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https://en.wikipedia.org/wiki/Cantor%20function | In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Though it is continuous everywhere and has zero derivative almost everywhere... |
https://en.wikipedia.org/wiki/Constant%20function | In mathematics, a constant function is a function whose (output) value is the same for every input value. For example, the function is a constant function because the value of is 4 regardless of the input value (see image).
Basic properties
As a real-valued function of a real-valued argument, a constant function ha... |
https://en.wikipedia.org/wiki/Symmedian | In geometry, symmedians are three particular lines associated with every triangle. They are constructed by taking a median of the triangle (a line connecting a vertex with the midpoint of the opposite side), and reflecting the line over the corresponding angle bisector (the line through the same vertex that divides the... |
https://en.wikipedia.org/wiki/Lemoine%20point | In geometry, the Lemoine point, Grebe point or symmedian point is the intersection of the three symmedians (medians reflected at the associated angle bisectors) of a triangle.
Ross Honsberger called its existence "one of the crown jewels of modern geometry".
In the Encyclopedia of Triangle Centers the symmedian poin... |
https://en.wikipedia.org/wiki/Tessellation | A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.
A periodic tiling has a repeating pattern. Some special kinds include r... |
https://en.wikipedia.org/wiki/Cunningham%20chain | In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes.
Definition
A Cunningham chain of the first kind of length n is a sequence of prime numbers (p1, ..., pn) such that pi+1 ... |
https://en.wikipedia.org/wiki/Multiply%20perfect%20number | In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number.
For a given natural number k, a number n is called (or perfect) if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if a... |
https://en.wikipedia.org/wiki/Abundant%20number | In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. Th... |
https://en.wikipedia.org/wiki/Deficient%20number | In number theory, a deficient number or defective number is a positive integer for which the sum of divisors of is less than . Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than . For example, the proper divisors of 8 are , and their sum is less than 8, so 8 is deficient... |
https://en.wikipedia.org/wiki/Deficiency | A deficiency is generally a lack of something. It may also refer to:
A deficient number, in mathematics, a number n for which σ(n) < 2n
Angular deficiency, in geometry, the difference between a sum of angles and the corresponding sum in a Euclidean plane
Deficiency (graph theory), a property describing how far a giv... |
https://en.wikipedia.org/wiki/Cullen%20number | In mathematics, a Cullen number is a member of the integer sequence (where is a natural number). Cullen numbers were first studied by James Cullen in 1905. The numbers are special cases of Proth numbers.
Properties
In 1976 Christopher Hooley showed that the natural density of positive integers for which Cn is a pr... |
https://en.wikipedia.org/wiki/Quasiperfect%20number | In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1. Equivalently, n is the sum of its non-trivial divisors (that is, its divisors excluding 1 and n). No quasiperfect numbers have been found so far.
The quasiperfect numbers ar... |
https://en.wikipedia.org/wiki/Semiperfect%20number | In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number.
The first few semiperfect numbers are: 6, 12, 18, 20, 24, 28, 30, 36, 40, ..... |
https://en.wikipedia.org/wiki/Weird%20number | In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.
Examples
The smallest weird number is 7... |
https://en.wikipedia.org/wiki/Primeval%20number | In recreational number theory, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permuting some or all of its digits (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by M... |
https://en.wikipedia.org/wiki/Woodall%20number | In number theory, a Woodall number (Wn) is any natural number of the form
for some natural number n. The first few Woodall numbers are:
1, 7, 23, 63, 159, 383, 895, … .
History
Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the simi... |
https://en.wikipedia.org/wiki/Riesel%20number | In mathematics, a Riesel number is an odd natural number k for which is composite for all natural numbers n . In other words, when k is a Riesel number, all members of the following set are composite:
If the form is instead , then k is a Sierpinski number.
Riesel problem
In 1956, Hans Riesel showed that there are ... |
https://en.wikipedia.org/wiki/Almost%20perfect%20number | In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum of all divisors of n (the sum-of-divisors function σ(n)) is equal to 2n − 1, the sum of all proper divisors of n, s(n) = σ(n) − n, then being equal to n − 1. The only kno... |
https://en.wikipedia.org/wiki/Hyperperfect%20number | In number theory, a -hyperperfect number is a natural number for which the equality holds, where is the divisor function (i.e., the sum of all positive divisors of ). A hyperperfect number is a -hyperperfect number for some integer . Hyperperfect numbers generalize perfect numbers, which are 1-hyperperfect.
The fir... |
https://en.wikipedia.org/wiki/Zermelo%20set%20theory | Zermelo set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF) and its extensions, such as von Neumann–Bernays–Gödel set theory (NBG). It bears certain differences from its descendants, which are not always understood, an... |
https://en.wikipedia.org/wiki/Theoretical%20computer%20science | Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, formal language theory, the lambda calculus and type theory.
It is difficult to circumscribe the theoretical areas precisely. The ACM's ... |
https://en.wikipedia.org/wiki/Regularization | Regularization may refer to:
Regularization (linguistics)
Regularization (mathematics)
Regularization (physics)
Regularization (solid modeling)
Regularization Law, an Israeli law intended to retroactively legalize settlements
See also
Matrix regularization |
https://en.wikipedia.org/wiki/Israel%20Central%20Bureau%20of%20Statistics | The Israel Central Bureau of Statistics (, HaLishka HaMerkazit LiStatistika; ), abbreviated CBS, is an Israeli government office established in 1949 to carry out research and publish statistical data on all aspects of Israeli life, including population, society, economy, industry, education, and physical infrastructure... |
https://en.wikipedia.org/wiki/Wieferich%20prime | In number theory, a Wieferich prime is a prime number p such that p2 divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides . Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem, at which time both ... |
https://en.wikipedia.org/wiki/Wilson%20prime | In number theory, a Wilson prime is a prime number such that divides , where "" denotes the factorial function; compare this with Wilson's theorem, which states that every prime divides . Both are named for 18th-century English mathematician John Wilson; in 1770, Edward Waring credited the theorem to Wilson, althoug... |
https://en.wikipedia.org/wiki/Wall%E2%80%93Sun%E2%80%93Sun%20prime | In number theory, a Wall–Sun–Sun prime or Fibonacci–Wieferich prime is a certain kind of prime number which is conjectured to exist, although none are known.
Definition
Let be a prime number. When each term in the sequence of Fibonacci numbers is reduced modulo , the result is a periodic sequence.
The (minimal) pe... |
https://en.wikipedia.org/wiki/Regular%20prime | In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli numbers.
The first few regular odd primes are:
3, 5, 7, 11, 13, 17, 19, 23, 2... |
https://en.wikipedia.org/wiki/Newman%E2%80%93Shanks%E2%80%93Williams%20prime | In mathematics, a Newman–Shanks–Williams prime (NSW prime) is a prime number p which can be written in the form
NSW primes were first described by Morris Newman, Daniel Shanks and Hugh C. Williams in 1981 during the study of finite simple groups with square order.
The first few NSW primes are 7, 41, 239, 9369319, 630... |
https://en.wikipedia.org/wiki/Finite%20group | In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and p... |
https://en.wikipedia.org/wiki/Office%20for%20National%20Statistics | The Office for National Statistics (ONS; ) is the executive office of the UK Statistics Authority, a non-ministerial department which reports directly to the UK Parliament.
Overview
The ONS is responsible for the collection and publication of statistics related to the economy, population and society of the UK; respon... |
https://en.wikipedia.org/wiki/Palestinian%20Central%20Bureau%20of%20Statistics | The Palestinian Central Bureau of Statistics (PCBS; ) is the official
statistical institution of the State of Palestine. Its main task is to provide credible statistical figures at the national and international levels. It is a state institution that provides service to the governmental, non – governmental and private ... |
https://en.wikipedia.org/wiki/Isadore%20Singer | Isadore Manuel Singer (May 3, 1924 – February 11, 2021) was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley.
Singer is noted for his work wit... |
https://en.wikipedia.org/wiki/Financial%20engineering | Financial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance.
Fina... |
https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer%20index%20theorem | In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some to... |
https://en.wikipedia.org/wiki/Baby%20monster%20group | In the area of modern algebra known as group theory, the baby monster group B (or, more simply, the baby monster) is a sporadic simple group of order
241313567211131719233147
= 4154781481226426191177580544000000
= 4,154,781,481,226,426,191,177,580,544,000,000
≈ 4.
B is one of the 26 sporadic groups and has the ... |
https://en.wikipedia.org/wiki/Sporadic%20group | In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.
A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself. The classification theorem states that the list of finite simple groups consists of 18... |
https://en.wikipedia.org/wiki/Bimonster%20group | In mathematics, the bimonster is a group that is the wreath product of the monster group M with Z2:
The Bimonster is also a quotient of the Coxeter group corresponding to the Dynkin diagram Y555, a Y-shaped graph with 16 nodes:
John H. Conway conjectured that a presentation of the bimonster could be given by addin... |
https://en.wikipedia.org/wiki/Ethnomathematics | In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture. Often associated with "cultures without written expression", it may also be defined as "the mathematics which is practised among identifiable cultural groups". It refers to a broad cluster of ideas ranging from ... |
https://en.wikipedia.org/wiki/Radical%20center | The term radical center can refer to:
Radical centrism, a political movement
a mathematical construct: also called the power center (geometry) |
https://en.wikipedia.org/wiki/Modular%20group | In mathematics, the modular group is the projective special linear group of matrices with integer coefficients and determinant 1. The matrices and are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation... |
https://en.wikipedia.org/wiki/Domain%20theory | Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory. The field has major applications in computer science, where it is used to specify denotational semantics, especially ... |
https://en.wikipedia.org/wiki/Kirkland%20Lake | Kirkland Lake is a town and municipality in Timiskaming District of Northeastern Ontario. The 2016 population, according to Statistics Canada, was 7,981.
The community name was based on a nearby lake which in turn was named after Winnifred Kirkland, a secretary of the Ontario Department of Mines in Toronto. The lake w... |
https://en.wikipedia.org/wiki/Successor%20function | In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by S, so S(n) = n +1. For example, S(1) = 2 and S(2) = 3. The successor function is one of the basic components used to build a primitive recursive function.
Successor operations are ... |
https://en.wikipedia.org/wiki/Hopf%20algebra | In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property. The re... |
https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer%20primality%20test | In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1878 and subsequently proved by Derrick Henry Lehmer in 1930.
The test
The Lucas–Lehmer test works as follows. Let Mp = 2p − 1 be the Mersenne number to test with p an odd prime. ... |
https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices... |
https://en.wikipedia.org/wiki/Graph%20drawing | Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
A drawing of a graph or networ... |
https://en.wikipedia.org/wiki/Extendible%20cardinal | In mathematics, extendible cardinals are large cardinals introduced by , who was partly motivated by reflection principles. Intuitively, such a cardinal represents a point beyond which initial pieces of the universe of sets start to look similar, in the sense that each is elementarily embeddable into a later one.
Def... |
https://en.wikipedia.org/wiki/Isoperimetric%20inequality | In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In -dimensional space the inequality lower bounds the surface area or perimeter of a set by its volume ,
,
where is a unit sphere. The equality holds only when is a sphere in .
On a plane, i.e... |
https://en.wikipedia.org/wiki/Power%20center%20%28geometry%29 | In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical axes of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles ... |
https://en.wikipedia.org/wiki/Covering%20lemma | In the foundations of mathematics, a covering lemma is used to prove that the non-existence of certain large cardinals leads to the existence of a canonical inner model, called the core model, that is, in a sense, maximal and approximates the structure of the von Neumann universe V. A covering lemma asserts that under ... |
https://en.wikipedia.org/wiki/Reverse%20mathematics | Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of deriving theorems from axiom... |
https://en.wikipedia.org/wiki/Finitely%20generated%20module | In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type.
Related concepts include finitely cogenerated modules, finitely presented modules, finitely related module... |
https://en.wikipedia.org/wiki/Free%20module | In mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.
Given any set an... |
https://en.wikipedia.org/wiki/Mathematics%20education | In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
Although research into mathematics education is primarily concerned with the tools, method... |
https://en.wikipedia.org/wiki/Brahmagupta%E2%80%93Fibonacci%20identity | In algebra, the Brahmagupta–Fibonacci identity expresses the product of two sums of two squares as a sum of two squares in two different ways. Hence the set of all sums of two squares is closed under multiplication. Specifically, the identity says
For example,
The identity is also known as the Diophantus identity, a... |
https://en.wikipedia.org/wiki/Ramsey%20cardinal | In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by and named after Frank P. Ramsey, whose theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize to the uncountable case.
Let [κ]<ω denote the set of all finite subsets of κ. A cardinal number κ is... |
https://en.wikipedia.org/wiki/Erd%C5%91s%20cardinal | In mathematics, an Erdős cardinal, also called a partition cardinal is a certain kind of large cardinal number introduced by .
A cardinal κ is called α-Erdős if for every function there is a set of order type that is homogeneous for . In the notation of the partition calculus, κ is α-Erdős if
.
The existence of ze... |
https://en.wikipedia.org/wiki/Subtle%20cardinal | In mathematics, subtle cardinals and ethereal cardinals are closely related kinds of large cardinal number.
A cardinal κ is called subtle if for every closed and unbounded C ⊂ κ and for every sequence A of length κ for which element number δ (for an arbitrary δ), Aδ ⊂ δ, there exist α, β, belonging to C, with α < β, s... |
https://en.wikipedia.org/wiki/Alan%20Sokal | Alan David Sokal (; born January 24, 1955) is an American professor of mathematics at University College London and professor emeritus of physics at New York University. He works in statistical mechanics and combinatorics. He is a critic of postmodernism, and caused the Sokal affair in 1996 when his deliberately nonsen... |
https://en.wikipedia.org/wiki/Urysohn%20and%20completely%20Hausdorff%20spaces | In topology, a discipline within mathematics, an Urysohn space, or T2½ space, is a topological space in which any two distinct points can be separated by closed neighborhoods. A completely Hausdorff space, or functionally Hausdorff space, is a topological space in which any two distinct points can be separated by a con... |
https://en.wikipedia.org/wiki/Fischer%20group | In the area of modern algebra known as group theory, the Fischer groups are the three sporadic simple groups Fi22, Fi23 and Fi24 introduced by .
3-transposition groups
The Fischer groups are named after Bernd Fischer who discovered them while investigating 3-transposition groups.
These are groups G with the followi... |
https://en.wikipedia.org/wiki/Decagon | In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°.
Regular decagon
A regular decagon has all sides of equal length and each internal angle will always be equal to 144°. Its Schläfli symbol ... |
https://en.wikipedia.org/wiki/Sabi%20%28Korea%29 | {
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126.87149047851564,
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https://en.wikipedia.org/wiki/Pick%27s%20theorem | In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. It was popularized in English by Hugo Steinhaus in the 1950 edition of ... |
https://en.wikipedia.org/wiki/Annihilator%20%28ring%20theory%29 | In mathematics, the annihilator of a subset of a module over a ring is the ideal formed by the elements of the ring that give always zero when multiplied by each element of .
Over an integral domain, a module that has a nonzero annihilator is a torsion module, and a finitely generated torsion module has a nonzero an... |
https://en.wikipedia.org/wiki/Solid%20of%20revolution | In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary). The surface created by this revolution and which bounds the solid is the surface of revolution.
Assuming that the... |
https://en.wikipedia.org/wiki/Disk%20%28mathematics%29 | In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not.
For a radius, , an open disk is usually denoted as and a closed disk is . However in the field of topology the closed disk... |
https://en.wikipedia.org/wiki/Stationary%20process | In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over ... |
https://en.wikipedia.org/wiki/Discretization | In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is t... |
https://en.wikipedia.org/wiki/Kernel%20%28set%20theory%29 | In set theory, the kernel of a function (or equivalence kernel) may be taken to be either
the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function can tell", or
the corresponding partition of the domain.
An unrelated notion is that of the kernel of a ... |
https://en.wikipedia.org/wiki/Differentiable%20function | In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well... |
https://en.wikipedia.org/wiki/Row%20echelon%20form | In linear algebra, a matrix is in row echelon form if it can be obtained as the result of Gaussian elimination. In particular, every matrix can be put in row echelon form by a succession of elementary row operations. The term echelon comes from the French "échelon" ("level" or step of a ladder), and refers to the fact ... |
https://en.wikipedia.org/wiki/Rank%E2%80%93nullity%20theorem | The rank–nullity theorem is a theorem in linear algebra, which asserts:
the number of columns of a matrix is the sum of the rank of and the nullity of ; and
the dimension of the domain of a linear transformation is the sum of the rank of (the dimension of the image of ) and the nullity of (the dimension of the k... |
https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes%20integral | In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes. It serves as an instructive and useful precursor of the Lebesgue integral, and an invaluable to... |
https://en.wikipedia.org/wiki/Disc%20integration | Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution. This method models the resulting three-dimensional shape as a stack of an infinite number o... |
https://en.wikipedia.org/wiki/Monoidal%20category | In mathematics, a monoidal category (or tensor category) is a category equipped with a bifunctor
that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism. The associated natural isomorphisms are subject to certain coherence condit... |
https://en.wikipedia.org/wiki/Shell%20integration | Shell integration (the shell method in integral calculus) is a method for calculating the volume of a solid of revolution, when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.
Definition
The ... |
https://en.wikipedia.org/wiki/Squeeze%20theorem | In calculus, the squeeze theorem (also known as the sandwich theorem, among other names) is a theorem regarding the limit of a function that is trapped between two other functions.
The squeeze theorem is used in calculus and mathematical analysis, typically to confirm the limit of a function via comparison with two ot... |
https://en.wikipedia.org/wiki/Saharon%20Shelah | Saharon Shelah (; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.
Biography
Shelah was born in Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist Yonatan Ratosh. He received his... |
https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose%20inverse | In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix is the most widely known generalization of the inverse matrix. It was independently described by E. H. Moore in 1920, Arne Bjerhammar in 1951, and Roger Penrose in 1955. Earlier, Erik Ivar Fredholm had introduced the concept of a ... |
https://en.wikipedia.org/wiki/Kuratowski%20closure%20axioms | In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms that can be used to define a topological structure on a set. They are equivalent to the more commonly used open set definition. They were first formalized by Kazimierz Kuratowski, and the idea was further studied by mathe... |
https://en.wikipedia.org/wiki/Prime-counting%20function | In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by (x) (unrelated to the number ).
Growth rate
Of great interest in number theory is the growth rate of the prime-counting function. It was conjectured in the end of... |
https://en.wikipedia.org/wiki/Algebra%20homomorphism | In mathematics, an algebra homomorphism is a homomorphism between two algebras. More precisely, if A and B are algebras over a field (or a ring) K, it is a function such that, for all k in K and x, y in A, one has
The first two conditions say that F is a K-linear map, and the last condition says that F preserv... |
https://en.wikipedia.org/wiki/F-distribution | In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the... |
https://en.wikipedia.org/wiki/Ian%20Stewart%20%28mathematician%29 | Ian Nicholas Stewart (born 24 September 1945) is a British mathematician and a popular-science and science-fiction writer. He is Emeritus Professor of Mathematics at the University of Warwick, England.
Education and early life
Stewart was born in 1945 in Folkestone, England. While in the sixth form at Harvey Gramma... |
https://en.wikipedia.org/wiki/Sociable%20number | In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence. They are generalizations of the concepts of perfect numbers and amicable numbers. The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918. In a sociable sequ... |
https://en.wikipedia.org/wiki/Rate%20%28mathematics%29 | In mathematics, a rate is the quotient of two quantities in different units of measurement, often represented as a fraction. If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent var... |
https://en.wikipedia.org/wiki/Media%20access%20unit | A media access unit (MAU), also known as a multistation access unit (MAU or MSAU), is a device to attach multiple network stations in a star topology as a Token Ring network, internally wired to connect the stations into a logical ring (generally passive i.e. non-switched and unmanaged; however managed Token Ring MAUs ... |
https://en.wikipedia.org/wiki/Primitive%20element | In mathematics, the term primitive element can mean:
Primitive root modulo n, in number theory
Primitive element (field theory), an element that generates a given field extension
Primitive element (finite field), an element that generates the multiplicative group of a finite field
Primitive element (lattice), an el... |
https://en.wikipedia.org/wiki/Hereditarily%20finite%20set | In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of its elements are finite sets, recursively all the way down to the empty set.
Formal definition
A recursive definition of well-founded ... |
https://en.wikipedia.org/wiki/Quotient | In arithmetic, a quotient (from 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division), or as a fraction or a ratio (in the case of a... |
https://en.wikipedia.org/wiki/Fluctuation%20theorem | The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predict... |
https://en.wikipedia.org/wiki/Regular%20polygon | In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle,... |
https://en.wikipedia.org/wiki/Michael%20Spivak | Michael David Spivak (May 25, 1940October 1, 2020) was an American mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. Spivak was the author of the five-volume A Comprehensive Introduction to Differential Geometry.
Biography
Spivak was born in ... |
https://en.wikipedia.org/wiki/Nowhere%20continuous%20function | In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If is a function from real numbers to real numbers, then is nowhere continuous if for each point there is some such that for every we can find a point s... |
https://en.wikipedia.org/wiki/Free%20object | In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the alg... |
https://en.wikipedia.org/wiki/Ultrametric%20space | In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to . Sometimes the associated metric is also called a non-Archimedean metric or super-metric.
Formal definition
An ultrametric on a set is a real-valued function
(where denote the real numbers), such that for a... |
https://en.wikipedia.org/wiki/Isolated%20singularity | In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it. In other words, a complex number z0 is an isolated singularity of a function f if there exists an open disk D centered at z0 such that f is holomorphic on D \ {z0}, that is, on the set obtained from... |
https://en.wikipedia.org/wiki/Self-healing%20ring | A self-healing ring, or SHR, is a telecommunications term for loop network topology, a common configuration in telecommunications transmission systems. Like roadway and water distribution systems, a loop or ring is used to provide redundancy. SDH, SONET and WDM systems are often configured in self-healing rings.
Desc... |
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