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https://en.wikipedia.org/wiki/Regularization%20%28mathematics%29 | In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting.
Although regularization procedures can be divide... |
https://en.wikipedia.org/wiki/Ivor%20Grattan-Guinness | Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic.
Life
Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (E... |
https://en.wikipedia.org/wiki/Ceiling%20effect%20%28statistics%29 | The "ceiling effect" is one type of scale attenuation effect; the other scale attenuation effect is the "floor effect". The ceiling effect is observed when an independent variable no longer has an effect on a dependent variable, or the level above which variance in an independent variable is no longer measurable. The s... |
https://en.wikipedia.org/wiki/Sparsely%20totient%20number | In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n,
where is Euler's totient function. The first few sparsely totient numbers are:
2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690,... |
https://en.wikipedia.org/wiki/Surface%20bundle%20over%20the%20circle | In mathematics, a surface bundle over the circle is a fiber bundle with base space a circle, and with fiber space a surface. Therefore the total space has dimension 2 + 1 = 3. In general, fiber bundles over the circle are a special case of mapping tori.
Here is the construction: take the Cartesian product of a surfa... |
https://en.wikipedia.org/wiki/Schiffler%20point | In geometry, the Schiffler point of a triangle is a triangle center, a point defined from the triangle that is equivariant under Euclidean transformations of the triangle. This point was first defined and investigated by Schiffler et al. (1985).
Definition
A triangle with the incenter has its Schiffler point at the ... |
https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20Sweden | This article lists various Swedish football records for the various Swedish football leagues and competitions and the Sweden national team.
National team
Men's national team
Largest victory: 12–0
vs. Latvia, 29 May 1927
Largest loss: 1–12
vs. England Amateur, 20 October 1908
Most appearances, career: 148
Anders S... |
https://en.wikipedia.org/wiki/Exact%20differential%20equation | In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in Physics and engineering.
Definition
Given a simply connected and open subset D of and two functions I and J which are continuous on D, an implicit first-order ordin... |
https://en.wikipedia.org/wiki/Alexandre%20Deulofeu | Alexandre Deulofeu i Torres (20 September 1903, in L'Armentera – 27 December 1978, in Figueres) was a Catalan politician and philosopher of history. He wrote about what he called the Mathematics of History, a cyclical theory on the evolution of civilizations.
Biography
Deulofeu was born at l'Armentera in the province... |
https://en.wikipedia.org/wiki/Qutb%20al-Din%20al-Shirazi | Qotb al-Din Mahmoud b. Zia al-Din Mas'ud b. Mosleh Shirazi (1236–1311) () was a 13th-century Persian polymath and poet who made contributions to astronomy, mathematics, medicine, physics, music theory, philosophy and Sufism.
Biography
He was born in Kazerun in October 1236 to a family with a tradition of Sufism. His... |
https://en.wikipedia.org/wiki/Henry%20Marshall%20Tory%20Medal | The Henry Marshall Tory Medal is an award of the Royal Society of Canada "for outstanding research in a branch of astronomy, chemistry, mathematics, physics, or an allied science". It is named in honour of Henry Marshall Tory and is awarded bi-annually. The award consists of a gold plated silver medal.
Recipients
Sour... |
https://en.wikipedia.org/wiki/Factor%20graph | A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to represent factorization of a probability distribution function, enabling efficient computations, such as the computation of marginal distributions through the sum–prod... |
https://en.wikipedia.org/wiki/Spidron | This article discusses the geometric figure; for the science-fiction character see Spidron (character).
In geometry, a spidron is a continuous flat geometric figure composed entirely of triangles, where, for every pair of joining triangles, each has a leg of the other as one of its legs, and neither has any point insi... |
https://en.wikipedia.org/wiki/James%20Curley%20%28astronomer%29 | James Curley (26 October 1796 – 24 July 1889) was an Irish-American astronomer.
He was born at Athleague, County Roscommon, Ireland. His early education was limited, though his talent for mathematics was discovered, and to some extent developed, by a teacher in his native town. He left Ireland in his youth, arriving i... |
https://en.wikipedia.org/wiki/Likely | Likely may refer to:
Probability
Likelihood function
Likely (surname)
Likely, British Columbia, Canada, a community
Likely, California, United States, a census-designated place
Likely McBrien (1892-1956), leading Australian rules football administrator in the Victorian Football League
In the nomenclature of political ... |
https://en.wikipedia.org/wiki/Bernard%20Koopman | Bernard Osgood Koopman (January 19, 1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research.
Education and work
After living in France and Italy, Koopman emigrated to the United States in 1915. K... |
https://en.wikipedia.org/wiki/Mathematical%20formulation%20of%20the%20Standard%20Model | This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group . The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
The Stan... |
https://en.wikipedia.org/wiki/Erik%20Prosperin | Erik Prosperin (25 July 1739 – 4 April 1803) was a Swedish astronomer.
Prosperin was a lecturer in mathematics and physics at Uppsala University in 1767, professor of observational astronomy (Observator) in 1773 – 1796, and professor of Astronomy in 1797 – 1798. He became a member of the Royal Swedish Academy of Scie... |
https://en.wikipedia.org/wiki/Zernike%20polynomials | In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel Prize in Physics and the inventor of phase-contrast microscopy, they play important roles in various optics branches such as beam optics and... |
https://en.wikipedia.org/wiki/Z-matrix | Z-matrix may mean:
Z-matrix (chemistry), a table of the locations of atoms comprising a molecule
Z-matrix (mathematics), a matrix whose off-diagonal entries are less than or equal to zero
It may also refer to:
The matrix of Z-parameters, a matrix characterizing an electrical network |
https://en.wikipedia.org/wiki/Hyperbolic%20secant%20distribution | In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus ... |
https://en.wikipedia.org/wiki/Oval | An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry of an ellipse. In common English, the term is used in... |
https://en.wikipedia.org/wiki/Variational%20perturbation%20theory | In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say
,
into a convergent series in powers
,
where is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the h... |
https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%80%93Lewy%20condition | In mathematics, the convergence condition by Courant–Friedrichs–Lewy is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically. It arises in the numerical analysis of explicit time integration schemes, when these are used for the numerical soluti... |
https://en.wikipedia.org/wiki/List%20of%20cities%20and%20towns%20in%20Kosovo | This is a list of cities and towns in the Kosovo in alphabetical order categorised by municipality or district, according to the criteria used by the Kosovo Agency of Statistics (KAS). Kosovo's population is distributed in 1,467 settlements with 26 per cent of its population concentrated in 7 urban areas, also known as... |
https://en.wikipedia.org/wiki/Schanuel%27s%20conjecture | In mathematics, specifically transcendental number theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions of the rational numbers.
Statement
The conjecture is as follows:
Given any complex numbers that are linearly indepen... |
https://en.wikipedia.org/wiki/Axiality | Axiality may refer to:
Axiality (geometry), a measure of the axial symmetry of a two-dimensional shape
Axiality and rhombicity in mathematics, measures of the directional symmetry of a three-dimensional tensor
Axiality, a principle behind the art and poetry of George Quasha
Axiality in architecture, organization around... |
https://en.wikipedia.org/wiki/Painlev%C3%A9%20transcendents | In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions. They were discovered by
,
,
, and
.
H... |
https://en.wikipedia.org/wiki/Back-and-forth%20method | In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular it can be used to prove that
any two countably infinite densely ordered sets (i.e., linearly ordered in such... |
https://en.wikipedia.org/wiki/Covering%20set | In mathematics, a covering set for a sequence of integers refers to a set of prime numbers such that every term in the sequence is divisible by at least one member of the set. The term "covering set" is used only in conjunction with sequences possessing exponential growth.
Sierpinski and Riesel numbers
The use of the... |
https://en.wikipedia.org/wiki/154%20%28number%29 | 154 (one hundred [and] fifty-four) is the natural number following 153 and preceding 155.
In mathematics
154 is a nonagonal number. Its factorization makes 154 a sphenic number
There is no integer with exactly 154 coprimes below it, making 154 a noncototient, nor is there, in base 10, any integer that added up to its... |
https://en.wikipedia.org/wiki/Gibbs%27%20inequality | In information theory, Gibbs' inequality is a statement about the information entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are derived from Gibbs' inequality, including Fano's inequality.
It was first presented by J. Willard Gibbs in the 19th century.
... |
https://en.wikipedia.org/wiki/Abstract%20analytic%20number%20theory | Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to a variety of different mathematical fields. The classical prime number theorem serves as a prototypical example, and the emphasis is on abstract asymptotic distribution... |
https://en.wikipedia.org/wiki/EHP | EHP may refer to:
E.H.P., a 1920s French automobile manufacturer
Eastern Highlands Province in Papua New Guinea
EHP spectral sequence in mathematics
(), Labourist Movement Party, a political party in Turkey
Environmental Health Perspectives, a scholarly journal
Environmental Planning & Historic Preservation (EHP)... |
https://en.wikipedia.org/wiki/Paper%20bag%20problem | In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.
According to Anthony C. Robin, an approximate formula... |
https://en.wikipedia.org/wiki/Trigamma%20function | In mathematics, the trigamma function, denoted or , is the second of the polygamma functions, and is defined by
.
It follows from this definition that
where is the digamma function. It may also be defined as the sum of the series
making it a special case of the Hurwitz zeta function
Note that the last ... |
https://en.wikipedia.org/wiki/Lens%20%28geometry%29 | In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex). This shape can be formed as the intersection of two circular disks. It can also be formed as the union of two circ... |
https://en.wikipedia.org/wiki/Homotopy%20category | In mathematics, the homotopy category is a category built from the category of topological spaces which in a sense identifies two spaces that have the same shape. The phrase is in fact used for two different (but related) categories, as discussed below.
More generally, instead of starting with the category of topologi... |
https://en.wikipedia.org/wiki/Cassini%20oval | In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points (foci) is constant. This may be contrasted with an ellipse, for which the sum of the distances is constant, rather than the product. Cassini ovals are the special c... |
https://en.wikipedia.org/wiki/Wilhelm%20Wirtinger | Wilhelm Wirtinger (19 July 1865 – 16 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory.
Biography
He was born at Ybbs on the Danube and studied at the University of Vienna, where he received his doctorate in 1887, and his habilitatio... |
https://en.wikipedia.org/wiki/Damodar%20Dharmananda%20Kosambi | Damodar Dharmananda Kosambi (31 July 1907 – 29 June 1966) was an Indian polymath with interests in mathematics, statistics, philology, history, and genetics. He contributed to genetics by introducing the Kosambi map function. In statistics, he was the first person to develop orthogonal infinite series expressions for s... |
https://en.wikipedia.org/wiki/Nuclear%20cross%20section | The nuclear cross section of a nucleus is used to describe the probability that a nuclear reaction will occur. The concept of a nuclear cross section can be quantified physically in terms of "characteristic area" where a larger area means a larger probability of interaction. The standard unit for measuring a nuclear... |
https://en.wikipedia.org/wiki/Petrov%20classification | In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.
It is most often applied in studying exact solutions of Einstein's field equations, but... |
https://en.wikipedia.org/wiki/Segre%20classification | The Segre classification is an algebraic classification of rank two symmetric tensors. The resulting types are then known as Segre types. It is most commonly applied to the energy–momentum tensor (or the Ricci tensor) and primarily finds application in the classification of exact solutions in general relativity.
See a... |
https://en.wikipedia.org/wiki/Abraham%20Nemeth | Abraham Nemeth (October 16, 1918 – October 2, 2013) was an American mathematician. He was professor of mathematics at the University of Detroit Mercy in Detroit, Michigan. Nemeth was blind and is known for developing Nemeth Braille, a system for blind people to read and write mathematics.
Early life
Nemeth was born in... |
https://en.wikipedia.org/wiki/Coincidence%20point | In mathematics, a coincidence point (or simply coincidence) of two functions is a point in their common domain having the same image.
Formally, given two functions
we say that a point x in X is a coincidence point of f and g if f(x) = g(x).
Coincidence theory (the study of coincidence points) is, in most settings, a... |
https://en.wikipedia.org/wiki/Gradient%20%28disambiguation%29 | Gradient in vector calculus is a vector field representing the maximum rate of increase of a scalar field or a multivariate function and the direction of this maximal rate.
Gradient may also refer to:
Gradient sro, a Czech aircraft manufacturer
Image gradient, a gradual change or blending of color
Color gradient, a ... |
https://en.wikipedia.org/wiki/Polarization%20identity | In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space.
If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely ... |
https://en.wikipedia.org/wiki/Joel%20Brawley | Joel Vincent Brawley, Jr. is the Alumni Distinguished Professor of Mathematical Sciences at Clemson University. Brawley is reputed nationally for being a prolific mathematics educator and is regarded highly for his teaching abilities. Brawley is also a prominent researcher in the field of algebra, specifically finite f... |
https://en.wikipedia.org/wiki/La%20Granja%2C%20Chile | La Granja (Spanish for "the farm") is a commune of Chile located in Santiago Province, Santiago Metropolitan Region.
Demographics
According to the 2002 census of the National Statistics Institute, La Granja spans an area of and has 132,520 inhabitants (64,750 men and 67,770 women), and the commune is an entirely urba... |
https://en.wikipedia.org/wiki/Kumaraswamy%20distribution | In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval (0,1). It is similar to the Beta distribution, but much simpler to use especially in simulation studies since its probability density function, cumulative distribution... |
https://en.wikipedia.org/wiki/Renca | Renca is a commune of Chile located in Santiago Province, Santiago Metropolitan Region. It was founded on 6 May 1894.
Demographics
According to the 2002 census of the National Statistics Institute, Renca spans an area of and has 133,500 inhabitants, and the commune is an entirely urban area. The population grew by 3.... |
https://en.wikipedia.org/wiki/Sampling%20frame | In statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.
Importance of the sampling frame is stressed by Jessen and Salant and Dillman.
Obtaining and organiz... |
https://en.wikipedia.org/wiki/APV | APV may refer to:
Actuarial present value, a probability weighted present value often used in insurance
Adjusted present value, a variation of the net present value (NPV)
Advanced Power Virtualization (renamed PowerVM), a software virtualization technique used by IBM
Alavuden Peli-Veikot, a multi-sport club in Alav... |
https://en.wikipedia.org/wiki/Hypergeometric%20function | In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linea... |
https://en.wikipedia.org/wiki/Zhou%20Kexi | Zhou Kexi (), born 1942, is a Chinese translator of French literature.
Biography
Zhou gained a degree in mathematics from Fudan University. He acquired the French language and became interested in French literature while studying at École Normale Supérieure in Paris. He became a full-time literary editor in the 1980s,... |
https://en.wikipedia.org/wiki/Substructure%20%28mathematics%29 | In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are restricted to the substructure's domain. Some examples of subalgebras are subgroups, submonoids, subrings, subfields, subalgebras of algeb... |
https://en.wikipedia.org/wiki/Pre-algebra | Prealgebra is a common name for a course in middle school mathematics in the United States, usually taught in the 7th grade or 8th grade. The objective of it is to prepare students for the study of algebra. Usually, algebra is taught in the 8th and 9th grade.
As an intermediate stage after arithmetic, prealgebra helps... |
https://en.wikipedia.org/wiki/Academy%20for%20Mathematics%2C%20Science%2C%20and%20Engineering | The Academy for Mathematics, Science, and Engineering (AMSE) is a four-year magnet public high school program intended to prepare students for STEM careers. Housed on the campus of Morris Hills High School in Rockaway, New Jersey, United States, it is a joint endeavor between the Morris County Vocational School Distric... |
https://en.wikipedia.org/wiki/List%20of%20set%20theory%20topics | This page is a list of articles related to set theory.
Articles on individual set theory topics
Lists related to set theory
Glossary of set theory
List of large cardinal properties
List of properties of sets of reals
List of set identities and relations
Set theorists
Societies and organizations
Associati... |
https://en.wikipedia.org/wiki/K-function | In mathematics, the -function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the gamma function.
Definition
Formally, the -function is defined as
It can also be given in closed form as
where denotes the derivative of the ... |
https://en.wikipedia.org/wiki/Barnes%20G-function | In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written in terms of the double gamma functio... |
https://en.wikipedia.org/wiki/Municipality%20of%20the%20District%20of%20Barrington | Barrington, officially named the Municipality of the District of Barrington, is a district municipality in western Shelburne County, Nova Scotia, Canada. Statistics Canada classifies the district municipality as a municipal district.
Geography
The Municipality of the District of Barrington forms the southernmost part ... |
https://en.wikipedia.org/wiki/Victor%20Wickerhauser | Mladen Victor Wickerhauser was born in Zagreb, SR Croatia, in 1959. He is a graduate of the California Institute of Technology and Yale University.
He is currently a professor of Mathematics and of Biomedical Engineering at Washington University in St. Louis. He has six U.S. patents and more than 100 publications. One... |
https://en.wikipedia.org/wiki/StatSoft | StatSoft is the original developer of Statistica. Dell acquired it in March 2014. Statistica is an analytics software portfolio that provides enterprise and desktop software for statistics, data analysis, data management, data visualization, data mining, which is also called predictive analytics, and quality control.
... |
https://en.wikipedia.org/wiki/Symplectic%20integrator | In mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, acceler... |
https://en.wikipedia.org/wiki/Bruce%20Price | Bruce Price (December 12, 1845 – May 29, 1903) was an American architect and an innovator in the Shingle Style. The stark geometry and compact massing of his cottages in Tuxedo Park, New York, influenced Modernist architects, including Frank Lloyd Wright and Robert Venturi.
He also designed Richardsonian Romanesque i... |
https://en.wikipedia.org/wiki/Claude%20Mydorge | Claude Mydorge (1585 – July 1647) was a French mathematician. His primary contributions were in geometry and physics.
Mydorge served on a scientific committee (whose members included Pierre Hérigone and Étienne Pascal) set up to determine whether Jean-Baptiste Morin's scheme for determining longitude from the Moon's m... |
https://en.wikipedia.org/wiki/1997%20NBA%20draft | The 1997 NBA draft took place on June 25, 1997, at Charlotte Coliseum in Charlotte, North Carolina. The Vancouver Grizzlies had the highest probability to win the NBA draft lottery, but since they were an expansion team along with the Toronto Raptors they were not allowed to select first in this draft. Although the B... |
https://en.wikipedia.org/wiki/Sticking%20probability | The sticking probability is the probability that molecules are trapped on surfaces and adsorb chemically. From Langmuir's adsorption isotherm, molecules cannot adsorb on surfaces when the adsorption sites are already occupied by other molecules, so the sticking probability can be expressed as follows:
where is the in... |
https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz%20theorem | In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left half-plane. Polynomials with this property are called Hurwitz stable polynomials. The Routh–Hurwitz theorem is important in dynamical systems and control theory, because the characteristic polyno... |
https://en.wikipedia.org/wiki/Pentation | In mathematics, pentation (or hyper-5) is the next hyperoperation (infinite sequence of arithmetic operations) after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity), just as tetration is iterated right-associative exponentiation. It is a binary operation defi... |
https://en.wikipedia.org/wiki/List%20of%20chaotic%20maps | In mathematics, a chaotic map is a map (namely, an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
Chaot... |
https://en.wikipedia.org/wiki/Tent%20map | In mathematics, the tent map with parameter μ is the real-valued function fμ defined by
the name being due to the tent-like shape of the graph of fμ. For the values of the parameter μ within 0 and 2, fμ maps the unit interval [0, 1] into itself, thus defining a discrete-time dynamical system on it (equivalently, a rec... |
https://en.wikipedia.org/wiki/Costas%20array | In mathematics, a Costas array can be regarded geometrically as a set of n points, each at the center of a square in an n×n square tiling such that each row or column contains only one point, and all of the n(n − 1)/2 displacement vectors between each pair of dots are distinct. This results in an ideal "thumbtack" auto... |
https://en.wikipedia.org/wiki/Stability%20radius | In mathematics, the stability radius of an object (system, function, matrix, parameter) at a given nominal point is the radius of the largest ball, centered at the nominal point, all of whose elements satisfy pre-determined stability conditions. The picture of this intuitive notion is this:
where denotes the nomi... |
https://en.wikipedia.org/wiki/Schwarz%20triangle | In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere (spherical tiling), possibly overlapping, through reflections in its edges. They were classified in .
These can be defined more generally as tessellations of the sphere, the Euclidean plane, or the h... |
https://en.wikipedia.org/wiki/Triangle%20group | In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane... |
https://en.wikipedia.org/wiki/Lebesgue%27s%20lemma | For Lebesgue's lemma for open covers of compact spaces in topology see Lebesgue's number lemma
In mathematics, Lebesgue's lemma is an important statement in approximation theory. It provides a bound for the projection error, controlling the error of approximation by a linear subspace based on a linear projection rela... |
https://en.wikipedia.org/wiki/Popular%20mathematics | Popular mathematics is mathematical presentation aimed at a general audience. Sometimes this is in the form of books which require no mathematical background and in other cases it is in the form of expository articles written by professional mathematicians to reach out to others working in different areas.
Notable wor... |
https://en.wikipedia.org/wiki/156%20%28number%29 | 156 (one hundred [and] fifty-six) is the natural number, following 155 and preceding 157.
In mathematics
156 is an abundant number, a pronic number, a dodecagonal number, and a refactorable number.
156 is the number of graphs on 6 unlabeled nodes.
156 is a repdigit in base 5 (1111), and also in bases 25, 38, 51, 77... |
https://en.wikipedia.org/wiki/Heun%20function | In mathematics, the local Heun function is the solution of Heun's differential equation that is holomorphic and 1 at the singular point z = 0. The local Heun function is called a Heun function, denoted Hf, if it is also regular at z = 1, and is called a Heun polynomial, denoted Hp, if it is regular at all three fi... |
https://en.wikipedia.org/wiki/Lebesgue%20constant | In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomial approximation of the function (the degree of the polynomials are fixed). The Lebesgue constant for polynomials of de... |
https://en.wikipedia.org/wiki/Heinz-Otto%20Kreiss | Heinz-Otto Kreiss (14 September 1930 – 16 December 2015) was a German mathematician in the fields of numerical analysis, applied mathematics, and what was the new area of computing in the early 1960s. Born in Hamburg, Germany, he earned his Ph.D. at Kungliga Tekniska Högskolan in 1959. Over the course of his long caree... |
https://en.wikipedia.org/wiki/Q-theta%20function | In mathematics, the q-theta function (or modified Jacobi theta function) is a type of q-series which is used to define elliptic hypergeometric series.
It is given by
where one takes 0 ≤ |q| < 1. It obeys the identities
It may also be expressed as:
where is the q-Pochhammer symbol.
See also
elliptic hypergeometr... |
https://en.wikipedia.org/wiki/Elliptic%20gamma%20function | In mathematics, the elliptic gamma function is a generalization of the q-gamma function, which is itself the q-analog of the ordinary gamma function. It is closely related to a function studied by , and can be expressed in terms of the triple gamma function. It is given by
It obeys several identities:
and
where θ is... |
https://en.wikipedia.org/wiki/Lattice%20group | In mathematics, the term lattice group is used for two distinct notions:
a lattice (group), a discrete subgroup of Rn and its generalizations
a lattice ordered group, a group that with a partial ordering that is a lattice order |
https://en.wikipedia.org/wiki/Pretopological%20space | In general topology, a pretopological space is a generalization of the concept of topological space.
A pretopological space can be defined in terms of either filters or a preclosure operator.
The similar, but more abstract, notion of a Grothendieck pretopology is used to form a Grothendieck topology, and is covered i... |
https://en.wikipedia.org/wiki/Picard%E2%80%93Fuchs%20equation | In mathematics, the Picard–Fuchs equation, named after Émile Picard and Lazarus Fuchs, is a linear ordinary differential equation whose solutions describe the periods of elliptic curves.
Definition
Let
be the j-invariant with and the modular invariants of the elliptic curve in Weierstrass form:
Note that the j-inv... |
https://en.wikipedia.org/wiki/Modular%20invariant | In mathematics, a modular invariant may be
A modular invariant of a group acting on a vector space of positive characteristic
The elliptic modular function, giving the modular invariant of an elliptic curve. |
https://en.wikipedia.org/wiki/Riemann%27s%20differential%20equation | In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and . The equation is also known as the Papperitz equation.
The hyp... |
https://en.wikipedia.org/wiki/Willmore%20energy | In differential geometry, the Willmore energy is a quantitative measure of how much a given surface deviates from a round sphere. Mathematically, the Willmore energy of a smooth closed surface embedded in three-dimensional Euclidean space is defined to be the integral of the square of the mean curvature minus the Gaus... |
https://en.wikipedia.org/wiki/Principal%20curvature | In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. They measure how the surface bends by different amounts in different directions at that point.
Discussion
At eac... |
https://en.wikipedia.org/wiki/Category%20of%20small%20categories | In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms.
The initial ob... |
https://en.wikipedia.org/wiki/Manifold | In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space.
... |
https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin%20constant | In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted , is a mathematical constant, related to the -function and the Barnes -function. The constant appears in a number of sums and integrals, especially those involving gamma functions and zeta functions. It is named after mathematicia... |
https://en.wikipedia.org/wiki/Ernst%20Gottfried%20Fischer | Ernst Gottfried Fischer (17 July 1754 – 27 January 1831) was a German chemist. He was born in Hoheneiche near Saalfeld. After studying theology and mathematics at the University of Halle, he was a teacher in Berlin before becoming Professor of Physics in 1810. He translated Claude Berthollet's publication Recherches ... |
https://en.wikipedia.org/wiki/Holyhedron | In mathematics, a holyhedron is a type of 3-dimensional geometric body: a polyhedron each of whose faces contains at least one polygon-shaped hole, and whose holes' boundaries share no point with each other or the face's boundary.
The concept was first introduced by John H. Conway; the term "holyhedron" was coined by... |
https://en.wikipedia.org/wiki/COT | A cot is a camp bed or infant bed.
Cot or COT may also refer to:
In arts and entertainment
Chicago Opera Theater, an opera company
In mathematics, science, and technology
Car of Tomorrow, a car design used in NASCAR racing
Cost of transport, an energy calculation
Cottage developed from the word cot, which can be... |
https://en.wikipedia.org/wiki/Baire%20space%20%28set%20theory%29 | In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology. This space is commonly used in descriptive set theory, to the extent that its elements are often called "reals". It is denoted NN, ωω, by the symbol or also ωω, not to be confused with the countable ordina... |
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