source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/Tetrakis%20square%20tiling | In geometry, the tetrakis square tiling is a tiling of the Euclidean plane. It is a square tiling with each square divided into four isosceles right triangles from the center point, forming an infinite arrangement of lines. It can also be formed by subdividing each square of a grid into two triangles by a diagonal, wit... |
https://en.wikipedia.org/wiki/Theta%20%28disambiguation%29 | Theta is the eighth Greek letter, written Θ (uppercase) or θ (lowercase).
Theta may also refer to:
Science and mathematics
Θ (set theory), the least ordinal α such that there is no surjection from the reals onto α
Theta (gastropod), a genus of sea snails
Theta functions, special functions of several complex variab... |
https://en.wikipedia.org/wiki/Hirzebruch%E2%80%93Riemann%E2%80%93Roch%20theorem | In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing the classical Riemann–Roch theorem on Riemann surfaces to all complex algebraic varieties of higher dimensions. The result paved the way for the Grothendieck... |
https://en.wikipedia.org/wiki/Operating%20surplus | Operating surplus is an accounting concept used in national accounts statistics (such as United Nations System of National Accounts (UNSNA)) and in corporate and government accounts. It is the balancing item of the Generation of Income Account in the UNSNA. It may be used in macro-economics as a proxy for total pre-ta... |
https://en.wikipedia.org/wiki/FIVB%20Volleyball%20World%20League%20statistics | This article gives the summarized final standings of each FIVB Volleyball World League tournament, an annual competition involving national men's volleyball teams. The most successful teams, , have been: Brazil, 9 times (1993, 2001, 2003–07, 2009–10) and Italy, 8 times (1990–92, 1994–95, 1997, 1999–2000). The competiti... |
https://en.wikipedia.org/wiki/National%20Longitudinal%20Surveys | The National Longitudinal Surveys (NLS) are a set of surveys sponsored by the Bureau of Labor Statistics (BLS) of the U.S. Department of Labor. These surveys have gathered information at multiple points in time on the labor market experiences and other significant life events of several groups of men and women. Each of... |
https://en.wikipedia.org/wiki/Model%20category | In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations' satisfying certain axioms relating them. These abstract from the category of topological spaces or of chain complexes (derived ca... |
https://en.wikipedia.org/wiki/Fluent%20%28disambiguation%29 | Fluent is an adjective related to fluency, the ability to communicate in a language quickly and accurately.
Fluent or fluency may also refer to:
Fluent (mathematics), in mathematics, a continuous function
Fluent (artificial intelligence), in artificial intelligence, a condition that varies over time
Fluent, Inc., a... |
https://en.wikipedia.org/wiki/Event%20calculus | The event calculus is a logical language for representing and reasoning about events and their effects first presented by Robert Kowalski and Marek Sergot in 1986. It was extended by Murray Shanahan and Rob Miller in the 1990s. Similar to other languages for reasoning about change, the event calculus represents the eff... |
https://en.wikipedia.org/wiki/Tomita%E2%80%93Takesaki%20theory | In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita–Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution. It is essential for the theory of type III factors, and has led to a go... |
https://en.wikipedia.org/wiki/Perspective | Perspective may refer to:
Vision and mathematics
Perspectivity, the formation of an image in a picture plane of a scene viewed from a fixed point, and its modeling in geometry
Perspective (graphical), representing the effects of visual perspective in graphic arts
Aerial perspective, the effect the atmosphere has o... |
https://en.wikipedia.org/wiki/Matplotlib | Matplotlib is a plotting library for the Python programming language and its numerical mathematics extension NumPy. It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK. There is also a procedural "pylab" interface based on a stat... |
https://en.wikipedia.org/wiki/Upper%20set | In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set is a subset with the following property: if s is in S and if x in X is larger than s (that is, if ), then x is in S. In other words, this means that any x element of X that is to some element ... |
https://en.wikipedia.org/wiki/Daniell%20integral | In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced. One of the main difficulties with the traditional formulation of the Lebesgue integral is that it requires the initial dev... |
https://en.wikipedia.org/wiki/Olav%20Reiers%C3%B8l | Olav Reiersøl (28 June 1908 – 14 February 2001) was a Norwegian statistician and econometrician, who made several substantial contributions to econometrics and statistics. His works on identifiability and instrumental variables are standard references both in econometrics and statistics, and his work on genetic algebra... |
https://en.wikipedia.org/wiki/Pandigital%20number | 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 pandigital number in base 10. The first few... |
https://en.wikipedia.org/wiki/Doubly%20stochastic%20matrix | In mathematics, especially in probability and combinatorics, a doubly stochastic matrix
(also called bistochastic matrix) is a square matrix of nonnegative real numbers, each of whose rows and columns sums to 1, i.e.,
Thus, a doubly stochastic matrix is both left stochastic and right stochastic.
Indeed, any matrix ... |
https://en.wikipedia.org/wiki/Kurosh%20problem | In mathematics, the Kurosh problem is one general problem, and several more special questions, in ring theory. The general problem is known to have a negative solution, since one of the special cases has been shown to have counterexamples. These matters were brought up by Aleksandr Gennadievich Kurosh as analogues of t... |
https://en.wikipedia.org/wiki/Pencil%20%28geometry%29 | In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane.
Although the definition of a pencil is rather vague, the common characteristic is that the pencil ... |
https://en.wikipedia.org/wiki/David%20E.%20Rowe | David E. Rowe (born August 11, 1950) is an American mathematician and historian. He studied mathematics and the history of science at the University of Oklahoma, and took a second doctorate in history at the Graduate Center of the City University of New York. He served as book review editor, managing editor, and editor... |
https://en.wikipedia.org/wiki/Behrens%E2%80%93Fisher%20problem | In statistics, the Behrens–Fisher problem, named after Walter-Ulrich Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on... |
https://en.wikipedia.org/wiki/Studentization | In statistics, Studentization, named after William Sealy Gosset, who wrote under the pseudonym Student, is the adjustment consisting of division of a first-degree statistic derived from a sample, by a sample-based estimate of a population standard deviation. The term is also used for the standardisation of a higher-de... |
https://en.wikipedia.org/wiki/Klein%20geometry | In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which acts as the symmetry group of the geometry.
For background and motivation see the article on... |
https://en.wikipedia.org/wiki/Serre%27s%20modularity%20conjecture | In mathematics, Serre's modularity conjecture, introduced by , states that an odd, irreducible, two-dimensional Galois representation over a finite field arises from a modular form. A stronger version of this conjecture specifies the weight and level of the modular form. The conjecture in the level 1 case was proved by... |
https://en.wikipedia.org/wiki/Truncation%20%28disambiguation%29 | Truncation is the term used for limiting the number of digits right of the decimal point by discarding the least significant ones.
Truncation may also refer to:
Mathematics
Truncation (statistics) refers to measurements which have been cut off at some value
Truncation (numerical analysis) refers to truncating an in... |
https://en.wikipedia.org/wiki/Forest-fire%20model | In applied mathematics, a forest-fire model is any of a number of dynamical systems displaying self-organized criticality. Note, however, that according to Pruessner et al. (2002, 2004) the forest-fire model does not behave critically on very large, i.e. physically relevant scales. Early versions go back to Henley (198... |
https://en.wikipedia.org/wiki/Trisectrix | In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool. Such a method falls outside those allowed by compass and straightedge constructions, so they do not contradict the well known theorem which states that an arbitrary angle can... |
https://en.wikipedia.org/wiki/Great%20dirhombicosidodecahedron | In geometry, the great dirhombicosidodecahedron (or great snub disicosidisdodecahedron) is a nonconvex uniform polyhedron, indexed last as . It has 124 faces (40 triangles, 60 squares, and 24 pentagrams), 240 edges, and 60 vertices.
This is the only non-degenerate uniform polyhedron with more than six faces meeting at... |
https://en.wikipedia.org/wiki/Andrew%20Granville | Andrew James Granville (born 7 September 1962) is a British mathematician, working in the field of number theory.
He has been a faculty member at the Université de Montréal since 2002. Before moving to Montreal he was a mathematics professor at the University of Georgia (UGA) from 1991 until 2002. He was a section spe... |
https://en.wikipedia.org/wiki/Fril | Fril is a programming language for first-order predicate calculus. It includes the semantics of Prolog as a subset, but takes its syntax from the of Logic Programming Associates and adds support for fuzzy sets, support logic, and metaprogramming.
Fril was originally developed by Trevor Martin and Jim Baldwin at the ... |
https://en.wikipedia.org/wiki/Mathematics%20of%20Sudoku | Mathematics can be used to study Sudoku puzzles to answer questions such as "How many filled Sudoku grids are there?", "What is the minimal number of clues in a valid puzzle?" and "In what ways can Sudoku grids be symmetric?" through the use of combinatorics and group theory.
The analysis of Sudoku is generally divide... |
https://en.wikipedia.org/wiki/Topological%20K-theory | In mathematics, topological -theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological -theory is due to Michael Atiyah and Friedrich Hirzebr... |
https://en.wikipedia.org/wiki/Ergodic%20sequence | In mathematics, an ergodic sequence is a certain type of integer sequence, having certain equidistribution properties.
Definition
Let be an infinite, strictly increasing sequence of positive integers. Then, given an integer q, this sequence is said to be ergodic mod q if, for all integers , one has
where
and card ... |
https://en.wikipedia.org/wiki/Tautological%20bundle | In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of -dimensional subspaces of , given a point in the Grassmannian corresponding to a -dimensional vector subspace , the fiber over is the subspace itself. In the case of projective... |
https://en.wikipedia.org/wiki/Chinaman%27s%20chance | Chinaman's chance is an American idiom which means that a person has little or no chance at success, synonymous with similar idioms of improbability such as a snowball's chance in hell or when pigs fly. Although the origin of the phrase is unclear, it may refer to the historical misfortunes which were suffered by Chine... |
https://en.wikipedia.org/wiki/Milnor%20conjecture | In mathematics, the Milnor conjecture was a proposal by of a description of the Milnor K-theory (mod 2) of a general field F with characteristic different from 2, by means of the Galois (or equivalently étale) cohomology of F with coefficients in Z/2Z. It was proved by .
Statement
Let F be a field of characteristic d... |
https://en.wikipedia.org/wiki/Milnor%20K-theory | In mathematics, Milnor K-theory is an algebraic invariant (denoted for a field ) defined by as an attempt to study higher algebraic K-theory in the special case of fields. It was hoped this would help illuminate the structure for algebraic and give some insight about its relationships with other parts of mathematics... |
https://en.wikipedia.org/wiki/Spin%20connection | In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine connection. It can also be regarded as the gauge field generated by local Lorentz transformations. In some canonical formulations of general relativity, a spin... |
https://en.wikipedia.org/wiki/Orbifold%20notation | In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature. The advantage of the notation is that it describes these groups in a way which indic... |
https://en.wikipedia.org/wiki/Dissection%20problem | In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the... |
https://en.wikipedia.org/wiki/Dissection%20%28disambiguation%29 | Dissection is the dismembering of the body of a deceased animal or plant to study its anatomical structure.
Dissection may also refer to:
The dissection problem in geometry
Dissection (medical), a tear in a blood vessel
Dissection (band), a Swedish extreme metal band
Dissection (album), a 1997 Crimson Thorn album
D... |
https://en.wikipedia.org/wiki/List%20of%20combinatorial%20computational%20geometry%20topics | List of combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects as discrete entities and hence the methods of their solution are mostly theories and algorithms of combinatorial character.
See List of numerical computational geometry... |
https://en.wikipedia.org/wiki/List%20of%20numerical%20computational%20geometry%20topics | List of numerical computational geometry topics enumerates the topics of computational geometry that deals with geometric objects as continuous entities and applies methods and algorithms of nature characteristic to numerical analysis. This area is also called "machine geometry", computer-aided geometric design, and ge... |
https://en.wikipedia.org/wiki/Cabri%20Geometry | Cabri Geometry is a commercial interactive geometry software produced by the French company Cabrilog for teaching and learning geometry and trigonometry. It was designed with ease-of-use in mind. The program allows the user to animate geometric figures, proving a significant advantage over those drawn on a blackboard.... |
https://en.wikipedia.org/wiki/David%20Salsburg | David S. Salsburg (born 1931) is an author. His 2002 book The Lady Tasting Tea, subtitled How Statistics Revolutionized Science in the Twentieth Century, provides a layman's overview of important developments in the field of statistics in the late 19th and early 20th century, particularly in the areas of experiment des... |
https://en.wikipedia.org/wiki/Separatrix%20%28mathematics%29 | In mathematics, a separatrix is the boundary separating two modes of behaviour in a differential equation.
Example: simple pendulum
Consider the differential equation describing the motion of a simple pendulum:
where denotes the length of the pendulum, the gravitational acceleration and the angle between the pend... |
https://en.wikipedia.org/wiki/Dihedral%20symmetry%20in%20three%20dimensions | In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as an abstract group is a dihedral group Dihn (for n ≥ 2).
Types
There are 3 types of dihedral symmetry in three dimensions, each shown below in 3 notations: Schön... |
https://en.wikipedia.org/wiki/The%20Lady%20Tasting%20Tea | The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century () is a book by David Salsburg about the history of modern statistics and the role it played in the development of science and industry.
The title comes from the "lady tasting tea", an example from the famous book, The Design of Exper... |
https://en.wikipedia.org/wiki/Interprime | In mathematics, an interprime is the average of two consecutive odd primes. For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are:
4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, ...
Interprimes cannot be prime themselves (otherwis... |
https://en.wikipedia.org/wiki/Odious%20number | In number theory, an odious number is a positive integer that has an odd number of 1s in its binary expansion. Non-negative integers that are not odious are called evil numbers.
In computer science, an odious number is said to have odd parity.
Examples
The first odious numbers are:
Properties
If denotes the th odio... |
https://en.wikipedia.org/wiki/Cyclic%20symmetry%20in%20three%20dimensions | In three dimensional geometry, there are four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) that does not change the object.
They are the finite symmetry groups on a cone. For n = ∞ they correspond to four frieze groups.... |
https://en.wikipedia.org/wiki/Square%20root%20of%20a%20matrix | In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix is said to be a square root of if the matrix product is equal to .
Some authors use the name square root or the notation only for the specific case when is positive semidefinite, to denote the unique ... |
https://en.wikipedia.org/wiki/Zvi%20Hecker | Zvi Hecker (; 31 May 1931 – 24 September 2023) was a Polish-born Israeli architect. His work is known for its emphasis on geometry and asymmetry.
Biography
Zvi Hecker was born as Tadeusz Hecker in Kraków, Poland. He grew up in Poland and Samarkand. He began his education in architecture at the Cracow University of Tec... |
https://en.wikipedia.org/wiki/MIMA | MIMA may refer to:
Member of the Institute of Mathematics and its Applications
MiMA (building), an apartment building whose name means Middle of Manhattan, New York City, United States
Middlesbrough Institute of Modern Art, art gallery in Middlesbrough, England
Modern Improvisational Music Association, a public c... |
https://en.wikipedia.org/wiki/Logarithm%20of%20a%20matrix | In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do ha... |
https://en.wikipedia.org/wiki/Infinity%20%28disambiguation%29 | Infinity (symbol: ) is a mathematical concept that is involved in almost all branches of mathematics, and used in many scientific and non-scientific areas.
Infinity or infinities may also refer to:
Infinity (philosophy), a related philosophical and metaphysical concept
Mathematics
Infinity symbol
Aleph number, s... |
https://en.wikipedia.org/wiki/Circles%20of%20Apollonius | The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereo... |
https://en.wikipedia.org/wiki/GCD%20domain | In mathematics, a GCD domain is an integral domain R with the property that any two elements have a greatest common divisor (GCD); i.e., there is a unique minimal principal ideal containing the ideal generated by two given elements. Equivalently, any two elements of R have a least common multiple (LCM).
A GCD domain g... |
https://en.wikipedia.org/wiki/Euler%20class | In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the classical notion of Euler characte... |
https://en.wikipedia.org/wiki/Robion%20Kirby | Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant for classifying the piecewise linear structures on a topological manifold. H... |
https://en.wikipedia.org/wiki/Klein%20quadric | In mathematics, the lines of a 3-dimensional projective space, S, can be viewed as points of a 5-dimensional projective space, T. In that 5-space, the points that represent each line in S lie on a quadric, Q known as the Klein quadric.
If the underlying vector space of S is the 4-dimensional vector space V, then T has... |
https://en.wikipedia.org/wiki/Plane%20partition | In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers (with positive integer indices i and j) that is nonincreasing in both indices. This means that
and for all i and j.
Moreover, only finitely many of the may be nonzero. Plane partitions are a general... |
https://en.wikipedia.org/wiki/Quantum%20calculus | Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. It defines "q-calculus" and "h-calculus", where h ostensibly stands for Planck's constant while q stands for quantum. The two parameters are related by the formula
where is the... |
https://en.wikipedia.org/wiki/Quasi-algebraically%20closed%20field | In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree. The idea of quasi-algebraically closed fields was investigated by C. C. Tsen, a student of Emmy Noether, in a... |
https://en.wikipedia.org/wiki/Chevalley%E2%80%93Warning%20theorem | In number theory, the Chevalley–Warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions. It was proved by and a slightly weaker form of the theorem, known as Chevalley's theorem, was proved by . Chevalley's theorem implied Artin's and Dickson's conje... |
https://en.wikipedia.org/wiki/Noetherian%20topological%20space | In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the complements of the closed subsets. The Noetherian pr... |
https://en.wikipedia.org/wiki/Concordance%20%28genetics%29 | In genetics, concordance is the probability that a pair of individuals will both have a certain characteristic (phenotypic trait) given that one of the pair has the characteristic. Concordance can be measured with concordance rates, reflecting the odds of one person having the trait if the other does. Important clinica... |
https://en.wikipedia.org/wiki/Greater%20Manchester%20Built-up%20Area | The Greater Manchester Built-up Area is an area of land defined by the Office for National Statistics (ONS), consisting of the large conurbation that encompasses the urban element of the city of Manchester and the metropolitan area that forms much of Greater Manchester in North West England. According to the United Kin... |
https://en.wikipedia.org/wiki/Ancestral%20graph | In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that takes the form of a directed acyclic graph.
Definition
Ancestral graphs are mixed graphs used with three kinds of edges: ... |
https://en.wikipedia.org/wiki/M-separation | In statistics, m-separation is a measure of disconnectedness in ancestral graphs and a generalization of d-separation for directed acyclic graphs. It is the opposite of m-connectedness.
Suppose G is an ancestral graph. For given source and target nodes s and t and a set Z of nodes in G\{s, t}, m-connectedness can be ... |
https://en.wikipedia.org/wiki/Adragon%20De%20Mello | Adragon De Mello (born October 8, 1976) graduated from the University of California, Santa Cruz with a degree in computational mathematics in 1988, at age 11. At the time, he was the youngest college graduate in U.S. history, a record broken in 1994 by Michael Kearney. His early achievements may have been more due to ... |
https://en.wikipedia.org/wiki/Breusch%E2%80%93Pagan%20test | In statistics, the Breusch–Pagan test, developed in 1979 by Trevor Breusch and Adrian Pagan, is used to test for heteroskedasticity in a linear regression model. It was independently suggested with some extension by R. Dennis Cook and Sanford Weisberg in 1983 (Cook–Weisberg test). Derived from the Lagrange multiplier t... |
https://en.wikipedia.org/wiki/Carus%20Mathematical%20Monographs | The Carus Mathematical Monographs is a monograph series published by the Mathematical Association of America. Books in this series are intended to appeal to a wide range of readers in mathematics and science.
Scope and audience
While the books are intended to cover nontrivial material, the emphasis is on exposition an... |
https://en.wikipedia.org/wiki/Lefschetz%20zeta%20function | In mathematics, the Lefschetz zeta-function is a tool used in topological periodic and fixed point theory, and dynamical systems. Given a continuous map , the zeta-function is defined as the formal series
where is the Lefschetz number of the -th iterate of . This zeta-function is of note in topological periodic point... |
https://en.wikipedia.org/wiki/Scalar%20boson | A scalar boson is a boson whose spin equals zero. A boson is a particle whose wave function is symmetric under particle exchange and therefore follows Bose–Einstein statistics. The spin–statistics theorem implies that all bosons have an integer-valued spin. Scalar bosons are the subset of bosons with zero-valued spin.
... |
https://en.wikipedia.org/wiki/Hemicontinuity | In mathematics, the notion of the continuity of functions is not immediately extensible to set-valued functions between two sets A and B.
The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension.
A set-valued function that has both properties is said to be continuous in an analo... |
https://en.wikipedia.org/wiki/Saturated%20measure | In mathematics, a measure is said to be saturated if every locally measurable set is also measurable. A set , not necessarily measurable, is said to be a if for every measurable set of finite measure, is measurable. -finite measures and measures arising as the restriction of outer measures are saturated.
Referenc... |
https://en.wikipedia.org/wiki/Stable%20homotopy%20theory | In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states that given any pointed space ... |
https://en.wikipedia.org/wiki/Tokyo%20International%20Film%20Festival | The is a film festival established in 1985. The event was held biennially from 1985 to 1991 and annually thereafter. According to FIAPF statistics, it is one of Asia's competitive film festivals, is considered to be the second largest film festival in Asia behind the Shanghai International Film Festival, and the only... |
https://en.wikipedia.org/wiki/European%20Cup%20and%20UEFA%20Champions%20League%20records%20and%20statistics | This page details statistics of the European Cup and Champions League. Unless noted, these statistics concern all seasons since the inception of the European Cup in the 1955–56 season, and renamed since 1992 as the UEFA Champions League. This does not include the qualifying rounds of the UEFA Champions League, unless o... |
https://en.wikipedia.org/wiki/Matthew%20Stephens%20%28statistician%29 | Matthew Stephens (born 1970) is a Bayesian statistician and professor in the departments of human genetics and statistics at the University of Chicago. He is known for the Li and Stephens model as an efficient coalescent.
Education
Stephens has a PhD from Magdalen College, Oxford University where his advisor was Bri... |
https://en.wikipedia.org/wiki/Wythoff%20construction | In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic construction.
Construction process
The method is based on the idea of tiling a sphere, with spherical triangles ... |
https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Wold%20theorem | In mathematics, the Cramér–Wold theorem in measure theory states that a Borel probability measure on is uniquely determined by the totality of its one-dimensional projections. It is used as a method for proving joint convergence results. The theorem is named after Harald Cramér and Herman Ole Andreas Wold.
Let
and
... |
https://en.wikipedia.org/wiki/Wedge%20%28geometry%29 | In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices.
A wedge is a subclass of the prismatoids with the base and opposite ridge in two parallel planes.
A wedge can also be classified as a digonal cupola.
Comparisons:
A w... |
https://en.wikipedia.org/wiki/Medial | Medial may refer to:
Mathematics
Medial magma, a mathematical identity in algebra
Geometry
Medial axis, in geometry the set of all points having more than one closest point on an object's boundary
Medial graph, another graph that represents the adjacencies between edges in the faces of a plane graph
Medial tria... |
https://en.wikipedia.org/wiki/Filtered%20algebra | In mathematics, a filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and representation theory.
A filtered algebra over the field is an algebra over that has an increasing sequence of subspaces of such that
... |
https://en.wikipedia.org/wiki/Cairo%20pentagonal%20tiling | In geometry, a Cairo pentagonal tiling is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations of the plane by hexagons and named for its use as a paving design in Cairo. It is also called MacMahon's net after Percy Alexander MacMahon, who depicted it in his 1921 p... |
https://en.wikipedia.org/wiki/Rational%20point | In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers is generally understood. If the field is the field of real numbers, a rational point is more commonly called a real point. ... |
https://en.wikipedia.org/wiki/Weil%20cohomology%20theory | In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups. The name is in honor of André Weil. Any Weil cohomology theory factors uniquely through the category of Chow motives, but the category of Chow... |
https://en.wikipedia.org/wiki/Immigration%20to%20France | According to the French National Institute of Statistics INSEE, the 2021 census counted nearly 7 million immigrants (foreign-born people) in France, representing 10.3% of the total population. This is a decrease from INSEE statistics in 2018 in which there were 9 million immigrants (foreign-born people) in France, whic... |
https://en.wikipedia.org/wiki/Fluent%20calculus | The fluent calculus is a formalism for expressing dynamical domains in first-order logic. It is a variant of the situation calculus; the main difference is that situations are considered representations of states. A binary function symbol is used to concatenate the terms that represent facts that hold in a situation. ... |
https://en.wikipedia.org/wiki/Blattner%27s%20conjecture | In mathematics, Blattner's conjecture or Blattner's formula is a description of the discrete series representations of a general semisimple group G in terms of their restricted representations to a maximal compact subgroup K (their so-called K-types). It is named after Robert James Blattner, despite not being formulate... |
https://en.wikipedia.org/wiki/Naum%20Sekulovski | Naum Sekulovski (born 14 May 1982) is an Australian soccer player who plays for Preston Lions in the NPL 2 Victoria competition.
A League career statistics
(Correct as of 21 March 2010)
Honours
Perth Glory FC
Best Clubman: 2010
References
External links
Perth Glory profile
Oz Football profile
1982 births
Livin... |
https://en.wikipedia.org/wiki/Solvable%20Lie%20algebra | In mathematics, a Lie algebra is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra of the Lie algebra is the subalgebra of , denoted
that consists of all linear combinations of Lie brackets of pairs of elements of . The derived series is the sequence of subalgebras
If the der... |
https://en.wikipedia.org/wiki/Final%20stellation%20of%20the%20icosahedron | In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three intersecting face planes of the icosahedral core intersect either on a vertex ... |
https://en.wikipedia.org/wiki/Weil%20reciprocity%20law | In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then
f((g)) = g((f))
where the notation has this meaning: (h) is the divisor of the functio... |
https://en.wikipedia.org/wiki/Joseph%20Wedderburn | Joseph Henry Maclagan Wedderburn FRSE FRS (2 February 1882 – 9 October 1948) was a Scottish mathematician, who taught at Princeton University for most of his career. A significant algebraist, he proved that a finite division algebra is a field, and part of the Artin–Wedderburn theorem on simple algebras. He also worked... |
https://en.wikipedia.org/wiki/Tonelli%27s%20theorem | In mathematics, Tonelli's theorem may refer to
Tonelli's theorem in measure theory, a successor of Fubini's theorem
Tonelli's theorem in functional analysis, a fundamental result on the weak lower semicontinuity of nonlinear functionals on Lp spaces |
https://en.wikipedia.org/wiki/Penrose%20graphical%20notation | In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions or tensors proposed by Roger Penrose in 1971. A diagram in the notation consists of several shapes linked together by lines.
The notation widely appears in modern quan... |
https://en.wikipedia.org/wiki/Idempotent%20matrix | In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix is idempotent if and only if . For this product to be defined, must necessarily be a square matrix. Viewed this way, idempotent matrices are idempotent elements of matrix rings.
Example
Examples ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.