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Minuscule representation Summary Minuscule_representation The minuscule representations are indexed by the weight lattice modulo the root lattice, or equivalently by irreducible representations of the center of the simply connected compact group. For the simple Lie algebras, the dimensions of the minuscule representati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minuscule representation Summary Minuscule_representation An (n+1k) for 0 ≤ k ≤ n (exterior powers of vector representation). Quasi-minuscule: n2+2n (adjoint) Bn 1 (trivial), 2n (spin). Quasi-minuscule: 2n+1 (vector) Cn 1 (trivial), 2n (vector). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minuscule representation Summary Minuscule_representation Quasi-minuscule: 2n2–n–1 if n>1 Dn 1 (trivial), 2n (vector), 2n−1 (half spin), 2n−1 (half spin). Quasi-minuscule: 2n2–n (adjoint) E6 1, 27, 27. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minuscule representation Summary Minuscule_representation Quasi-minuscule: 78 (adjoint) E7 1, 56. Quasi-minuscule: 133 (adjoint) E8 1. Quasi-minuscule: 248 (adjoint) F4 1. Quasi-minuscule: 26 G2 1. Quasi-minuscule: 7 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coherent set of characters Summary Coherent_set_of_characters In mathematical representation theory, coherence is a property of sets of characters that allows one to extend an isometry from the degree-zero subspace of a space of characters to the whole space. The general notion of coherence was developed by Feit (1960,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eisenstein integral Summary Eisenstein_integral In mathematical representation theory, the Eisenstein integral is an integral introduced by Harish-Chandra in the representation theory of semisimple Lie groups, analogous to Eisenstein series in the theory of automorphic forms. Harish-Chandra used Eisenstein integrals to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hecke algebra of a pair Summary Hecke_algebra_of_a_pair In mathematical representation theory, the Hecke algebra of a pair (g,K) is an algebra with an approximate identity, whose approximately unital modules are the same as K-finite representations of the pairs (g,K). Here K is a compact subgroup of a Lie group with Li... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Naimark equivalence Summary Naimark_equivalence In mathematical representation theory, two representations of a group on topological vector spaces are called Naimark equivalent (named after Mark Naimark) if there is a closed bijective linear map between dense subspaces preserving the group action. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baumgartner's axiom Summary Baumgartner's_axiom In mathematical set theory, Baumgartner's axiom (BA) can be one of three different axioms introduced by James Earl Baumgartner. A subset of the real line is said to be ℵ 1 {\displaystyle \aleph _{1}} -dense if every two points are separated by exactly ℵ 1 {\displaystyle \... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baumgartner's axiom Summary Baumgartner's_axiom Baumgartner's axiom is a consequence of the proper forcing axiom. It is consistent with a combination of ZFC, Martin's axiom, and the negation of the continuum hypothesis, but not implied by those hypotheses.Another axiom introduced by Baumgartner (1975) states that Marti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor's theorem Summary Cantor's_theorem In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle A} , the set of all subsets of A , {\displaystyle A,} the power set of A , {\displaystyle A,} has a strictly greater cardinality than A {\displaystyle A} itself.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor's theorem Summary Cantor's_theorem As a consequence, the cardinality of the real numbers, which is the same as that of the power set of the integers, is strictly larger than the cardinality of the integers; see Cardinality of the continuum for details. The theorem is named for German mathematician Georg Cantor, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor's theorem Summary Cantor's_theorem Cantor's theorem had immediate and important consequences for the philosophy of mathematics. For instance, by iteratively taking the power set of an infinite set and applying Cantor's theorem, we obtain an endless hierarchy of infinite cardinals, each strictly larger than the o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chang's model Summary Chang's_model In mathematical set theory, Chang's model is the smallest inner model of set theory closed under countable sequences. It was introduced by Chang (1971). More generally Chang introduced the smallest inner model closed under taking sequences of length less than κ for any infinite cardi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohen algebra Summary Cohen_algebra In mathematical set theory, a Cohen algebra, named after Paul Cohen, is a type of Boolean algebra used in the theory of forcing. A Cohen algebra is a Boolean algebra whose completion is isomorphic to the completion of a free Boolean algebra (Koppelberg 1993). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Permutation model Summary Hereditarily_symmetric_set In mathematical set theory, a permutation model is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms. A symmetric model is similar except that it is a model of ZF (without atoms) and is constructed using a group of permutat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pseudo-intersection number Summary Pseudo-intersection_number In mathematical set theory, a pseudo-intersection of a family of sets is an infinite set S such that each element of the family contains all but a finite number of elements of S. The pseudo-intersection number, sometimes denoted by the fraktur letter 𝔭, is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hereditarily ordinal definable Summary Hereditarily_ordinal_definable In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first-order formula. Ordinal definable sets were introduced by Gödel (1965). A drawback to this informa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hereditarily ordinal definable Summary Hereditarily_ordinal_definable However there is a different way of stating the definition that can be so formalized. In this approach, a set S is formally defined to be ordinal definable if there is some collection of ordinals α1, ..., αn such that S ∈ V α 1 {\displaystyle S\in V_... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hereditarily ordinal definable Summary Hereditarily_ordinal_definable In other words, S is the unique object such that φ(S, α2...αn) holds with its quantifiers ranging over V α 1 {\displaystyle V_{\alpha _{1}}} . The class of all ordinal definable sets is denoted OD; it is not necessarily transitive, and need not be a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hereditarily ordinal definable Summary Hereditarily_ordinal_definable The class of hereditarily ordinal definable sets is denoted by HOD, and is a transitive model of ZFC, with a definable well ordering. It is consistent with the axioms of set theory that all sets are ordinal definable, and so hereditarily ordinal defi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hereditarily ordinal definable Summary Hereditarily_ordinal_definable It follows from V = L, and is equivalent to the existence of a (definable) well-ordering of the universe. Note however that the formula expressing V = HOD need not hold true within HOD, as it is not absolute for models of set theory: within HOD, the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Square principle Summary Global_square In mathematical set theory, a square principle is a combinatorial principle asserting the existence of a cohering sequence of short closed unbounded (club) sets so that no one (long) club set coheres with them all. As such they may be viewed as a kind of incompactness phenomenon. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countable transitive model Summary Countable_transitive_model In mathematical set theory, a transitive model is a model of set theory that is standard and transitive. Standard means that the membership relation is the usual one, and transitive means that the model is a transitive set or class. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Worldly cardinal Summary Worldly_cardinal In mathematical set theory, a worldly cardinal is a cardinal κ such that the rank Vκ is a model of Zermelo–Fraenkel set theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Aronszajn line Summary Aronszajn_line In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality ℵ 1 {\displaystyle \aleph _{1}} which contains no subset order-isomorphic to ω 1 {\displaystyle \omega _{1}} with the usual ordering the reverse of ω 1 {\displaystyle \... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ulam matrix Summary Ulam_matrix In mathematical set theory, an Ulam matrix is an array of subsets of a cardinal number with certain properties. Ulam matrices were introduced by Stanislaw Ulam in his 1930 work on measurable cardinals: they may be used, for example, to show that a real-valued measurable cardinal is weakl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jónsson function Summary Jónsson_function In mathematical set theory, an ω-Jónsson function for a set x of ordinals is a function f: ω → x {\displaystyle f:^{\omega }\to x} with the property that, for any subset y of x with the same cardinality as x, the restriction of f {\displaystyle f} to ω {\displaystyle ^{\omega... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jónsson function Summary Jónsson_function Erdős and Hajnal (1966) showed that for every ordinal λ there is an ω-Jónsson function for λ. Kunen's proof of Kunen's inconsistency theorem uses a Jónsson function for cardinals λ such that 2λ = λℵ0, and Kunen observed that for this special case there is a simpler proof of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor tree Summary Cantor_tree In mathematical set theory, the Cantor tree is either the full binary tree of height ω + 1, or a topological space related to this by joining its points with intervals, that was introduced by Robert Lee Moore in the late 1920s as an example of a non-metrizable Moore space (Jones 1966). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mitchell order Summary Mitchell_order In mathematical set theory, the Mitchell order is a well-founded preorder on the set of normal measures on a measurable cardinal κ. It is named for William Mitchell. We say that M ◅ N (this is a strict order) if M is in the ultrapower model defined by N. Intuitively, this means tha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mitchell order Summary Mitchell_order Well-foundedness fails specifically for rank-into-rank extenders; but Itay Neeman showed in 2004 that it holds for all weaker types of extender. The Mitchell rank of a measure is the order type of its predecessors under ◅; since ◅ is well-founded this is always an ordinal. Using th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mostowski model Summary Mostowski_model In mathematical set theory, the Mostowski model is a model of set theory with atoms where the full axiom of choice fails, but every set can be linearly ordered. It was introduced by Mostowski (1939). The Mostowski model can be constructed as the permutation model corresponding to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Axiom of Adjunction Summary Axiom_of_Adjunction In mathematical set theory, the axiom of adjunction states that for any two sets x, y there is a set w = x ∪ {y} given by "adjoining" the set y to the set x. It is stated as ∀ x . ∀ y . ∃ w . ∀ z . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Axiom of Adjunction Summary Axiom_of_Adjunction ( z ∈ w ↔ ( z ∈ x ∨ z = y ) ) . {\displaystyle \forall x.\forall y.\exists w.\forall z. {\big (}z\in w\leftrightarrow (z\in x\lor z=y){\big )}.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Axiom of Adjunction Summary Axiom_of_Adjunction Bernays (1937, page 68, axiom II (2)) introduced the axiom of adjunction as one of the axioms for a system of set theory that he introduced in about 1929. It is a weak axiom, used in some weak systems of set theory such as general set theory or finitary set theory. The ad... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiverse (set theory) Summary Multiverse_(set_theory) In mathematical set theory, the multiverse view is that there are many models of set theory, but no "absolute", "canonical" or "true" model. The various models are all equally valid or true, though some may be more useful or attractive than others. The opposite vi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiverse (set theory) Summary Multiverse_(set_theory) The collection of countable transitive models of ZFC (in some universe) is called the hyperverse and is very similar to the "multiverse". A typical difference between the universe and multiverse views is the attitude to the continuum hypothesis. In the universe vi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Illness narrative Mathematical-sociology approach Illness_narrative > Social-sciences approaches > Mathematical-sociology approach In mathematical sociology, the theory of comparative narratives was devised in order to describe and compare the structures (expressed as "and" in a directed graph where multiple causal lin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haar's theorem Mathematical statistics Haar's_theorem > Uses > Mathematical statistics In mathematical statistics, Haar measures are used for prior measures, which are prior probabilities for compact groups of transformations. These prior measures are used to construct admissible procedures, by appeal to the characteri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haar's theorem Mathematical statistics Haar's_theorem > Uses > Mathematical statistics For the group of affine transformations on the parameter space of the normal distribution, the right Haar measure is the Jeffreys prior measure. Unfortunately, even right Haar measures sometimes result in useless priors, which cannot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Standardized variable Standardizing in mathematical statistics Z_score > Standardizing in mathematical statistics In mathematical statistics, a random variable X is standardized by subtracting its expected value E {\displaystyle \operatorname {E} } and dividing the difference by its standard deviation σ ( X ) = Var ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic estimate Asymptotic distribution Asymptotic_theory > Asymptotic distribution In mathematical statistics, an asymptotic distribution is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. A distribution is an ordered set of random variables Zi for i = 1, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Asymptotic estimate Asymptotic distribution Asymptotic_theory > Asymptotic distribution This is based on the notion of an asymptotic function which cleanly approaches a constant value (the asymptote) as the independent variable goes to infinity; "clean" in this sense meaning that for any desired closeness epsilon there... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Growth curve (statistics) Other uses Growth_curve_(statistics) > Other uses In mathematical statistics, growth curves such as those used in biology are often modeled as being continuous stochastic processes, e.g. as being sample paths that almost surely solve stochastic differential equations. Growth curves have been a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Darmois–Skitovich theorem Summary Darmois–Skitovich_theorem In mathematical statistics, the Darmois–Skitovich theorem characterizes the normal distribution (the Gaussian distribution) by the independence of two linear forms from independent random variables. This theorem was proved independently by G. Darmois and V. P.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Singular statistical model Summary Fisher_matrix In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the varianc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Singular statistical model Summary Fisher_matrix It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covaria... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kullback–Leibler divergence Summary Information_gain In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} , is a type of statistical distance: a measure of how one probability distribution P is dif... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Total curvature Summary Total_curvature In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length: ∫ a b k ( s ) d s = 2 π N . {\displaystyle \int _{a}^{b}k(s)\,ds=2\pi N.} The total curvature ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multidimensional systems Summary Multidimensional_systems In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one independent variable exists (like time), but there are several independent variables. Important problems such as factorization and stability of m-D systems ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Financial result Calculation formula Financial_result > Calculation formula In mathematical terms financial result is defined as follows: Financial result = Interest income − Interest expense ± Write-downs/write-ups for financial assets ± Write-downs/write-ups for marketable securities + Other financial income and expe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eddy covariance Mathematical foundation Eddy_covariance > Mathematical foundation In mathematical terms, "eddy flux" is computed as a covariance between instantaneous deviation in vertical wind speed ( w ′ {\displaystyle w'} ) from the mean value ( w ¯ {\displaystyle {\bar {w}}} ) and instantaneous deviation in gas con... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Alfvén's Theorem Mathematical statement Frozen-in_flux_theorem > Mathematical statement In mathematical terms, Alfvén's theorem states that, in an electrically conducting fluid in the limit of a large magnetic Reynolds number, the magnetic flux ΦB through an orientable, open material surface advected by a macroscopic, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multi-objective linear programming Problem formulation Multi-objective_linear_programming > Problem formulation In mathematical terms, a MOLP can be written as: min x P x s.t. a ≤ B x ≤ b , ℓ ≤ x ≤ u {\displaystyle \min _{x}Px\quad {\text{s.t. }}\quad a\leq Bx\leq b,\;\ell \leq x\leq u} where B {\displaystyle B} is an ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Statistical modeling Formal definition Statistical_Model > Formal definition In mathematical terms, a statistical model is usually thought of as a pair ( S , P {\displaystyle S,{\mathcal {P}}} ), where S {\displaystyle S} is the set of possible observations, i.e. the sample space, and P {\displaystyle {\mathcal {P}}} i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Statistical modeling Formal definition Statistical_Model > Formal definition Indeed, as Burnham & Anderson state, "A model is a simplification or approximation of reality and hence will not reflect all of reality"—hence the saying "all models are wrong". The set P {\displaystyle {\mathcal {P}}} is almost always paramet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Statistical modeling Formal definition Statistical_Model > Formal definition The set of distributions Θ {\displaystyle \Theta } defines the parameters of the model. A parameterization is generally required to have distinct parameter values give rise to distinct distributions, i.e. F θ 1 = F θ 2 ⇒ θ 1 = θ 2 {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector optimization Problem formulation Vector_optimization > Problem formulation In mathematical terms, a vector optimization problem can be written as: C - min x ∈ S f ( x ) {\displaystyle C\operatorname {-} \min _{x\in S}f(x)} where f: X → Z {\displaystyle f:X\to Z} for a partially ordered vector space Z {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Point transformation Modern mathematical description Canonical_transformation > Modern mathematical description In mathematical terms, canonical coordinates are any coordinates on the phase space (cotangent bundle) of the system that allow the canonical one-form to be written as up to a total differential (exact form).... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inverse demand function Definition Inverse_demand_function > Definition In mathematical terms, if the demand function is d e m a n d = f ( p r i c e ) {\displaystyle {demand}=f({price})} , then the inverse demand function is p r i c e = f − 1 ( d e m a n d ) {\displaystyle {price}=f^{-1}({demand})} . The value of the i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inverse demand function Definition Inverse_demand_function > Definition The inverse demand function is the same as the average revenue function, since P = AR.To compute the inverse demand function, simply solve for P from the demand function. For example, if the demand function has the form Q = 240 − 2 P {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quantum discord Definition and mathematical relations Quantum_discord > Definition and mathematical relations In mathematical terms, quantum discord is defined in terms of the quantum mutual information. More specifically, quantum discord is the difference between two expressions which each, in the classical limit, rep... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quantum discord Definition and mathematical relations Quantum_discord > Definition and mathematical relations The notation J represents the part of the correlations that can be attributed to classical correlations and varies in dependence on the chosen eigenbasis; therefore, in order for the quantum discord to reflect ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quantum discord Definition and mathematical relations Quantum_discord > Definition and mathematical relations Other conditions have been identified which can be seen in analogy to the Peres–Horodecki criterion and in relation to the strong subadditivity of the von Neumann entropy.Efforts have been made to extend the de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jahn–Teller distortion Mexican-hat potential Jahn–Teller_effect > Theory > Potential energy surfaces > Mexican-hat potential In mathematical terms, the APESs characterising the JT distortion arise as the eigenvalues of the potential energy matrix. Generally, the APESs take the characteristic appearance of a double cone... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jahn–Teller distortion Mexican-hat potential Jahn–Teller_effect > Theory > Potential energy surfaces > Mexican-hat potential The conical shape near the degeneracy at the origin makes it immediately clear that this point cannot be stationary, that is, the system is unstable against asymmetric distortions, which leads to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jahn–Teller distortion Mexican-hat potential Jahn–Teller_effect > Theory > Potential energy surfaces > Mexican-hat potential The Q i {\displaystyle Q_{i}} giving these distortions are arranged in a circle, as shown by the red curve in the figure. Quadratic coupling or cubic elastic terms lead to a warping along this "m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary Golay code Mathematical definition Extended_binary_Golay_code > Mathematical definition In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F242 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary Golay code Mathematical definition Extended_binary_Golay_code > Mathematical definition They can also be described as subsets of a set of 24 elements, where addition is defined as taking the symmetric difference of the subsets. In the extended binary Golay code, all code words have Hamming weights of 0, 8, 12, 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary Golay code Mathematical definition Extended_binary_Golay_code > Mathematical definition Octads of the code G24 are elements of the S(5,8,24) Steiner system. There are 759 = 3 × 11 × 23 octads and 759 complements thereof. It follows that there are 2576 = 24 × 7 × 23 dodecads. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary Golay code Mathematical definition Extended_binary_Golay_code > Mathematical definition Two octads intersect (have 1's in common) in 0, 2, or 4 coordinates in the binary vector representation (these are the possible intersection sizes in the subset representation). An octad and a dodecad intersect at 2, 4, or 6 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary Golay code Mathematical definition Extended_binary_Golay_code > Mathematical definition That is, the spheres of radius three around code words form a partition of the vector space. G23 is a 12-dimensional subspace of the space F232. The automorphism group of the perfect binary Golay code G23 (meaning the subgrou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary Golay code Mathematical definition Extended_binary_Golay_code > Mathematical definition The automorphism group of the extended binary Golay code is the Mathieu group M 24 {\displaystyle M_{24}} , of order 210 × 33 × 5 × 7 × 11 × 23. M 24 {\displaystyle M_{24}} is transitive on octads and on dodecads. The other M... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euler top Mathematical description of phase space Lagrange,_Euler,_and_Kovalevskaya_tops > Hamiltonian formulation of classical tops > Mathematical description of phase space In mathematical terms, the spatial configuration of the body is described by a point on the Lie group S O ( 3 ) {\displaystyle SO(3)} , the three... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Strict Summary Strict In mathematical writing, the term strict refers to the property of excluding equality and equivalence and often occurs in the context of inequality and monotonic functions. It is often attached to a technical term to indicate that the exclusive meaning of the term is to be understood. The opposite... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hylozoism Literature Hylozoism > In popular culture > Literature In mathematician and writer Rudy Rucker's novels Postsingular and Hylozoic, the emergent sentience of all material things is described as a property of the technological singularity. The Hylozoist is one of the Culture ships mentioned in Iain M. Banks's n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Semicircle Summary Semicircle In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, π radians, or a half-turn). It has only one line of symmetry (reflection symmetry). In non-technical usage,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Major index Summary Major_index In mathematics (and particularly in combinatorics), the major index of a permutation is the sum of the positions of the descents of the permutation. In symbols, the major index of the permutation w is maj ( w ) = ∑ w ( i ) > w ( i + 1 ) i . {\displaystyle \operatorname {maj} (w)=\sum _... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Major index Summary Major_index This statistic is named after Major Percy Alexander MacMahon who showed in 1913 that the distribution of the major index on all permutations of a fixed length is the same as the distribution of inversions. That is, the number of permutations of length n with k inversions is the same as t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Major index Summary Major_index In fact, a stronger result is true: the number of permutations of length n with major index k and i inversions is the same as the number of permutations of length n with major index i and k inversions, that is, the two statistics are equidistributed. For example, the number of permutatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kronecker foliation Summary Foliation_theory In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space Rn into the cos... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kronecker foliation Summary Foliation_theory The number p (the dimension of the leaves) is called the dimension of the foliation and q = n − p is called its codimension. In some papers on general relativity by mathematical physicists, the term foliation (or slicing) is used to describe a situation where the relevant Lo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Colored operad Summary Colored_operad In mathematics (especially category theory), a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a multicategory are analogous to functions of seve... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Convolution operation Summary Convolution_kernel In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function ( f ∗ g {\displaystyle f*g} ) that expresses how the shape of one is modified by the other. The term convolution refers ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Convolution operation Summary Convolution_kernel The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution ( f ∗ g {\displaystyle f*g} ) differs from c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Convolution operation Summary Convolution_kernel Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations.The convolution can be defined for functions on Euclidean spac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear recurrence with constant coefficients Summary Linear_recurrence In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients: ch. 17: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear recurrence with constant coefficients Summary Linear_recurrence A linear recurrence denotes the evolution of some variable over time, with the current time period or discrete moment in time denoted as t, one period earlier denoted as t − 1, one period later as t + 1, etc. The solution of such an equation is a fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Faddeev–LeVerrier algorithm Summary Faddeev–LeVerrier_algorithm In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial p A ( λ ) = det ( λ I n − A ) {\displaystyle p_{A}(\lambda )=\det(\lambda I_{n}-A)} of a square matrix, A,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Faddeev–LeVerrier algorithm Summary Faddeev–LeVerrier_algorithm It was first published in 1840 by Urbain Le Verrier, subsequently redeveloped by P. Horst, Jean-Marie Souriau, in its present form here by Faddeev and Sominsky, and further by J. S. Frame, and others. (For historical points, see Householder. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Faddeev–LeVerrier algorithm Summary Faddeev–LeVerrier_algorithm An elegant shortcut to the proof, bypassing Newton polynomials, was introduced by Hou. The bulk of the presentation here follows Gantmacher, p. 88.) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group cohomology Summary Group_homology In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a grou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group cohomology Summary Group_homology Group cohomology plays a role in the investigation of fixed points of a group action in a module or space and the quotient module or space with respect to a group action. Group cohomology is used in the fields of abstract algebra, homological algebra, algebraic topology and algeb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group cohomology Summary Group_homology The techniques of group cohomology can also be extended to the case that instead of a G-module, G acts on a nonabelian G-group; in effect, a generalization of a module to non-Abelian coefficients. These algebraic ideas are closely related to topological ideas. The group cohomolog... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group cohomology Summary Group_homology Thus, the group cohomology of Z {\displaystyle \mathbb {Z} } can be thought of as the singular cohomology of the circle S1, and similarly for Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } and P ∞ ( R ) . {\displaystyle \mathbb {P} ^{\infty }(\mathbb {R} ).} A great deal is k... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Argument of a complex number Summary Argument_of_a_complex_number In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as φ {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Shear matrix Summary Shear_matrix In mathematics (particularly linear algebra), a shear matrix or transvection is an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity matrix and replacing one of the zero elements with a non-... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volume integral Summary Volume_integral In mathematics (particularly multivariable calculus), a volume integral (∭) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Radon metric Summary Outer_regular_measure In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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