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c_5mxn1tlhaya8 | In mathematics, the Wallis product for π, published in 1656 by John Wallis, states that π 2 = ∏ n = 1 ∞ 4 n 2 4 n 2 − 1 = ∏ n = 1 ∞ ( 2 n 2 n − 1 ⋅ 2 n 2 n + 1 ) = ( 2 1 ⋅ 2 3 ) ⋅ ( 4 3 ⋅ 4 5 ) ⋅ ( 6 5 ⋅ 6 7 ) ⋅ ( 8 7 ⋅ 8 9 ) ⋅ ⋯ {\displaystyle {\begin{aligned}{\frac {\pi }{2}}&=\prod _{n=1}^{\infty }{\frac {4n^{2}}{4n... | Wallis product |
c_41pee7u5fgbb | In mathematics, the Wallman compactification, generally called Wallman–Shanin compactification is a compactification of T1 topological spaces that was constructed by Wallman (1938). | Wallman compactification |
c_1uskfmts79sz | In mathematics, the Walter theorem, proved by John H. Walter (1967, 1969), describes the finite groups whose Sylow 2-subgroup is abelian. Bender (1970) used Bender's method to give a simpler proof. | Walter's theorem |
c_e13ms690txsr | In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space M {\displaystyle M} . It is named after Leonid Vaseršteĭn. Intuitively, if each distribution is viewed as a unit amount of earth (soil) piled on M {\displays... | Kantorovich metric |
c_qthu2yjdmxwe | Because of this analogy, the metric is known in computer science as the earth mover's distance. The name "Wasserstein distance" was coined by R. L. Dobrushin in 1970, after learning of it in the work of Leonid Vaseršteĭn on Markov processes describing large systems of automata (Russian, 1969). However the metric was fi... | Kantorovich metric |
c_9p72tq5la6rk | In mathematics, the Weber modular functions are a family of three functions f, f1, and f2, studied by Heinrich Martin Weber. | Weber modular function |
c_ys97pzp5257n | In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead link. It has volume approximately equal to 0.942707… (OEIS: A126774) and David Gabai, Robert Meyerhoff, and Peter Milley (2009) showed ... | Weeks manifold |
c_upcc4jiazahn | In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or co... | Weierstrass M-test |
c_fetvst775n6j | In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the the... | Weierstrass elliptic function |
c_cn69owae4ek8 | In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass. | Weierstrass function |
c_p1d2ycoj4ru1 | The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. Weierstrass's demonstration that continuity did not imply alm... | Weierstrass function |
c_p9mr50461uql | In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta, and ℘ {\displaystyle \wp } functions is analogous to that between the sine, cotangent, and squared cos... | Weierstrass sigma function |
c_d7cxflko223c | In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic, and whose coefficients of lower d... | Weierstrass preparation theorem |
c_mw6an1zqmy2d | In mathematics, the Weierstrass product inequality states that for any real numbers 0 ≤ x1, ..., xn ≤ 1 we have ( 1 − x 1 ) ( 1 − x 2 ) ( 1 − x 3 ) ( 1 − x 4 ) . . . . | Weierstrass product inequality |
c_c22zb8b1abtv | ( 1 − x n ) ≥ 1 − S n , {\displaystyle (1-x_{1})(1-x_{2})(1-x_{3})(1-x_{4})....(1-x_{n})\geq 1-S_{n},} ( 1 + x 1 ) ( 1 + x 2 ) ( 1 + x 3 ) ( 1 + x 4 ) . . . | Weierstrass product inequality |
c_r06ojj7d0u5r | . ( 1 + x n ) ≥ 1 + S n , {\displaystyle (1+x_{1})(1+x_{2})(1+x_{3})(1+x_{4})....(1+x_{n})\geq 1+S_{n},} where S n = x 1 + x 2 + x 3 + x 4 + . . | Weierstrass product inequality |
c_bzg6tb3xy3fz | . . + x n . {\displaystyle S_{n}=x_{1}+x_{2}+x_{3}+x_{4}+....+x_{n}.} The inequality is named after the German mathematician Karl Weierstrass. | Weierstrass product inequality |
c_vfbjmdzu6p4n | In mathematics, the Weierstrass transform of a function f: R → R, named after Karl Weierstrass, is a "smoothed" version of f(x) obtained by averaging the values of f, weighted with a Gaussian centered at x. Specifically, it is the function F defined by F ( x ) = 1 4 π ∫ − ∞ ∞ f ( y ) e − ( x − y ) 2 4 d y = 1 4 π ∫ − ∞... | Weierstrass transform |
c_fhpedgxzf6uq | Instead of F(x) one also writes W(x). Note that F(x) need not exist for every real number x, when the defining integral fails to converge. The Weierstrass transform is intimately related to the heat equation (or, equivalently, the diffusion equation with constant diffusion coefficient). If the function f describes the ... | Weierstrass transform |
c_vtf8zdsiio8u | In mathematics, the Weierstrass–Enneper parameterization of minimal surfaces is a classical piece of differential geometry. Alfred Enneper and Karl Weierstrass studied minimal surfaces as far back as 1863. Let f {\displaystyle f} and g {\displaystyle g} be functions on either the entire complex plane or the unit disk, ... | Weierstrass–Enneper parameterization |
c_gv2ds9cscjf4 | In mathematics, the Weil conjecture on Tamagawa numbers is the statement that the Tamagawa number τ ( G ) {\displaystyle \tau (G)} of a simply connected simple algebraic group defined over a number field is 1. In this case, simply connected means "not having a proper algebraic covering" in the algebraic group theory se... | Weil conjecture for Tamagawa numbers |
c_vpdd2v2200j1 | In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory. The conjectures concern the generating functions (known as l... | Weil conjectures |
c_pdh746inz3k5 | The generating function has coefficients derived from the numbers Nk of points over the extension field with qk elements. Weil conjectured that such zeta functions for smooth varieties are rational functions, satisfy a certain functional equation, and have their zeros in restricted places. The last two parts were consc... | Weil conjectures |
c_8mmz9u2ws7eo | In mathematics, the Weil conjectures were some highly influential proposals by André Weil (1949) on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. A variety V over a finite field with q elements has a finite number of ration... | Conjecture |
c_yirdxh83aywq | Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis. The rationality was proved by Dwork (1960), the ... | Conjecture |
c_02r3c9c301es | In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. More generally there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduced... | Weil pairing |
c_5efb6oc80inj | In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then f((g)) = g((f))where the notation has this meaning: (h) is the divisor of the function h... | Weil reciprocity |
c_fo9l9ldh81cd | When f and g both take the values 0 or ∞ at P, the definition is essentially in limiting or removable singularity terms, by considering (up to sign) fagbwith a and b such that the function has neither a zero nor a pole at P. This is achieved by taking a to be the multiplicity of g at P, and −b the multiplicity of f at ... | Weil reciprocity |
c_h5vax3s6p0a6 | In mathematics, the Weil–Petersson metric is a Kähler metric on the Teichmüller space Tg,n of genus g Riemann surfaces with n marked points. It was introduced by André Weil (1958, 1979) using the Petersson inner product on forms on a Riemann surface (introduced by Hans Petersson). | Weil–Petersson metric |
c_a8wfj3cfsuui | In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the conjecture claims that on a compact contact manifold, its Reeb vector field should carry at least one periodic orbit. By definition, a level set of contact type ... | Weinstein conjecture |
c_l8mwzpbwsl91 | It is a fact that any contact manifold (M,α) can be embedded into a canonical symplectic manifold, called the symplectization of M, such that M is a contact type level set (of a canonically defined Hamiltonian) and the Reeb vector field is a Hamiltonian flow. That is, any contact manifold can be made to satisfy the req... | Weinstein conjecture |
c_nq14r024fgc8 | It has been known that any contact form is isotopic to a form that admits a closed Reeb orbit; for example, for any contact manifold there is a compatible open book decomposition, whose binding is a closed Reeb orbit. This is not enough to prove the Weinstein conjecture, though, because the Weinstein conjecture states ... | Weinstein conjecture |
c_3rx6v7dzjxqe | In several cases, the existence of a periodic orbit was known. For instance, Rabinowitz showed that on star-shaped level sets of a Hamiltonian function on a symplectic manifold, there were always periodic orbits (Weinstein independently proved the special case of convex level sets). Weinstein observed that the hypothes... | Weinstein conjecture |
c_b372nzf5lrrd | (Weinstein's original conjecture included the condition that the first de Rham cohomology group of the level set is trivial; this hypothesis turned out to be unnecessary). The Weinstein conjecture was first proved for contact hypersurfaces in R 2 n {\displaystyle \mathbb {R} ^{2n}} in 1986 by Viterbo, then extended to ... | Weinstein conjecture |
c_bvb0cz4ccv0l | All these cases dealt with the situation where the contact manifold is a contact submanifold of a symplectic manifold. A new approach without this assumption was discovered in dimension 3 by Hofer and is at the origin of contact homology.The Weinstein conjecture has now been proven for all closed 3-dimensional manifold... | Weinstein conjecture |
c_qb9b9wpiqbah | In mathematics, the Weinstein–Aronszajn identity states that if A {\displaystyle A} and B {\displaystyle B} are matrices of size m × n and n × m respectively (either or both of which may be infinite) then, provided A B {\displaystyle AB} (and hence, also B A {\displaystyle BA} ) is of trace class, det ( I m + A B ) = d... | Sylvester's determinant theorem |
c_kefctgys62nl | In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights. It was proved by Hermann Weyl (1925, 1926a, 1926b). There is a closely related formula for the character of an irreducible representation o... | Weyl character formula |
c_owxxghax2t4i | In Weyl's approach to the representation theory of connected compact Lie groups, the proof of the character formula is a key step in proving that every dominant integral element actually arises as the highest weight of some irreducible representation. Important consequences of the character formula are the Weyl dimensi... | Weyl character formula |
c_pbhgjrq3292v | The irreducible representations in this case are all finite-dimensional (this is part of the Peter–Weyl theorem); so the notion of trace is the usual one from linear algebra. Knowledge of the character χ {\displaystyle \chi } of π {\displaystyle \pi } gives a lot of information about π {\displaystyle \pi } itself. Weyl... | Weyl character formula |
c_5e12j90eeln0 | In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group G in terms of a maximal torus T. Precisely, it says there exists a real-valued continuous function u on T such that for every class function f on G: ∫ G f ( g ) d g = ∫ T f ( t ) u ( t )... | Weyl integration formula |
c_ap5y3gq702yn | In mathematics, the Weyl–von Neumann theorem is a result in operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator (Weyl (1909)) or Hilbert–Schmidt operator (von Neumann (1935)) of arbitrarily small norm, a bounded self-adjoint operator or unitary operator on ... | Weyl–von Neumann theorem |
c_je2eetx8mx9d | The theorem and its generalizations were one of the starting points of operator K-homology, developed first by Lawrence G. Brown, Ronald Douglas and Peter Fillmore and, in greater generality, by Gennadi Kasparov. In 1958 Kuroda showed that the Weyl–von Neumann theorem is also true if the Hilbert–Schmidt class is replac... | Weyl–von Neumann theorem |
c_entp11ywkj56 | In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to R 3 . {\displaystyle \mathbb {R} ^{3}.} J. H. C. Whitehead (1935) discovered this puzzling object while he was trying to prove the Poincaré conjecture, correcting an error in an earlier paper Whitehead (1934, theo... | Whitehead continuum |
c_c1tpl51ljazb | A contractible manifold is one that can continuously be shrunk to a point inside the manifold itself. For example, an open ball is a contractible manifold. All manifolds homeomorphic to the ball are contractible, too. | Whitehead continuum |
c_3jsjh56lx1cg | One can ask whether all contractible manifolds are homeomorphic to a ball. For dimensions 1 and 2, the answer is classical and it is "yes". In dimension 2, it follows, for example, from the Riemann mapping theorem. Dimension 3 presents the first counterexample: the Whitehead manifold. | Whitehead continuum |
c_ua5sx2y49wvs | In mathematics, the Whitehead product is a graded quasi-Lie algebra structure on the homotopy groups of a space. It was defined by J. H. C. Whitehead in (Whitehead 1941). The relevant MSC code is: 55Q15, Whitehead products and generalizations. | Whitehead product |
c_avif3bnzb3eq | In mathematics, the Whitney inequality gives an upper bound for the error of best approximation of a function by polynomials in terms of the moduli of smoothness. It was first proved by Hassler Whitney in 1957, and is an important tool in the field of approximation theory for obtaining upper estimates on the errors of ... | Whitney inequality |
c_1lgzk6ntlncu | In mathematics, the Wielandt theorem characterizes the gamma function, defined for all complex numbers z {\displaystyle z} for which R e z > 0 {\displaystyle \mathrm {Re} \,z>0} by Γ ( z ) = ∫ 0 + ∞ t z − 1 e − t d t , {\displaystyle \Gamma (z)=\int _{0}^{+\infty }t^{z-1}\mathrm {e} ^{-t}\,\mathrm {d} t,} as the only f... | Wielandt theorem |
c_0i04nc5uh7y0 | In mathematics, the Wiener algebra, named after Norbert Wiener and usually denoted by A(T), is the space of absolutely convergent Fourier series. Here T denotes the circle group. | Wiener algebra |
c_abn3wjauaah5 | In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the p... | Wiener integral |
c_e2eiaetashyv | In pure mathematics, the Wiener process gave rise to the study of continuous time martingales. It is a key process in terms of which more complicated stochastic processes can be described. As such, it plays a vital role in stochastic calculus, diffusion processes and even potential theory. | Wiener integral |
c_b2mlnjpwnsb7 | It is the driving process of Schramm–Loewner evolution. In applied mathematics, the Wiener process is used to represent the integral of a white noise Gaussian process, and so is useful as a model of noise in electronics engineering (see Brownian noise), instrument errors in filtering theory and disturbances in control ... | Wiener integral |
c_p3beluainywv | In physics it is used to study Brownian motion, the diffusion of minute particles suspended in fluid, and other types of diffusion via the Fokker–Planck and Langevin equations. It also forms the basis for the rigorous path integral formulation of quantum mechanics (by the Feynman–Kac formula, a solution to the Schrödin... | Wiener integral |
c_0odpe0slmb52 | In mathematics, the Wiener series, or Wiener G-functional expansion, originates from the 1958 book of Norbert Wiener. It is an orthogonal expansion for nonlinear functionals closely related to the Volterra series and having the same relation to it as an orthogonal Hermite polynomial expansion has to a power series. For... | Wiener series |
c_380oytybq8gp | The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of white noise. This property allows the terms to be identified in applications by the Lee–Schetzen method. The Wiener series is important in nonlinear system identification. | Wiener series |
c_3i8wou996op8 | In this context, the series approximates the functional relation of the output to the entire history of system input at any time. The Wiener series has been applied mostly to the identification of biological systems, especially in neuroscience. The name Wiener series is almost exclusively used in system theory. In the ... | Wiener series |
c_7x2m8p4nndv1 | In mathematics, the Wiener–Wintner theorem, named after Norbert Wiener and Aurel Wintner, is a strengthening of the ergodic theorem, proved by Wiener and Wintner (1941). | Wiener–Wintner theorem |
c_33m8udg0ib31 | In mathematics, the Wirtinger plane sextic curve, studied by Wirtinger, is a degree 6 genus 4 plane curve with double points at the 6 vertices of a complete quadrilateral. | Wirtinger sextic |
c_elgk4ppavcnk | In mathematics, the Witten zeta function, is a function associated to a root system that encodes the degrees of the irreducible representations of the corresponding Lie group. These zeta functions were introduced by Don Zagier who named them after Edward Witten's study of their special values (among other things). Note... | Witten zeta function |
c_e0dwqa197p8j | In mathematics, the Wright omega function or Wright function, denoted ω, is defined in terms of the Lambert W function as: ω ( z ) = W ⌈ I m ( z ) − π 2 π ⌉ ( e z ) . {\displaystyle \omega (z)=W_{{\big \lceil }{\frac {\mathrm {Im} (z)-\pi }{2\pi }}{\big \rceil }}(e^{z}).} | Wright Omega function |
c_uut6i5is81ci | In mathematics, the Wythoff array is an infinite matrix of integers derived from the Fibonacci sequence and named after Dutch mathematician Willem Abraham Wythoff. Every positive integer occurs exactly once in the array, and every integer sequence defined by the Fibonacci recurrence can be derived by shifting a row of ... | Wythoff array |
c_z3fvp8uhg9u6 | In mathematics, the X-ray transform (also called ray transform or John transform) is an integral transform introduced by Fritz John in 1938 that is one of the cornerstones of modern integral geometry. It is very closely related to the Radon transform, and coincides with it in two dimensions. In higher dimensions, the X... | X-ray transform |
c_3bectgzbb2ce | The X-ray transform derives its name from X-ray tomography (used in CT scans) because the X-ray transform of a function ƒ represents the attenuation data of a tomographic scan through an inhomogeneous medium whose density is represented by the function ƒ. Inversion of the X-ray transform is therefore of practical impor... | X-ray transform |
c_zy3g2cwqje2j | In mathematics, the Yang–Mills–Higgs equations are a set of non-linear partial differential equations for a Yang–Mills field, given by a connection, and a Higgs field, given by a section of a vector bundle (specifically, the adjoint bundle). These equations are D A ∗ F A + = 0 , D A ∗ D A Φ = 0 {\displaystyle {\begin{... | Yang–Mills–Higgs equations |
c_qlckp9lx3g10 | Goganov and L.V. Kapitanskii have shown that the Cauchy problem for hyperbolic Yang–Mills–Higgs equations in Hamiltonian gauge on 4-dimensional Minkowski space have a unique global solution with no restrictions at the spatial infinity. Furthermore, the solution has the finite propagation speed property. | Yang–Mills–Higgs equations |
c_ri25jmys7bag | 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... | Yoneda lemma |
c_ynwwyj2zarlq | It also clarifies how the embedded category, of representable functors and their natural transformations, relates to the other objects in the larger functor category. It is an important tool that underlies several modern developments in algebraic geometry and representation theory. It is named after Nobuo Yoneda. | Yoneda lemma |
c_u3qpad2v5t6k | In mathematics, the Young–Deruyts development is a method of writing invariants of an action of a group on an n-dimensional vector space V in terms of invariants depending on at most n–1 vectors (Dieudonné & Carrell 1970, 1971, p.36, 39). | Young–Deruyts development |
c_2whypsjk4ixp | In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. Any digit sequence of this type can be assigned a rank, the sum of its digits: for instance, the rank of 11212 is 1 + 1 + ... | Young–Fibonacci lattice |
c_9981prkjhx70 | The Young–Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph. The Young–Fibonacci graph and the Young–Fibonacci lattice were both initially studied in two papers by Fomin (1988) and Stanley (1988). They are named after the clo... | Young–Fibonacci lattice |
c_eewyn3cam4jt | In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in t... | Z function |
c_gf1tmx1t9cq3 | It follows from the functional equation of the Riemann zeta function that the Z function is real for real values of t. It is an even function, and real analytic for real values. It follows from the fact that the Riemann-Siegel theta function and the Riemann zeta function are both holomorphic in the critical strip, wher... | Z function |
c_4mfv4zetmcq1 | In mathematics, the Zahlbericht (number report) was a report on algebraic number theory by Hilbert (1897, 1998, (English translation)). | Zahlbericht |
c_tuklfzs5vwte | In mathematics, the Zak transform (also known as the Gelfand mapping) is a certain operation which takes as input a function of one variable and produces as output a function of two variables. The output function is called the Zak transform of the input function. The transform is defined as an infinite series in which ... | Zak transform |
c_b04m5lgk2o83 | The signal may be real valued or complex-valued, defined on a continuous set (for example, the real numbers) or a discrete set (for example, the integers or a finite subset of integers). The Zak transform is a generalization of the discrete Fourier transform.The Zak transform had been discovered by several people in di... | Zak transform |
c_edfxi06nl4nq | In mathematics, the Zakharov system is a system of non-linear partial differential equations, introduced by Vladimir Zakharov in 1972 to describe the propagation of Langmuir waves in an ionized plasma. The system consists of a complex field u and a real field n satisfying the equations i ∂ t u + ∇ 2 u = u n ◻ n = − ∇ 2... | Zakharov system |
c_6e5dvpwlv07g | In mathematics, the Zakharov–Schulman system is a system of nonlinear partial differential equations introduced in Zakharov & Schulman (1980) to describe the interactions of small amplitude, high frequency waves with acoustic waves. The equations are i ∂ t u + L 1 u = ϕ u {\displaystyle i\partial _{t}^{}u+L_{1}u=\phi u... | Zakharov–Schulman system |
c_q6irdtafx60t | In mathematics, the Zassenhaus algorithm is a method to calculate a basis for the intersection and sum of two subspaces of a vector space. It is named after Hans Zassenhaus, but no publication of this algorithm by him is known. It is used in computer algebra systems. | Zassenhaus algorithm |
c_tqz0iau2ptfy | In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex K {\displaystyle K} , the space K × {\displaystyle K\times } is collapsible. The conjecture, due to Christopher Zeeman, implies the Poincaré conjecture and the Andrews–Curtis co... | Zeeman conjecture |
c_lip6j1gqzt3y | In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel Prize in Physics and the inventor of phase-contrast microscopy, they play important roles in various optics branches such as beam optics and... | Zernike polynomial |
c_vadc3rg2a5t0 | In mathematics, the Zilber–Pink conjecture is a far-reaching generalisation of many famous Diophantine conjectures and statements, such as André–Oort, Manin–Mumford, and Mordell–Lang. For algebraic tori and semiabelian varieties it was proposed by Boris Zilber and independently by Enrico Bombieri, David Masser, Umberto... | Zilber–Pink conjecture |
c_xcmnkpo0rh0o | In the case of algebraic tori, Zilber called it the Conjecture on Intersection with Tori (CIT). The general version is now known as the Zilber–Pink conjecture. It states roughly that atypical or unlikely intersections of an algebraic variety with certain special varieties are accounted for by finitely many special vari... | Zilber–Pink conjecture |
c_86wx2aculnht | In mathematics, the absolute Galois group GK of a field K is the Galois group of Ksep over K, where Ksep is a separable closure of K. Alternatively it is the group of all automorphisms of the algebraic closure of K that fix K. The absolute Galois group is well-defined up to inner automorphism. It is a profinite group. ... | Absolute Galois group |
c_zn7xjvt27eha | In mathematics, the absolute value or modulus of a real number x {\displaystyle x} , denoted | x | {\displaystyle |x|} , is the non-negative value of x {\displaystyle x} without regard to its sign. Namely, | x | = x {\displaystyle |x|=x} if x {\displaystyle x} is a positive number, and | x | = − x {\displaystyle |x|=-x... | Modulus of a complex number |
c_fqvjfhttpamh | The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absol... | Modulus of a complex number |
c_1mw8ome4g5ne | In mathematics, the abstract additive Schwarz method, named after Hermann Schwarz, is an abstract version of the additive Schwarz method for boundary value problems on partial differential equations, formulated only in terms of linear algebra without reference to domains, subdomains, etc. Many if not all domain decompo... | Abstract additive Schwarz method |
c_3r8keedzpe54 | In mathematics, the actuarial polynomials a(β)n(x) are polynomials studied by Toscano (1950) given by the generating function ∑ n a n ( β ) ( x ) n ! t n = exp ( β t + x ( 1 − e t ) ) {\displaystyle \displaystyle \sum _{n}{\frac {a_{n}^{(\beta )}(x)}{n! }}t^{n}=\exp(\beta t+x(1-e^{t}))} (Roman 1984, 4.3.4), Boas & Bu... | Actuarial polynomials |
c_9xxr7792uk18 | In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results. | Additive Schwarz method |
c_6v4pmpo06qd4 | In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures w... | Additive identity |
c_pwbjn7eqal4i | In mathematics, the additive inverse of a number a (sometimes called the opposite of a) is the number that, when added to a, yields zero. The operation taking a number to its additive inverse is known as sign change or negation. For a real number, it reverses its sign: the additive inverse (opposite number) of a positi... | Opposite number |
c_dlyf0k3u3u5s | The additive inverse of a is denoted by unary minus: −a (see also § Relation to subtraction below). For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0. Similarly, the additive inverse of a − b is −(a − b) which can be simplified to b − a. ... | Opposite number |
c_41auicfn5xrl | In mathematics, the additive polynomials are an important topic in classical algebraic number theory. | Additive polynomial |
c_sleimxcmp543 | In mathematics, the adele ring of a global field (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic number theory. It is the restricted product of all the completions of the global field and is an example of a self-dual topological ring. An adele derive... | Valuation vector |
c_r9bb27wxye8x | The word stands for 'ideal element' (abbreviated: id.el.). Adele (French: "adèle") stands for 'additive idele' (that is, additive ideal element). | Valuation vector |
c_fwghgrrs4ec4 | The ring of adeles allows one to describe the Artin reciprocity law, which is a generalisation of quadratic reciprocity, and other reciprocity laws over finite fields. In addition, it is a classical theorem from Weil that G {\displaystyle G} -bundles on an algebraic curve over a finite field can be described in terms o... | Valuation vector |
c_barxrcdpo79c | In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite length. Noetherian objects are named after Emmy Noether, who was the first to... | Noetherian |
c_fzfgc38vlcjg | Noetherian module, a module that satisfies the ascending chain condition on submodules. More generally, an object in a category is said to be Noetherian if there is no infinitely increasing filtration of it by subobjects. A category is Noetherian if every object in it is Noetherian. | Noetherian |
c_38r5cb1zvpfx | Noetherian relation, a binary relation that satisfies the ascending chain condition on its elements. Noetherian topological space, a topological space that satisfies the descending chain condition on closed sets. Noetherian induction, also called well-founded induction, a proof method for binary relations that satisfy ... | Noetherian |
c_4l960103dyqq | In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces). The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the... | Triviality (mathematics) |
c_xybc3xn8meus | The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple, or that a statement or a theorem is not easy to prove.The judgement of whether a situation under consideration is trivial or not depends on who considers it since the situation is obviously true for so... | Triviality (mathematics) |
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