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Translation of axes Summary Translation_of_axes In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Translation of axes Summary Translation_of_axes For example, if the xy-system is translated a distance h to the right and a distance k upward, then P will appear to have been translated a distance h to the left and a distance k downward in the x'y'-system . A translation of axes in more than two dimensions is defined s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Translation plane Summary Translation_plane In mathematics, a translation plane is a projective plane which admits a certain group of symmetries (described below). Along with the Hughes planes and the Figueroa planes, translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Translation plane Summary Translation_plane A line l in a projective plane Π is a translation line if the group of all elations with axis l acts transitively on the points of the affine plane obtained by removing l from the plane Π, Πl (the affine derivative of Π). A projective plane with a translation line is called a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transverse knot Summary Transverse_link In mathematics, a transverse knot is a smooth embedding of a circle into a three-dimensional contact manifold such that the tangent vector at every point of the knot is transverse to the contact plane at that point. Any Legendrian knot can be C0-perturbed in a direction transvers... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
XML tree Representation as trees XML_tree > Representation as trees In mathematics, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. Any connected graph without simple cycles is a tree. A tree data structure simulates a hierarchical tree structure with a set of linked no... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
XML tree Representation as trees XML_tree > Representation as trees A hierarchy consists of an order defined on a set. The term hierarchy is used to stress a hierarchical relation among the elements. The XML specification defines an XML document as a well-formed text if it satisfies a list of syntax rules defined in th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
XML tree Representation as trees XML_tree > Representation as trees This specification is long, however 2 key points relating to the tree structure of an XML document are: The begin, end, and empty-element tags that delimit the elements are correctly nested, with none missing and none overlapping A single "root" elemen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
XML tree Representation as trees XML_tree > Representation as trees The JavaScript (E4X) extension explicitly defines two specific objects (XML and XMLList), which support XML document nodes and XML node lists as distinct objects and use a dot-notation specifying parent-child relationships. These data structures repres... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
XML tree Representation as trees XML_tree > Representation as trees For instance, the XML document and the ASCII tree have the same structure. XML Trees do not show the content in an Instance document, only the structure of the document. In this example Product is the Root Element of the tree and the two child nodes of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tree of primitive Pythagorean triples Summary Tree_of_Pythagorean_triples In mathematics, a tree of primitive Pythagorean triples is a data tree in which each node branches to three subsequent nodes with the infinite set of all nodes giving all (and only) primitive Pythagorean triples without duplication. A Pythagorean... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tree of primitive Pythagorean triples Summary Tree_of_Pythagorean_triples This was first discovered by B. Berggren in 1934.F. J. M. Barning showed that when any of the three matrices A = B = C = {\displaystyle {\begin{array}{lcr}A={\begin{bmatrix}1&-2&2\\2&-1&2\\2&-2&3\end{bmatrix}}&B={\begin{bmatrix}1&2&2\\2&1&2\\2... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tree of primitive Pythagorean triples Summary Tree_of_Pythagorean_triples Thus each primitive Pythagorean triple has three "children". All primitive Pythagorean triples are descended in this way from the triple (3, 4, 5), and no primitive triple appears more than once. The result may be graphically represented as an in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Triangle group Summary Triangle_group In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry gro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Triangular form Summary Triangular_matrices In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. B... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exact triangle Summary Triangulated_functor In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles ge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exact triangle Summary Triangulated_functor In the 1960s, a typical use of triangulated categories was to extend properties of sheaves on a space X to complexes of sheaves, viewed as objects of the derived category of sheaves on X. More recently, triangulated categories have become objects of interest in their own righ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tricategory Summary Tricategory In mathematics, a tricategory is a kind of structure of category theory studied in higher-dimensional category theory. Whereas a weak 2-category is said to be a bicategory, a weak 3-category is said to be a tricategory (Gordon, Power & Street 1995; Baez & Dolan 1996; Leinster 1998).Tetra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trident curve Summary Trident_curve In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula: x y + a x 3 + b x 2 + c x = d {\displaystyle xy+ax^{3}+bx^{2}+cx=d} Trident curves are cubic plane curves with an ordinary double point in th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trinomial expansion Summary Trinomial_expansion In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by ( a + b + c ) n = ∑ i , j , k i + j + k = n ( n i , j , k ) a i b j c k , {\displaystyle (a+b+c)^{n}=\sum _{{i,j,k} \atop {i+j+k=n}}{n \choo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trinomial expansion Summary Trinomial_expansion k ! . {\displaystyle {n \choose i,j,k}={\frac {n!}{i!\,j!\,k!}}\,.} This formula is a special case of the multinomial formula for m = 3. The coefficients can be defined with a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trivial group Summary Zero_group In mathematics, a trivial group or zero group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: 0 , 1 , {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trivial group Summary Zero_group {\displaystyle e\cdot e=e.} The similarly defined trivial monoid is also a group since its only element is its own inverse, and is hence the same as the trivial group. The trivial group is distinct from the empty set, which has no elements, hence lacks an identity element, and so cannot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trivial semigroup Summary Trivial_semigroup In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of distinct nonisomorphic semigroups with one element is one. If S = { a } is a semigroup with one element, then the Cayley tab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trivial semigroup Summary Trivial_semigroup It is the starting point for understanding the structure of semigroups. It serves as a counterexample in illuminating many situations. For example, the semigroup with one element is the only semigroup in which 0 = 1, that is, the zero element and the identity element are equa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tube domain Summary Tube_domain In mathematics, a tube domain is a generalization of the notion of a vertical strip (or half-plane) in the complex plane to several complex variables. A strip can be thought of as the collection of complex numbers whose real part lie in a given subset of the real line and whose imaginary... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tube domain Summary Tube_domain Tubes over convex sets are domains of holomorphy. The Hardy spaces on tubes over convex cones have an especially rich structure, so that precise results are known concerning the boundary values of Hp functions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tube domain Summary Tube_domain In mathematical physics, the future tube is the tube domain associated to the interior of the past null cone in Minkowski space, and has applications in relativity theory and quantum gravity. Certain tubes over cones support a Bergman metric in terms of which they become bounded symmetri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tubular neighborhood Summary Tubular_neighborhood In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle. The idea behind a tubular neighborhood can be explained in a simple example. Consider a smooth curve in the plane without self-intersectio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tubular neighborhood Summary Tubular_neighborhood Unless the curve is straight, these lines will intersect among themselves in a rather complicated fashion. However, if one looks only in a narrow band around the curve, the portions of the lines in that band will not intersect, and will cover the entire band without gap... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tubular neighborhood Summary Tubular_neighborhood In general, let S be a submanifold of a manifold M, and let N be the normal bundle of S in M. Here S plays the role of the curve and M the role of the plane containing the curve. Consider the natural map i: N 0 → S {\displaystyle i:N_{0}\to S} which establishes a biject... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty tuple Summary Tuple In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty tuple Summary Tuple Tuple may be formally defined from ordered pairs by recurrence by starting from ordered pairs; indeed, a n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element. Tuples are usually written by listing the elements within parentheses "( )", separated by ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty tuple Summary Tuple Braces "{ }" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term tuple can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Empty tuple Summary Tuple Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Twisted cubic Summary Twisted_cubic In mathematics, a twisted cubic is a smooth, rational curve C of degree three in projective 3-space P3. It is a fundamental example of a skew curve. It is essentially unique, up to projective transformation (the twisted cubic, therefore). In algebraic geometry, the twisted cubic is a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncommutative polynomials Summary Noncommutative_polynomials In mathematics, a twisted polynomial is a polynomial over a field of characteristic p {\displaystyle p} in the variable τ {\displaystyle \tau } representing the Frobenius map x ↦ x p {\displaystyle x\mapsto x^{p}} . In contrast to normal polynomials, multipl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Twisted sheaf Summary Twisted_sheaf In mathematics, a twisted sheaf is a variant of a coherent sheaf. Precisely, it is specified by: an open covering in the étale topology Ui, coherent sheaves Fi over Ui, a Čech 2-cocycle θ on the covering Ui as well as the isomorphisms g i j: F j | U i j → ∼ F i | U i j {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Two-graph Summary Two-graph In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set X, such that every (unordered) quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unary function Summary Unary_function In mathematics, a unary function is a function that takes one argument. A unary operator belongs to a subset of unary functions, in that its range coincides with its domain. In contrast, a unary function's domain may or may not coincide with its range. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unary functional symbol Summary Unary_operator In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function f: A → A, where A is a set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unary functional symbol Summary Unary_operator The function f is a unary operation on A. Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial n! ), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well, for example, in the case of t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unicoherent space Summary Unicoherent_space In mathematics, a unicoherent space is a topological space X {\displaystyle X} that is connected and in which the following property holds: For any closed, connected A , B ⊂ X {\displaystyle A,B\subset X} with X = A ∪ B {\displaystyle X=A\cup B} , the intersection A ∩ B {\dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniform matroid Summary Uniform_matroid In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer r. An alternative definition is that every permutation of the elements is a symmetry. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniform tree Summary Uniform_tree In mathematics, a uniform tree is a locally finite tree which is the universal cover of a finite graph. Equivalently, the full automorphism group G=Aut(X) of the tree, which is a locally compact topological group, is unimodular and G\X is finite. Also equivalent is the existence of a u... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniformly bounded Summary Uniform_boundedness In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is larger than or equal to the absolute value of any value of any of the functions in the family. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniformly bounded representation Summary Uniformly_bounded_representation In mathematics, a uniformly bounded representation T {\displaystyle T} of a locally compact group G {\displaystyle G} on a Hilbert space H {\displaystyle H} is a homomorphism into the bounded invertible operators which is continuous for the stron... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniformly bounded representation Summary Uniformly_bounded_representation The result on unitarizability of uniformly bounded representations was extended in 1950 by Dixmier, Day and Nakamura-Takeda to all locally compact amenable groups, following essentially the method of proof of Sz-Nagy. The result is known to fail ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniformly disconnected space Summary Uniformly_disconnected_space In mathematics, a uniformly disconnected space is a metric space ( X , d ) {\displaystyle (X,d)} for which there exists λ > 0 {\displaystyle \lambda >0} such that no pair of distinct points x , y ∈ X {\displaystyle x,y\in X} can be connected by a λ {\dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniformly smooth space Summary Uniformly_smooth_space In mathematics, a uniformly smooth space is a normed vector space X {\displaystyle X} satisfying the property that for every ϵ > 0 {\displaystyle \epsilon >0} there exists δ > 0 {\displaystyle \delta >0} such that if x , y ∈ X {\displaystyle x,y\in X} with ‖ x ‖ = 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Totally unimodular Summary Total_unimodularity In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule). Thus every... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unimodular polynomial matrix Summary Unimodular_polynomial_matrix In mathematics, a unimodular polynomial matrix is a square polynomial matrix whose inverse exists and is itself a polynomial matrix. Equivalently, a polynomial matrix A is unimodular if its determinant det(A) is a nonzero constant. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unipotent group Summary Unipotent_group In mathematics, a unipotent element r of a ring R is one such that r − 1 is a nilpotent element; in other words, (r − 1)n is zero for some n. In particular, a square matrix M is a unipotent matrix if and only if its characteristic polynomial P(t) is a power of t − 1. Thus all the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unipotent representation Summary Unipotent_representation In mathematics, a unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups. Informally, Langlands philosophy suggests that there should be a correspondence between representations of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unique factorisation Summary Unique_factorization_domain In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unique sink orientation Summary Unique_sink_orientation In mathematics, a unique sink orientation is an orientation of the edges of a polytope such that, in every face of the polytope (including the whole polytope as one of the faces), there is exactly one vertex for which all adjoining edges are oriented inward (i.e. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniqueness theorem Summary Uniqueness_theorem In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions. Examples of uniqueness theorems include: Alexandrov's uni... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Uniqueness theorem Summary Uniqueness_theorem Fundamental theorem of arithmetic, the uniqueness of prime factorization. Holmgren's uniqueness theorem for linear partial differential equations with real analytic coefficients. Picard–Lindelöf theorem, the uniqueness of solutions to first-order differential equations. Tho... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unistochastic matrix Summary Unistochastic_matrix In mathematics, a unistochastic matrix (also called unitary-stochastic) is a doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some unitary matrix. A square matrix B of size n is doubly stochastic (or bistochastic) if all it... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unistochastic matrix Summary Unistochastic_matrix Since all orthogonal matrices are necessarily unitary matrices, all orthostochastic matrices are also unistochastic. The converse, however, is not true. First, all 2-by-2 doubly stochastic matrices are both unistochastic and orthostochastic, but for larger n this is not... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unistochastic matrix Summary Unistochastic_matrix For example, take n = 3 {\displaystyle n=3} and consider the following doubly stochastic matrix: B = 1 2 . {\displaystyle B={\frac {1}{2}}{\begin{bmatrix}1&1&0\\0&1&1\\1&0&1\end{bmatrix}}.} This matrix is not unistochastic, since any two vectors with moduli equal to th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit circle Summary Unit_circle In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit circle Summary Unit_circle Thus, by the Pythagorean theorem, x and y satisfy the equation Since x2 = (−x)2 for all x, and since the reflection of any point on the unit circle about the x- or y-axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not only those in the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit ball Summary Unit_ball In mathematics, a unit sphere is simply a sphere of radius one around a given center. More generally, it is the set of points of distance 1 from a fixed central point, where different norms can be used as general notions of "distance". A unit ball is the closed set of points of distance less... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit ball Summary Unit_ball Special cases are the unit circle and the unit disk. The importance of the unit sphere is that any sphere can be transformed to a unit sphere by a combination of translation and scaling. In this way the properties of spheres in general can be reduced to the study of the unit sphere. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit square Summary Unit_square In mathematics, a unit square is a square whose sides have length 1. Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points (0, 0), (1, 0), (0, 1), and (1, 1). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hat operator Unit vector Hat_operator > Unit vector In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in v ^ {\displaystyle {\hat {\mathbf {v} }}} (pronounced "v-hat"). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit vector Summary Normalized_vector In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in v ^ {\displaystyle {\hat {\mathbf {v} }}} (pronounced "v-hat"). The term direction vector... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit vector Summary Normalized_vector 2D spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3D are equivalent to a point on the unit sphere. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., u ^ = u ‖ u ‖ {\displaystyle \math... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unitary representation Summary Unitary_dual In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in the case that G is a locally compact (Hausdorff) topological grou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spider diagram Summary Spider_diagram In mathematics, a unitary spider diagram adds existential points to an Euler or a Venn diagram. The points indicate the existence of an attribute described by the intersection of contours in the Euler diagram. These points may be joined forming a shape like a spider. Joined points ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unitary transformation Summary Antiunitary_transformation In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate Summary Univariate_and_multivariate In mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one variable are multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for ex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate Summary Univariate_and_multivariate In statistics, a univariate distribution characterizes one variable, although it can be applied in other ways as well. For example, univariate data are composed of a single scalar component. In time series analysis, the whole time series is the "variable": a univariate tim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Univariate Summary Univariate_and_multivariate Correspondingly, a "multivariate time series" characterizes the changing values over time of several quantities. In some cases, the terminology is ambiguous, since the values within a univariate time series may be treated using certain types of multivariate statistical ana... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Properties of polynomial roots Summary Geometrical_properties_of_polynomial_roots In mathematics, a univariate polynomial of degree n with real or complex coefficients has n complex roots, if counted with their multiplicities. They form a multiset of n points in the complex plane. This article concerns the geometry of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Properties of polynomial roots Summary Geometrical_properties_of_polynomial_roots Such bounds are widely used for root-finding algorithms for polynomials, either for tuning them, or for computing their computational complexity. Some other properties are probabilistic, such as the expected number of real roots of a rand... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal C*-algebra Summary Universal_C*-algebra In mathematics, a universal C*-algebra is a C*-algebra described in terms of generators and relations. In contrast to rings or algebras, where one can consider quotients by free rings to construct universal objects, C*-algebras must be realizable as algebras of bounded ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal graph Summary Universal_graph In mathematics, a universal graph is an infinite graph that contains every finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type was first constructed by Richard Rado and is now called the Rado graph or random graph. More recent work has focus... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal graph Summary Universal_graph However it is not the smallest such graph: it is known that there is a universal graph for n-vertex trees, with only n vertices and O(n log n) edges, and that this is optimal. A construction based on the planar separator theorem can be used to show that n-vertex planar graphs hav... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal graph Summary Universal_graph It is also possible to construct universal graphs for planar graphs that have n1+o(1) vertices.Sumner's conjecture states that tournaments are universal for polytrees, in the sense that every tournament with 2n − 2 vertices contains every polytree with n vertices as a subgraph.A ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal quadratic form Summary Universal_quadratic_form In mathematics, a universal quadratic form is a quadratic form over a ring that represents every element of the ring. A non-singular form over a field which represents zero non-trivially is universal. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal space (topology) Summary Universal_space_(topology) In mathematics, a universal space is a certain metric space that contains all metric spaces whose dimension is bounded by some fixed constant. A similar definition exists in topological dynamics. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wonders of Numbers Vampire numbers and other mathematical highlights Clifford_A._Pickover > Work > Vampire numbers and other mathematical highlights In mathematics, a vampire number or true vampire number is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y ea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wonders of Numbers Vampire numbers and other mathematical highlights Clifford_A._Pickover > Work > Vampire numbers and other mathematical highlights Similarly, 136,948 is a vampire because 136,948 = 146 × 938. Vampire numbers first appeared in a 1994 post by Clifford A. Pickover to the Usenet group sci.math, and the ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Wonders of Numbers Vampire numbers and other mathematical highlights Clifford_A._Pickover > Work > Vampire numbers and other mathematical highlights In 1990, he asked "Is There a Double Smoothly Undulating Integer? ", and he computed "All Known Replicating Fibonacci Digits Less than One Billion". With his colleague Joh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Variable (logics) Summary Variable_(logics) In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.Algebraic computations with variabl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Variational inequalities Summary Variational_inequality In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector bundle morphism Summary Bundle_projection In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X {\displaystyle X} (for example X {\displaystyle X} could be a topological space, a manifold, or an algebraic variety): ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector bundle morphism Summary Bundle_projection Tangent bundles are not, in general, trivial bundles. For example, the tangent bundle of the sphere is non-trivial by the hairy ball theorem. In general, a manifold is said to be parallelizable if, and only if, its tangent bundle is trivial. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector bundle morphism Summary Bundle_projection Vector bundles are almost always required to be locally trivial, which means they are examples of fiber bundles. Also, the vector spaces are usually required to be over the real or complex numbers, in which case the vector bundle is said to be a real or complex vector bu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Flat vector bundle Summary Flat_vector_bundle In mathematics, a vector bundle is said to be flat if it is endowed with a linear connection with vanishing curvature, i.e. a flat connection. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lyapunov's theorem Summary Lyapunov_vector-measure_theorem In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization of the concept of finite measure, which takes nonnegative real values only. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector-valued differential form Summary Vector_valued_differential_form In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit quaternion Summary Unit_quaternion In mathematics, a versor is a quaternion of norm one (a unit quaternion). Each versor has the form q = exp ( a r ) = cos a + r sin a , r 2 = − 1 , a ∈ , {\displaystyle q=\exp(a\mathbf {r} )=\cos a+\mathbf {r} \sin a,\quad \mathbf {r} ^{2}=-1,\quad a\in ,} where the r2 = −1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vertex cycle cover Summary Vertex_cycle_cover In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vertex cycle cover Summary Vertex_cycle_cover Similar definitions exist for digraphs, in terms of directed cycles. Finding a vertex-disjoint cycle cover of a directed graph can also be performed in polynomial time by a similar reduction to perfect matching. However, adding the condition that each cycle should have leng... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vertex algebra Summary Vertex_algebras In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts suc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vertex algebra Summary Vertex_algebras Borcherds formulated the notion of vertex algebra by axiomatizing the relations between the lattice vertex operators, producing an algebraic structure that allows one to construct new Lie algebras by following Frenkel's method. The notion of vertex operator algebra was introduced ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vertex algebra Summary Vertex_algebras Motivated by this observation, they added the Virasoro action and bounded-below property as axioms. We now have post-hoc motivation for these notions from physics, together with several interpretations of the axioms that were not initially known. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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