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Representation rigid group Summary Representation_rigid_group In mathematics, in the representation theory of groups, a group is said to be representation rigid if for every n {\displaystyle n} , it has only finitely many isomorphism classes of complex irreducible representations of dimension n {\displaystyle n} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Limit cycle Summary Limit_cycle In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hartman–Grobman theorem Summary Hartman–Grobman_theorem In mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. It asserts that linearisation—a natural simp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hutchinson operator Summary Hutchinson_operator In mathematics, in the study of fractals, a Hutchinson operator is the collective action of a set of contractions, called an iterated function system. The iteration of the operator converges to a unique attractor, which is the often self-similar fixed set of the operator. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Periodic mapping Summary Periodic_orbit In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mapping class group Summary Mapping_class_group In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hopf algebroid Summary Hopf_algebroid In mathematics, in the theory of Hopf algebras, a Hopf algebroid is a generalisation of weak Hopf algebras, certain skew Hopf algebras and commutative Hopf k-algebroids. If k is a field, a commutative k-algebroid is a cogroupoid object in the category of k-algebras; the category of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hopf algebroid Summary Hopf_algebroid The generalization of Hopf algebroids and its main part of the structure, associative bialgebroids, to the noncommutative base algebra was introduced by J.-H. Lu in 1996 as a result on work on groupoids in Poisson geometry (later shown equivalent in nontrivial way to a construction... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear stability Summary Unstable_equilibrium In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form d r / d t = A r {\displays... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Superrigidity theorem Summary Superrigidity_theorem In mathematics, in the theory of discrete groups, superrigidity is a concept designed to show how a linear representation ρ of a discrete group Γ inside an algebraic group G can, under some circumstances, be as good as a representation of G itself. That this phenomeno... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Superrigidity theorem Summary Superrigidity_theorem One simplified statement is this: take G to be a simply connected semisimple real algebraic group in GLn, such that the Lie group of its real points has real rank at least 2 and no compact factors. Suppose Γ is an irreducible lattice in G. For a local field F and ρ a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer tree Summary Brauer_tree In mathematics, in the theory of finite groups, a Brauer tree is a tree that encodes the characters of a block with cyclic defect group of a finite group. In fact, the trees encode the group algebra up to Morita equivalence. Such algebras coming from Brauer trees are called Brauer tree a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Domain of holomorphy Summary Domain_of_holomorphy In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a domain which is maximal in the sense that there exists a holomorphic function on this domain which cannot be extended to a bigger domain. Formally, an open set Ω {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lax form Summary Lax_form In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation. Lax pairs were introduced by Peter Lax to discuss solitons in continuous media. The inverse scattering ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Radical of a module Summary Radical_of_a_module In mathematics, in the theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization of the Jacobson radical for rings. In many ways, it is the dual notion to that of the socle soc(M) of M. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Regular singular points Summary Regular_singular_points In mathematics, in the theory of ordinary differential equations in the complex plane C {\displaystyle \mathbb {C} } , the points of C {\displaystyle \mathbb {C} } are classified into ordinary points, at which the equation's coefficients are analytic functions, an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newman's lemma Summary Newman's_lemma In mathematics, in the theory of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating (or strongly normalizing) abstract rewriting system (ARS), that is, one in which there are no infinite reduction sequences, is confluent if it is lo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Levi problem Summary Stein_space In mathematics, in the theory of several complex variables and complex manifolds, a Stein manifold is a complex submanifold of the vector space of n complex dimensions. They were introduced by and named after Karl Stein (1951). A Stein space is similar to a Stein manifold but is allowed... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop theorem Summary Loop_theorem In mathematics, in the topology of 3-manifolds, the loop theorem is a generalization of Dehn's lemma. The loop theorem was first proven by Christos Papakyriakopoulos in 1956, along with Dehn's lemma and the Sphere theorem. A simple and useful version of the loop theorem states that if ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop theorem Summary Loop_theorem Let N ⊂ π 1 ( S ) {\displaystyle N\subset \pi _{1}(S)} be a normal subgroup such that k e r ( π 1 ( S ) → π 1 ( M ) ) − N ≠ ∅ {\displaystyle \mathop {\mathrm {ker} } (\pi _{1}(S)\to \pi _{1}(M))-N\neq \emptyset } . Let f: D 2 → M {\displaystyle f\colon D^{2}\to M} be a continuous map... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop theorem Summary Loop_theorem Then there exists an embedding g: D 2 → M {\displaystyle g\colon D^{2}\to M} such that g ( ∂ D 2 ) ⊂ S {\displaystyle g(\partial D^{2})\subset S} and ∉ N . {\displaystyle \notin N.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop theorem Summary Loop_theorem Furthermore if one starts with a map f in general position, then for any neighborhood U of the singularity set of f, we can find such a g with image lying inside the union of image of f and U. Stalling's proof utilizes an adaptation, due to Whitehead and Shapiro, of Papakyriakopoulos' ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop theorem Summary Loop_theorem There is also a version of Dehn's lemma for minimal discs due to Meeks and S.-T. Yau, which also crucially relies on the tower construction. A proof not utilizing the tower construction exists of the first version of the loop theorem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop theorem Summary Loop_theorem This was essentially done 30 years ago by Friedhelm Waldhausen as part of his solution to the word problem for Haken manifolds; although he recognized this gave a proof of the loop theorem, he did not write up a detailed proof. The essential ingredient of this proof is the concept of H... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sphere theorem (3-manifolds) Summary Sphere_theorem_(3-manifolds) In mathematics, in the topology of 3-manifolds, the sphere theorem of Christos Papakyriakopoulos (1957) gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres. One example is the following: Let M ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sphere theorem (3-manifolds) Summary Sphere_theorem_(3-manifolds) Another more general version (also called the projective plane theorem, and due to David B. A. Epstein) is: Let M {\displaystyle M} be any 3-manifold and N {\displaystyle N} a π 1 ( M ) {\displaystyle \pi _{1}(M)} -invariant subgroup of π 2 ( M ) {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Incidence geometry Summary Incidence_geometry In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles, continuity, betweenness, and incidence. An incidence structure is what is obtain... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Incidence geometry Summary Incidence_geometry Such fundamental results remain valid when additional concepts are added to form a richer geometry. It sometimes happens that authors blur the distinction between a study and the objects of that study, so it is not surprising to find that some authors refer to incidence str... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Incidence geometry Summary Incidence_geometry In graph theory they are called hypergraphs, and in combinatorial design theory they are called block designs. Besides the difference in terminology, each area approaches the subject differently and is interested in questions about these objects relevant to that discipline.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Incidence geometry Summary Incidence_geometry It is, however, possible to translate the results from one discipline into the terminology of another, but this often leads to awkward and convoluted statements that do not appear to be natural outgrowths of the topics. In the examples selected for this article we use only ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inertial manifold Summary Inertial_manifold In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponentially qui... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inertial manifold Summary Inertial_manifold Some say that the small wavelengths are enslaved by the large (e.g. synergetics). Inertial manifolds may also appear as slow manifolds common in meteorology, or as the center manifold in any bifurcation. Computationally, numerical schemes for partial differential equations se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arrow notation (Ramsey theory) Summary Combinatorial_set_theory In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom. Recent de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinite compositions of analytic functions Summary Infinite_compositions_of_analytic_functions In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products and other infinite expansions, and the theory evolving from such composition... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinite compositions of analytic functions Summary Infinite_compositions_of_analytic_functions For infinite compositions of a single function see Iterated function. For compositions of a finite number of functions, useful in fractal theory, see Iterated function system. Although the title of this article specifies ana... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinite difference method Summary Infinite_difference_method In mathematics, infinite difference methods are numerical methods for solving differential equations by approximating them with difference equations, in which infinite differences approximate the derivatives. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinite-dimensional holomorphy Summary Analytic_functional In mathematics, infinite-dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces (or Fréchet spaces more generally), ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinitesimal cohomology Summary Infinitesimal_cohomology In mathematics, infinitesimal cohomology is a cohomology theory for algebraic varieties introduced by Grothendieck (1966). In characteristic 0 it is essentially the same as crystalline cohomology. In nonzero characteristic p Ogus (1975) showed that it is closely... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Infinity plus one Summary Infinity_plus_one In mathematics, infinity plus one is a concept which has a well-defined formal meaning in some number systems, and may refer to: Transfinite numbers, numbers that are larger than all finite numbers Cardinal numbers, representations of sizes (cardinalities) of abstract sets, w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lemma (mathematics) Summary Lemma_(mathematics) In mathematics, informal logic and argument mapping, a lemma (PL: lemmas or lemmata) is a generally minor, proven proposition which is used as a stepping stone to a larger result. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclid's orchard Summary Euclid's_orchard In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional "trees" of unit height planted at the lattice points in one quadrant of a square lattice. More formally, Euclid's orchard is the set of line segments from (x, y, 0) to (x, y, 1), where x and y ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclid's orchard Summary Euclid's_orchard If the orchard is projected relative to the origin onto the plane x + y = 1 (or, equivalently, drawn in perspective from a viewpoint at the origin) the tops of the trees form a graph of Thomae's function. The point (x, y, 1) projects to ( x x + y , y x + y , 1 x + y ) . {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijection, injection and surjection Summary Bijection,_injection_and_surjection In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijection, injection and surjection Summary Bijection,_injection_and_surjection Notationally: ∀ x , x ′ ∈ X , f ( x ) = f ( x ′ ) ⟹ x = x ′ , {\displaystyle \forall x,x'\in X,f(x)=f(x')\implies x=x',} or, equivalently (using logical transposition), ∀ x , x ′ ∈ X , x ≠ x ′ ⟹ f ( x ) ≠ f ( x ′ ) . {\displaystyle \forall ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijection, injection and surjection Summary Bijection,_injection_and_surjection That is, the image and the codomain of the function are equal. A surjective function is a surjection. Notationally: ∀ y ∈ Y , ∃ x ∈ X such that y = f ( x ) . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijection, injection and surjection Summary Bijection,_injection_and_surjection {\displaystyle \forall y\in Y,\exists x\in X{\text{ such that }}y=f(x).} The function is bijective (one-to-one and onto, one-to-one correspondence, or invertible) if each element of the codomain is mapped to by exactly one element of the do... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijection, injection and surjection Summary Bijection,_injection_and_surjection A bijective function is also called a bijection. That is, combining the definitions of injective and surjective, ∀ y ∈ Y , ∃ ! x ∈ X such that y = f ( x ) , {\displaystyle \forall y\in Y,\exists !x\in X{\text{ such that }}y=f(x),} where ∃ ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bijection, injection and surjection Summary Bijection,_injection_and_surjection x {\displaystyle \exists !x} means "there exists exactly one x".In any case (for any function), the following holds: ∀ x ∈ X , ∃ ! y ∈ Y such that y = f ( x ) . {\displaystyle \forall x\in X,\exists !y\in Y{\text{ such that }}y=f(x).} An in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Acyclic sheaf Summary Acyclic_sheaf In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext). There is a further group of related concepts applied to sheaves: flabby (flasque in French), fine, soft (mou in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Acyclic sheaf Summary Acyclic_sheaf The other classes of sheaves are historically older notions. The abstract framework for defining cohomology and derived functors does not need them. However, in most concrete situations, resolutions by acyclic sheaves are often easier to construct. Acyclic sheaves therefore serve for... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completely integrable system Summary Integrable_Systems In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals that its ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completely integrable system Summary Integrable_Systems The latter generally have no conserved quantities, and are asymptotically intractable, since an arbitrarily small perturbation in initial conditions may lead to arbitrarily large deviations in their trajectories over a sufficiently large time. Many systems studied... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completely integrable system Summary Integrable_Systems Other elementary examples include the motion of a rigid body about its center of mass (the Euler top) and the motion of an axially symmetric rigid body about a point in its axis of symmetry (the Lagrange top). In the late 1960's, it was realized that there are com... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completely integrable system Summary Integrable_Systems In the special case of Hamiltonian systems, if there are enough independent Poisson commuting first integrals for the flow parameters to be able to serve as a coordinate system on the invariant level sets (the leaves of the Lagrangian foliation), and if the flows ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Singular integral equations Summary Integral_equation In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where I i ( u ) {\displaystyle I^{i}(u)} is an integral operator ac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Singular integral equations Summary Integral_equation For example, one method of solving a boundary value problem is by converting the differential equation with its boundary conditions into an integral equation and solving the integral equation. In addition, because one can convert between the two, differential equati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Integral geometry Summary Integral_geometry In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformations from the space of function... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Integral of inverse functions Summary Inverse_function_integration In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle f^{-1}} of a continuous and invertible function f {\displaystyle f} , in terms of f − 1 {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unlikely intersections Summary Self-intersection_number In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem on curves and elimina... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Intransitive preference Summary Intransitive_preference In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger property of antitransitivity, which describes a relation th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical anti-realism Intuitionism Mathematical_anti-realism > Contemporary schools of thought > Intuitionism In mathematics, intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths" (L. E. J. Brouwer). From this springboard, intuitionists seek to rec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical anti-realism Intuitionism Mathematical_anti-realism > Contemporary schools of thought > Intuitionism The axiom of choice is also rejected in most intuitionistic set theories, though in some versions it is accepted. In intuitionism, the term "explicit construction" is not cleanly defined, and that has led t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Factorization system Summary Factorization_system In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Comparison operator Operator chaining Test_operator > Syntax > Operator chaining In mathematics, it is common practice to chain relational operators, such as in 3 < x < y < 20 (meaning 3 < x and x < y and y < 20). The syntax is clear since these relational operators in mathematics are transitive. However, many recent p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Comparison operator Operator chaining Test_operator > Syntax > Operator chaining However, it does compile in C/C++ and some other languages, yielding surprising result (as true would be represented by the number 1 here). It is possible to give the expression x < y < z its familiar mathematical meaning, and some program... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iterated forcing Summary Iterated_forcing In mathematics, iterated forcing is a method for constructing models of set theory by repeating Cohen's forcing method a transfinite number of times. Iterated forcing was introduced by Solovay and Tennenbaum (1971) in their construction of a model of set theory with no Suslin t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iterated forcing Summary Iterated_forcing If α+1 is a successor ordinal then Pα+1 is often constructed from Pα using a forcing notion in VPα, while if α is a limit ordinal then Pα is often constructed as some sort of limit (such as the direct limit) of the Pβ for β<α. A key consideration is that, typically, it is neces... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iterated forcing Summary Iterated_forcing This is often accomplished by the use of a preservation theorem such as: Finite support iteration of c.c.c. forcings (see countable chain condition) are c.c.c. and thus preserve ω 1 {\displaystyle \omega _{1}} . Countable support iterations of proper forcings are proper (see Fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iterated Function Systems Summary Iterated_function_system In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iterated Function Systems Summary Iterated_function_system IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iterated Function Systems Summary Iterated_function_system The functions are normally contractive, which means they bring points closer together and make shapes smaller. Hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of its... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Iteration Mathematics Iterate_(math) > Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hessian equation Summary Hessian_equation In mathematics, k-Hessian equations (or Hessian equations for short) are partial differential equations (PDEs) based on the Hessian matrix. More specifically, a Hessian equation is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. Whe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Least-squares function approximation Summary Least_squares_(function_approximation) In mathematics, least squares function approximation applies the principle of least squares to function approximation, by means of a weighted sum of other functions. The best approximation can be defined as that which minimizes the diff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Leximin order Summary Leximin_order In mathematics, leximin order is a total preorder on finite-dimensional vectors. A more accurate, but less common term is leximin preorder. The leximin order is particularly important in social choice theory and fair division. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lifting theory Summary Lifting_theory In mathematics, lifting theory was first introduced by John von Neumann in a pioneering paper from 1931, in which he answered a question raised by Alfréd Haar. The theory was further developed by Dorothy Maharam (1958) and by Alexandra Ionescu Tulcea and Cassius Ionescu Tulcea (196... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Combining like terms Summary Combining_like_terms In mathematics, like terms are summands in a sum that differ only by a numerical factor. Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Combining like terms Summary Combining_like_terms For example, when considering a quadratic equation, one considers often the expression ( x − r ) ( x − s ) , {\displaystyle (x-r)(x-s),} where r {\displaystyle r} and s {\displaystyle s} are the roots of the equation and may be considered as parameters. Then, expanding ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weak limit cardinal Summary Weak_limit_cardinal In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. These cardinals are somet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear interpolation Summary Linear_interpolation In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Discontinuous linear functional Summary Discontinuous_linear_functional In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions (see linear approximation). If the spaces involved are ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearization Summary Linearization In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the lo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
List chromatic index Summary List_edge-coloring In mathematics, list edge-coloring is a type of graph coloring that combines list coloring and edge coloring. An instance of a list edge-coloring problem consists of a graph together with a list of allowed colors for each edge. A list edge-coloring is a choice of a color ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
List chromatic index Summary List_edge-coloring A graph G is k-edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has a proper coloring. The edge choosability, or list edge colorability, list edge chromatic number, or ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local class field theory Summary Local_class_field_theory In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite residue field: h... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Serre C-theory Summary Serre_C-theory In mathematics, localization of a category consists of adding to a category inverse morphisms for some collection of morphisms, constraining them to become isomorphisms. This is formally similar to the process of localization of a ring; it in general makes objects isomorphic that w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Log-polar coordinates Summary Log-polar_coordinates In mathematics, log-polar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two numbers, one for the logarithm of the distance to a certain point, and one for an angle. Log-polar coordinates are clo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic Sobolev inequalities Summary Logarithmic_Sobolev_inequalities In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient ∇ f {\displaystyle \nabla f} . These inequalities were discovered and named by Leonard Gross, who est... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic growth Summary Logarithmic_growth In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log (x). Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant. Logarithmic gro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic growth Summary Logarithmic_growth In more advanced mathematics, the partial sums of the harmonic series 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ {\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots } grow logarithmically. In the design of computer algorithms, logarithmic growth, and rela... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic growth Summary Logarithmic_growth Petersburg paradox.In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing is proportional to the population. This terminological confusion ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive language Summary Recursive_language In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive language Summary Recursive_language Recursive languages are also called decidable. The concept of decidability may be extended to other models of computation. For example, one may speak of languages decidable on a non-deterministic Turing machine. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive language Summary Recursive_language Therefore, whenever an ambiguity is possible, the synonym used for "recursive language" is Turing-decidable language, rather than simply decidable. The class of all recursive languages is often called R, although this name is also used for the class RP. This type of languag... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recognizable language Summary Recursively_enumerable_language In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possib... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Impredicativity Summary Predicative_mathematics In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Impredicativity Summary Predicative_mathematics The opposite of impredicativity is predicativity, which essentially entails building stratified (or ramified) theories where quantification over lower levels results in variables of some new type, distinguished from the lower types that the variable ranges over. A prototy... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Impredicativity Summary Predicative_mathematics The paradox is that such a set cannot exist: If it would exist, the question could be asked whether it contains itself or not — if it does then by definition it should not, and if it does not then by definition it should. The greatest lower bound of a set X, glb(X), also ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
System of types Summary Typed_logic In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Undefined term Summary Primitive_notion In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory, relations betwe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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