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Kervaire invariant Summary Kervaire_invariant In mathematics, the Kervaire invariant is an invariant of a framed ( 4 k + 2 ) {\displaystyle (4k+2)} -dimensional manifold that measures whether the manifold could be surgically converted into a sphere. This invariant evaluates to 0 if the manifold can be converted to a sp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kervaire invariant Summary Kervaire_invariant It can be thought of as the simply-connected quadratic L-group L 4 k + 2 {\displaystyle L_{4k+2}} , and thus analogous to the other invariants from L-theory: the signature, a 4 k {\displaystyle 4k} -dimensional invariant (either symmetric or quadratic, L 4 k ≅ L 4 k {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kervaire invariant Summary Kervaire_invariant The Kervaire invariant problem is the problem of determining in which dimensions the Kervaire invariant can be nonzero. For differentiable manifolds, this can happen in dimensions 2, 6, 14, 30, 62, and possibly 126, and in no other dimensions. The final case of dimension 12... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kervaire semi-characteristic Summary Kervaire_semi-characteristic In mathematics, the Kervaire semi-characteristic, introduced by Michel Kervaire (1956), is an invariant of closed manifolds M of dimension 4 n + 1 {\displaystyle 4n+1} taking values in Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } , given by k ( M )... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Face-splitting product Summary Face-splitting_product In mathematics, the Khatri–Rao product of matrices is defined as A ∗ B = ( A i j ⊗ B i j ) i j {\displaystyle \mathbf {A} \ast \mathbf {B} =\left(\mathbf {A} _{ij}\otimes \mathbf {B} _{ij}\right)_{ij}} in which the ij-th block is the mipi × njqj sized Kronecker prod... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Khinchin integral Summary Khinchin_integral In mathematics, the Khinchin integral (sometimes spelled Khintchine integral), also known as the Denjoy–Khinchin integral, generalized Denjoy integral or wide Denjoy integral, is one of a number of definitions of the integral of a function. It is a generalization of the Riema... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Khintchine inequality Summary Khintchine_inequality In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick N {\displaystyle N} complex num... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Killing form Summary Killing_form In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras. Cartan's criteria (criterion of solvability and criterion of semisimplicity) show that Killing form has a close relationsh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kirby calculus Summary Kirby_moves In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kirby calculus Summary Kirby_moves Different presentations of "Kirby calculus" have a different set of moves and these are sometimes called Kirby moves. Kirby's original formulation involved two kinds of move, the "blow-up" and the "handle slide"; Roger Fenn and Colin Rourke exhibited an equivalent construction in term... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kirby calculus Summary Kirby_moves This allows an extension of the Kirby calculus to rational surgeries. There are also various tricks to modify surgery diagrams. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kirby calculus Summary Kirby_moves One such useful move is the slam-dunk. An extended set of diagrams and moves are used for describing 4-manifolds. A framed link in the 3-sphere encodes instructions for attaching 2-handles to the 4-ball. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kirby calculus Summary Kirby_moves (The 3-dimensional boundary of this manifold is the 3-manifold interpretation of the link diagram mentioned above.) 1-handles are denoted by either a pair of 3-balls (the attaching region of the 1-handle) or, more commonly, unknotted circles with dots. The dot indicates that a neighbo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kleene–Rosser paradox Summary Kleene–Rosser_paradox In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda calculus, introduced in 1932... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Klein bottle Summary Klein_bottle In mathematics, the Klein bottle () is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. More formally, the Klein bottle is a two-dimensional m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Klein bottle Summary Klein_bottle While a Möbius strip is a surface with boundary, a Klein bottle has no boundary. For comparison, a sphere is an orientable surface with no boundary. The Klein bottle was first described in 1882 by the mathematician Felix Klein. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Klein 4-group Summary Klein_4-group In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces the identity) and in which composing any two of the three non-identity elements produces the third one. It can be described as the sym... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Klein 4-group Summary Klein_4-group The Klein four-group, with four elements, is the smallest group that is not a cyclic group. There is only one other group of order four, up to isomorphism, the cyclic group of order 4. Both are abelian groups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kneser's theorem (differential equations) Summary Kneser's_theorem_(differential_equations) In mathematics, the Kneser theorem can refer to two distinct theorems in the field of ordinary differential equations: the first one, named after Adolf Kneser, provides criteria to decide whether a differential equation is oscil... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kneser–Tits conjecture Summary Kneser–Tits_conjecture In mathematics, the Kneser–Tits problem, introduced by Tits (1964) based on a suggestion by Martin Kneser, asks whether the Whitehead group W(G,K) of a semisimple simply connected isotropic algebraic group G over a field K is trivial. The Whitehead group is the quot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kodaira embedding theorem Summary Kodaira_embedding_theorem In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds. In effect it says precisely which complex manifolds are defined by homogeneous polynomials. Kunihiko Koda... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kodaira embedding theorem Summary Kodaira_embedding_theorem The converse that projective manifolds are Hodge manifolds is more elementary and was already known. Kodaira also proved (Kodaira 1963), by recourse to the classification of compact complex surfaces, that every compact Kähler surface is a deformation of a proj... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kodaira vanishing theorem Summary Kodaira_vanishing_theory In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the grou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kodaira–Spencer map Summary Kodaira–Spencer_map In mathematics, the Kodaira–Spencer map, introduced by Kunihiko Kodaira and Donald C. Spencer, is a map associated to a deformation of a scheme or complex manifold X, taking a tangent space of a point of the deformation space to the first cohomology group of the sheaf of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Koenigs function Summary Koenigs_function In mathematics, the Koenigs function is a function arising in complex analysis and dynamical systems. Introduced in 1884 by the French mathematician Gabriel Koenigs, it gives a canonical representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kolakoski sequence Summary Kolakoski_sequence In mathematics, the Kolakoski sequence, sometimes also known as the Oldenburger–Kolakoski sequence, is an infinite sequence of symbols {1,2} that is the sequence of run lengths in its own run-length encoding. It is named after the recreational mathematician William Kolakosk... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kolmogorov continuity theorem Summary Kolmogorov_continuity_theorem In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments of its increments will be continuous (or, more precisely, have a "continuous version"). It is cre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kolmogorov extension theorem Summary Kolmogorov_extension_theorem In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Konhauser polynomials Summary Konhauser_polynomials In mathematics, the Konhauser polynomials, introduced by Konhauser (1967), are biorthogonal polynomials for the distribution function of the Laguerre polynomials. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kontorovich–Lebedev transform Summary Kontorovich–Lebedev_transform In mathematics, the Kontorovich–Lebedev transform is an integral transform which uses a Macdonald function (modified Bessel function of the second kind) with imaginary index as its kernel. Unlike other Bessel function transforms, such as the Hankel tra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kontorovich–Lebedev transform Summary Kontorovich–Lebedev_transform Laguerre previously studied a similar transform regarding Laguerre function as: g ( y ) = ∫ 0 ∞ f ( x ) e − x L y ( x ) d x {\displaystyle g(y)=\int _{0}^{\infty }f(x)e^{-x}L_{y}(x)\,dx} f ( x ) = ∫ 0 ∞ g ( y ) Γ ( y ) L y ( x ) d y . {\displaystyle f(... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kontsevich quantization formula Summary Kontsevich_quantization_formula In mathematics, the Kontsevich quantization formula describes how to construct a generalized ★-product operator algebra from a given arbitrary finite-dimensional Poisson manifold. This operator algebra amounts to the deformation quantization of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Korteweg de Vries equation Summary KdV_equation In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an integrable PDE and exhibits many of the expe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kostant polynomial Summary Kostant_polynomial In mathematics, the Kostant polynomials, named after Bertram Kostant, provide an explicit basis of the ring of polynomials over the ring of polynomials invariant under the finite reflection group of a root system. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kostka number Summary Kostka_number In mathematics, the Kostka number K λ μ {\displaystyle K_{\lambda \mu }} (depending on two integer partitions λ {\displaystyle \lambda } and μ {\displaystyle \mu } ) is a non-negative integer that is equal to the number of semistandard Young tableaux of shape λ {\displaystyle \lambda... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Koszul cohomology Summary Koszul_cohomology In mathematics, the Koszul cohomology groups K p , q ( X , L ) {\displaystyle K_{p,q}(X,L)} are groups associated to a projective variety X with a line bundle L. They were introduced by Mark Green (1984, 1984b), and named after Jean-Louis Koszul as they are closely related to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Koszul complex Summary Koszul_complex In mathematics, the Koszul complex was first introduced to define a cohomology theory for Lie algebras, by Jean-Louis Koszul (see Lie algebra cohomology). It turned out to be a useful general construction in homological algebra. As a tool, its homology can be used to tell when a se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kronecker delta function Summary Kronecker_delta In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: or with use of Iverson brackets: For example, δ 12 = 0 {\displaystyle \d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kronecker delta function Summary Kronecker_delta In linear algebra, the n × n {\displaystyle n\times n} identity matrix I {\displaystyle \mathbf {I} } has entries equal to the Kronecker delta: where i {\displaystyle i} and j {\displaystyle j} take the values 1 , 2 , ⋯ , n {\displaystyle 1,2,\cdots ,n} , and the inner p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kronecker sum of discrete Laplacians Summary Kronecker_sum_of_discrete_Laplacians In mathematics, the Kronecker sum of discrete Laplacians, named after Leopold Kronecker, is a discrete version of the separation of variables for the continuous Laplacian in a rectangular cuboid domain. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Krull–Schmidt theorem Summary Krull–Schmidt_theorem In mathematics, the Krull–Schmidt theorem states that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Krylov–Bogolyubov theorem Summary Krylov–Bogolyubov_theorem In mathematics, the Krylov–Bogolyubov theorem (also known as the existence of invariant measures theorem) may refer to either of the two related fundamental theorems within the theory of dynamical systems. The theorems guarantee the existence of invariant meas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kubilius model Summary Kubilius_model In mathematics, the Kubilius model relies on a clarification and extension of a finite probability space on which the behaviour of additive arithmetic functions can be modeled by sum of independent random variables.The method was introduced in Jonas Kubilius's monograph Tikimybinia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kummer variety Summary Kummer_variety In mathematics, the Kummer variety of an abelian variety is its quotient by the map taking any element to its inverse. The Kummer variety of a 2-dimensional abelian variety is called a Kummer surface. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vandiver conjecture Summary Kummer–Vandiver_conjecture In mathematics, the Kummer–Vandiver conjecture, or Vandiver conjecture, states that a prime p does not divide the class number hK of the maximal real subfield K = Q ( ζ p ) + {\displaystyle K=\mathbb {Q} (\zeta _{p})^{+}} of the p-th cyclotomic field. The conjectur... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kuramoto–Sivashinsky equation Summary Kuramoto–Sivashinsky_equation In mathematics, the Kuramoto–Sivashinsky equation (also called the KS equation or flame equation) is a fourth-order nonlinear partial differential equation. It is named after Yoshiki Kuramoto and Gregory Sivashinsky, who derived the equation in the lat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kuratowski and Ryll-Nardzewski measurable selection theorem Summary Kuratowski_and_Ryll-Nardzewski_measurable_selection_theorem In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable sel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kuratowski–Ulam theorem Summary Kuratowski–Ulam_theorem In mathematics, the Kuratowski–Ulam theorem, introduced by Kazimierz Kuratowski and Stanislaw Ulam (1932), called also the Fubini theorem for category, is an analog of Fubini's theorem for arbitrary second countable Baire spaces. Let X and Y be second countable Ba... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kuratowski–Ulam theorem Summary Kuratowski–Ulam_theorem comeager) in Y } {\displaystyle \{x\in X:A_{x}{\text{ is meager (resp. comeager) in }}Y\}} is comeager in X, where A x = π Y {\displaystyle A_{x}=\pi _{Y}} , where π Y {\displaystyle \pi _{Y}} is the projection onto Y.Even if A does not have the Baire property, 2... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kurosh problem Summary Kurosh_problem In mathematics, the Kurosh problem is one general problem, and several more special questions, in ring theory. The general problem is known to have a negative solution, since one of the special cases has been shown to have counterexamples. These matters were brought up by Aleksandr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kurosh problem Summary Kurosh_problem A special case is whether or not every nil algebra is locally nilpotent. For PI-algebras the Kurosh problem has a positive solution. Golod showed a counterexample to that case, as an application of the Golod–Shafarevich theorem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kurosh problem Summary Kurosh_problem The Kurosh problem on group algebras concerns the augmentation ideal I. If I is a nil ideal, is the group algebra locally nilpotent? There is an important problem which is often referred as the Kurosh's problem on division rings. The problem asks whether there exists an algebraic (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Köthe conjecture Summary Köthe_conjecture In mathematics, the Köthe conjecture is a problem in ring theory, open as of 2022. It is formulated in various ways. Suppose that R is a ring. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Köthe conjecture Summary Köthe_conjecture One way to state the conjecture is that if R has no nil ideal, other than {0}, then it has no nil one-sided ideal, other than {0}. This question was posed in 1930 by Gottfried Köthe (1905–1989). The Köthe conjecture has been shown to be true for various classes of rings, such a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Functional equation (L-function) Summary Functional_equation_(L-function) In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations. There is an elaborate theory of what these equations should be, much of which... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Labs septic Summary Labs_septic In mathematics, the Labs septic surface is a degree-7 (septic) nodal surface with 99 nodes found by Labs (2006). As of 2015, it has the largest known number of nodes of a degree-7 surface, though this number is still less than the best known upper bound of 104 nodes given by Varchenko (1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lagrange number Summary Lagrange_number In mathematics, the Lagrange numbers are a sequence of numbers that appear in bounds relating to the approximation of irrational numbers by rational numbers. They are linked to Hurwitz's theorem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lagrange reversion theorem Summary Lagrange_reversion_theorem In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions. Let v be a function of x and y in terms of another function f such that v = x ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lagrange reversion theorem Summary Lagrange_reversion_theorem {\displaystyle g(v)=g(x)+\sum _{k=1}^{\infty }{\frac {y^{k}}{k! }}\left({\frac {\partial }{\partial x}}\right)^{k-1}\left(f(x)^{k}g'(x)\right).} If g is the identity, this becomes v = x + ∑ k = 1 ∞ y k k ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lagrange reversion theorem Summary Lagrange_reversion_theorem ( ∂ ∂ x ) k − 1 ( f ( x ) k ) {\displaystyle v=x+\sum _{k=1}^{\infty }{\frac {y^{k}}{k! }}\left({\frac {\partial }{\partial x}}\right)^{k-1}\left(f(x)^{k}\right)} In which case the equation can be derived using perturbation theory. In 1770, Joseph Louis Lagr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lagrangian Grassmannian Summary Lagrangian_Grassmannian In mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is 1/2n(n + 1) (where the dimension of V is 2n). It may be identified with the homogeneous space U(n)/O(n),where U(n) is t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Variational bicomplex Summary Variational_bicomplex In mathematics, the Lagrangian theory on fiber bundles is globally formulated in algebraic terms of the variational bicomplex, without appealing to the calculus of variations. For instance, this is the case of classical field theory on fiber bundles (covariant classic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laguerre form Summary Laguerre_form In mathematics, the Laguerre form is generally given as a third degree tensor-valued form, that can be written as, L = ( w 1 ) 2 D a 11 + 2 w 1 w 2 D a 12 + ( w 2 ) 2 D a 22 {\displaystyle {\mathfrak {L}}=(w^{1})^{2}Da_{11}+2w^{1}w^{2}Da_{12}+(w^{2})^{2}Da_{22}} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laguerre functions Summary Laguerre_polynomials In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laguerre functions Summary Laguerre_polynomials More generally, a Laguerre function is a solution when n is not necessarily a non-negative integer. The Laguerre polynomials are also used for Gaussian quadrature to numerically compute integrals of the form These polynomials, usually denoted L0, L1, …, are a polynomial s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laguerre functions Summary Laguerre_polynomials Further see the Tricomi–Carlitz polynomials. The Laguerre polynomials arise in quantum mechanics, in the radial part of the solution of the Schrödinger equation for a one-electron atom. They also describe the static Wigner functions of oscillator systems in quantum mechan... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laguerre functions Summary Laguerre_polynomials They further enter in the quantum mechanics of the Morse potential and of the 3D isotropic harmonic oscillator. Physicists sometimes use a definition for the Laguerre polynomials that is larger by a factor of n! than the definition used here. (Likewise, some physicists ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lambert W-function Summary Lambert's_W_function In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f(w) = wew, where w is any complex number and ew is the exponential function. For each inte... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lambert W-function Summary Lambert's_W_function {\displaystyle w=W_{k}(z)\ \ {\text{ for some integer }}k.} When dealing with real numbers only, the two branches W0 and W−1 suffice: for real numbers x and y the equation y e y = x {\displaystyle ye^{y}=x} can be solved for y only if x ≥ −1/e; we get y = W0(x) if x ≥ 0 a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lambert W-function Summary Lambert's_W_function The Lambert W relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance, in the enumeration of trees. It can be used to solve various equations involving exponentials (e.g. the maxima of the Planck, Bose–Einstein, and Fermi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lanczos approximation Summary Lanczos_approximation In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's approximation for calculating the gamma function with fixed precisi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Landau–Kolmogorov inequality Summary Landau–Kolmogorov_inequality In mathematics, the Landau–Kolmogorov inequality, named after Edmund Landau and Andrey Kolmogorov, is the following family of interpolation inequalities between different derivatives of a function f defined on a subset T of the real numbers: ‖ f ( k ) ‖ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Landweber exact functor theorem Summary Landweber_exact_functor_theorem In mathematics, the Landweber exact functor theorem, named after Peter Landweber, is a theorem in algebraic topology. It is known that a complex orientation of a homology theory leads to a formal group law. The Landweber exact functor theorem (or L... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Langlands decomposition Summary Langlands_decomposition In mathematics, the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product P = M A N {\displaystyle P=MAN} of a reductive subgroup M, an abelian subgroup A, and a nilpotent subgroup N. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Langlands–Deligne local constant Summary Langlands–Deligne_local_constant In mathematics, the Langlands–Deligne local constant, also known as the local epsilon factor or local Artin root number (up to an elementary real function of s), is an elementary function associated with a representation of the Weil group of a lo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Langlands–Shahidi method Summary Langlands–Shahidi_method In mathematics, the Langlands–Shahidi method provides the means to define automorphic L-functions in many cases that arise with connected reductive groups over a number field. This includes Rankin–Selberg products for cuspidal automorphic representations of gene... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace limit Summary Laplace_limit In mathematics, the Laplace limit is the maximum value of the eccentricity for which a solution to Kepler's equation, in terms of a power series in the eccentricity, converges. It is approximately 0.66274 34193 49181 58097 47420 97109 25290.Kepler's equation M = E − ε sin E relates t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace limit Summary Laplace_limit It is the radius of convergence of the power series. It is given by the solution to the transcendental equation x exp ( 1 + x 2 ) 1 + 1 + x 2 = 1. {\displaystyle {\frac {x\exp({\sqrt {1+x^{2}}})}{1+{\sqrt {1+x^{2}}}}}=1.} No closed-form expression or infinite series is known for th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace operator Summary Vector_Laplacian In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols ∇ ⋅ ∇ {\displaystyle \nabla \cdot \nabla } , ∇ 2 {\displaystyle \nabla ^{2}} (where... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace operator Summary Vector_Laplacian Informally, the Laplacian Δf (p) of a function f at a point p measures by how much the average value of f over small spheres or balls centered at p deviates from f (p). The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace operator Summary Vector_Laplacian The Laplacian occurs in many differential equations describing physical phenomena. Poisson's equation describes electric and gravitational potentials; the diffusion equation describes heat and fluid flow; the wave equation describes wave propagation; and the Schrödinger equatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace transform applied to differential equations Summary Laplace_transform_applied_to_differential_equations Note that if the initial conditions are all zero, i.e. f ( i ) ( 0 ) = c i = 0 ∀ i ∈ { 0 , 1 , 2 , . . . n } {\displaystyle f^{(i)}(0)=c_{i}=0\quad \forall i\in \{0,1,2,...\ n\}} then the formula simplifies t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complex frequency Summary S_domain In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle s} (in the complex fr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplace–Carson transform Summary Laplace–Carson_transform In mathematics, the Laplace–Carson transform, named after Pierre Simon Laplace and John Renshaw Carson, is an integral transform with significant applications in the field of physics and engineering, particularly in the field of railway engineering. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laplacian of the indicator Summary Laplacian_of_the_indicator In mathematics, the Laplacian of the indicator of the domain D is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the surface of D. It can be viewed as the surface delta prime function. It is analo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primary submodule Summary Lasker-Noether_theorem In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primary submodule Summary Lasker-Noether_theorem The theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components. It has a straightforward extension to modules stating that every submodule of a finitely generated m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primary submodule Summary Lasker-Noether_theorem This also generalizes the primary decomposition form of the structure theorem for finitely generated modules over a principal ideal domain, and for the special case of polynomial rings over a field, it generalizes the decomposition of an algebraic set into a finite union... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Laurent power series Summary Laurent_series In mathematics, the Laurent series of a complex function f ( z ) {\displaystyle f(z)} is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lebedev–Milin inequality Summary Lebedev–Milin_inequality In mathematics, the Lebedev–Milin inequality is any of several inequalities for the coefficients of the exponential of a power series, found by Lebedev and Milin (1965) and Isaak Moiseevich Milin (1977). It was used in the proof of the Bieberbach conjecture, as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lebedev–Milin inequality Summary Lebedev–Milin_inequality {\displaystyle |\beta _{n}|^{2}\leq \exp \left(\sum _{k=1}^{n}(k|\alpha _{k}|^{2}-1/k)\right).} See also exponential formula (on exponentiation of power series). == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lebesgue constant (interpolation) Summary Lebesgue_constant_(interpolation) In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomial approximation of the function (the degree... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological dimension Summary Lebesgue_covering_dimension In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lebesgue differentiation theorem Summary Lebesgue_differentiation_theorem In mathematics, the Lebesgue differentiation theorem is a theorem of real analysis, which states that for almost every point, the value of an integrable function is the limit of infinitesimal averages taken about the point. The theorem is named f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Leech lattice Summary Leech_lattice In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by John Leech (1967). It may also have been discovered (but not published) by Ernst Witt in 1940. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lefschetz–Hopf theorem Summary Lefschetz–Hopf_theorem In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X {\displaystyle X} to itself by means of traces of the induced mappings on the homology groups of X {\displaystyle X... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lefschetz zeta function Summary Lefschetz_zeta_function In mathematics, the Lefschetz zeta-function is a tool used in topological periodic and fixed point theory, and dynamical systems. Given a continuous map f: X → X {\displaystyle f\colon X\to X} , the zeta-function is defined as the formal series ζ f ( t ) = exp (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Legendre chi function Summary Legendre_chi_function In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by As such, it resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as The Legend... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Legendre form Summary Legendre_form In mathematics, the Legendre forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced. Legendre chose the name elliptic integrals because the second kind gives the arc length of an ellipse of unit semi-major axis and eccentricity ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Legendre sieve Summary Legendre_sieve In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set of integers. Because it is a simple ext... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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