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Sierpinski space Summary Sierpinski_space In mathematics, the Sierpiński space (or the connected two-point set) is a finite topological space with two points, only one of which is closed. It is the smallest example of a topological space which is neither trivial nor discrete. It is named after Wacław Sierpiński. The Si... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Silverman–Toeplitz theorem Summary Matrix_summability_method In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a matrix transformation of a convergent sequenc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Simon problems Summary Simon_problems In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilber... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sims conjecture Summary Sims_conjecture In mathematics, the Sims conjecture is a result in group theory, originally proposed by Charles Sims. He conjectured that if G {\displaystyle G} is a primitive permutation group on a finite set S {\displaystyle S} and G α {\displaystyle G_{\alpha }} denotes the stabilizer of the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sims conjecture Summary Sims_conjecture Thus, in a primitive permutation group with "large" stabilizers, these stabilizers cannot have any small orbit. A consequence of their proof is that there exist only finitely many connected distance-transitive graphs having degree greater than 2. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sister Beiter conjecture Summary Sister_Beiter_conjecture In mathematics, the Sister Beiter conjecture is a conjecture about the size of coefficients of ternary cyclotomic polynomials (i.e. where the index is the product of three prime numbers). It is named after Marion Beiter, a Catholic nun who first proposed it in 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Skolem problem Summary Skolem_problem In mathematics, the Skolem problem is the problem of determining whether the values of a constant-recursive sequence include the number zero. The problem can be formulated for recurrences over different types of numbers, including integers, rational numbers, and algebraic numbers. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Skolem problem Summary Skolem_problem This theorem states that, if such a sequence has zeros, then with finitely many exceptions the positions of the zeros repeat regularly. Skolem proved this for recurrences over the rational numbers, and Mahler and Lech extended it to other systems of numbers. However, the proofs of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Skolem problem Summary Skolem_problem There does exist an algorithm to test whether a constant-recursive sequence has infinitely many zeros, and if so to construct a decomposition of the positions of those zeros into periodic subsequences, based on the algebraic properties of the roots of the characteristic polynomial ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Smith conjecture Summary Smith_conjecture In mathematics, the Smith conjecture states that if f is a diffeomorphism of the 3-sphere of finite order, then the fixed point set of f cannot be a nontrivial knot. Paul A. Smith (1939, remark after theorem 4) showed that a non-trivial orientation-preserving diffeomorphism of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Smith conjecture Summary Smith_conjecture The proof of the general case was described by John Morgan and Hyman Bass (1984) and depended on several major advances in 3-manifold theory, In particular the work of William Thurston on hyperbolic structures on 3-manifolds, and results by William Meeks and Shing-Tung Yau on m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Smith normal form Summary Smith_normal_form In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries in a principal ideal domain (PID). The Smith normal form of a matrix is diagonal, and can be obtained from the original ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Siegel mass formula Summary Smith–Minkowski–Siegel_mass_formula In mathematics, the Smith–Minkowski–Siegel mass formula (or Minkowski–Siegel mass formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism groups. The mas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Siegel mass formula Summary Smith–Minkowski–Siegel_mass_formula It was rediscovered by H. Minkowski (1885), and an error in Minkowski's paper was found and corrected by C. L. Siegel (1935). Many published versions of the mass formula have errors; in particular the 2-adic densities are difficult to get right, and it is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Smith–Volterra–Cantor set Summary Smith–Volterra–Cantor_set In mathematics, the Smith–Volterra–Cantor set (SVC), fat Cantor set, or ε-Cantor set is an example of a set of points on the real line that is nowhere dense (in particular it contains no intervals), yet has positive measure. The Smith–Volterra–Cantor set is na... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck–Springer simultaneous resolution Summary Springer_resolution In mathematics, the Springer resolution is a resolution of the variety of nilpotent elements in a semisimple Lie algebra, or the unipotent elements of a reductive algebraic group, introduced by Tonny Albert Springer in 1969. The fibers of this re... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stallings–Zeeman theorem Summary Stallings–Zeeman_theorem In mathematics, the Stallings–Zeeman theorem is a result in algebraic topology, used in the proof of the Poincaré conjecture for dimension greater than or equal to five. It is named after the mathematicians John R. Stallings and Christopher Zeeman. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Steinberg representation Summary Steinberg_representation In mathematics, the Steinberg representation, or Steinberg module or Steinberg character, denoted by St, is a particular linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is analogous to the 1-... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Steinberg representation Summary Steinberg_representation Over a finite field of characteristic p, the Steinberg representation has degree equal to the largest power of p dividing the order of the group. The Steinberg representation is the Alvis–Curtis dual of the trivial 1-dimensional representation. Matsumoto (1969),... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
3D4 Summary 3D4 In mathematics, the Steinberg triality groups of type 3D4 form a family of Steinberg or twisted Chevalley groups. They are quasi-split forms of D4, depending on a cubic Galois extension of fields K ⊂ L, and using the triality automorphism of the Dynkin diagram D4. Unfortunately the notation for the grou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
3D4 Summary 3D4 The group 3D4 is very similar to an orthogonal or spin group in dimension 8. Over finite fields these groups form one of the 18 infinite families of finite simple groups, and were introduced by Steinberg (1959). They were independently discovered by Jacques Tits in Tits (1958) and Tits (1959). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stein–Strömberg theorem Summary Stein–Strömberg_theorem In mathematics, the Stein–Strömberg theorem or Stein–Strömberg inequality is a result in measure theory concerning the Hardy–Littlewood maximal operator. The result is foundational in the study of the problem of differentiation of integrals. The result is named af... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stiefel manifold Summary Stiefel_manifold In mathematics, the Stiefel manifold V k ( R n ) {\displaystyle V_{k}(\mathbb {R} ^{n})} is the set of all orthonormal k-frames in R n . {\displaystyle \mathbb {R} ^{n}.} That is, it is the set of ordered orthonormal k-tuples of vectors in R n . {\displaystyle \mathbb {R} ^{n}.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stiefel manifold Summary Stiefel_manifold It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold V k ( C n ) {\displaystyle V_{k}(\mathbb {C} ^{n})} of orthonormal k-frames in C n {\displaystyle \mathbb {C} ^{n}} and the quaternionic Stiefel manifold V k ( H n ) {\dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stieltjes constants Summary Stieltjes_constants In mathematics, the Stieltjes constants are the numbers γ k {\displaystyle \gamma _{k}} that occur in the Laurent series expansion of the Riemann zeta function: ζ ( 1 + s ) = 1 s + ∑ n = 0 ∞ ( − 1 ) n n ! γ n s n . {\displaystyle \zeta (1+s)={\frac {1}{s}}+\sum _{n=0}^{\i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stieltjes moment problem Summary Stieltjes_moment_problem In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2, ...) to be of the form m n = ∫ 0 ∞ x n d μ ( x ) {\displaystyle m_{n}=\int _{0}^{\infty }x^{n}\,d\mu (x)} fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stieltjes polynomials Summary Stieltjes_polynomials In mathematics, the Stieltjes polynomials En are polynomials associated to a family of orthogonal polynomials Pn. They are unrelated to the Stieltjes polynomial solutions of differential equations. Stieltjes originally considered the case where the orthogonal polynomi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stirling polynomial Summary Stirling_polynomial In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stolarsky mean Summary Stolarsky_mean In mathematics, the Stolarsky mean is a generalization of the logarithmic mean. It was introduced by Kenneth B. Stolarsky in 1975. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stolz–Cesàro theorem Summary Stolz–Cesàro_theorem In mathematics, the Stolz–Cesàro theorem is a criterion for proving the convergence of a sequence. The theorem is named after mathematicians Otto Stolz and Ernesto Cesàro, who stated and proved it for the first time. The Stolz–Cesàro theorem can be viewed as a generaliz... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stone functor Summary Stone_functor In mathematics, the Stone functor is a functor S: Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space X the Boolean algebra S(X) of its clopen subsets, and to each m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stoneham number Summary Stoneham_number In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G. Stoneham (1920–1996). For coprime numbers b, c > 1, the Stoneham number αb,c is defined as α b , c = ∑ n = c k > 1 1 b n n = ∑ k = 1 ∞ 1 b c k c k {\displaystyle \alpha ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Strahler stream order Summary Strahler_number In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology, as a way of measuring the complexity of rivers and streams, by Robert E. Horton (1945) a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Strömberg wavelet Summary Strömberg_wavelet In mathematics, the Strömberg wavelet is a certain orthonormal wavelet discovered by Jan-Olov Strömberg and presented in a paper published in 1983. Even though the Haar wavelet was earlier known to be an orthonormal wavelet, Strömberg wavelet was the first smooth orthonormal ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sturm theorem Summary Sturm_theorem In mathematics, the Sturm sequence of a univariate polynomial p is a sequence of polynomials associated with p and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval in terms of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sturm theorem Summary Sturm_theorem By subdividing the intervals containing some roots, it can isolate the roots into arbitrarily small intervals, each containing exactly one root. This yields the oldest real-root isolation algorithm, and arbitrary-precision root-finding algorithm for univariate polynomials. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sturm theorem Summary Sturm_theorem For computing over the reals, Sturm's theorem is less efficient than other methods based on Descartes' rule of signs. However, it works on every real closed field, and, therefore, remains fundamental for the theoretical study of the computational complexity of decidability and quanti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sturm series Summary Sturm_series In mathematics, the Sturm series associated with a pair of polynomials is named after Jacques Charles François Sturm. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sugeno integral Summary Sugeno_integral In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure. Let ( X , Ω ) {\displaystyle (X,\Omega )} be a measurable space and let h: X → {\displaystyle h:X\to } be an Ω {\displaystyle \Omega } -measurable function. The Sug... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suita conjecture Summary Suita_conjecture In mathematics, the Suita conjecture is a conjecture related to the theory of the Riemann surface, the boundary behavior of conformal maps, the theory of Bergman kernel, and the theory of the L2 extension. The conjecture states the following: Suita (1972): Let R be an Riemann s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suita conjecture Summary Suita_conjecture Let c β ( z ) {\displaystyle c_{\beta }(z)} be the logarithmic capacity which is locally defined by c β ( z 0 ) := exp lim ξ → z ( G R ( z , z 0 ) − log | ω ( z ) | ) {\displaystyle c_{\beta }(z_{0}):=\exp \lim _{\xi \to z}(G_{R}(z,z_{0})-\log |\omega (z)|)} on R. Then, the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Singular homology of abstract algebraic varieties Summary Singular_homology_of_abstract_algebraic_varieties In mathematics, the Suslin homology is a homology theory attached to algebraic varieties. It was proposed by Suslin in 1987, and developed by Suslin and Voevodsky (1996). It is sometimes called singular homology ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suslin scheme Summary Suslin_scheme In mathematics, the Suslin operation 𝓐 is an operation that constructs a set from a collection of sets indexed by finite sequences of positive integers. The Suslin operation was introduced by Alexandrov (1916) and Suslin (1917). In Russia it is sometimes called the A-operation after... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Séminaire de Géométrie Algébrique du Bois Marie Summary Séminaire_de_Géométrie_Algébrique_du_Bois_Marie In mathematics, the Séminaire de Géométrie Algébrique du Bois Marie (SGA) was an influential seminar run by Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathemati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
T(1) theorem Summary T(1)_theorem In mathematics, the T(1) theorem, first proved by David & Journé (1984), describes when an operator T given by a kernel can be extended to a bounded linear operator on the Hilbert space L2(Rn). The name T(1) theorem refers to a condition on the distribution T(1), given by the operator ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
T-square (fractal) Summary T-square_(fractal) In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing instrument known as a T-square. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tamagawa number Summary Tamagawa_number In mathematics, the Tamagawa number τ ( G ) {\displaystyle \tau (G)} of a semisimple algebraic group defined over a global field k is the measure of G ( A ) / G ( k ) {\displaystyle G(\mathbb {A} )/G(k)} , where A {\displaystyle \mathbb {A} } is the adele ring of k. Tamagawa numb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taniyama group Summary Taniyama_group In mathematics, the Taniyama group is a group that is an extension of the absolute Galois group of the rationals by the Serre group. It was introduced by Langlands (1977) using an observation by Deligne, and named after Yutaka Taniyama. It was intended to be the group scheme whose ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tarski–Seidenberg theorem Summary Tarski–Seidenberg_theorem In mathematics, the Tarski–Seidenberg theorem states that a set in (n + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tarski–Seidenberg theorem Summary Tarski–Seidenberg_theorem An important consequence is the decidability of the theory of real-closed fields. Although the original proof of the theorem was constructive, the resulting algorithm has a computational complexity that is too high for using the method on a computer. George E.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tate curve Summary Tate_curve In mathematics, the Tate curve is a curve defined over the ring of formal power series Z ] {\displaystyle \mathbb {Z} ]} with integer coefficients. Over the open subscheme where q is invertible, the Tate curve is an elliptic curve. The Tate curve can also be defined for q as an element of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tate topology Summary Tate_topology In mathematics, the Tate topology is a Grothendieck topology of the space of maximal ideals of a k-affinoid algebra, whose open sets are the admissible open subsets and whose coverings are the admissible open coverings. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taylor polynomial Summary Taylor_series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taylor polynomial Summary Taylor_series The partial sum formed by the first n + 1 terms of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally more accurate as n increases. Taylor's theorem give... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taylor polynomial Summary Taylor_series If the Taylor series of a function is convergent, its sum is the limit of the infinite sequence of the Taylor polynomials. A function may differ from the sum of its Taylor series, even if its Taylor series is convergent. A function is analytic at a point x if it is equal to the s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Teichmüller cocycle Summary Teichmüller_cocycle In mathematics, the Teichmüller cocycle is a certain 3-cocycle associated to a simple algebra A over a field L which is a finite Galois extension of a field K and which has the property that any automorphism of L over K extends to an automorphism of A. The Teichmüller coc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Teichmüller theory Summary Bers_compactification In mathematics, the Teichmüller space T ( S ) {\displaystyle T(S)} of a (real) topological (or differential) surface S {\displaystyle S} , is a space that parametrizes complex structures on S {\displaystyle S} up to the action of homeomorphisms that are isotopic to the i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Teichmüller theory Summary Bers_compactification It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it with a natural topology for which it is homeomorphic to a ball of dimension 6 g − 6 {\displaystyle 6g-6} for a surface of genus g ≥ 2 {\displaystyle g\geq 2} . In this w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Low dimensional topology Teichmüller space Low-dimensional_topology > Two dimensions > Teichmüller space In mathematics, the Teichmüller space TX of a (real) topological surface X, is a space that parameterizes complex structures on X up to the action of homeomorphisms that are isotopic to the identity homeomorphism. E... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tukey's lemma Summary Teichmüller–Tukey_lemma In mathematics, the Teichmüller–Tukey lemma (sometimes named just Tukey's lemma), named after John Tukey and Oswald Teichmüller, is a lemma that states that every nonempty collection of finite character has a maximal element with respect to inclusion. Over Zermelo–Fraenkel ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thom spectrum Summary Thom_spectrum In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thomas–Fermi equation Summary Thomas–Fermi_equation In mathematics, the Thomas–Fermi equation for the neutral atom is a second order non-linear ordinary differential equation, named after Llewellyn Thomas and Enrico Fermi, which can be derived by applying the Thomas–Fermi model to atoms. The equation reads d 2 y d x 2 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson groups Summary Thompson_groups In mathematics, the Thompson groups (also called Thompson's groups, vagabond groups or chameleon groups) are three groups, commonly denoted F ⊆ T ⊆ V {\displaystyle F\subseteq T\subseteq V} , that were introduced by Richard Thompson in some unpublished handwritten notes in 1965 a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson groups Summary Thompson_groups The groups T and V are (rare) examples of infinite but finitely-presented simple groups. The group F is not simple but its derived subgroup is and the quotient of F by its derived subgroup is the free abelian group of rank 2. F is totally ordered, has exponential growth, and doe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thue-Morse Sequence Summary Thue-Morse_Sequence In mathematics, the Thue–Morse sequence or Prouhet–Thue–Morse sequence or parity sequence is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thurston boundary Summary Thurston_boundary In mathematics, the Thurston boundary of Teichmüller space of a surface is obtained as the boundary of its closure in the projective space of functionals on simple closed curves on the surface. The Thurston boundary can be interpreted as the space of projective measured folia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thurston norm Summary Thurston_norm In mathematics, the Thurston norm is a function on the second homology group of an oriented 3-manifold introduced by William Thurston, which measures in a natural way the topological complexity of homology classes represented by surfaces. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tits alternative Summary Tits_alternative In mathematics, the Tits alternative, named after Jacques Tits, is an important theorem about the structure of finitely generated linear groups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Toda bracket Summary Toda_bracket In mathematics, the Toda bracket is an operation on homotopy classes of maps, in particular on homotopy groups of spheres, named after Hiroshi Toda, who defined them and used them to compute homotopy groups of spheres in (Toda 1962). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Todd class Summary Todd_class In mathematics, the Todd class is a certain construction now considered a part of the theory in algebraic topology of characteristic classes. The Todd class of a vector bundle can be defined by means of the theory of Chern classes, and is encountered where Chern classes exist — most notabl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tonelli–Hobson test Summary Tonelli–Hobson_test In mathematics, the Tonelli–Hobson test gives sufficient criteria for a function ƒ on R2 to be an integrable function. It is often used to establish that Fubini's theorem may be applied to ƒ. It is named for Leonida Tonelli and E. W. Hobson. More precisely, the Tonelli–Ho... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tor functor Summary Torsion_functor In mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central concepts of homological algebra, in which ideas from algebraic topology are used to construct invariants of algebraic structur... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tor functor Summary Torsion_functor In the special case of abelian groups, Tor was introduced by Eduard Čech (1935) and named by Samuel Eilenberg around 1950. It was first applied to the Künneth theorem and universal coefficient theorem in topology. For modules over any ring, Tor was defined by Henri Cartan and Eilenbe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Torelli's theorem Summary Torelli's_theorem In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) C is determined by its Jacobian variety J(C), when th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Torelli's theorem Summary Torelli's_theorem Generalizations are in two directions. Firstly, to geometric questions about that morphism, for example the local Torelli theorem. Secondly, to other period mappings. A case that has been investigated deeply is for K3 surfaces (by Viktor S. Kulikov, Ilya Pyatetskii-Shapiro, I... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trefftz method Summary Trefftz_method In mathematics, the Trefftz method is a method for the numerical solution of partial differential equations named after the German mathematician Erich Trefftz(de) (1888–1937). It falls within the class of finite element methods. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tricomi–Carlitz polynomial Summary Tricomi–Carlitz_polynomial In mathematics, the Tricomi–Carlitz polynomials or (Carlitz–)Karlin–McGregor polynomials are polynomials studied by Tricomi (1951) and Carlitz (1958) and Karlin and McGregor (1959), related to random walks on the positive integers. They are given in terms of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trombi–Varadarajan theorem Summary Trombi–Varadarajan_theorem In mathematics, the Trombi–Varadarajan theorem, introduced by Trombi and Varadarjan (1971), gives an isomorphism between a certain space of spherical functions on a semisimple Lie group, and a certain space of holomorphic functions defined on a tubular neigh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Turán number Summary Turán_number In mathematics, the Turán number T(n,k,r) for r-uniform hypergraphs of order n is the smallest number of r-edges such that every induced subgraph on k vertices contains an edge. This number was determined for r = 2 by Turán (1941), and the problem for general r was introduced in Turán ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tutte homotopy theorem Summary Tutte_homotopy_theorem In mathematics, the Tutte homotopy theorem, introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly that closed paths can be written as compositions of elementary closed paths, so that in some sense they are homotopi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Twisted Hessian curves Summary Twisted_Hessian_curves In mathematics, the Twisted Hessian curve represents a generalization of Hessian curves; it was introduced in elliptic curve cryptography to speed up the addition and doubling formulas and to have strongly unified arithmetic. In some operations (see the last section... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ulam numbers Summary Ulam_numbers In mathematics, the Ulam numbers comprise an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with U1 = 1 and U2 = 2. Then for n > 2, Un is defined to be the smallest integer that is the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Valentiner group Summary Valentiner_group In mathematics, the Valentiner group is the perfect triple cover of the alternating group on 6 points, and is a group of order 1080. It was found by Herman Valentiner (1889) in the form of an action of A6 on the complex projective plane, and was studied further by Wiman (1896).... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Veblen functions Summary Veblen_hierarchy In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in Veblen (1908). If φ0 is any normal function, then for any non-zero ordinal α, φα is the function enumera... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Veblen–Young theorem Summary Veblen–Young_theorem In mathematics, the Veblen–Young theorem, proved by Oswald Veblen and John Wesley Young (1908, 1910, 1917), states that a projective space of dimension at least 3 can be constructed as the projective space associated to a vector space over a division ring. Non-Desargues... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Veronese surface Summary Veronese_surface In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics. It is named after Giuseppe Veronese (1854–1917). It... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Verschiebung operator Summary Verschiebung_operator In mathematics, the Verschiebung or Verschiebung operator V is a homomorphism between affine commutative group schemes over a field of nonzero characteristic p. For finite group schemes it is the Cartier dual of the Frobenius homomorphism. It was introduced by Witt (1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Virasoro algebra Summary Virasoro_algebra In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vitali covering lemma Summary Vitali_covering_lemma In mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. This lemma is an intermediate step, of independent interest, in the proof of the Vitali covering theorem. The covering theorem is cre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vitali–Carathéodory theorem Summary Vitali–Carathéodory_theorem In mathematics, the Vitali–Carathéodory theorem is a result in real analysis that shows that, under the conditions stated below, integrable functions can be approximated in L1 from above and below by lower- and upper-semicontinuous functions, respectively.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vitali–Hahn–Saks theorem Summary Vitali–Hahn–Saks_theorem In mathematics, the Vitali–Hahn–Saks theorem, introduced by Vitali (1907), Hahn (1922), and Saks (1933), proves that under some conditions a sequence of measures converging point-wise does so uniformly and the limit is also a measure. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vogel plane Summary Vogel_plane In mathematics, the Vogel plane is a method of parameterizing simple Lie algebras by eigenvalues α, β, γ of the Casimir operator on the symmetric square of the Lie algebra, which gives a point (α: β: γ) of P2/S3, the projective plane P2 divided out by the symmetric group S3 of permutatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volterra integral equation Summary Volterra_equation In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind. A linear Volterra equation of the first kind is f ( t ) = ∫ a t K ( t , s ) x ( s ) d s {\displays... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volterra integral equation Summary Volterra_equation {\displaystyle x(t)=f(t)+\int _{a}^{t}K(t,s)x(s)\,ds.} In operator theory, and in Fredholm theory, the corresponding operators are called Volterra operators. A useful method to solve such equations, the Adomian decomposition method, is due to George Adomian. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volterra integral equation Summary Volterra_equation A linear Volterra integral equation is a convolution equation if x ( t ) = f ( t ) + ∫ t 0 t K ( t − s ) x ( s ) d s . {\displaystyle x(t)=f(t)+\int _{t_{0}}^{t}K(t-s)x(s)\,ds.} The function K {\displaystyle K} in the integral is called the kernel. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volterra integral equation Summary Volterra_equation Such equations can be analyzed and solved by means of Laplace transform techniques. For a weakly singular kernel of the form K ( t , s ) = ( t 2 − s 2 ) − α {\displaystyle K(t,s)=(t^{2}-s^{2})^{-\alpha }} with 0 < α < 1 {\displaystyle 0<\alpha <1} , Volterra integral... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volterra lattice Summary Volterra_lattice In mathematics, the Volterra lattice, also known as the discrete KdV equation, the Kac–van Moerbeke lattice, and the Langmuir lattice, is a system of ordinary differential equations with variables indexed by some of the points of a 1-dimensional lattice. It was introduced by Ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volterra lattice Summary Volterra_lattice The Volterra lattice also behaves like a discrete version of the KdV equation. The Volterra lattice is an integrable system, and is related to the Toda lattice. It is also used as a model for Langmuir waves in plasmas. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Voorhoeve index Summary Voorhoeve_index In mathematics, the Voorhoeve index is a non-negative real number associated with certain functions on the complex numbers, named after Marc Voorhoeve. It may be used to extend Rolle's theorem from real functions to complex functions, taking the role that for real functions is pl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vámos matroid Summary Vámos_matroid In mathematics, the Vámos matroid or Vámos cube is a matroid over a set of eight elements that cannot be represented as a matrix over any field. It is named after English mathematician Peter Vámos, who first described it in an unpublished manuscript in 1968. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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