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Wallis product Summary Wallis_formula 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}}&=\p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wallman compactification Summary Wallman_compactification In mathematics, the Wallman compactification, generally called Wallman–Shanin compactification is a compactification of T1 topological spaces that was constructed by Wallman (1938). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Walter's theorem Summary Walter_theorem 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kantorovich metric Summary Kantorovich-Rubinstein_theorem 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 vie... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kantorovich metric Summary Kantorovich-Rubinstein_theorem 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 syst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weber modular function Summary Weber_modular_function In mathematics, the Weber modular functions are a family of three functions f, f1, and f2, studied by Heinrich Martin Weber. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weeks manifold Summary Weeks_manifold 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 Meye... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass M-test Summary Weierstrass_M-test 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 deter... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass elliptic function Summary Weierstrass_P_function 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 un... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass function Summary Weierstrass_function 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass function Summary Weierstrass_function 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass sigma function Summary Weierstrass_zeta_function 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 a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass preparation theorem Summary Weierstrass_preparation_theorem 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass product inequality Summary Weierstrass_product_inequality 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 ) . . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass product inequality Summary Weierstrass_product_inequality ( 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 ) . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass product inequality Summary Weierstrass_product_inequality . ( 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 + . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass product inequality Summary Weierstrass_product_inequality . . + 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass transform Summary Weierstrass_transform 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass transform Summary Weierstrass_transform 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 diff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass–Enneper parameterization Summary Weierstrass–Enneper_parameterization 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 {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil conjecture for Tamagawa numbers Summary Weil's_conjecture_on_Tamagawa_numbers 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 connec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil conjectures Summary Weil_conjectures 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 co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil conjectures Summary Weil_conjectures 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 restri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Conjecture Weil conjectures Conjecture > Important examples > Weil conjectures 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Conjecture Weil conjectures Conjecture > Important examples > Weil conjectures 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 fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil pairing Summary Weil_pairing 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 varie... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil reciprocity Summary Weil_reciprocity_law 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil reciprocity Summary Weil_reciprocity_law 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 multiplici... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil–Petersson metric Summary Weil–Petersson_metric 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 Han... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weinstein conjecture Summary Weinstein_conjecture 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weinstein conjecture Summary Weinstein_conjecture 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, a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weinstein conjecture Summary Weinstein_conjecture 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weinstein conjecture Summary Weinstein_conjecture 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weinstein conjecture Summary Weinstein_conjecture (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 \mathb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weinstein conjecture Summary Weinstein_conjecture 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sylvester's determinant theorem Summary Sylvester's_determinant_theorem 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl character formula Summary Weyl-Kac_character_formula 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 fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl character formula Summary Weyl-Kac_character_formula 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl character formula Summary Weyl-Kac_character_formula 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 lo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl integration formula Summary Weyl_integration_formula 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 cl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl–von Neumann theorem Summary Weyl–von_Neumann_theorem 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 nor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl–von Neumann theorem Summary Weyl–von_Neumann_theorem 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 t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whitehead continuum Summary Whitehead_continuum 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whitehead continuum Summary Whitehead_continuum 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whitehead continuum Summary Whitehead_continuum 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 Whiteh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whitehead product Summary Whitehead_product 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whitney inequality Summary Whitney_inequality 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 f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wielandt theorem Summary Wielandt_theorem 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}\mathr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener algebra Summary Wiener_algebra 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener integral Summary Wiener_Process 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener integral Summary Wiener_Process 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 potentia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener integral Summary Wiener_Process 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 filter... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener integral Summary Wiener_Process 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–... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener series Summary Wiener_series 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener series Summary Wiener_series 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener series Summary Wiener_series 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 exclus... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wiener–Wintner theorem Summary Wiener–Wintner_theorem 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). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wirtinger sextic Summary Wirtinger_sextic 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Witten zeta function Summary Witten_zeta_function 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wright Omega function Summary Wright_Omega_function 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wythoff array Summary Wythoff_array 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
X-ray transform Summary X-ray_transform 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
X-ray transform Summary X-ray_transform 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 t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Yang–Mills–Higgs equations Summary Yang–Mills–Higgs_equation 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 a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Yang–Mills–Higgs equations Summary Yang–Mills–Higgs_equation 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 soluti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Yoneda lemma Summary Yoneda_lemma 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 jus... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Yoneda lemma Summary Yoneda_lemma 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Young–Deruyts development Summary Young–Deruyts_development 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). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Young–Fibonacci lattice Summary Young–Fibonacci_lattice 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Young–Fibonacci lattice Summary Young–Fibonacci_lattice 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z function Summary Z_function 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 fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Z function Summary Z_function 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 holomorph... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zahlbericht Summary Zahlbericht In mathematics, the Zahlbericht (number report) was a report on algebraic number theory by Hilbert (1897, 1998, (English translation)). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zak transform Summary Zak_transform 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 def... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zak transform Summary Zak_transform 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 bee... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zakharov system Summary Zakharov_system 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 equ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zakharov–Schulman system Summary Zakharov–Schulman_system 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zassenhaus algorithm Summary Zassenhaus_algorithm 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zeeman conjecture Summary Zeeman_conjecture 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 P... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zernike polynomial Summary Zernike_polynomials 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zilber–Pink conjecture Summary Zilber–Pink_conjecture 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 i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zilber–Pink conjecture Summary Zilber–Pink_conjecture 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 var... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Absolute Galois group Summary Absolute_Galois_group 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modulus of a complex number Summary Modulus_of_complex_number 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modulus of a complex number Summary Modulus_of_complex_number 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 q... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Abstract additive Schwarz method Summary Abstract_additive_Schwarz_method 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 wit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Actuarial polynomials Summary Actuarial_polynomials 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Additive Schwarz method Summary Additive_Schwarz_method 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Additive identity Summary Additive_identity 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 identit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Opposite number Summary Unary_minus 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 i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Opposite number Summary Unary_minus 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Additive polynomial Summary Additive_polynomial In mathematics, the additive polynomials are an important topic in classical algebraic number theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Valuation vector Summary Ring_of_adeles 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 sel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Valuation vector Summary Ring_of_adeles The word stands for 'ideal element' (abbreviated: id.el.). Adele (French: "adèle") stands for 'additive idele' (that is, additive ideal element). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Valuation vector Summary Ring_of_adeles 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noetherian Summary Noetherian 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noetherian Summary Noetherian 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noetherian Summary Noetherian 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Triviality (mathematics) Summary Triviality_(mathematics) 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 techn... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Triviality (mathematics) Summary Triviality_(mathematics) 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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