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Parshin's conjecture Summary Parshin's_conjecture In mathematics, more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson–Parshin conjecture) states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion: K i ( X ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Griffiths group Summary Griffiths_group In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold X measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles. More precisely, it... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal morphism Summary Universal_arrow In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently from the method chosen for construc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal morphism Summary Universal_arrow In particular, the concept of universal property allows a simple proof that all constructions of real numbers are equivalent: it suffices to prove that they satisfy the same universal property. Technically, a universal property is defined in terms of categories and functors by... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal morphism Summary Universal_arrow Universal properties occur almost everywhere in mathematics, and the use of the concept allows the use of general properties of universal properties for easily proving some properties that would need boring verifications otherwise. For example, given a commutative ring R, the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Internal category Summary Internal_category In mathematics, more specifically in category theory, internal categories are a generalisation of the notion of small category, and are defined with respect to a fixed ambient category. If the ambient category is taken to be the category of sets then one recovers the theory o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Redshift conjecture Summary Redshift_conjecture In mathematics, more specifically in chromatic homotopy theory, the redshift conjecture states, roughly, that algebraic K-theory K ( R ) {\displaystyle K(R)} has chromatic level one higher than that of a complex-oriented ring spectrum R. It was formulated by John Rognes i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Straight-line program Summary Straight-line_program In mathematics, more specifically in computational algebra, a straight-line program (SLP) for a finite group G = ⟨S⟩ is a finite sequence L of elements of G such that every element of L either belongs to S, is the inverse of a preceding element, or the product of two ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Straight-line program Summary Straight-line_program Babai and Szemerédi prove that every element of a finite group G has an SLP of length O(log2|G|) in every generating set. An efficient solution to the constructive membership problem is crucial to many group-theoretic algorithms. It can be stated in terms of SLPs as f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Straight-line program Summary Straight-line_program Given a finite group G = ⟨S⟩ and g ∈ G, find a straight-line program computing g over S. The constructive membership problem is often studied in the setting of black box groups. The elements are encoded by bit strings of a fixed length. Three oracles are provided for ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Straight-line program Summary Straight-line_program A black box algorithm is one which uses only these oracles. Hence, straight-line programs for black box groups are black box algorithms. Explicit straight-line programs are given for a wealth of finite simple groups in the online ATLAS of Finite Groups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Milnor–Wood inequality Summary Milnor–Wood_inequality In mathematics, more specifically in differential geometry and geometric topology, the Milnor–Wood inequality is an obstruction to endow circle bundles over surfaces with a flat structure. It is named after John Milnor and John W. Wood. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maps of manifolds Summary Maps_of_manifolds In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they shed | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of averaging Summary Method_of_averaging In mathematics, more specifically in dynamical systems, the method of averaging (also called averaging theory) exploits systems containing time-scales separation: a fast oscillation versus a slow drift. It suggests that we perform an averaging over a given amount of time ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of averaging Summary Method_of_averaging It turns out to be a customary problem where there exists the trade off between how good is the approximated solution balanced by how much time it holds to be close to the original solution. More precisely, the system has the following form of a phase space variable x . {... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Method of averaging Summary Method_of_averaging The fast oscillation is given by f {\displaystyle f} versus a slow drift of x ˙ {\displaystyle {\dot {x}}} . The averaging method yields an autonomous dynamical system which approximates the solution curves of x ˙ {\displaystyle {\dot {x}}} inside a connected and compact ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Banach Spaces Summary Banach_space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
K-space (functional analysis) Summary K-space_(functional_analysis) In mathematics, more specifically in functional analysis, a K-space is an F-space V {\displaystyle V} such that every extension of F-spaces (or twisted sum) of the form is equivalent to the trivial one where R {\displaystyle \mathbb {R} } is the real l... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive linear functional Summary Positive_linear_functional In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space ( V , ≤ ) {\displaystyle (V,\leq )} is a linear functional f {\displaystyle f} on V {\displaystyle V} so that for all positive elements v ∈ V , ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive linear functional Summary Positive_linear_functional As in the case when V {\displaystyle V} is a C*-algebra with its partially ordered subspace of self-adjoint elements, sometimes a partial order is placed on only a subspace W ⊆ V , {\displaystyle W\subseteq V,} and the partial order does not extend to all of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive linear operator Summary Positive_linear_operator In mathematics, more specifically in functional analysis, a positive linear operator from an preordered vector space ( X , ≤ ) {\displaystyle (X,\leq )} into a preordered vector space ( Y , ≤ ) {\displaystyle (Y,\leq )} is a linear operator f {\displaystyle f} o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Total subset Summary Total_subset In mathematics, more specifically in functional analysis, a subset T {\displaystyle T} of a topological vector space X {\displaystyle X} is said to be a total subset of X {\displaystyle X} if the linear span of T {\displaystyle T} is a dense subset of X . {\displaystyle X.} This condit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore–Smith limit Summary Cluster_point_of_a_net In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence. In essence, a sequence is a function whose domain is the natural numbers. The codomain of this function is usually s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore–Smith limit Summary Cluster_point_of_a_net In particular, the following two conditions are, in general, not equivalent for a map f {\displaystyle f} between topological spaces X {\displaystyle X} and Y {\displaystyle Y}: The map f {\displaystyle f} is continuous in the topological sense; Given any point x {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore–Smith limit Summary Cluster_point_of_a_net The concept of a net, first introduced by E. H. Moore and Herman L. Smith in 1922, is to generalize the notion of a sequence so that the above conditions (with "sequence" being replaced by "net" in condition 2) are in fact equivalent for all maps of topological spaces. I... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore–Smith limit Summary Cluster_point_of_a_net Therefore, while sequences do not encode sufficient information about functions between topological spaces, nets do, because collections of open sets in topological spaces are much like directed sets in behavior. The term "net" was coined by John L. Kelley.Nets are one o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tychonoff cube Summary Tychonoff_cube In mathematics, more specifically in general topology, the Tychonoff cube is the generalization of the unit cube from the product of a finite number of unit intervals to the product of an infinite, even uncountable number of unit intervals. The Tychonoff cube is named after Andrey ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kirby–Siebenmann class Summary Kirby–Siebenmann_class In mathematics, more specifically in geometric topology, the Kirby–Siebenmann class is an obstruction for topological manifolds to allow a PL-structure. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grün's lemma Summary Perfect_group In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no non-trivial abelian quotients (equivalently, its abelianization, which is the universal abelian quotient, is trivial). In sym... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Orthogonality relations Summary Ordinary_character In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Orthogonality relations Summary Ordinary_character This is possible because a complex representation of a finite group is determined (up to isomorphism) by its character. The situation with representations over a field of positive characteristic, so-called "modular representations", is more delicate, but Richard Brauer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Walsh function Summary Walsh_function In mathematics, more specifically in harmonic analysis, Walsh functions form a complete orthogonal set of functions that can be used to represent any discrete function—just like trigonometric functions can be used to represent any continuous function in Fourier analysis. They can t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Walsh function Summary Walsh_function The system of Walsh functions is known as the Walsh system. It is an extension of the Rademacher system of orthogonal functions.Walsh functions, the Walsh system, the Walsh series, and the fast Walsh–Hadamard transform are all named after the American mathematician Joseph L. Walsh.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homotopy sheaf Summary Homotopy_sheaf In mathematics, more specifically in homotopy theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets). Equivalently, a simplici... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homotopy sheaf Summary Homotopy_sheaf Thus, a simplicial scheme, a simplicial object in the site, represents a simplicial presheaf (in fact, often a simplicial sheaf). Example: Let G be a presheaf of groupoids. Then taking nerves section-wise, one obtains a simplicial presheaf B G {\displaystyle BG} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homotopy sheaf Summary Homotopy_sheaf For example, one might set B GL = lim → B G L n {\displaystyle B\operatorname {GL} =\varinjlim B\operatorname {GL_{n}} } . These types of examples appear in K-theory. If f: X → Y {\displaystyle f:X\to Y} is a local weak equivalence of simplicial presheaves, then the induced map Z... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spark (mathematics) Summary Spark_(mathematics) In mathematics, more specifically in linear algebra, the spark of a m × n {\displaystyle m\times n} matrix A {\displaystyle A} is the smallest integer k {\displaystyle k} such that there exists a set of k {\displaystyle k} columns in A {\displaystyle A} which are linearly... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cesaro's theorem Summary Cauchy_product In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis Cauchy. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baire set Summary Baire_set In mathematics, more specifically in measure theory, the Baire sets form a σ-algebra of a topological space that avoids some of the pathological properties of Borel sets. There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a locally compac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baire set Summary Baire_set Every Baire set is a Borel set. The converse holds in many, but not all, topological spaces. Baire sets avoid some pathological properties of Borel sets on spaces without a countable base for the topology. In practice, the use of Baire measures on Baire sets can often be replaced by the use ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Alternating multilinear map Summary Alternating_map In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a multilinear form) that is zero whenever any pair of arguments is equa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Biconjugate gradient method Summary Biconjugate_gradient_method In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations A x = b . {\displaystyle Ax=b.\,} Unlike the conjugate gradient method, this algorithm does not require the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bendixson derivative Summary Bendixson_derivative In mathematics, more specifically in point-set topology, the derived set of a subset S {\displaystyle S} of a topological space is the set of all limit points of S . {\displaystyle S.} It is usually denoted by S ′ . {\displaystyle S'.} The concept was first introduced b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean ring Summary Norm-Euclidean_field In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of integers. This generalized Euclidean alg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean ring Summary Norm-Euclidean_field It is important to compare the class of Euclidean domains with the larger class of principal ideal domains (PIDs). An arbitrary PID has much the same "structural properties" of a Euclidean domain (or, indeed, even of the ring of integers), but when an explicit algorithm for E... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean ring Summary Norm-Euclidean_field So, given an integral domain R, it is often very useful to know that R has a Euclidean function: in particular, this implies that R is a PID. However, if there is no "obvious" Euclidean function, then determining whether R is a PID is generally a much easier problem than dete... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cyclic module Summary Cyclic_module In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is a generalization of the notion of a cyclic group, that is, an Abelian group (i.e. Z-module) that is generated by one element... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maximal submodule Summary Maximal_submodule In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R. Maximal ideals are... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Krull intersection theorem Summary Krull_intersection_theorem In mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commutative ring theory Noetherian rings Commutative_ring_theory > Main tools and results > Noetherian rings In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non-empty set of ideals has a maximal element. Equivale... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commutative ring theory Noetherian rings Commutative_ring_theory > Main tools and results > Noetherian rings The notion of a Noetherian ring is of fundamental importance in both commutative and noncommutative ring theory, due to the role it plays in simplifying the ideal structure of a ring. For instance, the ring of i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quantization commutes with reduction Summary Quantization_commutes_with_reduction In mathematics, more specifically in the context of geometric quantization, quantization commutes with reduction states that the space of global sections of a line bundle L satisfying the quantization condition on the symplectic quotient ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Siegel zero Summary Siegel_zero In mathematics, more specifically in the field of analytic number theory, a Landau–Siegel zero or simply Siegel zero (also known as exceptional zero), named after Edmund Landau and Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solvable groups Summary Insoluble_group In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Invariant basis number Summary Invariant_basis_number In mathematics, more specifically in the field of ring theory, a ring has the invariant basis number (IBN) property if all finitely generated free left modules over R have a well-defined rank. In the case of fields, the IBN property becomes the statement that finite... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lienard equation Summary Lienard_equation In mathematics, more specifically in the study of dynamical systems and differential equations, a Liénard equation is a second order differential equation, named after the French physicist Alfred-Marie Liénard. During the development of radio and vacuum tube technology, Liénard... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
PBW theorem Summary PBW_theorem In mathematics, more specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a Lie algebra. It is named after Henri Poincaré, Garrett Birkhoff, and Ernst Witt. The te... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Variance reduction Summary Variance_reduction In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. Every output random variable from the simulation is associated ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Variance reduction Summary Variance_reduction The main ones are common random numbers, antithetic variates, control variates, importance sampling, stratified sampling, moment matching, conditional Monte Carlo and quasi random variables. For simulation with black-box models subset simulation and line sampling can also b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extension of a topological group Summary Extension_of_a_topological_group In mathematics, more specifically in topological groups, an extension of topological groups, or a topological extension, is a short exact sequence 0 → H → ı X → π G → 0 {\displaystyle 0\to H{\stackrel {\imath }{\to }}X{\stackrel {\pi }{\to }}G\to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Closed map Summary Open_mapping In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function f: X → Y {\displaystyle f:X\to Y} is open if for any open set U {\displaystyle U} in X , {\displaystyle X,} the image f ( U ) {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Closed map Summary Open_mapping A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa.Open and closed maps are not necessarily continuous. Further, continuity is independent of openness and closedness in the general case and a continuous function may have one, both, o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Closed map Summary Open_mapping Recall that, by definition, a function f: X → Y {\displaystyle f:X\to Y} is continuous if the preimage of every open set of Y {\displaystyle Y} is open in X . {\displaystyle X.} (Equivalently, if the preimage of every closed set of Y {\displaystyle Y} is closed in X {\displaystyle X} ). ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volodin space Summary Volodin_space In mathematics, more specifically in topology, the Volodin space X {\displaystyle X} of a ring R is a subspace of the classifying space B G L ( R ) {\displaystyle BGL(R)} given by X = ⋃ n , σ B ( U n ( R ) σ ) {\displaystyle X=\bigcup _{n,\sigma }B(U_{n}(R)^{\sigma })} where U n ( R ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equivariant stable homotopy theory Summary Equivariant_stable_homotopy_theory In mathematics, more specifically in topology, the equivariant stable homotopy theory is a subfield of equivariant topology that studies a spectrum with group action instead of a space with group action, as in stable homotopy theory. The fiel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Portmanteau theorem Summary Portmanteau_lemma In mathematics, more specifically measure theory, there are various notions of the convergence of measures. For an intuitive general sense of what is meant by convergence of measures, consider a sequence of measures μn on a space, sharing a common collection of measurable s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jacobson density theorem Summary Jacobson_density_theorem In mathematics, more specifically non-commutative ring theory, modern algebra, and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring R.The theorem can be applied to show that any primitive ring can be viewed as a "den... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore space (topology) Summary Moore_space_(topology) In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, a topological space X is a Moore space if the following conditions hold: Any two distinct points can be separated by neighbourhoods, and any closed... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore space (topology) Summary Moore_space_(topology) (X is a developable space. )Moore spaces are generally interesting in mathematics because they may be applied to prove interesting metrization theorems. The concept of a Moore space was formulated by R. L. Moore in the earlier part of the 20th century. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Levitzky's theorem Summary Levitzky's_theorem In mathematics, more specifically ring theory and the theory of nil ideals, Levitzky's theorem, named after Jacob Levitzki, states that in a right Noetherian ring, every nil one-sided ideal is necessarily nilpotent. Levitzky's theorem is one of the many results suggesting t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Atomic domain Summary Atomic_domain In mathematics, more specifically ring theory, an atomic domain or factorization domain is an integral domain in which every non-zero non-unit can be written in at least one way as a finite product of irreducible elements. Atomic domains are different from unique factorization domain... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nilpotent ideal Summary Nilpotent_ideal In mathematics, more specifically ring theory, an ideal I of a ring R is said to be a nilpotent ideal if there exists a natural number k such that I k = 0. By I k, it is meant the additive subgroup generated by the set of all products of k elements in I. Therefore, I is nilpotent... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jacobson radical Summary Jacobson_radical In mathematics, more specifically ring theory, the Jacobson radical of a ring R {\displaystyle R} is the ideal consisting of those elements in R {\displaystyle R} that annihilate all simple right R {\displaystyle R} -modules. It happens that substituting "left" in place of "rig... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jacobson radical Summary Jacobson_radical The Jacobson radical of a ring has numerous internal characterizations, including a few definitions that successfully extend the notion to rings without unity. The radical of a module extends the definition of the Jacobson radical to include modules. The Jacobson radical plays ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exceptional inverse image functor Summary Exceptional_inverse_image_functor In mathematics, more specifically sheaf theory, a branch of topology and algebraic geometry, the exceptional inverse image functor is the fourth and most sophisticated in a series of image functors for sheaves. It is needed to express Verdier d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local homeomorphism Summary Locally_homeomorphic In mathematics, more specifically topology, a local homeomorphism is a function between topological spaces that, intuitively, preserves local (though not necessarily global) structure. If f: X → Y {\displaystyle f:X\to Y} is a local homeomorphism, X {\displaystyle X} is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local homeomorphism Summary Locally_homeomorphic Typical examples of local homeomorphisms are covering maps. A topological space X {\displaystyle X} is locally homeomorphic to Y {\displaystyle Y} if every point of X {\displaystyle X} has a neighborhood that is homeomorphic to an open subset of Y . {\displaystyle Y.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local homeomorphism Summary Locally_homeomorphic For example, a manifold of dimension n {\displaystyle n} is locally homeomorphic to R n . {\displaystyle \mathbb {R} ^{n}.} If there is a local homeomorphism from X {\displaystyle X} to Y , {\displaystyle Y,} then X {\displaystyle X} is locally homeomorphic to Y , {\disp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mixed volume Summary Mixed_volume In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to a tuple of convex bodies in R n {\displaystyle \mathbb {R} ^{n}} . This number depends on the size and shape of the bodies, and their relative orientation to each othe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Motivic L-function Summary Motivic_L-function In mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v acting on the v-inertial invarian... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multipliers and centralizers (Banach spaces) Summary Multipliers_and_centralizers_(Banach_spaces) In mathematics, multipliers and centralizers are algebraic objects in the study of Banach spaces. They are used, for example, in generalizations of the Banach–Stone theorem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near sets Summary Near_sets In mathematics, near sets are either spatially close or descriptively close. Spatially close sets have nonempty intersection. In other words, spatially close sets are not disjoint sets, since they always have at least one element in common. Descriptively close sets contain elements that have... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near sets Summary Near_sets Such sets can be either disjoint or non-disjoint sets. Spatially near sets are also descriptively near sets. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near sets Summary Near_sets The underlying assumption with descriptively close sets is that such sets contain elements that have location and measurable features such as colour and frequency of occurrence. The description of the element of a set is defined by a feature vector. Comparison of feature vectors provides a b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near sets Summary Near_sets Near set theory provides a formal basis for the observation, comparison, and classification of elements in sets based on their closeness, either spatially or descriptively. Near sets offer a framework for solving problems based on human perception that arise in areas such as image processing... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near sets Summary Near_sets From the beginning, descriptively near sets have proved to be useful in applications of topology, and visual pattern recognition , spanning a broad spectrum of applications that include camouflage detection, micropaleontology, handwriting forgery detection, biomedical image analysis, content... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negacyclic convolution Summary Negacyclic_convolution In mathematics, negacyclic convolution is a convolution between two vectors a and b. It is also called skew circular convolution or wrapped convolution. It results from multiplication of a skew circulant matrix, generated by vector a, with vector b. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negafibonacci coding Summary Negafibonacci_coding In mathematics, negafibonacci coding is a universal code which encodes nonzero integers into binary code words. It is similar to Fibonacci coding, except that it allows both positive and negative integers to be represented. All codes end with "11" and have no "11" befor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative definite Summary Negative_definiteness In mathematics, negative definiteness is a property of any object to which a bilinear form may be naturally associated, which is negative-definite. See, in particular: Negative-definite bilinear form Negative-definite quadratic form Negative-definite matrix Negative-defin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nilpotent orbit Summary Nilpotent_orbit In mathematics, nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple Lie groups and semisimple Lie algebras. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-Archimedean geometry Summary Non-Archimedean_geometry In mathematics, non-Archimedean geometry is any of a number of forms of geometry in which the axiom of Archimedes is negated. An example of such a geometry is the Dehn plane. Non-Archimedean geometries may, as the example indicates, have properties significantly... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-Euclidean space Summary Non-Euclidian_geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either re... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-abelian class field theory Summary Non-abelian_class_field_theory In mathematics, non-abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and classical set of results on abelian extensions of any number field K, to the general Galois exten... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian algebraic topology Summary Nonabelian_algebraic_topology In mathematics, nonabelian algebraic topology studies an aspect of algebraic topology that involves (inevitably noncommutative) higher-dimensional algebras. Many of the higher-dimensional algebraic structures are noncommutative and, therefore, their st... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian algebraic topology Summary Nonabelian_algebraic_topology An important part of nonabelian algebraic topology is concerned with the properties and applications of homotopy groupoids and filtered spaces. Noncommutative double groupoids and double algebroids are only the first examples of such higher-dimensional... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian algebraic topology Summary Nonabelian_algebraic_topology Cubical omega-groupoids, higher homotopy groupoids, crossed modules, crossed complexes and Galois groupoids are key concepts in developing applications related to homotopy of filtered spaces, higher-dimensional space structures, the construction of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian algebraic topology Summary Nonabelian_algebraic_topology A related example is that of van Kampen theorems for categories of covering morphisms in lextensive categories. Other reports of generalisations of the van Kampen theorem include statements for 2-categories and a topos of topoi . Important results in h... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncommutative harmonic analysis Summary Non-commutative_harmonic_analysis In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups that are not commutative. Since locally compact abelian groups have a well-understood theory, Pontryagin dual... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncommutative harmonic analysis Summary Non-commutative_harmonic_analysis The interesting examples include many Lie groups, and also algebraic groups over p-adic fields. These examples are of interest and frequently applied in mathematical physics, and contemporary number theory, particularly automorphic representatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncommutative harmonic analysis Summary Non-commutative_harmonic_analysis He showed that if the von Neumann group algebra of G is of type I, then L2(G) as a unitary representation of G is a direct integral of irreducible representations. It is parametrized therefore by the unitary dual, the set of isomorphism classes ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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