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https://en.wikipedia.org/wiki/Mertens%20conjecture | In mathematics, the Mertens conjecture is the statement that the Mertens function is bounded by . Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in ), and again in print by , and disproved by .
... |
https://en.wikipedia.org/wiki/Linear%20differential%20equation | In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form
where and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unkn... |
https://en.wikipedia.org/wiki/Spline | Spline may refer to:
Mathematics
Spline (mathematics), a mathematical function used for interpolation or smoothing
Smoothing spline, a method of smoothing using a spline function
Devices
Spline (mechanical), a mating feature for rotating elements
Flat spline, a device to draw curves
Spline drive, a type of scre... |
https://en.wikipedia.org/wiki/Janko%20group | In the area of modern algebra known as group theory, the Janko groups are the four sporadic simple groups J1, J2, J3 and J4 introduced by Zvonimir Janko. Unlike the Mathieu groups, Conway groups, or Fischer groups, the Janko groups do not form a series, and the relation among the four groups is mainly historical ... |
https://en.wikipedia.org/wiki/Mathieu%20group | In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by . They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They are the first sporadic groups to be discovered.
Sometimes the notation M8 M9, M10, M20 an... |
https://en.wikipedia.org/wiki/Stone%20space | In topology and related areas of mathematics, a Stone space, also known as a profinite space or profinite set, is a compact totally disconnected Hausdorff space. Stone spaces are named after Marshall Harvey Stone who introduced and studied them in the 1930s in the course of his investigation of Boolean algebras, which ... |
https://en.wikipedia.org/wiki/Walsh%20function | In mathematics, more specifically in harmonic analysis, Walsh functions form a complete orthogonal set of functions that can be used to represent any discrete function—just like trigonometric functions can be used to represent any continuous function in Fourier analysis. They can thus be viewed as a discrete, digital ... |
https://en.wikipedia.org/wiki/Group%20algebra%20of%20a%20locally%20compact%20group | In functional analysis and related areas of mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that representations of the algebra are related to representations of the group. As such, they are similar to t... |
https://en.wikipedia.org/wiki/Support%20%28mathematics%29 | In mathematics, the support of a real-valued function is the subset of the function domain containing the elements which are not mapped to zero. If the domain of is a topological space, then the support of is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used ve... |
https://en.wikipedia.org/wiki/Function%20field%20%28scheme%20theory%29 | The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on that open set; in other words, KX(U)... |
https://en.wikipedia.org/wiki/Hilbert%27s%20sixteenth%20problem | Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics.
The original problem was posed as the Problem of the topology of algebraic curves and surfaces (Problem der Topologie algebraischer Kurve... |
https://en.wikipedia.org/wiki/Singleton%20%28mathematics%29 | In mathematics, a singleton, also known as a unit set or one-point set, is a set with exactly one element. For example, the set is a singleton whose single element is .
Properties
Within the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element of itself. This implies ... |
https://en.wikipedia.org/wiki/Lexicostatistics | Lexicostatistics is a method of comparative linguistics that involves comparing the percentage of lexical cognates between languages to determine their relationship. Lexicostatistics is related to the comparative method but does not reconstruct a proto-language. It is to be distinguished from glottochronology, which at... |
https://en.wikipedia.org/wiki/Fourier%20inversion%20theorem | In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely.
The th... |
https://en.wikipedia.org/wiki/Trivial%20topology | In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly called indiscrete, anti-discrete, concrete or codiscrete. Intuitively, this has the consequence that all points of the space are "lumped together" and cannot be di... |
https://en.wikipedia.org/wiki/Projective%20linear%20group | In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V). Explicitly, the projective linear group is the quotient... |
https://en.wikipedia.org/wiki/Congruence%20subgroup | In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of invertible 2 × 2 integer matrices of determinant 1 in which the off-diagonal entries are even. More generally, the notion of congruence sub... |
https://en.wikipedia.org/wiki/Cofiniteness | In mathematics, a cofinite subset of a set is a subset whose complement in is a finite set. In other words, contains all but finitely many elements of If the complement is not finite, but is countable, then one says the set is cocountable.
These arise naturally when generalizing structures on finite sets to infin... |
https://en.wikipedia.org/wiki/Birational%20geometry | In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the r... |
https://en.wikipedia.org/wiki/Polydivisible%20number | In mathematics a polydivisible number (or magic number) is a number in a given number base with digits abcde... that has the following properties:
Its first digit a is not 0.
The number formed by its first two digits ab is a multiple of 2.
The number formed by its first three digits abc is a multiple of 3.
The num... |
https://en.wikipedia.org/wiki/Seifert%E2%80%93Van%20Kampen%20theorem | In mathematics, the Seifert–Van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called Van Kampen's theorem, expresses the structure of the fundamental group of a topological space in terms of the fundamental groups of two open, path-connected subspaces that co... |
https://en.wikipedia.org/wiki/Cantor%E2%80%93Bernstein%20theorem | In set theory and order theory, the Cantor–Bernstein theorem states that the cardinality of the second type class, the class of countable order types, equals the cardinality of the continuum. It was used by Felix Hausdorff and named by him after Georg Cantor and Felix Bernstein. Cantor constructed a family of countable... |
https://en.wikipedia.org/wiki/Italian%20school%20of%20algebraic%20geometry | In relation to the history of mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered around Rome roughly from 1885 to 1935. There were 30 to 40 leading mathematicians who made major contributions, about half of t... |
https://en.wikipedia.org/wiki/Erich%20K%C3%A4hler | Erich Kähler (; 16 January 1906 – 31 May 2000) was a German mathematician with wide-ranging interests in geometry and mathematical physics, who laid important mathematical groundwork for algebraic geometry and for string theory.
Education and life
Erich Kähler was born in Leipzig, the son of a telegraph inspector Erns... |
https://en.wikipedia.org/wiki/Large%20cardinal | In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least α such that α=ωα). The proposition that such cardinals exist cannot be pr... |
https://en.wikipedia.org/wiki/General%20position | In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differ... |
https://en.wikipedia.org/wiki/Intersection%20number | In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency. One needs a definition of intersection number in order to state r... |
https://en.wikipedia.org/wiki/Solomon%20Lefschetz | Solomon Lefschetz (; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
Life
He was born in Moscow, the son of Alexander Lefschetz and his wif... |
https://en.wikipedia.org/wiki/W.%20V.%20D.%20Hodge | Sir William Vallance Douglas Hodge (; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer.
His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a ... |
https://en.wikipedia.org/wiki/Arithmetic%20of%20abelian%20varieties | In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both in terms of res... |
https://en.wikipedia.org/wiki/Ramification%20%28mathematics%29 | In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. The term is also used from the opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing o... |
https://en.wikipedia.org/wiki/Generalized%20flag%20variety | In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieti... |
https://en.wikipedia.org/wiki/Finsler%20manifold | In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold where a (possibly asymmetric) Minkowski norm is provided on each tangent space , that enables one to define the length of any smooth curve as
Finsler manifolds are more general than Riemannian manifolds since the tan... |
https://en.wikipedia.org/wiki/Inverse%20scattering%20problem | In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. It is the inverse problem to the direct scattering problem, which is to determine how radiation or particles are scattered based on the... |
https://en.wikipedia.org/wiki/Pontryagin%20class | In mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology groups with degrees a multiple of four.
Definition
Given a real vector bundle E over M, its k-th Pontryagin class is defined as
where:
denotes the... |
https://en.wikipedia.org/wiki/Irreducible%20representation | In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of .
Every finite-dimensional unitary representation on a Hilb... |
https://en.wikipedia.org/wiki/Eisenstein%27s%20criterion | In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into the product of non-constant polynomials with rational coefficients.
This criterion is not applicable to all polynomial... |
https://en.wikipedia.org/wiki/Isospectral | In mathematics, two linear operators are called isospectral or cospectral if they have the same spectrum. Roughly speaking, they are supposed to have the same sets of eigenvalues, when those are counted with multiplicity.
The theory of isospectral operators is markedly different depending on whether the space is finit... |
https://en.wikipedia.org/wiki/Homothety | In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number called its ratio, which sends point to a point by the rule
for a fixed number .
Using position vectors:
.
In case of (Origin):
,
which is a uni... |
https://en.wikipedia.org/wiki/Spectral%20radius | In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectrum. The spectral radius is often denoted by .
Definition
Matrices
Let b... |
https://en.wikipedia.org/wiki/Cartan | Cartan may refer to:
Élie Cartan (1869–1951), French mathematician who worked with Lie groups
Henri Cartan (1904–2008), French mathematician who worked in algebraic topology, son of Élie Cartan
Anna Cartan (1878–1923), French mathematician and teacher, sister of Élie Cartan
Cartan (crater), a lunar crater named fo... |
https://en.wikipedia.org/wiki/Digital%20geometry | Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space.
Simply put, digitizing is replacing an object by a discrete set of its points. The images we see on the TV screen, the raster display of a computer, or in news... |
https://en.wikipedia.org/wiki/Discrete%20geometry | Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, an... |
https://en.wikipedia.org/wiki/Constructive%20solid%20geometry | Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, potentially generating visually complex objects by combi... |
https://en.wikipedia.org/wiki/Newport%20Pagnell | Newport Pagnell is a town and civil parish in the City of Milton Keynes, Buckinghamshire, England. The Office for National Statistics records Newport Pagnell as part of the Milton Keynes urban area.
The town is separated from the rest of the urban area by the M1 motorway, on which Newport Pagnell Services, the secon... |
https://en.wikipedia.org/wiki/Incidence%20%28geometry%29 | In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, , and a line, , sometimes denoted . If the pair is called a flag.... |
https://en.wikipedia.org/wiki/Mellin%20transform | In mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is closely connected to the theory of Dirichlet series, and is
often used in number theory, mathematical statistics, and the theory of asymptotic e... |
https://en.wikipedia.org/wiki/Edward%20Nelson | Edward Nelson (May 4, 1932 – September 10, 2014) was an American mathematician. He was professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematical logic, he was noted especially for his internal set theory, and views on ultr... |
https://en.wikipedia.org/wiki/Sierpi%C5%84ski%20space | In mathematics, the Sierpiński space (or the connected two-point set) is a finite topological space with two points, only one of which is closed.
It is the smallest example of a topological space which is neither trivial nor discrete. It is named after Wacław Sierpiński.
The Sierpiński space has important relations to... |
https://en.wikipedia.org/wiki/Separation%20of%20variables | In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
Ordinary differential equations (ODE... |
https://en.wikipedia.org/wiki/Outline%20of%20probability | Probability is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition whose truth is not certain. The proposition of interest is usually of the form "A specific event will occur." The attitude of mind is of the form "How certain is it that the ... |
https://en.wikipedia.org/wiki/Cantor%20distribution | The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.
This distribution has neither a probability density function nor a probability mass function, since although its cumulative distribution function is a continuous function, the distribution is not abso... |
https://en.wikipedia.org/wiki/Cubic | Cubic may refer to:
Science and mathematics
Cube (algebra), "cubic" measurement
Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex
Cubic crystal system, a crystal system where the unit cell is in the shape of a cube
Cubic function, a polynomial fu... |
https://en.wikipedia.org/wiki/Bewick%20Bridge | Bewick Bridge (1767, Linton, Cambridgeshire – 15 May 1833, Cherry Hinton) was an English vicar and mathematical author.
In 1786, he was admitted as a sizar to study mathematics Peterhouse, Cambridge University, where he graduated as senior wrangler and won the Smith's Prize in 1790.
In October 1790, he was ordained a... |
https://en.wikipedia.org/wiki/Zipf%E2%80%93Mandelbrot%20law | In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution. Also known as the Pareto–Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mande... |
https://en.wikipedia.org/wiki/Legendre%20transformation | In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex o... |
https://en.wikipedia.org/wiki/Fano%20plane | In finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. These points and lines cannot exist with this pattern of incidences in Euclidean geometry, but they ... |
https://en.wikipedia.org/wiki/PSL%282%2C7%29 | In mathematics, the projective special linear group , isomorphic to , is a finite simple group that has important applications in algebra, geometry, and number theory. It is the automorphism group of the Klein quartic as well as the symmetry group of the Fano plane. With 168 elements, PSL(2, 7) is the smallest nonabeli... |
https://en.wikipedia.org/wiki/K%C3%A4hler%20manifold | In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähl... |
https://en.wikipedia.org/wiki/Isolated%20point | In mathematics, a point is called an isolated point of a subset (in a topological space ) if is an element of and there exists a neighborhood of that does not contain any other points of . This is equivalent to saying that the singleton is an open set in the topological space (considered as a subspace of ). Anot... |
https://en.wikipedia.org/wiki/Flag%20%28linear%20algebra%29 | In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration):
The term flag is motivated by a particular example resembling a flag: the zero point, a line, and a plane... |
https://en.wikipedia.org/wiki/Klein%20quartic | In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus with the highest possible order automorphism group for this genus, namely order orientation-preserving automorphisms, and automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz ... |
https://en.wikipedia.org/wiki/Stark%E2%80%93Heegner%20theorem | In number theory, the Baker–Heegner–Stark theorem establishes the complete list of the quadratic imaginary number fields whose rings of integers are unique factorization domains. It solves a special case of Gauss's class number problem of determining the number of imaginary quadratic fields that have a given fixed clas... |
https://en.wikipedia.org/wiki/Fluxion%20%28disambiguation%29 | A fluxion is a mathematical concept, first formulated by Isaac Newton.
Fluxion may also refer to:
Newton's method for solving an equation
Method of Fluxions, Newton's book on differential calculus
An alternate spelling of fluxon, a quantum of magnetic flux
Fluxion (electronic musician), real name Konstantinos Sou... |
https://en.wikipedia.org/wiki/Full%20Circle | Full Circle may refer to:
Geometry
Full circle (unit), a unit of plane angle
Books
Full Circle, a 1962 novel by Grace Lumpkin
Full Circle, a 1982 memoir by Janet Baker
Full Circle (novel), a 1984 novel by Danielle Steel
Full Circle: The Moral Force of Unified Science, a 1972 book co-written and edited by Edward ... |
https://en.wikipedia.org/wiki/Parametric | Parametric may refer to:
Mathematics
Parametric equation, a representation of a curve through equations, as functions of a variable
Parametric statistics, a branch of statistics that assumes data has come from a type of probability distribution
Parametric derivative, a type of derivative in calculus
Parametric model,... |
https://en.wikipedia.org/wiki/Connection%20%28vector%20bundle%29 | In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for whic... |
https://en.wikipedia.org/wiki/Cobordism | In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifol... |
https://en.wikipedia.org/wiki/81%20%28number%29 | 81 (eighty-one) is the natural number following 80 and preceding 82.
In mathematics
81 is:
the square of 9 and the second fourth-power of a prime; 34.
with an aliquot sum of 40; within an aliquot sequence of three composite numbers (81,40,50,43,1,0) to the Prime in the 43-aliquot tree.
a perfect totient number lik... |
https://en.wikipedia.org/wiki/82%20%28number%29 | 82 (eighty-two) is the natural number following 81 and preceding 83.
In mathematics
82 is:
the twenty-third semiprime and the twelfth of the form (2.q).
with an aliquot sum of 44, within an aliquot sequence of four composite numbers (82,44,40,50,43,1,0) to the Prime in the 43-aliquot tree.
a companion Pell number.
... |
https://en.wikipedia.org/wiki/83%20%28number%29 | 83 (eighty-three) is the natural number following 82 and preceding 84.
In mathematics
83 is:
the sum of three consecutive primes (23 + 29 + 31).
the sum of five consecutive primes (11 + 13 + 17 + 19 + 23).
the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89.
a Sophie Germain... |
https://en.wikipedia.org/wiki/84%20%28number%29 | 84 (eighty-four) is the natural number following 83 and preceding 85.
In mathematics
84 is a semiperfect number, being thrice a perfect number, and the sum of the sixth pair of twin primes .
It is the third (or second) dodecahedral number, and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28,... |
https://en.wikipedia.org/wiki/85%20%28number%29 | 85 (eighty-five) is the natural number following 84 and preceding 86.
In mathematics
85 is:
the product of two prime numbers (5 and 17), and is therefore a semiprime of the form (5.q) where q is prime.
specifically, the 24th Semiprime, it being the fourth of the form (5.q).
together with 86 and 87, forms the sec... |
https://en.wikipedia.org/wiki/86%20%28number%29 | 86 (eighty-six) is the natural number following 85 and preceding 87.
In mathematics
86 is:
nontotient and a noncototient.
the 25th distinct semiprime and the 13th of the form (2.q).
together with 85 and 87, forms the middle semiprime in the 2nd cluster of three consecutive semiprimes; the first comprising 33, 34, ... |
https://en.wikipedia.org/wiki/87%20%28number%29 | 87 (eighty-seven) is the natural number following 86 and preceding 88.
In mathematics
87 is:
the sum of the squares of the first four primes (87 = 22 + 32 + 52 + 72).
the sum of the sums of the divisors of the first 10 positive integers.
the thirtieth semiprime, and the twenty-sixth distinct semiprime and the eigh... |
https://en.wikipedia.org/wiki/89%20%28number%29 | 89 (eighty-nine) is the natural number following 88 and preceding 90.
In mathematics
89 is:
the 24th prime number, following 83 and preceding 97.
a Chen prime.
a Pythagorean prime.
the smallest Sophie Germain prime to start a Cunningham chain of the first kind of six terms, {89, 179, 359, 719, 1439, 2879}.
an E... |
https://en.wikipedia.org/wiki/77%20%28number%29 | 77 (seventy-seven) is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.
In mathematics
77 is:
the 22nd discrete semiprime and the first of the (7.q) family, where q is a higher prime.
with a prime aliquot sum of 19 within an aliquot ... |
https://en.wikipedia.org/wiki/79%20%28number%29 | 79 (seventy-nine) is the natural number following 78 and preceding 80.
In mathematics
79 is:
An odd number.
The smallest number that can not be represented as a sum of fewer than 19 fourth powers.
The 22nd prime number (between and )
An isolated prime without a twin prime, as 77 and 81 are composite.
The smalle... |
https://en.wikipedia.org/wiki/Shiing-Shen%20Chern | Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mat... |
https://en.wikipedia.org/wiki/71%20%28number%29 | 71 (seventy-one) is the natural number following 70 and preceding 72.
In mathematics
Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime. It is the largest number which occurs as a prime factor of an order of a sporadic simple group, the large... |
https://en.wikipedia.org/wiki/73%20%28number%29 | 73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.
In mathematics
73 is the 21st prime number, and emirp with 37, the 12th prime number. It is also the eighth twin prime, with 71. It is the largest minimal ... |
https://en.wikipedia.org/wiki/74%20%28number%29 | 74 (seventy-four) is the natural number following 73 and preceding 75.
In mathematics
74 is:
the twenty-first distinct semiprime and the eleventh of the form (2.q), where q is a higher prime.
with an aliquot sum of 40, within an aliquot sequence of three composite numbers (74,40,50,43,1,0) to the Prime in the 43-al... |
https://en.wikipedia.org/wiki/75%20%28number%29 | 75 (seventy-five) is the natural number following 74 and preceding 76.
In mathematics
75 is a self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number.
It is a... |
https://en.wikipedia.org/wiki/32%20%28number%29 | 32 (thirty-two) is the natural number following 31 and preceding 33.
In mathematics
32 is the fifth power of two (), making it the first non-unitary fifth-power of the form p5 where p is prime. 32 is the totient summatory function over the first 10 integers, and the smallest number with exactly 7 solutions for . The... |
https://en.wikipedia.org/wiki/34%20%28number%29 | 34 (thirty-four) is the natural number following 33 and preceding 35.
In mathematics
34 is the ninth distinct semiprime, with four divisors including 1 and itself. Specifically, 34 is the ninth distinct semiprime, it being the sixth of the form . Its neighbors 33 and 35 are also distinct semiprimes with four divisors ... |
https://en.wikipedia.org/wiki/Value%20distribution%20theory%20of%20holomorphic%20functions | In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. The purpose of the theory is to provide quantitative measures of the number of times a function f(z) assumes a value a, as z grows in size, refining the Picard theorem on behaviour close to an essential singul... |
https://en.wikipedia.org/wiki/31%20%28number%29 | 31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.
In mathematics
31 is the 11th prime number. It is a superprime and a self prime (after 3, 5, and 7), as no integer added up to its base 10 digits results in 31. It is the third Mersenne prime of the form 2n − 1, and the eighth ... |
https://en.wikipedia.org/wiki/Degenerate%20conic | In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. This means that the defining equation is factorable over the complex numbers (or more generally over an algebraically closed field) as the product of two linear... |
https://en.wikipedia.org/wiki/Directrix | In mathematics, a directrix is a curve associated with a process generating a geometric object, such as:
Directrix (conic section)
Directrix (generatrix)
Directrix (rational normal scroll)
Other uses
Directrix is a spaceship in the Lensman series of novels by E. E. Smith.
Directrix is the name of a Dubai-based alte... |
https://en.wikipedia.org/wiki/Unitary | Unitary may refer to:
Mathematics
Unitary divisor
Unitary element
Unitary group
Unitary matrix
Unitary morphism
Unitary operator
Unitary transformation
Unitary representation
Unitarity (physics)
E-unitary inverse semigroup
Politics
Unitary authority
Unitary state
See also
Unital (disambiguation)
Unitar... |
https://en.wikipedia.org/wiki/Jo%C3%ABl-Fran%C3%A7ois%20Durand | Joël-François Durand (born 17 September 1954) is a French composer.
Biography
Born in Orléans, Durand studied mathematics, music education and piano in Paris, then composition with Brian Ferneyhough in Freiburg im Breisgau, Germany (1981–84), and at Stony Brook University, New York, with Arel and Semegen (1984–86) . B... |
https://en.wikipedia.org/wiki/Rigged%20Hilbert%20space | In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study spectral theory in the broad sense. They bring together the 'bound state' (... |
https://en.wikipedia.org/wiki/Index%20set | In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set may be indexed or labeled by means of the elements of a set , then is an index set. The indexing consists of a surjective function from onto , and the indexed collection is typically ca... |
https://en.wikipedia.org/wiki/Comparison%20of%20topologies | In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can be used for comparison of the topologies.
Definition
A topology on a set may be defined as the collection of subsets which are considered to be "open". An alternative ... |
https://en.wikipedia.org/wiki/Chern%E2%80%93Gauss%E2%80%93Bonnet%20theorem | In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the Euler–Poincaré characteristic (a topological invariant defined as the alternating sum of the Betti numbers of a topological space) of a closed even-dimensional Ri... |
https://en.wikipedia.org/wiki/Dirichlet%20series | In mathematics, a Dirichlet series is any series of the form
where s is complex, and is a complex sequence. It is a special case of general Dirichlet series.
Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet seri... |
https://en.wikipedia.org/wiki/Gift%20wrapping%20algorithm | In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points.
Planar case
In the two-dimensional case the algorithm is also known as Jarvis march, after R. A. Jarvis, who published it in 1973; it has O(nh) time complexity, where n is the number of points... |
https://en.wikipedia.org/wiki/Beth%20number | In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written , where is the second Hebrew letter (beth). The beth numbers are related to the aleph numbers (), but unless the generalized continuum hypothesis ... |
https://en.wikipedia.org/wiki/Illinois%20Mathematics%20and%20Science%20Academy | The Illinois Mathematics and Science Academy, or IMSA, is a three-year residential public secondary education institution in Aurora, Illinois, United States, with an enrollment of approximately 650 students.
Enrollment is generally offered to incoming sophomores, although younger students who have had the equivalent o... |
https://en.wikipedia.org/wiki/S%C3%A9minaire%20de%20G%C3%A9om%C3%A9trie%20Alg%C3%A9brique%20du%20Bois%20Marie | In mathematics, the Séminaire de Géométrie Algébrique du Bois Marie (SGA) was an influential seminar run by Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the IHÉS near Paris. (The name came from the small wood on th... |
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