text stringlengths 42 3.65k | source stringclasses 1
value |
|---|---|
Swiss cheese (mathematics) Summary Swiss_cheese_(mathematics) In mathematics, a Swiss cheese is a compact subset of the complex plane obtained by removing from a closed disc some countable union of open discs, usually with some restriction on the centres and radii of the removed discs. Traditionally the deleted discs s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sylvester domain Summary Sylvester_domain In mathematics, a Sylvester domain, named after James Joseph Sylvester by Dicks & Sontag (1978), is a ring in which Sylvester's law of nullity holds. This means that if A is an m by n matrix, and B is an n by s matrix over R, then ρ(AB) ≥ ρ(A) + ρ(B) – nwhere ρ is the inner ran... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sylvester matrix Summary Sylvester_matrix In mathematics, a Sylvester matrix is a matrix associated to two univariate polynomials with coefficients in a field or a commutative ring. The entries of the Sylvester matrix of two polynomials are coefficients of the polynomials. The determinant of the Sylvester matrix of two... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Szegő polynomial Summary Szegő_polynomial In mathematics, a Szegő polynomial is one of a family of orthogonal polynomials for the Hermitian inner product ⟨ f | g ⟩ = ∫ − π π f ( e i θ ) g ( e i θ ) ¯ d μ {\displaystyle \langle f|g\rangle =\int _{-\pi }^{\pi }f(e^{i\theta }){\overline {g(e^{i\theta })}}\,d\mu } where dμ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Takiff algebra Summary Takiff_algebra In mathematics, a Takiff algebra is a Lie algebra over a truncated polynomial ring. More precisely, a Takiff algebra of a Lie algebra g over a field k is a Lie algebra of the form g/(xn+1) = g⊗kk/(xn+1) for some positive integer n. Sometimes these are called generalized Takiff alge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tamari lattice Summary Tamari_lattice In mathematics, a Tamari lattice, introduced by Dov Tamari (1962), is a partially ordered set in which the elements consist of different ways of grouping a sequence of objects into pairs using parentheses; for instance, for a sequence of four objects abcd, the five possible groupin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tamari lattice Summary Tamari_lattice In this partial order, any two groupings g1 and g2 have a greatest common predecessor, the meet g1 ∧ g2, and a least common successor, the join g1 ∨ g2. Thus, the Tamari lattice has the structure of a lattice. The Hasse diagram of this lattice is isomorphic to the graph of vertices... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tamari lattice Summary Tamari_lattice The number of elements in a Tamari lattice for a sequence of n + 1 objects is the nth Catalan number Cn. The Tamari lattice can also be described in several other equivalent ways: It is the poset of sequences of n integers a1, ..., an, ordered coordinatewise, such that i ≤ ai ≤ n a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tannakian duality Summary Tannakian_formalism In mathematics, a Tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to approximate, in some sense, the category of linear representations of an algebraic group G d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tannakian duality Summary Tannakian_formalism The pattern of the theory is that of Grothendieck's Galois theory, which is a theory about finite permutation representations of groups G which are profinite groups. The gist of the theory is that the fiber functor Φ of the Galois theory is replaced by a tensor functor T fr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tate module of a number field Summary Tate_module_of_a_number_field In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made in the following situation: G is a commutative group scheme over a field K, Ks is the separable cl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tate vector space Summary Tate_vector_space In mathematics, a Tate vector space is a vector space obtained from finite-dimensional vector spaces in a way that makes it possible to extend concepts such as dimension and determinant to an infinite-dimensional situation. Tate spaces were introduced by Alexander Beilinson, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Teichmüller modular form Summary Teichmüller_modular_form In mathematics, a Teichmüller modular form is an analogue of a Siegel modular form on Teichmüller space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thue equation Summary Thue_equation In mathematics, a Thue equation is a Diophantine equation of the form ƒ(x,y) = r,where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue, who in 1909 proved that a Thue equation can have ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tschirnhaus transformation Summary Tschirnhaus_transformation In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683.Simply, it is a method for transforming a polynomial equation of degree n ≥ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tschirnhaus transformation Summary Tschirnhaus_transformation , a n − 1 {\displaystyle a_{1},...,a_{n-1}} , such that some or all of the transformed intermediate coefficients, a 1 ′ , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tschirnhaus transformation Summary Tschirnhaus_transformation , a n − 1 ′ {\displaystyle a'_{1},...,a'_{n-1}} , are exactly zero. For example, finding a substitutionfor a cubic equation of degree n = 3 {\displaystyle n=3} ,such that substituting x = x ( y ) {\displaystyle x=x(y)} yields a new equationsuch that a 1 ′ = ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tutte–Grothendieck invariant Summary Tutte–Grothendieck_invariant In mathematics, a Tutte–Grothendieck (TG) invariant is a type of graph invariant that satisfies a generalized deletion–contraction formula. Any evaluation of the Tutte polynomial would be an example of a TG invariant. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
V-ring (ring theory) Summary V-ring_(ring_theory) In mathematics, a V-ring is a ring R such that every simple R-module is injective. The following three conditions are equivalent: Every simple left (resp. right) R-module is injective The radical of every left (resp. right) R-module is zero Every left (resp. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
V-ring (ring theory) Summary V-ring_(ring_theory) right) ideal of R is an intersection of maximal left (resp. right) ideals of RA commutative ring is a V-ring if and only if it is Von Neumann regular. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Verlinde formula Summary Verlinde_algebra In mathematics, a Verlinde algebra is a finite-dimensional associative algebra introduced by Erik Verlinde (1988), with a basis of elements φλ corresponding to primary fields of a rational two-dimensional conformal field theory, whose structure constants Nνλμ describe fusion of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vitali set Summary Vitali_set In mathematics, a Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali in 1905. The Vitali theorem is the existence theorem that there are such sets. There are uncountably many Vitali sets, and their existence depends on the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vogan diagram Summary Vogan_diagram In mathematics, a Vogan diagram, named after David Vogan, is a variation of the Dynkin diagram of a real semisimple Lie algebra that indicates the maximal compact subgroup. Although they resemble Satake diagrams they are a different way of classifying simple Lie algebras. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Voronoi decomposition Summary Thiessen_method In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding regi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Voronoi decomposition Summary Thiessen_method The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons. V... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Voronoi formula Summary Voronoi_formula In mathematics, a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either side. It can be regarded as a Poisson summation formula for non-abelian groups. The Voronoi (summation) formula for... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Waldhausen category Summary Waldhausen_category In mathematics, a Waldhausen category is a category C equipped with some additional data, which makes it possible to construct the K-theory spectrum of C using a so-called S-construction. It's named after Friedhelm Waldhausen, who introduced this notion (under the term ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wall polynomial Summary Wall_polynomial In mathematics, a Wall polynomial is a polynomial studied by Wall (1963) in his work on conjugacy classes in classical groups, and named by Andrews (1984). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Walsh matrix Summary Walsh_matrix In mathematics, a Walsh matrix is a specific square matrix of dimensions 2n, where n is some particular natural number. The entries of the matrix are either +1 or −1 and its rows as well as columns are orthogonal, i.e. dot product is zero. The Walsh matrix was proposed by Joseph L. Wal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Walsh matrix Summary Walsh_matrix The Walsh matrices are a special case of Hadamard matrices. The naturally ordered Hadamard matrix is defined by the recursive formula below, and the sequency-ordered Hadamard matrix is formed by rearranging the rows so that the number of sign changes in a row is in increasing order. Co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point In mathematics, a Weierstrass point P {\displaystyle P} on a nonsingular algebraic curve C {\displaystyle C} defined over the complex numbers is a point such that there are more functions on C {\displaystyle C} , with their poles restricted to P {\displaystyle P} only, than w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point In fact if g {\displaystyle g} is the genus of C {\displaystyle C} , the dimension from the k {\displaystyle k} -th term is known to be l ( k P ) = k − g + 1 , {\displaystyle l(kP)=k-g+1,} for k ≥ 2 g − 1. {\displaystyle k\geq 2g-1.} Our knowledge of the sequence is therefore... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point , ? , … , ? | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point , g , g + 1 , g + 2 , … . {\displaystyle 1,?,?,\dots ,?,g,g+1,g+2,\dots .} What we know about the ? | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point entries is that they can increment by at most 1 each time (this is a simple argument: L ( n P ) / L ( ( n − 1 ) P ) {\displaystyle L(nP)/L((n-1)P)} has dimension as most 1 because if f {\displaystyle f} and g {\displaystyle g} have the same order of pole at P {\displaystyle P... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point There will be g − 1 {\displaystyle g-1} steps up, and g − 1 {\displaystyle g-1} steps where there is no increment. A non-Weierstrass point of C {\displaystyle C} occurs whenever the increments are all as far to the right as possible: i.e. the sequence looks like 1 , 1 , … , 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point Any other case is a Weierstrass point. A Weierstrass gap for P {\displaystyle P} is a value of k {\displaystyle k} such that no function on C {\displaystyle C} has exactly a k {\displaystyle k} -fold pole at P {\displaystyle P} only. The gap sequence is 1 , 2 , … , g {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point For a Weierstrass point it contains at least one higher number. (The Weierstrass gap theorem or Lückensatz is the statement that there must be g {\displaystyle g} gaps.) For hyperelliptic curves, for example, we may have a function F {\displaystyle F} with a double pole at P ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point Its powers have poles of order 4 , 6 {\displaystyle 4,6} and so on. Therefore, such a P {\displaystyle P} has the gap sequence 1 , 3 , 5 , … , 2 g − 1. {\displaystyle 1,3,5,\dots ,2g-1.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point In general if the gap sequence is a , b , c , … {\displaystyle a,b,c,\dots } the weight of the Weierstrass point is ( a − 1 ) + ( b − 2 ) + ( c − 3 ) + … . {\displaystyle (a-1)+(b-2)+(c-3)+\dots .} This is introduced because of a counting theorem: on a Riemann surface the sum... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point {\displaystyle g(g^{2}-1).} For example, a hyperelliptic Weierstrass point, as above, has weight g ( g − 1 ) / 2. {\displaystyle g(g-1)/2.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point Therefore, there are (at most) 2 ( g + 1 ) {\displaystyle 2(g+1)} of them. The 2 g + 2 {\displaystyle 2g+2} ramification points of the ramified covering of degree two from a hyperelliptic curve to the projective line are all hyperelliptic Weierstrass points and these exhausts... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass point Summary Weierstrass_point Multiplication of functions gives the non-gaps a numerical semigroup structure, and an old question of Adolf Hurwitz asked for a characterization of the semigroups occurring. A new necessary condition was found by R.-O. Buchweitz in 1980 and he gave an example of a subsemigro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weierstrass ring Summary Weierstrass_ring In mathematics, a Weierstrass ring, named by Nagata after Karl Weierstrass, is a commutative local ring that is Henselian, pseudo-geometric, and such that any quotient ring by a prime ideal is a finite extension of a regular local ring. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weil group of a class formation Summary Weil_group_of_a_class_formation In mathematics, a Weil group, introduced by Weil (1951), is a modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F, its Weil group is generally denoted WF. There also exists "finite le... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weyl sequence Summary Weyl_sequence In mathematics, a Weyl sequence is a sequence from the equidistribution theorem proven by Hermann Weyl:The sequence of all multiples of an irrational α, 0, α, 2α, 3α, 4α, ... is equidistributed modulo 1.In other words, the sequence of the fractional parts of each term will be uniform... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whittaker function Summary Whittaker_functions In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by Whittaker (1903) to make the formulas involving the solutions more symmetric. More generally, Jacquet (1966, 1967) int... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whittaker function Summary Whittaker_functions {\displaystyle {\frac {d^{2}w}{dz^{2}}}+\left(-{\frac {1}{4}}+{\frac {\kappa }{z}}+{\frac {1/4-\mu ^{2}}{z^{2}}}\right)w=0.} It has a regular singular point at 0 and an irregular singular point at ∞. Two solutions are given by the Whittaker functions Mκ,μ(z), Wκ,μ(z), defi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Whittaker function Summary Whittaker_functions {\displaystyle W_{\kappa ,\mu }\left(z\right)=\exp \left(-z/2\right)z^{\mu +{\tfrac {1}{2}}}U\left(\mu -\kappa +{\tfrac {1}{2}},1+2\mu ,z\right).} The Whittaker function W κ , μ ( z ) {\displaystyle W_{\kappa ,\mu }(z)} is the same as those with opposite values of μ, in ot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wieferich pair Summary Wieferich_pair In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfy pq − 1 ≡ 1 (mod q2) and qp − 1 ≡ 1 (mod p2)Wieferich pairs are named after German mathematician Arthur Wieferich. Wieferich pairs play an important role in Preda Mihăilescu's 2002 proof of Mihăilescu's... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Witt–Grothendieck ring Summary Witt_ring_(forms) In mathematics, a Witt group of a field, named after Ernst Witt, is an abelian group whose elements are represented by symmetric bilinear forms over the field. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Young symmetrizer Summary Young_symmetrizer In mathematics, a Young symmetrizer is an element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V ⊗ n {\displaystyle V^{\otimes n}} obtained from the action of S ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Young tableau Summary Skew_tableau In mathematics, a Young tableau (; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. Young tabl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zariski geometry Summary Zariski_geometry In mathematics, a Zariski geometry consists of an abstract structure introduced by Ehud Hrushovski and Boris Zilber, in order to give a characterisation of the Zariski topology on an algebraic curve, and all its powers. The Zariski topology on a product of algebraic varieties i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zimmert set Summary Zimmert_set In mathematics, a Zimmert set is a set of positive integers associated with the structure of quotients of hyperbolic three-space by a Bianchi group. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zinbiel algebra Summary Zinbiel_algebra In mathematics, a Zinbiel algebra or dual Leibniz algebra is a module over a commutative ring with a bilinear product satisfying the defining identity: ( a ∘ b ) ∘ c = a ∘ ( b ∘ c ) + a ∘ ( c ∘ b ) . {\displaystyle (a\circ b)\circ c=a\circ (b\circ c)+a\circ (c\circ b).} Zinbiel a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zinbiel algebra Summary Zinbiel_algebra The name was proposed by Jean-Michel Lemaire as being "opposite" to Leibniz algebra.In any Zinbiel algebra, the symmetrised product a ⋆ b = a ∘ b + b ∘ a {\displaystyle a\star b=a\circ b+b\circ a} is associative. A Zinbiel algebra is the Koszul dual concept to a Leibniz algebra. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zorn ring Summary Zorn_ring In mathematics, a Zorn ring is an alternative ring in which for every non-nilpotent x there exists an element y such that xy is a non-zero idempotent (Kaplansky 1968, pages 19, 25). Kaplansky (1951) named them after Max August Zorn, who studied a similar condition in (Zorn 1941). For associa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zuckerman functor Summary Zuckerman_functor In mathematics, a Zuckerman functor is used to construct representations of real reductive Lie groups from representations of Levi subgroups. They were introduced by Gregg Zuckerman (1978). The Bernstein functor is closely related. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Balanced matrix Summary Balanced_matrix In mathematics, a balanced matrix is a 0-1 matrix (a matrix where every entry is either zero or one) that does not contain any square submatrix of odd order having all row sums and all column sums equal to 2. Balanced matrices are studied in linear programming. The importance of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
4-ball (mathematics) Summary Ball_(topology) In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three-dimensional Euc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
4-ball (mathematics) Summary Ball_(topology) Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
4-ball (mathematics) Summary Ball_(topology) In a one-dimensional space, a ball is a line segment. In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball. In the field of topology the closed n {\displaystyle n} -dimensional ball is often denoted as B n {\displaystyle B^... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Band (algebra) Summary Rectangular_band In mathematics, a band (also called idempotent semigroup) is a semigroup in which every element is idempotent (in other words equal to its own square). Bands were first studied and named by A. H. Clifford (1954). The lattice of varieties of bands was described independently in th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countable base Summary Weight_of_a_topological_space In mathematics, a base (or basis; PL: bases) for the topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is equal to the union of some sub-family of B {\displaystyle {\mat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countable base Summary Weight_of_a_topological_space Many important topological definitions such as continuity and convergence can be checked using only basic open sets instead of arbitrary open sets. Some topologies have a base of open sets with specific useful properties that may make checking such topological defini... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countable base Summary Weight_of_a_topological_space Under some conditions detailed below, a family of subsets will form a base for a (unique) topology on X {\displaystyle X} , obtained by taking all possible unions of subfamilies. Such families of sets are very frequently used to define topologies. A weaker notion rel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Base-orderable matroid Summary Base-orderable_matroid In mathematics, a base-orderable matroid is a matroid that has the following additional property, related to the bases of the matroid. For any two bases A {\displaystyle A} and B {\displaystyle B} there exists a feasible exchange bijection, defined as a bijection f ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Algebraic operation Summary Algebraic_operation In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). These operations may be performed on numbers... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Algebraic operation Summary Algebraic_operation An algebraic operation may also be defined simply as a function from a Cartesian power of a set to the same set.The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the dot product. In calculus... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Semi-algebraic sets Summary Semialgebraic_sets In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and function... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Blending function Summary Basis_function In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of bas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Basis of a matroid Summary Circuit_of_a_matroid In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bi-directional delay line Summary Bi-directional_delay_line In mathematics, a bi-directional delay line is a numerical analysis technique used in computer simulation for solving ordinary differential equations by converting them to hyperbolic equations. In this way an explicit solution scheme is obtained with highly ro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bi-directional delay line Summary Bi-directional_delay_line It was then found that it could be used as an efficient numerical technique for numerically insulating different parts of a simulation model in each times step. It is used in the HOPSAN simulation package (Krus et al. 1990). It is also known as the Transmissio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bialgebra Summary Bialgebra In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra. The algebraic and coalgebraic structures are made compatible with a few more axioms. Specifically, the comultiplication and the counit are bo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bialgebra Summary Bialgebra Similar bialgebras are related by bialgebra homomorphisms. A bialgebra homomorphism is a linear map that is both an algebra and a coalgebra homomorphism. As reflected in the symmetry of the commutative diagrams, the definition of bialgebra is self-dual, so if one can define a dual of B (whic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Biased graph Summary Biased_graph In mathematics, a biased graph is a graph with a list of distinguished circles (edge sets of simple cycles), such that if two circles in the list are contained in a theta graph, then the third circle of the theta graph is also in the list. A biased graph is a generalization of the comb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Biased graph Summary Biased_graph For instance, a circle belonging to B is balanced and one that does not belong to B is unbalanced. Biased graphs are interesting mostly because of their matroids, but also because of their connection with multiary quasigroups. See below. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bicategory Summary Bicategory In mathematics, a bicategory (or a weak 2-category) is a concept in category theory used to extend the notion of category to handle the cases where the composition of morphisms is not (strictly) associative, but only associative up to an isomorphism. The notion was introduced in 1967 by Je... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bidiagonal matrix Summary Bidiagonal_matrix In mathematics, a bidiagonal matrix is a banded matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below. This means there are exactly two non-zero diagonals in the matrix. When the diagonal above the main diagonal has the non-z... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bidiagonal matrix Summary Bidiagonal_matrix When the diagonal below the main diagonal has the non-zero entries the matrix is lower bidiagonal. For example, the following matrix is upper bidiagonal: ( 1 4 0 0 0 4 1 0 0 0 3 4 0 0 0 3 ) {\displaystyle {\begin{pmatrix}1&4&0&0\\0&4&1&0\\0&0&3&4\\0&0&0&3\\\end{pmatrix}}} and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijective relation Summary Bijective_map In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijective relation Summary Bijective_map For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets. A bijective function from a set to itself is also called a permutation, and the set of all permutations of a set forms the symme... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Radical of a quadratic space Summary Skew_symmetric_form In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B: V × V → K that is linear in each... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Separate continuity Summary Separate_continuity In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bilinear program Summary Bilinear_program In mathematics, a bilinear program is a nonlinear optimization problem whose objective or constraint functions are bilinear. An example is the pooling problem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary functions Summary Binary_functions In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs. Precisely stated, a function f {\displaystyle f} is binary if there exists sets X , Y , Z {\displaystyle X,Y,Z} such that f: X × Y → Z {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commutative operation Summary Commutative_operation In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commutative operation Summary Commutative_operation The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary operation Summary Binary_operations In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation on a set is a binary operat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary operation Summary Binary_operations Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a binary operation. For example, scalar multiplication o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary quadratic form Summary Binary_quadratic_form In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x,y)=ax^{2}+bxy+cy^{2},\,} where a, b, c are the coefficients. When the coefficients can be arbitrary complex numbers,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary quadratic form Summary Binary_quadratic_form This choice is motivated by their status as the driving force behind the development of algebraic number theory. Since the late nineteenth century, binary quadratic forms have given up their preeminence in algebraic number theory to quadratic and more general number f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary quadratic form Summary Binary_quadratic_form x 2 + y 2 , x 2 + 2 y 2 , x 2 − 3 y 2 {\displaystyle x^{2}+y^{2},x^{2}+2y^{2},x^{2}-3y^{2}} and so on are quadratic forms, and the theory of quadratic forms gives a unified way of looking at and proving these theorems. Another instance of quadratic forms is Pell's equ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Well-founded order Summary Hereditarily_well-founded_set In mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is, an element m ∈ S not related by s R m (for instance, "s is not smaller than ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Well-founded order Summary Hereditarily_well-founded_set In set theory, a set x is called a well-founded set if the set membership relation is well-founded on the transitive closure of x. The axiom of regularity, which is one of the axioms of Zermelo–Fraenkel set theory, asserts that all sets are well-founded. A relati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Irreflexive kernel Summary Reflexive_relation In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to ha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Anti-symmetric relation Summary Anti-symmetric_relation In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle X} each of which is related by R {\displaystyle R} to the other. More formally, R {\displaystyle R} is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Left-total relation Summary Left-total_relation In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x: there is a y with xRy }. Conversely, R is called right total if Y equals the range {y: there is an x with xRy }. When f: X → Y is a functi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.