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Nonlocal operator Summary Nonlocal_operator In mathematics, a nonlocal operator is a mapping which maps functions on a topological space to functions, in such a way that the value of the output function at a given point cannot be determined solely from the values of the input function in any neighbourhood of any point.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonnegative matrices Summary Non-negative_matrix In mathematics, a nonnegative matrix, written X ≥ 0 , {\displaystyle \mathbf {X} \geq 0,} is a matrix in which all the elements are equal to or greater than zero, that is, x i j ≥ 0 ∀ i , j . {\displaystyle x_{ij}\geq 0\qquad \forall {i,j}.} A positive matrix is a matrix... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonnegative matrices Summary Non-negative_matrix The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonrecursive filter Summary Nonrecursive_filter In mathematics, a nonrecursive filter only uses input values like x, unlike recursive filter where it uses previous output values like y. In signal processing, non-recursive digital filters are often known as Finite Impulse Response (FIR) filters, as a non-recursive digit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonstandard integer Summary Nonstandard_integer In mathematics, a nonstandard integer may refer to Hyperinteger, the integer part of a hyperreal number an integer in a non-standard model of arithmetic | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Norm form Summary Norm_form In mathematics, a norm form is a homogeneous form in n variables constructed from the field norm of a field extension L/K of degree n. That is, writing N for the norm mapping to K, and selecting a basis e1, ..., en for L as a vector space over K, the form is given by N(x1e1 + ... + xnen)in v... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector length Summary Normable_topology In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector length Summary Normable_topology A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a seminormed vector space. The term pseudonorm has been used for several related meanings. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector length Summary Normable_topology It may be a synonym of "seminorm". A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality " ≤ {\displaystyle \,\leq \,} " in the homogeneity axiom. It can also refer to a norm that can take infinite values, or to certain functions parametr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Norm variety Summary Norm_variety In mathematics, a norm variety is a particular type of algebraic variety V over a field F, introduced for the purposes of algebraic K-theory by Voevodsky. The idea is to relate Milnor K-theory of F to geometric objects V, having function fields F(V) that 'split' given 'symbols' (elemen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Norm variety Summary Norm_variety The conditions on a norm variety V are that V is irreducible and a non-singular complete variety. Further it should have dimension d equal to p n − 1 − 1. {\displaystyle p^{n-1}-1.\ } The key condition is in terms of the d-th Newton polynomial sd, evaluated on the (algebraic) total Che... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal invariants Summary Normal_invariant In mathematics, a normal map is a concept in geometric topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X (more geometrically a Poincaré space), a normal map on X endows the space, roughly speaking, with some of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal invariants Summary Normal_invariant If the dimension of X is ≥ {\displaystyle \geq } 5 there is then only the algebraic topology surgery obstruction due to C. T. C. Wall to X actually being homotopy equivalent to a closed manifold. Normal maps also apply to the study of the uniqueness of manifold structures with... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal invariants Summary Normal_invariant Depending on the category of manifolds (differentiable, piecewise-linear, or topological), there are similarly defined, but inequivalent, concepts of normal maps and normal invariants. It is possible to perform surgery on normal maps, meaning surgery on the domain manifold, an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal surface Summary Normal_surface In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron so that each component of intersection is a triangle or a quad (see figure). A triangle cuts off a vertex of the tetrahedron while a quad separates pairs of vertices. A n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal surface Summary Normal_surface Dually, a normal surface can be considered to be a surface that intersects each handle of a given handle structure on the 3-manifold in a prescribed manner similar to the above. The concept of normal surface can be generalized to arbitrary polyhedra. There are also related notions ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal surface Summary Normal_surface The concept of normal surface is due to Hellmuth Kneser, who utilized it in his proof of the prime decomposition theorem for 3-manifolds. Later Wolfgang Haken extended and refined the notion to create normal surface theory, which is at the basis of many of the algorithms in 3-manif... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normed algebra Summary Normed_algebra In mathematics, a normed algebra A is an algebra over a field which has a sub-multiplicative norm: ∀ x , y ∈ A ‖ x y ‖ ≤ ‖ x ‖ ‖ y ‖ . {\displaystyle \forall x,y\in A\qquad \|xy\|\leq \|x\|\|y\|.} Some authors require it to have a multiplicative identity 1A such that ║1A║ = 1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normed spaces Summary Normed_linear_space In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If V {\displaystyle V} is a vector space over K {\displayst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normed spaces Summary Normed_linear_space Absolute homogeneity: for every λ ∈ K {\displaystyle \lambda \in K} and x ∈ V {\displaystyle x\in V} , Triangle inequality: for every x ∈ V {\displaystyle x\in V} and y ∈ V {\displaystyle y\in V} ,If V {\displaystyle V} is a real or complex vector space as above, and ‖ ⋅ ‖ {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normed spaces Summary Normed_linear_space If this metric space is complete then the normed space is a Banach space. Every normed vector space can be "uniquely extended" to a Banach space, which makes normed spaces intimately related to Banach spaces. Every Banach space is a normed space but converse is not true. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normed spaces Summary Normed_linear_space For example, the set of the finite sequences of real numbers can be normed with the Euclidean norm, but it is not complete for this norm. An inner product space is a normed vector space whose norm is the square root of the inner product of a vector and itself. The Euclidean nor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nowhere commutative semigroup Summary Nowhere_commutative_semigroup In mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if and only if any two elements of S are inverses of each other. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nowhere continuous function Summary Nowhere_continuous_function In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f {\displaystyle f} is a function from real numbers to real numbers, then f {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Null semigroup Summary Right_zero_semigroup In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of a semigroup is a left zero then the semigroup is called a left zero semigroup; a right ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nullform Summary Nullform In mathematics, a nullform of a vector space acted on linearly by a group is a vector on which all invariants of the group vanish. Nullforms were introduced by Hilbert (1893). (Dieudonné & Carrell 1970, 1971, p.57). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harmonic (mathematics) Summary Harmonic_(mathematics) In mathematics, a number of concepts employ the word harmonic. The similarity of this terminology to that of music is not accidental: the equations of motion of vibrating strings, drums and columns of air are given by formulas involving Laplacians; the solutions to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fixed-point theorems in infinite-dimensional spaces Summary Fixed_point_theorems_in_infinite-dimensional_spaces In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for example, to the proof of existence theorems for partial ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fixed-point theorems in infinite-dimensional spaces Summary Fixed_point_theorems_in_infinite-dimensional_spaces One way in which fixed-point theorems of this kind have had a larger influence on mathematics as a whole has been that one approach is to try to carry over methods of algebraic topology, first proved for fini... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fixed-point theorems in infinite-dimensional spaces Summary Fixed_point_theorems_in_infinite-dimensional_spaces Tikhonov (Tychonoff) fixed-point theorem: Let V be a locally convex topological vector space. For any nonempty compact convex set X in V, any continuous function f: X → X has a fixed point. Browder fixed-poin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fixed-point theorems in infinite-dimensional spaces Summary Fixed_point_theorems_in_infinite-dimensional_spaces Then any non-expansive function f: K → K has a fixed point. (A function f {\displaystyle f} is called non-expansive if ‖ f ( x ) − f ( y ) ‖ ≤ ‖ x − y ‖ {\displaystyle \|f(x)-f(y)\|\leq \|x-y\|} for each x {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Numerical monoid Summary Numerical_monoid In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number and the binary operation is the operation of addition of integers. Also, the integer 0 must be an element of the semigroup. F... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Numerical monoid Summary Numerical_monoid Numerical semigroups are commutative monoids and are also known as numerical monoids.The definition of numerical semigroup is intimately related to the problem of determining nonnegative integers that can be expressed in the form x1n1 + x2 n2 + ... + xr nr for a given set {n1, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Data cube Mathematics Data_cube > Applications > Mathematics In mathematics, a one-dimensional array corresponds to a vector, a two-dimensional array resembles a matrix; more generally, a tensor may be represented as an n-dimensional data cube. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
1-parameter group Summary One-parameter_subgroup In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism φ: R → G {\displaystyle \varphi :\mathbb {R} \rightarrow G} from the real line R {\displaystyle \mathbb {R} } (as an additive group) to some other topological gr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
1-parameter group Summary One-parameter_subgroup It is these infinitesimal transformations that generate a Lie algebra that is used to describe a Lie group of any dimension. The action of a one-parameter group on a set is known as a flow. A smooth vector field on a manifold, at a point, induces a local flow - a one par... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adic distribution Summary P-adic_distribution In mathematics, a p-adic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of p-adic numbers. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adic modular form Summary P-adic_modular_form In mathematics, a p-adic modular form is a p-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. Serre (1973) introduced p-adic modular forms as limits of ordinary modular forms, and Katz (1973) shortly afterwards gave a g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adic zeta function Summary P-adic_zeta_function In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic (where p is a prime number). For example, the domain could be the p-a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adic zeta function Summary P-adic_zeta_function For example, Kubota–Leopoldt used Kummer's congruences for Bernoulli numbers to construct a p-adic L-function, the p-adic Riemann zeta function ζp(s), whose values at negative odd integers are those of the Riemann zeta function at negative odd integers (up to an explici... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adic zeta function Summary P-adic_zeta_function A p-adic L-function arising in this way is typically called an arithmetic p-adic L-function as it encodes arithmetic data of the Galois module involved. The main conjecture of Iwasawa theory (now a theorem due to Barry Mazur and Andrew Wiles) is the statement that the K... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-adically closed field Summary P-adically_closed_field In mathematics, a p-adically closed field is a field that enjoys a closure property that is a close analogue for p-adic fields to what real closure is to the real field. They were introduced by James Ax and Simon B. Kochen in 1965. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-constrained group Summary P-constrained_group In mathematics, a p-constrained group is a finite group resembling the centralizer of an element of prime order p in a group of Lie type over a finite field of characteristic p. They were introduced by Gorenstein and Walter (1964, p.169) in order to extend some of Thompso... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Packing in a hypergraph Summary Packing_in_a_hypergraph In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pair of pants (mathematics) Summary Pair_of_pants_(mathematics) In mathematics, a pair of pants is a surface which is homeomorphic to the three-holed sphere. The name comes from considering one of the removed disks as the waist and the two others as the cuffs of a pair of pants. Pairs of pants are used as building bloc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor's pairing function Summary Pairing_function In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number.Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pairing Summary Pairing In mathematics, a pairing is an R-bilinear map from the Cartesian product of two R-modules, where the underlying ring R is commutative. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Palindromic prime Summary Palindromic_prime In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such concerns. The first few decima... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 (one billion two hundred thirty four million five hundred sixty seven thousand eight hundred ninety) is a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number In a trivial sense, all positive integers are pandigital in unary (or tallying). In binary, all integers are pandigital except for 0 and numbers of the form 2 n − 1 {\displaystyle 2^{n}-1} (the Mersenne numbers). The larger the base, the rarer pandigital numbers become, thoug... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number Conversely, the smaller the base, the fewer pandigital numbers without redundant digits there are. 2 is the only such pandigital number in base 2, while there are more of these in base 10. Sometimes, the term is used to refer only to pandigital numbers with no redundant digit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number In some cases, a number might be called pandigital even if it doesn't have a zero as a significant digit, for example, 923456781 (these are sometimes referred to as "zeroless pandigital numbers"). No base 10 pandigital number can be a prime number if it doesn't have redundant... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number The first base 10 pandigital prime is 10123457689; OEIS: A050288 lists more. For different reasons, redundant digits are also required for a pandigital number (in any base except unary) to also be a palindromic number in that base. The smallest pandigital palindromic number i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number The largest pandigital number without redundant digits to be also a square number is 9814072356 = 990662. Two of the zeroless pandigital Friedman numbers are: 123456789 = ((86 + 2 × 7)5 − 91) / 34, and 987654321 = (8 × (97 + 6/2)5 + 1) / 34. A pandigital Friedman number witho... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pandigital number Summary Pandigital_number While much of what has been said does not apply to Roman numerals, there are pandigital numbers: MCDXLIV, MCDXLVI, MCDLXIV, MCDLXVI, MDCXLIV, MDCXLVI, MDCLXIV, MDCLXVI. These, listed in OEIS: A105416, use each of the digits just once, while OEIS: A105417 has pandigital Roman ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pantachy Summary Pantachy In mathematics, a pantachy or pantachie (from the Greek word πανταχη meaning everywhere) is a maximal totally ordered subset of a partially ordered set, especially a set of equivalence classes of sequences of real numbers. The term was introduced by du Bois-Reymond (1879, 1882) to mean a dense... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parabola Summary Parabolic_curve In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parabola Summary Parabolic_curve The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parabola Summary Parabolic_curve The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parabola Summary Parabolic_curve Any parabola can be repositioned and rescaled to fit exactly on any other parabola—that is, all parabolas are geometrically similar. Parabolas have the property that, if they are made of material that reflects light, then light that travels parallel to the axis of symmetry of a parabola... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parabola Summary Parabolic_curve The same effects occur with sound and other waves. This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic mis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paracompact manifold Summary Paracompact_manifold In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a H... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paracompact manifold Summary Paracompact_manifold Sometimes paracompact spaces are defined so as to always be Hausdorff. Every closed subspace of a paracompact space is paracompact. While compact subsets of Hausdorff spaces are always closed, this is not true for paracompact subsets. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paracompact manifold Summary Paracompact_manifold A space such that every subspace of it is a paracompact space is called hereditarily paracompact. This is equivalent to requiring that every open subspace be paracompact. The notion of paracompact space is also studied in pointless topology, where it is more well-behave... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paracompact manifold Summary Paracompact_manifold For example, the product of any number of paracompact locales is a paracompact locale, but the product of two paracompact spaces may not be paracompact. Compare this to Tychonoff's theorem, which states that the product of any collection of compact topological spaces is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parallelization (mathematics) Summary Parallelization_(mathematics) In mathematics, a parallelization of a manifold M {\displaystyle M\,} of dimension n is a set of n global smooth linearly independent vector fields. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parametric formula Summary Parametric_representation In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parametric formula Summary Parametric_representation {\displaystyle (x,y)=(\cos t,\sin t).} Parametric representations are generally nonunique (see the "Examples in two dimensions" section below), so the same quantities may be expressed by a number of different parameterizations.In addition to curves and surfaces, para... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parametric formula Summary Parametric_representation Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter. Because of this application, a single parameter is often labeled t; however, parameters can represent other physica... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paramodular group Summary Paramodular_group In mathematics, a paramodular group is a special sort of arithmetic subgroup of the symplectic group. It is a generalization of the Siegel modular group, and has the same relation to polarized abelian varieties that the Siegel modular group has to principally polarized abelia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paramodular group Summary Paramodular_group The corresponding group over the reals is called the parasymplectic group and is conjugate to a (real) symplectic group. A paramodular form is a Siegel modular form for a paramodular group. Paramodular groups were introduced by Conforto (1952) and named by Shimura (1958, sect... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paraproduct Summary Paraproduct In mathematics, a paraproduct is a non-commutative bilinear operator acting on functions that in some sense is like the product of the two functions it acts on. According to Svante Janson and Jaak Peetre, in an article from 1988, "the name 'paraproduct' denotes an idea rather than a uniq... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paraproduct Summary Paraproduct {\displaystyle fg=\Lambda (f,g)+\Lambda (g,f).} For any appropriate functions f {\displaystyle f} and h {\displaystyle h} with h ( 0 ) = 0 {\displaystyle h(0)=0} , it is the case that h ( f ) = Λ ( f , h ′ ( f ) ) {\displaystyle h(f)=\Lambda (f,h'(f))} . It should satisfy some form of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paratopological group Summary Paratopological_group In mathematics, a paratopological group is a topological semigroup that is algebraically a group. In other words, it is a group G with a topology such that the group's product operation is a continuous function from G × G to G. This differs from the definition of a to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parent function Summary Base_function In mathematics, a parent function is the core representation of a function type without manipulations such as translation and dilation. For example, for the family of quadratic functions having the general form y = a x 2 + b x + c , {\displaystyle y=ax^{2}+bx+c\,,} the simplest fun... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parent function Summary Base_function For example, the graph of y = x2 − 4x + 7 can be obtained from the graph of y = x2 by translating +2 units along the X axis and +3 units along Y axis. This is because the equation can also be written as y − 3 = (x − 2)2. For many trigonometric functions, the parent function is usua... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parent function Summary Base_function For example, the graph of y = A sin(x) + B cos(x) can be obtained from the graph of y = sin(x) by translating it through an angle α along the positive X axis (where tan(α) = A⁄B), then stretching it parallel to the Y axis using a stretch factor R, where R2 = A2 + B2. This is becaus... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial cyclic order Summary Partial_cyclic_order In mathematics, a partial cyclic order is a ternary relation that generalizes a cyclic order in the same way that a partial order generalizes a linear order. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial derivatives Summary Partial_derivatives In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial derivatives Summary Partial_derivatives {\displaystyle {\tfrac {\partial z}{\partial x}}.} Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: The symbol used to denote partial derivatives ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear partial differential equation Summary Analytical_solutions_of_partial_differential_equations In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solve... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear partial differential equation Summary Analytical_solutions_of_partial_differential_equations Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear partial differential equation Summary Analytical_solutions_of_partial_differential_equations For instance, they are foundational in the modern scientific understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear partial differential equation Summary Analytical_solutions_of_partial_differential_equations As such, it is usually acknowledged that there is no "general theory" of partial differential equations, with specialist knowledge being somewhat divided between several essentially distinct subfields.Ordinary differenti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial equivalence relation Summary Partial_equivalence_relation In mathematics, a partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is symmetric and transitive. If the relation is also reflexive, then the rela... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial functions Summary Total_function In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the domain of definition or natural domain of f. If S equals X, that is, if ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial functions Summary Total_function This is the case in calculus, where, for example, the quotient of two functions is a partial function whose domain of definition cannot contain the zeros of the denominator. For this reason, in calculus, and more generally in mathematical analysis, a partial function is generall... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial functions Summary Total_function In computability theory, a general recursive function is a partial function from the integers to the integers; no algorithm can exist for deciding whether an arbitrary such function is in fact total. When arrow notation is used for functions, a partial function f {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial group algebra Summary Partial_group_algebra In mathematics, a partial group algebra is an associative algebra related to the partial representations of a group. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dense relation Summary Densely_ordered In mathematics, a partial order or total order < on a set X {\displaystyle X} is said to be dense if, for all x {\displaystyle x} and y {\displaystyle y} in X {\displaystyle X} for which x < y {\displaystyle x | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Knaster's condition Summary Knaster's_condition In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is name... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Knaster's condition Summary Knaster's_condition Knaster's condition implies the countable chain condition (ccc), and it is sometimes used in conjunction with a weaker form of Martin's axiom, where the ccc requirement is replaced with Knaster's condition. Not unlike ccc, Knaster's condition is also sometimes used as a p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partially ordered space Summary Partially_ordered_space In mathematics, a partially ordered space (or pospace) is a topological space X {\displaystyle X} equipped with a closed partial order ≤ {\displaystyle \leq } , i.e. a partial order whose graph { ( x , y ) ∈ X 2 ∣ x ≤ y } {\displaystyle \{(x,y)\in X^{2}\mid x\leq ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partition matroid Summary Partition_matroid In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which the elements are partitioned into different categories. For each category, there is a capacity constraint - a maximum numbe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Set partition Summary Set_partition In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partition of an interval Summary Partition_of_an_interval In mathematics, a partition of an interval on the real line is a finite sequence x0, x1, x2, …, xn of real numbers such that a = x0 < x1 < x2 < … < xn = b.In other terms, a partition of a compact interval I is a strictly increasing sequence of numbers (belongin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partition of unity Summary Partition_of_unity In mathematics, a partition of unity of a topological space X {\displaystyle X} is a set R {\displaystyle R} of continuous functions from X {\displaystyle X} to the unit interval such that for every point x ∈ X {\displaystyle x\in X}: there is a neighbourhood of x {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arc (topology) Summary Path_(topology) In mathematics, a path in a topological space X {\displaystyle X} is a continuous function from the closed unit interval {\displaystyle } into X . {\displaystyle X.} Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arc (topology) Summary Path_(topology) Any space may be broken up into path-connected components. The set of path-connected components of a space X {\displaystyle X} is often denoted π 0 ( X ) . {\displaystyle \pi _{0}(X).} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arc (topology) Summary Path_(topology) One can also define paths and loops in pointed spaces, which are important in homotopy theory. If X {\displaystyle X} is a topological space with basepoint x 0 , {\displaystyle x_{0},} then a path in X {\displaystyle X} is one whose initial point is x 0 {\displaystyle x_{0}} . Lik... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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