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https://en.wikipedia.org/wiki/Berkson%27s%20paradox | Berkson's paradox, also known as Berkson's bias, collider bias, or Berkson's fallacy, is a result in conditional probability and statistics which is often found to be counterintuitive, and hence a veridical paradox. It is a complicating factor arising in statistical tests of proportions. Specifically, it arises when th... |
https://en.wikipedia.org/wiki/Bethe%20lattice | In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite connected cycle-free graph where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by Hans Bethe in 1935. In such a graph, each node is connected to z neighb... |
https://en.wikipedia.org/wiki/Field%20equation | In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, a... |
https://en.wikipedia.org/wiki/Weak%20derivative | In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the Lp space .
The method of integration by parts holds that for differentiable functions and we have
A function u'... |
https://en.wikipedia.org/wiki/Science%20Museum%20of%20Minnesota | The Science Museum of Minnesota is an American museum focused on topics in technology, natural history, physical science, and mathematics education. Founded in 1907 and located in Saint Paul, Minnesota, the 501(c)(3) nonprofit institution has 385 employees and is supported by volunteers.
History
The museum was establ... |
https://en.wikipedia.org/wiki/Connected%20category | In category theory, a branch of mathematics, a connected category is a category in which, for every two objects X and Y there is a finite sequence of objects
with morphisms
or
for each 0 ≤ i < n (both directions are allowed in the same sequence). Equivalently, a category J is connected if each functor from J to a di... |
https://en.wikipedia.org/wiki/Incomplete%20polylogarithm | In mathematics, the Incomplete Polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral or the incomplete Bose–Einstein integral. It may be defined by:
Expanding about z=0 and integrating gives a series representation:
where Γ(s) is the gamma functi... |
https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel%20theta%20function | In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as
for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and holds, i.e., in the same way that the principal branch of the log-gamma function is defined.
It has an asymptotic ... |
https://en.wikipedia.org/wiki/Z%20function | In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in ... |
https://en.wikipedia.org/wiki/Fitting%20subgroup | In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it represents the smallest subgroup which "controls" the structure of G when G is solvable. When G is not sol... |
https://en.wikipedia.org/wiki/Tangent%20cone | In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities.
Definitions in nonlinear analysis
In nonlinear analysis, there are many definitions for a tangent cone, including the adjacent cone, Bouligand's contingent cone, and the... |
https://en.wikipedia.org/wiki/Constantin%20Le%20Paige | Constantin Marie Le Paige (9 March 1852 – 26 January 1929) was a Belgian mathematician.
Born in Liège, Belgium, Le Paige began studying mathematics in 1869 at the University of Liège. After studying analysis under Professor Eugène Charles Catalan, Le Paige became a professor at the Université de Liège in 1882.
While... |
https://en.wikipedia.org/wiki/Fuchsian%20model | In mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R as a quotient of the upper half-plane H by a Fuchsian group. Every hyperbolic Riemann surface admits such a representation. The concept is named after Lazarus Fuchs.
A more precise definition
By the uniformization theorem, every Ri... |
https://en.wikipedia.org/wiki/Municipality%20of%20the%20District%20of%20Lunenburg | The Municipality of the District of Lunenburg, is a district municipality in Lunenburg County, Nova Scotia, Canada. Statistics Canada classifies the district municipality as a municipal district.
Lunenburg surrounds the towns of Bridgewater, Lunenburg, and Mahone Bay, which are incorporated separately and not part of ... |
https://en.wikipedia.org/wiki/Regular%20matrix | Regular matrix may refer to:
Mathematics
Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive
The opposite of irregular matrix, a matrix with a different number of entries in each row
Regular Hadamard matrix, a Hadamard matrix whose row and column sums ar... |
https://en.wikipedia.org/wiki/Mediant%20%28mathematics%29 | In mathematics, the mediant of two fractions, generally made up of four positive integers
and is defined as
That is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively. It is sometimes called the freshman sum, as it is a common m... |
https://en.wikipedia.org/wiki/Mathlete | A mathlete is a person who competes in mathematics competitions at any level or any age. More specifically, a Mathlete is a student who participates in any of the MATHCOUNTS programs, as Mathlete is a registered trademark of the MATHCOUNTS Foundation in the United States. The term is a portmanteau of the words mathemat... |
https://en.wikipedia.org/wiki/Unbounded%20operator | In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.
The term "unbounded operator" can be misleading, since
"unbounded" should som... |
https://en.wikipedia.org/wiki/Joseph%20Tilly | Joseph Marie de Tilly (16 August 1837 – 4 August 1906) was a Belgian military man and mathematician.
He was born in Ypres, Belgium. In 1858, he became a teacher in mathematics at the regimental school. He began with studying geometry, particularly Euclid's fifth postulate and non-Euclidean geometry. He found similar r... |
https://en.wikipedia.org/wiki/Duality%20principle | Duality principle or principle of duality may refer to:
Duality (projective geometry)
Duality (order theory)
Duality principle (Boolean algebra)
Duality principle for sets
Duality principle (optimization theory)
Lagrange duality
Duality principle in functional analysis, used in large sieve method of analytic nu... |
https://en.wikipedia.org/wiki/Annales%20de%20l%27Institut%20Fourier | The Annales de l'Institut Fourier is a French mathematical journal publishing papers in all fields of mathematics. It was established in 1949. The journal publishes one volume per year, consisting of six issues. The current editor-in-chief is Hervé Pajot. Articles are published either in English or in French.
The jour... |
https://en.wikipedia.org/wiki/Differential%20equation | In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such rel... |
https://en.wikipedia.org/wiki/Eternal%20Majesty | Eternal Majesty is a French black metal band.
It was formed by four brothers under the original name of Enchantress Moon.
Statistics
Genre: Black metal
Country: France
Status: Active
Time: 1995 -
Discography
Albums
2002 - From War to Darkness (CD)
2003 - From War to Darkness (Picture disk)
2006 - Wounds of Hatred... |
https://en.wikipedia.org/wiki/Spherical%20space%20form%20conjecture | In geometric topology, the spherical space form conjecture (now a theorem) states that a finite group acting on the 3-sphere is conjugate to a group of isometries of the 3-sphere.
History
The conjecture was posed by Heinz Hopf in 1926 after determining the fundamental groups of three-dimensional spherical space forms ... |
https://en.wikipedia.org/wiki/F%C3%B8lner%20sequence | In mathematics, a Følner sequence for a group is a sequence of sets satisfying a particular condition. If a group has a Følner sequence with respect to its action on itself, the group is amenable. A more general notion of Følner nets can be defined analogously, and is suited for the study of uncountable groups. Følne... |
https://en.wikipedia.org/wiki/Holonomic | Holonomic (introduced by Heinrich Hertz in 1894 from the Greek ὅλος meaning whole, entire and νόμ-ος meaning law) may refer to:
Mathematics
Holonomic basis, a set of basis vector fields {ek} such that some coordinate system {xk} exists for which
Holonomic constraints, which are expressible as a function of the coor... |
https://en.wikipedia.org/wiki/Spray%20%28mathematics%29 | In differential geometry, a spray is a vector field H on the tangent bundle TM that encodes a quasilinear second order system of ordinary differential equations on the base manifold M. Usually a spray is required to be homogeneous in the sense that its integral curves t→ΦHt(ξ)∈TM obey the rule ΦHt(λξ)=ΦHλt(ξ) in positi... |
https://en.wikipedia.org/wiki/Fulkerson%20Prize | The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes ... |
https://en.wikipedia.org/wiki/Bungoma | {
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Bungoma is the headquarters of Bungoma County in Kenya. It ... |
https://en.wikipedia.org/wiki/Toshio%20Mura | was a professor of engineering.
He was born in Ono, a small port village of Kanazawa Japan, on December 7, 1925. He received a doctorate in the Department of Applied Mathematics of the University of Tokyo in 1954. He taught at Meiji University, Japan from 1954 to 1958. In 1958, he went to the United States to work ... |
https://en.wikipedia.org/wiki/MEI | MEI may refer to:
Education
MEI Academy, an international school
Mathematics in Education and Industry, an examination board affiliated with the OCR examination board
Mennonite Educational Institute, an independent grades K-12 school in Abbotsford, British Columbia
Businesses
MEI (company), manufacturer of cash... |
https://en.wikipedia.org/wiki/Coefficient%20of%20multiple%20correlation | In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.
The coefficien... |
https://en.wikipedia.org/wiki/Potential%20theory | In mathematics and mathematical physics, potential theory is the study of harmonic functions.
The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravity and the electrostatic force, could be modeled using functions called ... |
https://en.wikipedia.org/wiki/Mode%20%28statistics%29 | In statistics, the mode is the value that appears most often in a set of data values. If is a discrete random variable, the mode is the value at which the probability mass function takes its maximum value (i.e, ). In other words, it is the value that is most likely to be sampled.
Like the statistical mean and median... |
https://en.wikipedia.org/wiki/Paul%20Benacerraf | Paul Joseph Salomon Benacerraf (; born 26 March 1931) is a French-born American philosopher working in the field of the philosophy of mathematics who taught at Princeton University his entire career, from 1960 until his retirement in 2007. He was appointed Stuart Professor of Philosophy in 1974, and retired as the Jam... |
https://en.wikipedia.org/wiki/Schwarz%20lemma | In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is less celebrated than deeper theorems, such as the Riemann mapping theorem, which it helps to prove. It is, however, one of the simplest resu... |
https://en.wikipedia.org/wiki/Autoregressive%20model | In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own pr... |
https://en.wikipedia.org/wiki/ELT | ELT may refer to:
Education
English language teaching
Expanded learning time, an American education strategy
Kolb's experiential learning theory
Mathematics and science
Ending lamination theorem
Extremely large telescope, a type of telescope
Extremely Large Telescope, an astronomical observatory under constru... |
https://en.wikipedia.org/wiki/Voigt%20notation | In mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig of old ideas o... |
https://en.wikipedia.org/wiki/General%20algebraic%20modeling%20system | The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maint... |
https://en.wikipedia.org/wiki/134%20%28number%29 | 134 (one hundred [and] thirty-four) is the natural number following 133 and preceding 135.
In mathematics
134 is a nontotient since there is no integer with exactly 134 coprimes below it. And it is a noncototient since there is no integer with 134 integers with common factors below it.
134 is .
In Roman numerals, 13... |
https://en.wikipedia.org/wiki/Samurize | Serious Samurize (or simply Samurize) is a freeware system monitoring and desktop enhancement engine for Microsoft Windows.
The core of Samurize is the desktop client that displays PC statistics (similar to a widget or gadget) anywhere on the screen. There is also a taskbar client, a clock client, a server, and a scre... |
https://en.wikipedia.org/wiki/Symmetric%20polynomial | In mathematics, a symmetric polynomial is a polynomial in variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally, is a symmetric polynomial if for any permutation of the subscripts one has .
Symmetric polynomials arise naturally in the study of the relation betwee... |
https://en.wikipedia.org/wiki/IEP | IEP may refer to:
Science and technology
Immunoelectrophoresis, biochemistry method
Inclusion–exclusion principle, in the mathematics branch of combinatorics
Integrated electric propulsion, in marine propulsion
Isoelectric point, the pH where a molecule is electrically neutral
Education and research
Individ... |
https://en.wikipedia.org/wiki/Elementary%20symmetric%20polynomial | In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symmetric polynomials. That is, any symmetric polynomial is given by an ex... |
https://en.wikipedia.org/wiki/Triangulation%20%28geometry%29 | In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together.
In most instances, the triangles of a tria... |
https://en.wikipedia.org/wiki/Triangulation%20%28topology%29 | In mathematics, triangulation describes the replacement of topological spaces by piecewise linear spaces, i.e. the choice of a homeomorphism in a suitable simplicial complex. Spaces being homeomorphic to a simplicial complex are called triangulable. Triangulation has various uses in different branches of mathematics, f... |
https://en.wikipedia.org/wiki/Equilibrium%20point%20%28mathematics%29 | In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation.
Formal definition
The point is an equilibrium point for the differential equation
if for all .
Similarly, the point is an equilibrium point (or fixed point) for the difference equ... |
https://en.wikipedia.org/wiki/Transpose%20of%20a%20linear%20map | In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces.
The transpose or algebraic adjoint of a linear map is often used to study the original linear map. This concept is generalised by adjoint functors... |
https://en.wikipedia.org/wiki/Dual%20representation | In mathematics, if is a group and is a linear representation of it on the vector space , then the dual representation is defined over the dual vector space as follows:
is the transpose of , that is, = for all .
The dual representation is also known as the contragradient representation.
If is a Lie algebra an... |
https://en.wikipedia.org/wiki/Complex%20conjugate%20of%20a%20vector%20space | In mathematics, the complex conjugate of a complex vector space is a complex vector space , which has the same elements and additive group structure as but whose scalar multiplication involves conjugation of the scalars. In other words, the scalar multiplication of satisfies
where is the scalar multiplication of ... |
https://en.wikipedia.org/wiki/Complex%20conjugate%20representation | In mathematics, if is a group and is a representation of it over the complex vector space , then the complex conjugate representation is defined over the complex conjugate vector space as follows:
is the conjugate of for all in .
is also a representation, as one may check explicitly.
If is a real Lie algebr... |
https://en.wikipedia.org/wiki/Dave%20Bayer | David Allen Bayer (born November 29, 1955) is an American mathematician known for his contributions in algebra and symbolic computation and for his consulting work in the movie industry. He is a professor of mathematics at Barnard College, Columbia University.
Education and career
Bayer was educated at Swarthmore Coll... |
https://en.wikipedia.org/wiki/Natterer | Natterer may refer to:
People
Christian Natterer (born 1981), German politician
August Natterer (1868–1933), German artist
Frank Natterer (born 1941), German mathematics professor
Johann Natterer (1787–1843), Austrian explorer and naturalist
Other
Natterer's bat, Myotis nattereri |
https://en.wikipedia.org/wiki/Structure%20implies%20multiplicity | In diatonic set theory structure implies multiplicity is a quality of a collection or scale. For collections or scales which have this property, the interval series formed by the shortest distance around a diatonic circle of fifths between members of a series indicates the number of unique interval patterns (adjacently... |
https://en.wikipedia.org/wiki/Directional%20statistics | Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, Rn), axes (lines through the origin in Rn) or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian ma... |
https://en.wikipedia.org/wiki/Bessel%27s%20inequality | In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element in a Hilbert space with respect to an orthonormal sequence. The inequality was derived by F.W. Bessel in 1828.
Let be a Hilbert space, and suppose that is an orthonormal sequence in . Then, for a... |
https://en.wikipedia.org/wiki/Generated%20collection | In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. All scales with the deep scale property can be generate... |
https://en.wikipedia.org/wiki/Diatonic%20set%20theory | Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and analysis of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies mu... |
https://en.wikipedia.org/wiki/Generic%20and%20specific%20intervals | In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members. (Johnson 2003, p. 26)
A specific interval is the clockwise distance between pitch classes on the chromatic circle (interval class), i... |
https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman%20metric | The Kerr–Newman metric is the most general asymptotically flat, stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged, rotating mass. It generalizes the Kerr metric by taking into account the field energy of an... |
https://en.wikipedia.org/wiki/Visibility%20graph | In computational geometry and robot motion planning, a visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents a point location, and each edge represents a visible connection between them. That is, if the line segment ... |
https://en.wikipedia.org/wiki/Iterated%20function | In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the re... |
https://en.wikipedia.org/wiki/Conjugate%20gradient%20method | In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled ... |
https://en.wikipedia.org/wiki/Art%20gallery%20problem | The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem:
"In an art gallery, what is the minimum number of guards who together can observe the whole gallery?"
In the geometric version of the problem, the layout of... |
https://en.wikipedia.org/wiki/Degree%20matrix | In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. It is used together with the adjacency matrix to construct the Laplacian matrix of a graph: ... |
https://en.wikipedia.org/wiki/Bidiagonal%20matrix | In mathematics, a bidiagonal matrix is a banded matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below. This means there are exactly two non-zero diagonals in the matrix.
When the diagonal above the main diagonal has the non-zero entries the matrix is upper bidiagonal.... |
https://en.wikipedia.org/wiki/Statistics%20Norway | Statistics Norway (, abbreviated to SSB) is the Norwegian statistics bureau. It was established in 1876.
Relying on a staff of about 1,000, Statistics Norway publish about 1,000 new statistical releases every year on its web site. All releases are published both in Norwegian and English. In addition a number of edited... |
https://en.wikipedia.org/wiki/Nick%20Katz | Nicholas Michael Katz (born December 7, 1943) is an American mathematician, working in arithmetic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. He is currently a professor of Mathematics at Princeton University and an editor of the journal Annals of Mathematics.
Life and ... |
https://en.wikipedia.org/wiki/Band%20matrix | In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.
Band matrix
Bandwidth
Formally, consider an n×n matrix A=(ai,j ). If all matrix elements are ze... |
https://en.wikipedia.org/wiki/Universal%20graph | 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 focused on universal graphs for a graph ... |
https://en.wikipedia.org/wiki/Ludwig%20Schl%C3%A4fli | Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces. The concept of multidimensionality is pervasive in mathematics, has come t... |
https://en.wikipedia.org/wiki/Gotthold%20Eisenstein | Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician. He specialized in number theory and analysis, and proved several results that eluded even Gauss. Like Galois and Abel before him, Eisenstein died before the age of 30. He was born and died in Berlin, Prussia.
Early life
His... |
https://en.wikipedia.org/wiki/Hankel%20transform | In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind . The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r axis. The necessary coefficient of each Bessel function in t... |
https://en.wikipedia.org/wiki/Zn%C3%A1m%27s%20problem | In number theory, Znám's problem asks which sets of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám's problem is named after the Slovak mathematician Štefan Znám, who suggested it in 1972, although other mathematicians had conside... |
https://en.wikipedia.org/wiki/Null%20vector | In mathematics, given a vector space X with an associated quadratic form q, written , a null vector or isotropic vector is a non-zero element x of X for which .
In the theory of real bilinear forms, definite quadratic forms and isotropic quadratic forms are distinct. They are distinguished in that only for the latter ... |
https://en.wikipedia.org/wiki/Boxcar%20function | In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant, A. The function is named after its graph's resemblance to a boxcar, a type of railroad car. The boxcar function can be expressed in terms of the uniform distribution as... |
https://en.wikipedia.org/wiki/Sigma%20approximation | In mathematics, σ-approximation adjusts a Fourier summation to greatly reduce the Gibbs phenomenon, which would otherwise occur at discontinuities.
A σ-approximated summation for a series of period T can be written as follows:
in terms of the normalized sinc function
The term
is the Lanczos σ factor, which is respo... |
https://en.wikipedia.org/wiki/Pseudotensor | In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation (e.g. a proper rotation) but additionally changes sign under an orientation-reversing coordinate transformation (e.g., an improper rotation), which is a transformation... |
https://en.wikipedia.org/wiki/BEST%20theorem | In graph theory, a part of discrete mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of the names of people who discovered it: de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte.
Precise statement
Let G = (V, E) be a dire... |
https://en.wikipedia.org/wiki/Demographics%20of%20Montreal | The Demographics of Montreal concern population growth and structure for Montreal, Quebec, Canada. The information is analyzed by Statistics Canada and compiled every five years, with the most recent census having taken place in 2021.
Population history
According to Statistics Canada, at the time of the 2011 Canadian... |
https://en.wikipedia.org/wiki/Prime%20number%20theory | Prime number theory may refer to:
Prime number
Prime number theorem
Number theory
See also
Fundamental theorem of arithmetic, which explains prime factorization. |
https://en.wikipedia.org/wiki/Bessel | Bessel may refer to:
Bessel beam
Bessel ellipsoid
Bessel function in mathematics
Bessel's inequality in mathematics
Bessel's correction in statistics.
Bessel filter, a linear filter often used in audio crossover systems
Bessel Fjord, NE Greenland
Bessel Fjord, NW Greenland
Bessel (crater), a small lunar crater... |
https://en.wikipedia.org/wiki/Nesbitt%27s%20inequality | In mathematics, Nesbitt's inequality states that for positive real numbers a, b and c,
It is an elementary special case (N = 3) of the difficult and much studied Shapiro inequality, and was published at least 50 years earlier.
There is no corresponding upper bound as any of the 3 fractions in the inequality can be ma... |
https://en.wikipedia.org/wiki/Toy%20theorem | In mathematics, a toy theorem is a simplified instance (special case) of a more general theorem, which can be useful in providing a handy representation of the general theorem, or a framework for proving the general theorem. One way of obtaining a toy theorem is by introducing some simplifying assumptions in a theorem.... |
https://en.wikipedia.org/wiki/Rigidity%20%28mathematics%29 | In mathematics, a rigid collection C of mathematical objects (for instance sets or functions) is one in which every c ∈ C is uniquely determined by less information about c than one would expect.
The above statement does not define a mathematical property; instead, it describes in what sense the adjective "rigid" is ty... |
https://en.wikipedia.org/wiki/Stationary%20phase%20approximation | In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to functions given by integration against a rapidly-varying complex exponential.
This method originates from the 19th century, and is due to George Gabriel Stokes and Lord Kelvin.
It is closely related to Laplace's... |
https://en.wikipedia.org/wiki/Parallel%20tempering | Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting particles. It addresses the problem that at high temperatures, one may have a stable state different from low temperature, whereas simulations at low temperatures... |
https://en.wikipedia.org/wiki/Rigidity | Rigid or rigidity may refer to:
Mathematics and physics
Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity
Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges
Rigidity (electromagnetism), the resistance of... |
https://en.wikipedia.org/wiki/Chromatic%20polynomial | The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial by Hass... |
https://en.wikipedia.org/wiki/Cyclic%20homology | In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independently introduced by Boris Tsygan (homology) and Alain Connes (cohomology) i... |
https://en.wikipedia.org/wiki/Indeterminate%20%28variable%29 | In mathematics, particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else except itself. It may be used as a placeholder in objects such as polynomials and formal power series. In particular:
It does not designate a constant or a parameter of the ... |
https://en.wikipedia.org/wiki/Yakov%20Perelman | Yakov Isidorovich Perelman (; – 16 March 1942) was a Russian Empire and Soviet science writer and author of many popular science books, including Physics Can Be Fun and Mathematics Can Be Fun (both translated from Russian into English).
Life and work
Perelman was born in 1882 in the town of Białystok, Russian Empire.... |
https://en.wikipedia.org/wiki/Borel%27s%20lemma | In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations.
Statement
Suppose U is an open set in the Euclidean space Rn, and suppose that f0, f1, ... is a sequence of smooth functions on U.
If I is any open interval in... |
https://en.wikipedia.org/wiki/Riemann%E2%80%93Lebesgue%20lemma | In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, states that the Fourier transform or Laplace transform of an L1 function vanishes at infinity. It is of importance in harmonic analysis and asymptotic analysis.
Statement
Let be an integrable function, i.e. is a measurable ... |
https://en.wikipedia.org/wiki/Split-quaternion | In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers.
After introduction in the 20th century of coordinate-free definitions of rings and algebras, it wa... |
https://en.wikipedia.org/wiki/Dirichlet%E2%80%93Jordan%20test | In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at a point of continuity. Moreover, the behavior of the Fourier series at points of discontinuity is determined as well (it is the midpoint of the values of the disco... |
https://en.wikipedia.org/wiki/Progressive%20function | In mathematics, a progressive function ƒ ∈ L2(R) is a function whose Fourier transform is supported by positive frequencies only:
It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, if
The complex conjugate of a progressive function is regressive, and vice ve... |
https://en.wikipedia.org/wiki/Fixed-point%20space | In mathematics, a Hausdorff space X is called a fixed-point space if every continuous function has a fixed point.
For example, any closed interval [a,b] in is a fixed point space, and it can be proved from the intermediate value property of real continuous function. The open interval (a, b), however, is not a fixed... |
https://en.wikipedia.org/wiki/Local%20property | In mathematics, a mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object (e.g., on some sufficiently small or arbitrarily small neighborhoods of points).
Properties of a point on a function
Perhaps the best-known example of the idea of... |
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