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3-sphere Summary Three-dimensional_sphere In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. It may be embedded in 4-dimensional Euclidean space as the set of points equidistant from a fixed central point. Analogous to how the boundary of a ball in three dimensions is an ordi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
3-step group Summary 3-step_group In mathematics, a 3-step group is a special sort of group of Fitting length at most 3, that is used in the classification of CN groups and in the Feit–Thompson theorem. The definition of a 3-step group in these two cases is slightly different. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
4-manifold Summary 4-manifold In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds whi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
5-manifold Summary 5-manifold In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure. Non-simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups. Simply connected compact 5-manifolds were fir... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
5-manifold Summary 5-manifold In dimension 5, the smooth classification of simply connected manifolds is governed by classical algebraic topology. Namely, two simply connected, smooth 5-manifolds are diffeomorphic if and only if there exists an isomorphism of their second homology groups with integer coefficients, pres... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baer group Summary Baer_group In mathematics, a Baer group is a group in which every cyclic subgroup is subnormal. Every Baer group is locally nilpotent.Baer groups are named after Reinhold Baer. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bailey pair Summary Bailey_pair In mathematics, a Bailey pair is a pair of sequences satisfying certain relations, and a Bailey chain is a sequence of Bailey pairs. Bailey pairs were introduced by W. N. Bailey (1947, 1948) while studying the second proof Rogers 1917 of the Rogers–Ramanujan identities, and Bailey chains... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baire measure Summary Baire_measure In mathematics, a Baire measure is a measure on the σ-algebra of Baire sets of a topological space whose value on every compact Baire set is finite. In compact metric spaces the Borel sets and the Baire sets are the same, so Baire measures are the same as Borel measures that are fini... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Banach bundle (non-commutative geometry) Summary Banach_bundle_(non-commutative_geometry) In mathematics, a Banach bundle is a fiber bundle over a topological Hausdorff space, such that each fiber has the structure of a Banach space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Banach bundle Summary Banach_bundle In mathematics, a Banach bundle is a vector bundle each of whose fibres is a Banach space, i.e. a complete normed vector space, possibly of infinite dimension. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Banach manifold Summary Banach_manifold In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below). Banach manifolds are one possibil... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Barlow surface Summary Barlow_surface In mathematics, a Barlow surface is one of the complex surfaces introduced by Rebecca Barlow (1984, 1985). They are simply connected surfaces of general type with pg = 0. They are homeomorphic but not diffeomorphic to a projective plane blown up in 8 points. The Hodge diamond for t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Barnes integral Summary Barnes_integral In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by Ernest William Barnes (1908, 1910). They are closely related to generalized hypergeometric series. The integral is usually taken along... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Barnes zeta function Summary Barnes_zeta_function In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by E. W. Barnes (1901). It is further generalized by the Shintani zeta function. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Batalin–Vilkovisky formalism Batalin–Vilkovisky algebras Batalin–Vilkovisky_formalism > Batalin–Vilkovisky algebras In mathematics, a Batalin–Vilkovisky algebra is a graded supercommutative algebra (with a unit 1) with a second-order nilpotent operator Δ of degree −1. More precisely, it satisfies the identities | a b |... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Beatty sequence Summary Beatty_sequence In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are named after Samuel Beatty, who wrote about them in 1926. Rayleigh's theorem, na... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Beauville surface Summary Beauville_surface In mathematics, a Beauville surface is one of the surfaces of general type introduced by Arnaud Beauville (1996, exercise X.13 (4)). They are examples of "fake quadrics", with the same Betti numbers as quadric surfaces. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Benz plane Summary Benz_plane In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced sep... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Berkovich spectrum Summary Berkovich_space In mathematics, a Berkovich space, introduced by Berkovich (1990), is a version of an analytic space over a non-Archimedean field (e.g. p-adic field), refining Tate's notion of a rigid analytic space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel process Summary Bessel_processes In mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Beurling zeta function Summary Beurling_zeta_function In mathematics, a Beurling zeta function is an analogue of the Riemann zeta function where the ordinary primes are replaced by a set of Beurling generalized primes: any sequence of real numbers greater than 1 that tend to infinity. These were introduced by Beurling ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bianchi group Summary Bianchi_group In mathematics, a Bianchi group is a group of the form P S L 2 ( O d ) {\displaystyle PSL_{2}({\mathcal {O}}_{d})} where d is a positive square-free integer. Here, PSL denotes the projective special linear group and O d {\displaystyle {\mathcal {O}}_{d}} is the ring of integers of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bianchi group Summary Bianchi_group The quotient space M d = P S L 2 ( O d ) ∖ H 3 {\displaystyle M_{d}=PSL_{2}({\mathcal {O}}_{d})\backslash \mathbb {H} ^{3}} is a non-compact, hyperbolic 3-fold with finite volume, which is also called Bianchi orbifold. An exact formula for the volume, in terms of the Dedekind zeta fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bianchi group Summary Bianchi_group {\displaystyle \operatorname {vol} (\Gamma \backslash \mathbb {H} )={\frac {|D|^{3/2}}{4\pi ^{2}}}\zeta _{\mathbb {Q} ({\sqrt {-d}})}(2)\ .} The set of cusps of M d {\displaystyle M_{d}} is in bijection with the class group of Q ( − d ) {\displaystyle \mathbb {Q} ({\sqrt {-d}})} . It... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finitary boolean function Summary Switching_function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). Alternative names are switching function, used especially in older computer science literature, and truth functi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finitary boolean function Summary Switching_function A Boolean function with multiple outputs, f: { 0 , 1 } k → { 0 , 1 } m {\displaystyle f:\{0,1\}^{k}\to \{0,1\}^{m}} with m > 1 {\displaystyle m>1} is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography).There are 2 2 k {\displaystyle 2^{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finitary boolean function Summary Switching_function . . , x k {\displaystyle x_{1},...,x_{k}} , and two propositional formulas are logically equivalent if and only if they express the same Boolean function. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean matrix Summary Boolean_matrix In mathematics, a Boolean matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called a logical matrix. (In some contexts, particularly computer science, the term "Boolean matrix" implies this restriction.) Let ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean matrix Summary Boolean_matrix Intersection, union, complementation, and containment of elements is expressed in U. Let V be the collection of n × n matrices that have entries taken from U. Complementation of such a matrix is obtained by complementing each element. The intersection or union of two such matrices ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean matrix Summary Boolean_matrix The product of two Boolean matrices is expressed as follows: According to one author, "Matrices over an arbitrary Boolean algebra β satisfy most of the properties over β0 = {0, 1}. The reason is that any Boolean algebra is a sub-Boolean algebra of β 0 S {\displaystyle \beta _{0}^{S... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean rings Summary Boolean_ring In mathematics, a Boolean ring R is a ring for which x2 = x for all x in R, that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wightman functional Summary Wightman_functional In mathematics, a Borchers algebra or Borchers–Uhlmann algebra or BU-algebra is the tensor algebra of a vector space, often a space of smooth test functions. They were studied by H. J. Borchers (1962), who showed that the Wightman distributions of a quantum field could be... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel equivalence relation Summary Borel_equivalence_relation In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel isomorphism Summary Borel_isomorphism In mathematics, a Borel isomorphism is a measurable bijective function between two standard Borel spaces. By Souslin's theorem in standard Borel spaces (which says that a set that is both analytic and coanalytic is necessarily Borel), the inverse of any such measurable biject... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Log-concave measure Summary Log-concave_measure In mathematics, a Borel measure μ on n-dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is called logarithmically concave (or log-concave for short) if, for any compact subsets A and B of R n {\displaystyle \mathbb {R} ^{n}} and 0 < λ < 1, one has μ ( λ A ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel algebra Summary Borel_sigma-algebra In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel. For a topolog... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel algebra Summary Borel_sigma-algebra Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel algebra Summary Borel_sigma-algebra Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory. In some contexts, Borel sets are defined to be generated by the compact sets of the topological space, rather than the open sets. The two definitions are equivalent for many we... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bose–Mesner algebra Summary Bose–Mesner_algebra In mathematics, a Bose–Mesner algebra is a special set of matrices which arise from a combinatorial structure known as an association scheme, together with the usual set of rules for combining (forming the products of) those matrices, such that they form an associative al... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bost–Connes system Summary Bost–Connes_system In mathematics, a Bost–Connes system is a quantum statistical dynamical system related to an algebraic number field, whose partition function is related to the Dedekind zeta function of the number field. Bost & Connes (1995) introduced Bost–Connes systems by constructing on... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bratteli diagram Summary Bratteli_diagram In mathematics, a Bratteli diagram is a combinatorial structure: a graph composed of vertices labelled by positive integers ("level") and unoriented edges between vertices having levels differing by one. The notion was introduced by Ola Bratteli in 1972 in the theory of operato... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bratteli–Vershik diagram Summary Bratteli–Vershik_diagram In mathematics, a Bratteli–Veršik diagram is an ordered, essentially simple Bratteli diagram (V, E) with a homeomorphism on the set of all infinite paths called the Veršhik transformation. It is named after Ola Bratteli and Anatoly Vershik. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer algebra Summary Brauer_algebra In mathematics, a Brauer algebra is an associative algebra introduced by Richard Brauer in the context of the representation theory of the orthogonal group. It plays the same role that the symmetric group does for the representation theory of the general linear group in Schur–Weyl ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brieskorn sphere Summary Brieskorn_sphere In mathematics, a Brieskorn manifold or Brieskorn–Phạm manifold, introduced by Egbert Brieskorn (1966, 1966b), is the intersection of a small sphere around the origin with the singular, complex hypersurface x 1 k 1 + ⋯ + x n k n = 0 {\displaystyle x_{1}^{k_{1}}+\cdots +x_{n}^{k... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brieskorn–Grothendieck resolution Summary Brieskorn–Grothendieck_resolution In mathematics, a Brieskorn–Grothendieck resolution is a resolution conjectured by Alexander Grothendieck, that in particular gives a resolution of the universal deformation of a Kleinian singularity. Egbert Brieskorn (1971) announced the const... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brjuno number Summary Brjuno_number In mathematics, a Brjuno number (sometimes spelled Bruno or Bryuno) is a special type of irrational number named for Russian mathematician Alexander Bruno, who introduced them in Brjuno (1971). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Buekenhout geometry Summary Buekenhout_geometry In mathematics, a Buekenhout geometry or diagram geometry is a generalization of projective spaces, Tits buildings, and several other geometric structures, introduced by Buekenhout (1979). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Burniat surface Summary Burniat_surface In mathematics, a Burniat surface is one of the surfaces of general type introduced by Pol Burniat (1966). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Busemann G-space Summary Busemann_G-space It is a special case of the Bing–Borsuk conjecture. The Busemann conjecture is known to be true for dimensions 1 to 4. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Butler group Summary Butler_group In mathematics, a Butler group is a group that is the image of a completely decomposable abelian group of finite rank. They were introduced by M. C. R. Butler (1965). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bézout matrix Summary Bézout_matrix In mathematics, a Bézout matrix (or Bézoutian or Bezoutiant) is a special square matrix associated with two polynomials, introduced by James Joseph Sylvester (1853) and Arthur Cayley (1857) and named after Étienne Bézout. Bézoutian may also refer to the determinant of this matrix, wh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Böhmer integral Summary Böhmer_integral In mathematics, a Böhmer integral is an integral introduced by Böhmer (1939) generalizing the Fresnel integrals. There are two versions, given by C ( x , α ) = ∫ x ∞ t α − 1 cos ( t ) d t {\displaystyle \displaystyle C(x,\alpha )=\int _{x}^{\infty }t^{\alpha -1}\cos(t)\,dt} S (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
C0-semigroup Summary One-parameter_semigroup In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly conti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
CAT space Summary CAT(0)_space In mathematics, a CAT ( k ) {\displaystyle \mathbf {\operatorname {\textbf {CAT}} } (k)} space, where k {\displaystyle k} is a real number, is a specific type of metric space. Intuitively, triangles in a CAT ( k ) {\displaystyle \operatorname {CAT} (k)} space are "slimmer" than correspo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
CAT space Summary CAT(0)_space A notable special case is k = 0 {\displaystyle k=0} ; complete CAT ( 0 ) {\displaystyle \operatorname {CAT} (0)} spaces are known as "Hadamard spaces" after the French mathematician Jacques Hadamard. Originally, Aleksandrov called these spaces “ R k {\displaystyle {\mathfrak {R}}_{k}} d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
CAT(k) group Summary CAT(k)_group In mathematics, a CAT(k) group is a group that acts discretely, cocompactly and isometrically on a CAT(k) space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
CH-quasigroup Summary CH-quasigroup In mathematics, a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH" stands for cubic hypersurface. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
CM-field Summary CM-field In mathematics, a CM-field is a particular type of number field, so named for a close connection to the theory of complex multiplication. Another name used is J-field. The abbreviation "CM" was introduced by (Shimura & Taniyama 1961). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
CR manifold Summary Real-complex_manifold In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differenti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Caccioppoli set Summary Caccioppoli_set In mathematics, a Caccioppoli set is a set whose boundary is measurable and has (at least locally) a finite measure. A synonym is set of (locally) finite perimeter. Basically, a set is a Caccioppoli set if its characteristic function is a function of bounded variation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cannon–Thurston map Summary Cannon–Thurston_map In mathematics, a Cannon–Thurston map is any of a number of continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending a discrete isometric actions of the group on those spaces. The notion originated from a seminal 1980s preprint of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor algebra Summary Cantor_algebra In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete. The countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor algebra Summary Cantor_algebra The complete Cantor algebra is the complete Boolean algebra of Borel subsets of the reals modulo meager sets (Balcar & Jech 2006). It is isomorphic to the completion of the countable Cantor algebra. (The complete Cantor algebra is sometimes called the Cohen algebra, though "Cohen a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor cube Summary Cantor_cube In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself given the discrete topology). If A is a countably in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor cube Summary Cantor_cube (The literature can be unclear, so for safety, assume all spaces are Hausdorff.) Topologically, any Cantor cube is: homogeneous; compact; zero-dimensional; AE(0), an absolute extensor for compact zero-dimensional spaces. (Every map from a closed subset of such a space into a Cantor cube ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor cube Summary Cantor_cube )By a theorem of Schepin, these four properties characterize Cantor cubes; any space satisfying the properties is homeomorphic to a Cantor cube. In fact, every AE(0) space is the continuous image of a Cantor cube, and with some effort one can prove that every compact group is AE(0). It f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor space Summary Cantor_topology In mathematics, a Cantor space, named for Georg Cantor, is a topological abstraction of the classical Cantor set: a topological space is a Cantor space if it is homeomorphic to the Cantor set. In set theory, the topological space 2ω is called "the" Cantor space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carleman matrix Summary Carleman_matrix In mathematics, a Carleman matrix is a matrix used to convert function composition into matrix multiplication. It is often used in iteration theory to find the continuous iteration of functions which cannot be iterated by pattern recognition alone. Other uses of Carleman matrices... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carleson measure Summary Carleson_measure In mathematics, a Carleson measure is a type of measure on subsets of n-dimensional Euclidean space Rn. Roughly speaking, a Carleson measure on a domain Ω is a measure that does not vanish at the boundary of Ω when compared to the surface measure on the boundary of Ω. Carleson ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carlyle circle Summary Carlyle_circle In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the property that the solutions of the quadratic equation are the horizontal coordinates of the intersections of the cir... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carnot group Summary Carnot_group In mathematics, a Carnot group is a simply connected nilpotent Lie group, together with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra. The subbundle of the tangent bundle associated to this eigenspace is called horizontal. On a Carno... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan algebra Summary Cartan_algebra In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra h {\displaystyle {\mathfrak {h}}} of a Lie algebra g {\displaystyle {\mathfrak {g}}} that is self-normalising (if ∈ h {\displaystyle \in {\mathfrak {h}}} for all X ∈ h {\displaystyle X\in {\ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan algebra Summary Cartan_algebra In a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero (e.g., C {\displaystyle \mathbb {C} } ), a Cartan subalgebra is the same thing as a maximal abelian subalgebra consisting of elements x such that the adjoint endomorphism ad (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Casimir invariant Summary Casimir_invariant In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operator, which is a Casimir element... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catalan pseudoprime Summary Catalan_pseudoprime In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence ( − 1 ) n − 1 2 ⋅ C n − 1 2 ≡ 2 ( mod n ) , {\displaystyle (-1)^{\frac {n-1}{2}}\cdot C_{\frac {n-1}{2}}\equiv 2{\pmod {n}},} where Cm denotes the m-th Catalan number. The congrue... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catalan solid Summary Catalan_solid In mathematics, a Catalan solid, or Archimedean dual, is a polyhedron that is dual to an Archimedean solid. There are 13 Catalan solids. They are named for the Belgian mathematician Eugène Catalan, who first described them in 1865. The Catalan solids are all convex. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catalan solid Summary Catalan_solid They are face-transitive but not vertex-transitive. This is because the dual Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catalan solid Summary Catalan_solid However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles. Being face-transitive, Catalan solids are isohedra. Additionally, two of the Catalan solids are edge-transitive: the rhombic dodecahedron and the rhombic triacontahedron. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catalan solid Summary Catalan_solid These are the duals of the two quasi-regular Archimedean solids. Just as prisms and antiprisms are generally not considered Archimedean solids, bipyramids and trapezohedra are generally not considered Catalan solids, despite being face-transitive. Two of the Catalan solids are chiral... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catanese surface Summary Catanese_surface In mathematics, a Catanese surface is one of the surfaces of general type introduced by Fabrizio Catanese (1981). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy initial value problem Summary Cauchy_initial_value_problem In mathematics, a Cauchy (French: ) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy determinant Summary Cauchy_determinant In mathematics, a Cauchy matrix, named after Augustin-Louis Cauchy, is an m×n matrix with elements aij in the form a i j = 1 x i − y j ; x i − y j ≠ 0 , 1 ≤ i ≤ m , 1 ≤ j ≤ n {\displaystyle a_{ij}={\frac {1}{x_{i}-y_{j}}};\quad x_{i}-y_{j}\neq 0,\quad 1\leq i\leq m,\quad 1\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy sequence Summary Regular_Cauchy_sequence In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy sequence Summary Regular_Cauchy_sequence However, with growing values of n, the terms a n {\displaystyle a_{n}} become arbitrarily large. So, for any index n and distance d, there exists an index m big enough such that a m − a n > d . {\displaystyle a_{m}-a_{n}>d.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy sequence Summary Regular_Cauchy_sequence As a result, no matter how far one goes, the remaining terms of the sequence never get close to each other; hence the sequence is not Cauchy. The utility of Cauchy sequences lies in the fact that in a complete metric space (one where all such sequences are known to conver... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy-continuous function Summary Cauchy_continuity In mathematics, a Cauchy-continuous, or Cauchy-regular, function is a special kind of continuous function between metric spaces (or more general spaces). Cauchy-continuous functions have the useful property that they can always be (uniquely) extended to the Cauchy co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cayley graph Summary Cayley_diagram In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of gener... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cayley metric Summary Cayley–Klein_metric In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory of distance" where he calls the quadric the absolute. The con... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chevalley basis Summary Chevalley_basis In mathematics, a Chevalley basis for a simple complex Lie algebra is a basis constructed by Claude Chevalley with the property that all structure constants are integers. Chevalley used these bases to construct analogues of Lie groups over finite fields, called Chevalley groups. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chevalley basis Summary Chevalley_basis The generators of a Lie group are split into the generators H and E indexed by simple roots and their negatives ± α i {\displaystyle \pm \alpha _{i}} . The Cartan-Weyl basis may be written as = 0 {\displaystyle =0} = α i E α {\displaystyle =\alpha _{i}E_{\alpha }} Defining the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chevalley basis Summary Chevalley_basis We then call ( β , γ ) {\displaystyle (\beta ,\gamma )} an extraspecial pair of roots if they are both positive and β {\displaystyle \beta } is minimal among all β 0 {\displaystyle \beta _{0}} that occur in pairs of positive roots ( β 0 , γ 0 ) {\displaystyle (\beta _{0},\gamma _... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clifford multiplication Summary Clifford_Algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clifford bundle Summary Clifford_bundle In mathematics, a Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford algebra and whose local trivializations respect the algebra structure. There is a natural Clifford bundle associated to any (pseudo) Riemannian manifold M which is called the Clif... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clifford module Summary Clifford_module In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field K over which the quadratic form Q defining C is defined. The abstract theory of Clifford modules was f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clifford–Klein form Summary Clifford-Klein_form In mathematics, a Clifford–Klein form is a double coset space Γ\G/H,where G is a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space G/H. A suitable discrete subgroup Γ may or may not ex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohen–Macaulay ring Summary Cohen–Macaulay_ring In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohen–Macaulay ring Summary Cohen–Macaulay_ring All Cohen–Macaulay rings have the unmixedness property. For Noetherian local rings, there is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Colombeau algebra Summary Colombeau_algebra In mathematics, a Colombeau algebra is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Such... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Colombeau algebra Summary Colombeau_algebra As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory. These algebras have found numerous applications in the fields of partial ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coons surface Summary Coons_surface In mathematics, a Coons patch, is a type of surface patch or manifold parametrization used in computer graphics to smoothly join other surfaces together, and in computational mechanics applications, particularly in finite element method and boundary element method, to mesh problem do... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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