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https://en.wikipedia.org/wiki/Adolf%20Lindenbaum | Adolf Lindenbaum (12 June 1904 – August 1941) was a Polish-Jewish logician and mathematician best known for Lindenbaum's lemma and Lindenbaum–Tarski algebras.
He was born and brought up in Warsaw. He earned a Ph.D. in 1928 under Wacław Sierpiński and habilitated at the University of Warsaw in 1934. He published work... |
https://en.wikipedia.org/wiki/Aleksandr%20Khinchin | Aleksandr Yakovlevich Khinchin (, ; July 19, 1894 – November 18, 1959) was a Soviet mathematician and one of the most significant contributors to the Soviet school of probability theory.
Due to romanization conventions, his name is sometimes written as "Khinchin" and other times as "Khintchine".
Life and career
He w... |
https://en.wikipedia.org/wiki/Equidistributed%20sequence | In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carl... |
https://en.wikipedia.org/wiki/Minimum%20polynomial | Minimum polynomial can refer to:
Minimal polynomial (field theory)
Minimal polynomial (linear algebra) |
https://en.wikipedia.org/wiki/Surface%20%28disambiguation%29 | A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space.
Surface or surfaces may also refer to:
Mathematics
Surface (mathematics), a generalization of a plane which needs not be flat
Surface (differential geometry), a differentiable two-dimensional manifold
Sur... |
https://en.wikipedia.org/wiki/All%20one%20polynomial | In mathematics, an all one polynomial (AOP) is a polynomial in which all coefficients are one. Over the finite field of order two, conditions for the AOP to be irreducible are known, which allow this polynomial to be used to define efficient algorithms and circuits for multiplication in finite fields of characteristic ... |
https://en.wikipedia.org/wiki/Focus%20%28geometry%29 | In geometry, focuses or foci (; : focus) are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassi... |
https://en.wikipedia.org/wiki/Kitaro%20Nishida | was a Japanese moral
philosopher, philosopher of mathematics and science, and religious scholar. He was the founder of what has been called the Kyoto School of philosophy. He graduated from the University of Tokyo during the Meiji period in 1894 with a degree in philosophy. He was named professor of the Fourth Higher ... |
https://en.wikipedia.org/wiki/Marcinkiewicz%20interpolation%20theorem | In mathematics, the Marcinkiewicz interpolation theorem, discovered by , is a result bounding the norms of non-linear operators acting on Lp spaces.
Marcinkiewicz' theorem is similar to the Riesz–Thorin theorem about linear operators, but also applies to non-linear operators.
Preliminaries
Let f be a measurable func... |
https://en.wikipedia.org/wiki/Joseph%20Betts | Joseph Betts was an English mathematician. He held the Savilian Chair of Geometry at the University of Oxford in 1765.
Betts was an undergraduate and Fellow of University College, Oxford, where he was a tutor of William Jones. He had previously sought election as Savilian Professor of Astronomy with the support of the... |
https://en.wikipedia.org/wiki/Baden%20Powell%20%28mathematician%29 | Baden Powell, MA FRS FRGS (22 August 1796 – 11 June 1860) was an English mathematician and Church of England priest. He held the Savilian Chair of Geometry at the University of Oxford from 1827 to 1860. Powell was a prominent liberal theologian who put forward advanced ideas about evolution.
Origins
Baden Powell II w... |
https://en.wikipedia.org/wiki/Morava%20K-theory | In stable homotopy theory, a branch of mathematics, Morava K-theory is one of a collection of cohomology theories introduced in algebraic topology by Jack Morava in unpublished preprints in the early 1970s. For every prime number p (which is suppressed in the notation), it consists of theories K(n) for each nonnegative... |
https://en.wikipedia.org/wiki/Complex%20cobordism | In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it directly one uses some slightly weaker theories derived from it, such a... |
https://en.wikipedia.org/wiki/Spectrum%20%28topology%29 | In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This means that, given a cohomology theory,there exist spaces such that evaluating the cohomology theory... |
https://en.wikipedia.org/wiki/Reduction%20%28mathematics%29 | In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction". Rewriting a radical (or "root") expression w... |
https://en.wikipedia.org/wiki/Dixon%27s%20factorization%20method | In number theory, Dixon's factorization method (also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method. Unlike for other factor base methods, its run-time bound comes with a rigorous proof that does not rely on conjectures... |
https://en.wikipedia.org/wiki/Abraham%20Robertson | Abraham or Abram Robertson FRS (4 November 1751 – 4 December 1826), was a Scottish mathematician and astronomer. He held the Savilian Chair of Geometry at the University of Oxford from 1797 to 1809.
Robertson was born at Duns, Berwickshire, the son of Abraham Robertson, “a man of humble station”. He attended school ... |
https://en.wikipedia.org/wiki/Nigel%20Hitchin | Nigel James Hitchin FRS (born 2 August 1946) is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
Academic career
Hitchin attended Ecclesbourne School, Duffield, and ... |
https://en.wikipedia.org/wiki/Ioan%20James | Ioan Mackenzie James FRS (born 23 May 1928) is a British mathematician working in the field of topology, particularly in homotopy theory.
Biography
James was born in Croydon, Surrey, England, and was educated at St Paul's School, London and Queen's College, Oxford. In 1953 he earned a D. Phil. from the University of ... |
https://en.wikipedia.org/wiki/Scattering%20amplitude | In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process.
At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction
where is the positi... |
https://en.wikipedia.org/wiki/Smooth%20number | In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term see... |
https://en.wikipedia.org/wiki/Sieve%20theory | Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The prototypical example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the prototypical example of a sieve is the sieve ... |
https://en.wikipedia.org/wiki/Wittgenstein%27s%20rod | Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.
Description
A ray is drawn with its origin on a circle, through an external point and a point is chosen at some constant distance from the starting end of the ray; what figure does describe when all the initial ... |
https://en.wikipedia.org/wiki/Variation%20of%20parameters | In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations.
For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients wit... |
https://en.wikipedia.org/wiki/Kappa%20curve | In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter . The kappa curve was first studied by Gérard van Gutschoven around 1662. In the history of mathematics, it is remembered as one of the first examples of Isaac Barrow's application of rudimentary calculus... |
https://en.wikipedia.org/wiki/124%20%28number%29 | 124 (one hundred [and] twenty-four) is the natural number following 123 and preceding 125.
In mathematics
124 is an untouchable number, meaning that it is not the sum of proper divisors of any positive number.
It is a stella octangula number, the number of spheres packed in the shape of a stellated octahedron. It is... |
https://en.wikipedia.org/wiki/Proper%20linear%20model | In statistics, a proper linear model is a linear regression model in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion. Simple regression analysis is the most common example of a proper linear model. Unit-weighted regres... |
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Euler%20equation | In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of its particularly simple equidimensional structure, the differential equ... |
https://en.wikipedia.org/wiki/Cut%20rule | In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its meaning is that, if a formula A appears as a conclusion in one proof and a hypothesis in another, then another proof in which the formula A does not appear can be deduc... |
https://en.wikipedia.org/wiki/Sixth%20government%20of%20Jordi%20Pujol | The colors indicate the political party affiliation of each member:
So the statistics of the Government composition are:
Cabinets of Catalonia |
https://en.wikipedia.org/wiki/129%20%28number%29 | 129 (one hundred [and] twenty-nine) is the natural number following 128 and preceding 130.
In mathematics
129 is the sum of the first ten prime numbers. It is the smallest number that can be expressed as a sum of three squares in four different ways: , , , and .
129 is the product of only two primes, 3 and 43, making... |
https://en.wikipedia.org/wiki/Confidence%20region | In statistics, a confidence region is a multi-dimensional generalization of a confidence interval. It is a set of points in an n-dimensional space, often represented as an ellipsoid around a point which is an estimated solution to a problem, although other shapes can occur.
Interpretation
The confidence region is cal... |
https://en.wikipedia.org/wiki/Glossary%20of%20mathematical%20jargon | The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous argume... |
https://en.wikipedia.org/wiki/National%20Center%20for%20Health%20Statistics | The National Center for Health Statistics (NCHS) is a U.S. government agency that provides statistical information to guide actions and policies to improve the public health of the American people. It is a unit of the Centers for Disease Control and Prevention (CDC) and a principal agency of the U.S. Federal Statistica... |
https://en.wikipedia.org/wiki/131%20%28number%29 | 131 (one hundred [and] thirty-one) is the natural number following 130 and preceding 132.
In mathematics
131 is a Sophie Germain prime, an irregular prime, the second 3-digit palindromic prime, and also a permutable prime with 113 and 311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47.... |
https://en.wikipedia.org/wiki/Bertrand%27s%20ballot%20theorem | In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with p > q, what is the probability that A will be strictly ahead of B throughout the count?" The answer is
The result was first published by W. A. Whitworth in 1878, but is... |
https://en.wikipedia.org/wiki/Michel%20Lo%C3%A8ve | Michel Loève (January 22, 1907 – February 17, 1979) was a French-American probabilist and mathematical statistician, of Jewish origin. He is known in mathematical statistics and probability theory for the Karhunen–Loève theorem and Karhunen–Loève transform.
Michel Loève was born in Jaffa (then part of the Ottoman Empi... |
https://en.wikipedia.org/wiki/Nonlinear%20regression | In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.
General
In nonlinear regr... |
https://en.wikipedia.org/wiki/Multinomial%20distribution | In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k-sided die rolled n times. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a giv... |
https://en.wikipedia.org/wiki/133%20%28number%29 | 133 (one hundred [and] thirty-three) is the natural number following 132 and preceding 134.
In mathematics
133 is an n whose divisors (excluding n itself) added up divide φ(n). It is an octagonal number and a happy number.
133 is a Harshad number, because it is divisible by the sum of its digits.
133 is a repdigit i... |
https://en.wikipedia.org/wiki/Projection-valued%20measure | In mathematics, particularly in functional analysis, a projection-valued measure (PVM) is a function defined on certain subsets of a fixed set and whose values are self-adjoint projections on a fixed Hilbert space. Projection-valued measures are formally similar to real-valued measures, except that their values are se... |
https://en.wikipedia.org/wiki/Nerve%20%28disambiguation%29 | A nerve is a part of the peripheral nervous system.
Nerve or Nerves may also refer to:
Mathematics
Nerve of a covering, a construction in mathematical topology
Nerve (category theory), a construction in category theory
Film and television
Nerves (film), a 1919 film by the Austrian director and novelist Robert Rei... |
https://en.wikipedia.org/wiki/Recursive%20definition | In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set.
A re... |
https://en.wikipedia.org/wiki/Complete%20variety | In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety , such that for any variety the projection morphism
is a closed map (i.e. maps closed sets onto closed sets). This can be seen as an analogue of compactness in algebraic geometry: a topological space is compact... |
https://en.wikipedia.org/wiki/University%20of%20Bia%C5%82ystok | The University of Bialystok is the largest university in the north-eastern region of Poland, educating in various fields of study, including humanities, social and natural sciences and mathematics. It has nine faculties, including a foreign one in Vilnius. Four faculties have been awarded the highest scientific categor... |
https://en.wikipedia.org/wiki/Muirhead%27s%20Inequality | In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means.
Preliminary definitions
a-mean
For any real vector
define the "a-mean" [a] of positive real numbers x1, ..., xn by
where the sum extends ov... |
https://en.wikipedia.org/wiki/Algebraic%20normal%20form | In Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), Zhegalkin normal form, or Reed–Muller expansion is a way of writing propositional logic formulas in one of three subforms:
The entire formula is purely true or false:
One or more variables are combined into a term by AND (),... |
https://en.wikipedia.org/wiki/Apollonian%20gasket | In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named after Greek mathematician Apollonius of Perga.
Construction
The construction of the Ap... |
https://en.wikipedia.org/wiki/Wolfgang%20Gr%C3%B6bner | Wolfgang Gröbner (11 February 1899 – 20 August 1980) was an Austrian mathematician. His name is best known for the Gröbner basis, used for computations in algebraic geometry. However, the theory of Gröbner bases for polynomial rings was developed by his student Bruno Buchberger in 1965, who named them for Gröbner. Gröb... |
https://en.wikipedia.org/wiki/Quasidihedral%20group | In mathematics, the quasi-dihedral groups, also called semi-dihedral groups, are certain non-abelian groups of order a power of 2. For every positive integer n greater than or equal to 4, there are exactly four isomorphism classes of non-abelian groups of order 2n which have a cyclic subgroup of index 2. Two are wel... |
https://en.wikipedia.org/wiki/Laver%20table | In mathematics, Laver tables (named after Richard Laver, who discovered them towards the end of the 1980s in connection with his works on set theory) are tables of numbers that have certain properties of algebraic and combinatorial interest. They occur in the study of racks and quandles.
Definition
For any nonnegat... |
https://en.wikipedia.org/wiki/Szemer%C3%A9di%E2%80%93Trotter%20theorem | The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given points and lines in the Euclidean plane, the number of incidences (i.e., the number of point-line pairs, such that the point lies on the line) is
This bound cannot be improved, except in terms of the impl... |
https://en.wikipedia.org/wiki/Logarithmic%20form | In algebraic geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept was introduced by Pierre Deligne. In short, logarithmic differentials have the mildest possible singularities needed in order to give information about an open subm... |
https://en.wikipedia.org/wiki/Euler%20system | In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and the work of . Euler systems are named after Leonhard Euler because th... |
https://en.wikipedia.org/wiki/Sylvester%E2%80%93Gallai%20theorem | The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line that passes through all of them. It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of t... |
https://en.wikipedia.org/wiki/Statistical%20learning%20theory | Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields... |
https://en.wikipedia.org/wiki/G%26T | G&T can mean:
Gin and tonic
Geometry & Topology — a peer-refereed, international mathematics research journal.
Geometry and trigonometry
the Gifted And Talented
a Gifted And Talented program
Generation & Transmission cooperative (wholesale energy provider)
Gramophone & Typewriter Ltd
G&T Crampton, an Irish con... |
https://en.wikipedia.org/wiki/Stein%20manifold | In mathematics, in the theory of several complex variables and complex manifolds, a Stein manifold is a complex submanifold of the vector space of n complex dimensions. They were introduced by and named after . A Stein space is similar to a Stein manifold but is allowed to have singularities. Stein spaces are the analo... |
https://en.wikipedia.org/wiki/KSEG%20%28software%29 | KSEG is a free (GPL) interactive geometry software for exploring Euclidean geometry. It was created by Ilya Baran.
It runs on Unix-based platforms. It also compiles and runs on Mac OS X and should run on anything that Qt supports. Additionally, it was also ported to Microsoft Windows.
KSEG is a tool designed to let yo... |
https://en.wikipedia.org/wiki/Sheaf%20cohomology | In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructions to solving a geometric problem globally when it can be solved locally. The central work for the study of sheaf cohomo... |
https://en.wikipedia.org/wiki/Japanese%20mathematics | denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan, from wa ("Japanese") and san ("calculation"), was coined in the 1870s and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan).
In the history of mathematic... |
https://en.wikipedia.org/wiki/Completely%20multiplicative%20function | In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions. Outsi... |
https://en.wikipedia.org/wiki/Fundamental%20theorem%20of%20curves | In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size or scale) completely determined by its curvature and torsion.
Use
A curve can be described, and thereby defined, by a pair of scalar fields: cur... |
https://en.wikipedia.org/wiki/L%C3%A9vy%20C%20curve | In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and Georg Faber in 1910, but now bears the name of French mathematician Paul Lévy, who was the first to describe its self-similarity properties as well... |
https://en.wikipedia.org/wiki/Einstein%20tensor | In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner that... |
https://en.wikipedia.org/wiki/Super-Poincar%C3%A9%20algebra | In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-gr... |
https://en.wikipedia.org/wiki/Semigroup%20action | In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corres... |
https://en.wikipedia.org/wiki/Orthogonal%20complement | In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W⊥ of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement. It is a... |
https://en.wikipedia.org/wiki/Simple%20polygon | In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments. These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons.
The sum of external angles of a... |
https://en.wikipedia.org/wiki/Sun%20Zhihong | Sun Zhihong (, born October 16, 1965) is a Chinese mathematician, working primarily on number theory, combinatorics, and graph theory.
Sun and his twin brother Sun Zhiwei proved a theorem about what are now known as the Wall–Sun–Sun primes that guided the search for counterexamples to Fermat's Last Theorem.
External... |
https://en.wikipedia.org/wiki/Sun%20Zhiwei | Sun Zhiwei (, born October 16, 1965) is a Chinese mathematician, working primarily in number theory, combinatorics, and group theory. He is a professor at Nanjing University.
Biography
Sun Zhiwei was born in Huai'an, Jiangsu. Sun and his twin brother Sun Zhihong proved a theorem about what are now known as the Wall–S... |
https://en.wikipedia.org/wiki/Simplicial%20homology | In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of a given dimension in the complex. This generalizes the number of connected components (the case of dimension 0).
Simplicial homology arose as a way to study topologica... |
https://en.wikipedia.org/wiki/Basic%20Linear%20Algebra%20Subprograms | Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linea... |
https://en.wikipedia.org/wiki/Residual%20strength | Residual strength is the load or force (usually mechanical) that a damaged object or material can still carry without failing. Material toughness, fracture size and geometry as well as its orientation all contribute to residual strength.
References
Materials science |
https://en.wikipedia.org/wiki/GEMM | GEMM may refer to:
General matrix multiply gemm, one of the Basic Linear Algebra Subprograms
Genetically engineered mouse model
Gilt-edged market maker
Global Electronic Music Marketplace, a former online music market
CFU-GEMM, granulocyte-erythrocyte-monocyte-megakaryocyte colony forming unit
See also
Gem (disambigu... |
https://en.wikipedia.org/wiki/Associated%20Legendre%20polynomials | In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation
or equivalently
where the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsi... |
https://en.wikipedia.org/wiki/Mark%20Kac | Mark Kac ( ; Polish: Marek Kac; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, the idea of understanding the extent to which the spectrum allows one to read back th... |
https://en.wikipedia.org/wiki/Categorical%20logic |
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science.
In broad terms, categorical logic represents both syntax and semantics by a category, and an interpret... |
https://en.wikipedia.org/wiki/Ranked%20list%20of%20French%20regions | The following are ranked lists of French regions.
Population figures are from the 2016 census, with the exception of Mayotte, whose statistics are as of 2017.
Region boundaries are as of 2018.
By population
These figures are from the census in 2016. Statistics for Mayotte are from 2017.
By area
The total area of... |
https://en.wikipedia.org/wiki/Bose%20gas | An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin, and abide by Bose–Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for a photon gas, and extended to massive particl... |
https://en.wikipedia.org/wiki/Superreal%20number | In abstract algebra, the superreal numbers are a class of extensions of the real numbers, introduced by H. Garth Dales and W. Hugh Woodin as a generalization of the hyperreal numbers and primarily of interest in non-standard analysis, model theory, and the study of Banach algebras. The field of superreals is itself a ... |
https://en.wikipedia.org/wiki/Real%20closed%20field | In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers.
Definitions
A real closed field is a field F in which any of the following equiva... |
https://en.wikipedia.org/wiki/Characteristic%20%28algebra%29 | In mathematics, the characteristic of a ring , often denoted , is defined to be the smallest positive number of copies of the ring's multiplicative identity () that will sum to the additive identity (). If no such number exists, the ring is said to have characteristic zero.
That is, is the smallest positive number ... |
https://en.wikipedia.org/wiki/Salem%20number | In mathematics, a Salem number is a real algebraic integer whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in Diophantine approximation and harmonic analysis. They are named after Raphaël Salem.
Properties
Because... |
https://en.wikipedia.org/wiki/Formally%20real%20field | In mathematics, in particular in field theory and real algebra, a formally real field is a field that can be equipped with a (not necessarily unique) ordering that makes it an ordered field.
Alternative definitions
The definition given above is not a first-order definition, as it requires quantifiers over sets. Howeve... |
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Speiser%20theorem | In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of , which by the Kronecker–Weber theorem are isomorphic to subfields of cyclotomic fields.
Hilbert–Speiser Theorem. A finite abeli... |
https://en.wikipedia.org/wiki/L%C3%A9vy%27s%20constant | In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions.
In 1935, the Soviet mathematician Aleksandr Khinchin showed that the denominators qn of the convergents of the continued frac... |
https://en.wikipedia.org/wiki/Multimodal%20distribution | In statistics, a multimodal distribution is a probability distribution with more than one mode. These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and discrete data can all form multimodal distributions. Among univariate analyses, mu... |
https://en.wikipedia.org/wiki/Parabolic%20geometry | Parabolic geometry may refer to:
Parabolic geometry, former name for Euclidean geometry, a comprehensive and deductive mathematical system
Parabolic geometry (differential geometry): The homogeneous space defined by a semisimple Lie group modulo a parabolic subgroup, or the curved analog of such a space
Cartan p... |
https://en.wikipedia.org/wiki/Cohomology%20ring | In mathematics, specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication. Here 'cohomology' is usually understood as singular cohomology, but the ring structure is also present in other... |
https://en.wikipedia.org/wiki/Divide | Divide may refer to:
Mathematics
Division (mathematics)
Divides, redirects to Divisor
Geography
Drainage divide, a line separating two drainage basins
Great Divide Basin, in Wyoming
Places
Divide, Saskatchewan, Canada
Divide, Colorado, community
Divide, Illinois, an unincorporated community
Divide, Montana, ... |
https://en.wikipedia.org/wiki/Jean%20Dieudonn%C3%A9 | Jean Alexandre Eugène Dieudonné (; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendi... |
https://en.wikipedia.org/wiki/Total%20derivative | In mathematics, the total derivative of a function at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one. In many situations, thi... |
https://en.wikipedia.org/wiki/Fr%C3%A4nkel | Fränkel (or Fraenkel) is a surname. Notable people with the surname include:
Abraham Fraenkel (1891–1965), German-Israeli mathematician, known for Zermelo–Fraenkel set theory
Albert Fränkel (1848–1916), German physician
Aviezri Fraenkel (born 1929), Israeli mathematician
Baruch Fränkel-Teomim (1760–1828), rabbi, T... |
https://en.wikipedia.org/wiki/Hyperbolic%20quaternion | In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form
where the squares of i, j, and k are +1 and distinct elements of {i, j, k} multiply with the anti-commutative property.
The four-dimensional algebra of hyperbolic quaternions incorpor... |
https://en.wikipedia.org/wiki/Median%20%28disambiguation%29 | Median may refer to:
Mathematics and statistics
Median (statistics), in statistics, a number that separates the lowest- and highest-value halves
Median (geometry), in geometry, a line joining a vertex of a triangle to the midpoint of the opposite side
Median (graph theory), a vertex m(a,b,c) that belongs to shortest... |
https://en.wikipedia.org/wiki/Median%20%28geometry%29 | In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a media... |
https://en.wikipedia.org/wiki/Grothendieck%20universe | In mathematics, a Grothendieck universe is a set U with the following properties:
If x is an element of U and if y is an element of x, then y is also an element of U. (U is a transitive set.)
If x and y are both elements of U, then is an element of U.
If x is an element of U, then P(x), the power set of x, is also... |
https://en.wikipedia.org/wiki/Calculus%20of%20negligence | In the United States, the calculus of negligence, also known as the Hand rule, Hand formula, or BPL formula, is a term coined by Judge Learned Hand which describes a process for determining whether a legal duty of care has been breached (see negligence). The original description of the calculus was in United States v.... |
https://en.wikipedia.org/wiki/LIS | LIS or LiS may refer to:
Computing
LIS (programming language)
Lis (linear algebra library), library of iterative solvers for linear systems
Laboratory information system, databases oriented towards medical laboratories
Land information system, land mapping and cadastre GIS used by local governments
Language-indep... |
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