

Weyl's theorem on complete reducibility (2,447 words) [view diff] no match in snippet view article find links to article

In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation

Blaschke–Lebesgue theorem (1,062 words) [view diff] exact match in snippet view article find links to article

doi:10.1007/BF01458221, MR 1511839 Fujiwara, Matsusaburô (1927), "Analytic proof of Blaschke's theorem on the curve of constant breadth with minimum

Color confinement (1,223 words) [view diff] exact match in snippet view article find links to article

their parent hadron without producing new hadrons. There is not yet an analytic proof of color confinement in any non-abelian gauge theory. The phenomenon

Federer–Morse theorem (201 words) [view diff] case mismatch in snippet view article find links to article

York-London: Academic Press, Inc. L. W. Baggett and Arlan Ramsay, A Functional Analytic Proof of a Selection Lemma, Can. J. Math., vol. XXXII, no 2, 1980, pp. 441–448

Fundamental theorem of algebra (7,721 words) [view diff] exact match in snippet view article find links to article

obtain values p(z) smaller in absolute value than |p(z0)|. Another analytic proof can be obtained along this line of thought observing that, since |p(z)| > |p(0)|

Quantization commutes with reduction (266 words) [view diff] exact match in snippet view article find links to article

1006/aima.1997.1701, MR 1617809. Tian, Youliang; Zhang, Weiping (1998), "An analytic proof of the geometric quantization conjecture of Guillemin–Sternberg", Inventiones

Kodaira vanishing theorem (846 words) [view diff] exact match in snippet view article find links to article

known proof in characteristic zero was however based on the complex analytic proof and the GAGA comparison theorems. However, in 1987 Pierre Deligne and

Automated reasoning (1,352 words) [view diff] exact match in snippet view article find links to article

Residue HOL Light Harrison Classical 2008 Prime Number HOL Light Harrison Analytic proof 2012 Feit-Thompson Coq Gonthier et al. Bender, Glauberman and Peterfalvi

Analysis (2,486 words) [view diff] exact match in snippet view article find links to article

shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded

Liouville's theorem (complex analysis) (1,930 words) [view diff] no match in snippet view article

standard analytical proof uses the fact that holomorphic functions are analytic. Proof If f {\displaystyle f} is an entire function, it can be represented

Donald J. Newman (710 words) [view diff] exact match in snippet view article find links to article

Mathematical Society. ISBN 0-8218-1691-8. Newman, Donald J. (1980). "Simple analytic proof of the prime number theorem" (PDF). American Mathematical Monthly. 87

Yum-Tong Siu (570 words) [view diff] case mismatch in snippet view article find links to article

Yum-Tong (2006). "[math/0610740] A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring". arXiv:math.AG/0610740

Prime number theorem (8,186 words) [view diff] exact match in snippet view article find links to article

7.374, PMC 1063042, PMID 16588909 Newman, Donald J. (1980). "Simple analytic proof of the prime number theorem". American Mathematical Monthly. 87 (9):

Phragmén–Lindelöf principle (1,991 words) [view diff] exact match in snippet view article find links to article

bounded on its boundary. This statement can be used to give a complex analytic proof of the Hardy's uncertainty principle, which states that a function and

Compact space (5,681 words) [view diff] exact match in snippet view article find links to article

wenigstens eine reele Wurzel der Gleichung liege. Wilhelm Engelmann. (Purely analytic proof of the theorem that between any two values which give results of opposite

Radon–Nikodym theorem (3,596 words) [view diff] exact match in snippet view article find links to article

measure-theoretic proof of the theorem. There is also a functional-analytic proof, using Hilbert space methods, that was first given by von Neumann. For

Amenable group (3,135 words) [view diff] exact match in snippet view article find links to article

Although Tits' proof used algebraic geometry, Guivarc'h later found an analytic proof based on V. Oseledets' multiplicative ergodic theorem. Analogues of

Compact group (4,472 words) [view diff] exact match in snippet view article find links to article

approach, the construction is based on the Peter–Weyl theorem and an analytic proof of the Weyl character formula. Ultimately, the irreducible representations

Fermat's theorem (stationary points) (2,716 words) [view diff] exact match in snippet view article

However, making "behaves like a linear function" precise requires careful analytic proof. More precisely, the intuition can be stated as: if the derivative is

Pushdown automaton (4,019 words) [view diff] exact match in snippet view article find links to article

it is also recognized by a GPDA and vice versa. One can formulate an analytic proof for the equivalence of GPDA's and PDA's using the following simulation:

Prisoner's dilemma (8,842 words) [view diff] exact match in snippet view article find links to article

systems tend to produce tit-for-tat players,[clarification needed] but no analytic proof exists that this will always occur. In the strategy called win-stay

Atiyah–Singer index theorem (7,529 words) [view diff] exact match in snippet view article find links to article

ISBN 978-0-12-158860-1, Zbl 0478.57007 Sullivan, D.; Teleman, N. (1983), "An analytic proof of Novikov's theorem on rational Pontrjagin classes", Publications Mathématiques

Ian Gent (168 words) [view diff] exact match in snippet view article find links to article

Fields Computer science Institutions University of St Andrews Thesis Analytic proof systems for classical and modal logics of restricted quantification (1992)

List of unsolved problems in physics (11,425 words) [view diff] exact match in snippet view article find links to article

hadron without producing new hadrons. Is it possible to provide an analytic proof of color confinement in any non-abelian gauge theory? The QCD vacuum:

Shing-Tung Yau (10,422 words) [view diff] exact match in snippet view article find links to article

manifolds. The embedding of the solution given by Douglas–Morrey and an analytic proof of Dehn's lemma". Topology. 21 (4): 409–442. doi:10.1016/0040-9383(82)90021-0

Universal enveloping algebra (9,256 words) [view diff] exact match in snippet view article find links to article

group, one can use left-invariant differential operators to give an analytic proof of the Poincaré–Birkhoff–Witt theorem. Specifically, the algebra D (

Roth's theorem on arithmetic progressions (4,444 words) [view diff] exact match in snippet view article find links to article

_{3}^{n})=o(3^{n}).} In 1995, Roy Mesuhlam used a similar technique to the Fourier-analytic proof of Roth's theorem to show that r 3 ( F 3 n ) = O ( 3 n n ) . {\displaystyle

Analysis of Boolean functions (5,356 words) [view diff] exact match in snippet view article find links to article

was combinatorial. Bellare et al. gave an extremely simple Fourier-analytic proof, that also shows that if the test succeeds with probability 1 / 2 +

Oscillator representation (21,523 words) [view diff] exact match in snippet view article find links to article

physics, Gordon and Breach, pp. 27–63 Berg, M. C. (2000), The Fourier-analytic proof of quadratic reciprocity, Pure and Applied Mathematics, Wiley-Interscience