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https://en.wikipedia.org/wiki/Applications%20of%20randomness | Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized controlled trials helps scientists to test hypotheses, and random numbers or pseudorandom numbers help video games such as video poker.
These uses have different levels o... |
https://en.wikipedia.org/wiki/Eric%20Hehner | Eric "Rick" C. R. Hehner (born 16 September 1947) is a Canadian computer scientist. He was born in Ottawa. He studied mathematics and physics at Carleton University, graduating with a Bachelor of Science (B.Sc.) in 1969. He studied computer science at the University of Toronto, graduating with a Master of Science (M.Sc... |
https://en.wikipedia.org/wiki/Prime%20signature | In mathematics, the prime signature of a number is the multiset of (nonzero) exponents of its prime factorization. The prime signature of a number having prime factorization is the multiset .
For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the product... |
https://en.wikipedia.org/wiki/Robin%20Wilson%20%28mathematician%29 | Robin James Wilson (born 5 December 1943) is an emeritus professor in the Department of Mathematics at the Open University, having previously been Head of the Pure Mathematics Department and Dean of the Faculty. He was a stipendiary lecturer at Pembroke College, Oxford and, , Gresham Professor of Geometry at Gresham Co... |
https://en.wikipedia.org/wiki/Primefree%20sequence | In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. More specifically, it usually means a sequence defined by the same recurrence relation as the Fibonacci numbers, but with different initial conditions causing all members of the sequence to be composite numbers that ... |
https://en.wikipedia.org/wiki/Rectified%20600-cell | In geometry, the rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge has two octahedra and one icosahedron. Each vertex has five octahedra and two icosahedra. In total it has 3600 triangle faces, 3600 edges, and 720 vertices... |
https://en.wikipedia.org/wiki/Computational%20epidemiology | Computational epidemiology is a multidisciplinary field that uses techniques from computer science, mathematics, geographic information science and public health to better understand issues central to epidemiology such as the spread of diseases or the effectiveness of a public health intervention. Computational epidemi... |
https://en.wikipedia.org/wiki/Rectified%205-cell | In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron and two octahedra. Each vertex has two tetrahedra and three octahedra. In total it has 30 triangle faces, 30 edges, and 10 vertices. Each vertex is s... |
https://en.wikipedia.org/wiki/Evan%20Esar | Evan Esar (1899–1995) was an American humorist who wrote Esar's Comic Dictionary in 1943, Humorous English in 1961, and 20,000 Quips and Quotes in 1968.
He is known for quotes like "Statistics — the only science that enables different experts using the same figures to draw different conclusions." He also wrote The Le... |
https://en.wikipedia.org/wiki/Machin-like%20formula | In mathematics, Machin-like formulae are a popular technique for computing (the ratio of the circumference to the diameter of a circle) to a large number of digits. They are generalizations of John Machin's formula from 1706:
which he used to compute to 100 decimal places.
Machin-like formulas have the form
where... |
https://en.wikipedia.org/wiki/Dudeney%20number | In number theory, a Dudeney number in a given number base is a natural number equal to the perfect cube of another natural number such that the digit sum of the first natural number is equal to the second. The name derives from Henry Dudeney, who noted the existence of these numbers in one of his puzzles, Root Extrac... |
https://en.wikipedia.org/wiki/Multivector | In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra of a vector space . This algebra is graded, associative and alternating, and consists of linear combinations of simple -vectors (also known as decomposable -vectors or -blades) of the form
where a... |
https://en.wikipedia.org/wiki/Primary%20field | In theoretical physics, a primary field, also called a primary operator, or simply a primary, is a local operator in a conformal field theory which is annihilated by the part of the conformal algebra consisting of the lowering generators. From the representation theory point of view, a primary is the lowest dimension o... |
https://en.wikipedia.org/wiki/Resummation | In mathematics and theoretical physics, resummation is a procedure to obtain a finite result from a divergent sum (series) of functions. Resummation involves a definition of another (convergent) function in which the individual terms defining the original function are re-scaled, and an integral transformation of this n... |
https://en.wikipedia.org/wiki/2000%20Costa%20Rican%20census | The 2000 Costa Rican census was undertaken by the National Institute of Statistics and Census (Instituto Nacional de Estadística y Censos (INEC)).
Description
According to this census, Costa Rica had 3,810,179 inhabitants in 2000, a population density of 74.6/km², and 59% of the people lived in urban areas.
Results b... |
https://en.wikipedia.org/wiki/Resolvent | In mathematics, resolvent meaning "that which resolves" may refer to:
Resolvent formalism in operator theory
Resolvent set in operator theory, the set of points where an operator is "well-behaved"
in probability theory
Resolvent (Galois theory) of an equation for a permutation group, in particular:
Resolvent quad... |
https://en.wikipedia.org/wiki/INEC | INEC may refer to:
Ilocos Norte Electric Cooperative
Independent National Electoral Commission, Nigeria
National Institute of Statistics and Census (disambiguation) (Portuguese and Spanish abbreviation: INEC) |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20and%20Census%20of%20Costa%20Rica | The National Institute of Statistics and Census of Costa Rica (Instituto Nacional de Estadística y Censos de Costa Rica, or INEC, in Spanish) is the governmental institution entrusted with the running of censuses and official surveys in the country. Its main office is located in San José.
History
INEC was first calle... |
https://en.wikipedia.org/wiki/Napoleon%27s%20theorem | In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle.
The triangle thus formed is called the inner or outer Napoleon tr... |
https://en.wikipedia.org/wiki/Tensor%20product%20of%20Hilbert%20spaces | In mathematics, and in particular functional analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert spaces is another Hilbert space. Roughly speaking, the tensor product is the metric space completion of the ordinary... |
https://en.wikipedia.org/wiki/Glide%20plane | In geometry and crystallography, a glide plane (or transflection) is a symmetry operation describing how a reflection in a plane, followed by a translation parallel with that plane, may leave the crystal unchanged.
Glide planes are noted in the Hermann–Mauguin notation by a, b or c, depending on which axis the glide i... |
https://en.wikipedia.org/wiki/Matrix%20Template%20Library | The Matrix Template Library (MTL) is a linear algebra library for C++ programs.
The MTL uses template programming, which considerably reduces the code length. All matrices and vectors are available in all classical numerical formats: float, double, complex<float> or complex<double>.
Furthermore, generic programming a... |
https://en.wikipedia.org/wiki/Laning%20and%20Zierler%20system | The Laning and Zierler system (sometimes called "George" by its users) was the first operating algebraic compiler, that is, a system capable of accepting mathematical formulas in algebraic notation and producing equivalent machine code (the term compiler had not yet been invented and the system was referred to as "an i... |
https://en.wikipedia.org/wiki/GeoGebra | GeoGebra (a portmanteau of geometry and algebra) is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops (Windows, macOS and Linux), t... |
https://en.wikipedia.org/wiki/Constrained%20geometry%20complex | In organometallic chemistry, a "constrained geometry complex" (CGC) is a kind of catalyst used for the production of polyolefins such as polyethylene and polypropylene. The catalyst was one of the first major departures from metallocene-based catalysts and ushered in much innovation in the development of new plastics.
... |
https://en.wikipedia.org/wiki/Cantor%27s%20paradox | In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number. In informal terms, the paradox is that the collection of all possible "infinite sizes" is not only infinite, but so infinitely large that its own infinite size ca... |
https://en.wikipedia.org/wiki/Fr%C3%A9chet%20derivative | In mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued function of multiple real variables, and to define the functional derivative u... |
https://en.wikipedia.org/wiki/Psychographics | Psychographics is defined as "market research or statistics classifying population groups according to psychological variables" The term psychographics is derived from the words “psychological” and “demographics” Two common approaches to psychographics include analysis of consumers' activities, interests, and opinions ... |
https://en.wikipedia.org/wiki/Bicorn | In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation
It has two cusps and is symmetric about the y-axis.
History
In 1864, James Joseph Sylvester studied the curve
in connection with the classification of quintic equations; ... |
https://en.wikipedia.org/wiki/Bullet-nose%20curve | In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation
The bullet curve has three double points in the real projective plane, at and , and , and and , and is therefore a unicursal (rational) curve of genus zero.
If
then
are the two branches of the bu... |
https://en.wikipedia.org/wiki/Cl%C3%A9lie | In mathematics, a Clélie or Clelia curve is a curve on a sphere with the property:
If the surface of a sphere is described as usual by the longitude (angle ) and the colatitude (angle ) then
.
The curve was named by Luigi Guido Grandi after Clelia Borromeo.
Viviani's curve and spherical spirals are special cases ... |
https://en.wikipedia.org/wiki/Cochleoid | In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation
the Cartesian equation
or the parametric equations
The cochleoid is the inverse curve of Hippias' quadratrix.
Notes
References
Cochleoid in the Encyclopedia of Mathematics
Liliana Luca, Iulian P... |
https://en.wikipedia.org/wiki/Folium%20of%20Descartes | In geometry, the folium of Descartes (; named for René Descartes) is an algebraic curve defined by the implicit equation
History
The curve was first proposed and studied by René Descartes in 1638. Its claim to fame lies in an incident in the development of calculus. Descartes challenged Pierre de Fermat to find the t... |
https://en.wikipedia.org/wiki/Hessian%20form%20of%20an%20elliptic%20curve | In geometry, the Hessian curve is a plane curve similar to folium of Descartes. It is named after the German mathematician Otto Hesse.
This curve was suggested for application in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory than arithmetic in standard Weie... |
https://en.wikipedia.org/wiki/Hippopede | In geometry, a hippopede () is a plane curve determined by an equation of the form
where it is assumed that and since the remaining cases either reduce to a single point or can be put into the given form with a rotation. Hippopedes are bicircular, rational, algebraic curves of degree 4 and symmetric with respect to ... |
https://en.wikipedia.org/wiki/Strophoid | In geometry, a strophoid is a curve generated from a given curve and points (the fixed point) and (the pole) as follows: Let be a variable line passing through and intersecting at . Now let and be the two points on whose distance from is the same as the distance from to (i.e. ). The locus of such points an... |
https://en.wikipedia.org/wiki/Trident%20curve | In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula:
Trident curves are cubic plane curves with an ordinary double point in the real projective plane at x = 0, y = 1, z = 0; if we substitute x = and y = into the equation of the... |
https://en.wikipedia.org/wiki/Trochoid | In geometry, a trochoid () is a roulette curve formed by a circle rolling along a line. It is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line. If the point is on the circle, the trochoid is called common (also known as a cycl... |
https://en.wikipedia.org/wiki/Viviani%27s%20curve | In mathematics, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani. It is the intersection of a sphere with a cylinder that is tangent to the sphere and passes through two poles (a diameter) of the sphere (see diagram). Before Viv... |
https://en.wikipedia.org/wiki/Watt%27s%20curve | In mathematics, Watt's curve is a tricircular plane algebraic curve of degree six. It is generated by two circles of radius b with centers distance 2a apart (taken to be at (±a, 0)). A line segment of length 2c attaches to a point on each of the circles, and the midpoint of the line segment traces out the Watt curve as... |
https://en.wikipedia.org/wiki/Trisectrix%20of%20Maclaurin | In algebraic geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. It can be defined as locus of the point of intersection of two lines, each rotating at a uniform rate about separate points, so that the ratio of the rates of rotati... |
https://en.wikipedia.org/wiki/Primitive%20permutation%20group | In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into |X| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition... |
https://en.wikipedia.org/wiki/Osculating%20plane | In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point. The word osculate is from the Latin osculatus which is a past participle of osculari, meaning ... |
https://en.wikipedia.org/wiki/Hom%20functor | In mathematics, specifically in category theory, hom-sets (i.e. sets of morphisms between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous applications in category theory and other branches of mathematics.
Formal definition
Let C be a locally sm... |
https://en.wikipedia.org/wiki/Mathematical%20Association | The Mathematical Association is a professional society concerned with mathematics education in the UK.
History
It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in 1894. It was the first teachers' subject organisation formed in England. In... |
https://en.wikipedia.org/wiki/Naum%20Idelson | Naum Ilyich Idelson () (March 1(13), 1885, Saint Petersburg - July 14, 1951, Leningrad) was a Soviet theoretical astronomer and expert in history of physics and mathematics.
The crater Idelson on the Moon is named after him.
References
Further reading
Russian astronomers
1885 births
1951 deaths
Scientists from Sain... |
https://en.wikipedia.org/wiki/Quadrifolium | The quadrifolium (also known as four-leaved clover) is a type of rose curve with an angular frequency of 2. It has the polar equation:
with corresponding algebraic equation
Rotated counter-clockwise by 45°, this becomes
with corresponding algebraic equation
In either form, it is a plane algebraic curve of genus zer... |
https://en.wikipedia.org/wiki/Quasi-invariant%20measure | In mathematics, a quasi-invariant measure μ with respect to a transformation T, from a measure space X to itself, is a measure which, roughly speaking, is multiplied by a numerical function of T. An important class of examples occurs when X is a smooth manifold M, T is a diffeomorphism of M, and μ is any measure that l... |
https://en.wikipedia.org/wiki/Conchospiral | In mathematics, a conchospiral a specific type of space spiral on the surface of a cone (a conical spiral), whose floor projection is a logarithmic spiral.
Conchospirals are used in biology for modelling snail shells, and flight paths of insects and in electrical engineering for the construction of antennas.
Paramete... |
https://en.wikipedia.org/wiki/Crossed%20product | In mathematics, and more specifically in the theory of von Neumann algebras, a crossed product
is a basic method of constructing a new von Neumann algebra from
a von Neumann algebra acted on by a group. It is related to
the semidirect product construction for groups. (Roughly speaking, crossed product is the expected... |
https://en.wikipedia.org/wiki/Stability%20%28probability%29 | In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters. The distributions of random variables having this property are said to be "stable distributions". Results availa... |
https://en.wikipedia.org/wiki/Multiple%20integral | In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, or . Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables ove... |
https://en.wikipedia.org/wiki/Oricon | , established in 1999, is the holding company at the head of a Japanese corporate group that supplies statistics and information on music and the music industry in Japan and Western music. It started as, which was founded by Sōkō Koike in November 1967 and became known for its music charts. Oricon Inc. was originally s... |
https://en.wikipedia.org/wiki/Combinatorial%20design | Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as ... |
https://en.wikipedia.org/wiki/Five%20Equations%20That%20Changed%20the%20World | Five Equations That Changed the World: The Power and Poetry of Mathematics is a book by Michael Guillen, published in 1995.
It is divided into five chapters that talk about five different equations in physics and the people who have developed them.
The scientists and their equations are:
Isaac Newton (Universal Law o... |
https://en.wikipedia.org/wiki/State%20of%20Origin%20results%20and%20statistics | State of Origin results and statistics have been accumulating since the 1980 State of Origin game. Every game played under State of Origin selection rules, including the additional 1987 exhibition match and the matches played between New South Wales and Queensland for the Super League Tri-series are detailed below unle... |
https://en.wikipedia.org/wiki/The%20Geometer%27s%20Sketchpad | The Geometer's Sketchpad is a commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created as part of the NSF-funded Visual Geometry Project led by Eugene Klotz and Doris Schattschneider from 1986 to 1991 at Swarthmore College. Ni... |
https://en.wikipedia.org/wiki/Mary%20Everest%20Boole | Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as Philosophy and Fun of Algebra, and as the wife of fellow mathematician George Boole. Her progressive ideas on educat... |
https://en.wikipedia.org/wiki/Dirichlet%27s%20approximation%20theorem | In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers and , with , there exist integers and such that and
Here represents the integer part of .
This is a fundamental result in Diophantine approximation, showing that any ... |
https://en.wikipedia.org/wiki/Artin%20L-function | In mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced in 1923 by Emil Artin, in connection with his research into class field theory. Their fundamental properties, in particular the Artin conjecture described below,... |
https://en.wikipedia.org/wiki/Levi%20decomposition | In Lie theory and representation theory, the Levi decomposition, conjectured by Wilhelm Killing and Élie Cartan and proved by , states that any finite-dimensional real{Change real Lie algebra to a Lie algebra over a field of characterisitic 0} Lie algebra g is the semidirect product of a solvable ideal and a semisimp... |
https://en.wikipedia.org/wiki/Quasinormal%20subgroup | In mathematics, in the field of group theory, a quasinormal subgroup, or permutable subgroup, is a subgroup of a group that commutes (permutes) with every other subgroup with respect to the product of subgroups. The term quasinormal subgroup was introduced by Øystein Ore in 1937.
Two subgroups are said to permute (or ... |
https://en.wikipedia.org/wiki/Subnormal%20subgroup | In mathematics, in the field of group theory, a subgroup H of a given group G is a subnormal subgroup of G if there is a finite chain of subgroups of the group, each one normal in the next, beginning at H and ending at G.
In notation, is -subnormal in if there are subgroups
of such that is normal in for each .
... |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20and%20Census%20of%20Argentina | The National Institute of Statistics and Censuses (; INDEC) is an Argentine decentralized public body that operates within the Ministry of Economy, which exercises the direction of all official statistical activities carried out in the country.
In February 2013, the International Monetary Fund censured Argentina for f... |
https://en.wikipedia.org/wiki/Refinement%20calculus | The refinement calculus is a formalized approach to stepwise refinement for program construction. The required behaviour of the final executable program is specified as an abstract and perhaps non-executable "program", which is then refined by a series of correctness-preserving transformations into an efficiently execu... |
https://en.wikipedia.org/wiki/Ralph-Johan%20Back | Ralph-Johan Back is a Finnish computer scientist. Back originated the refinement calculus, an important approach to the formal development of programs using stepwise refinement, in his 1978 PhD thesis at the University of Helsinki, On the Correctness of Refinement Steps in Program Development. He has undertaken much su... |
https://en.wikipedia.org/wiki/Degree%20of%20an%20algebraic%20variety | In mathematics, the degree of an affine or projective variety of dimension is the number of intersection points of the variety
with hyperplanes in general position. For an algebraic set, the intersection points must be counted with their intersection multiplicity, because of the possibility of multiple components. Fo... |
https://en.wikipedia.org/wiki/Quaternion%20algebra | In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, is isomorphic to the 2 × 2 matrix al... |
https://en.wikipedia.org/wiki/Dense%20graph | In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often ... |
https://en.wikipedia.org/wiki/Extreme | Extreme may refer to:
Science and mathematics
Mathematics
Extreme point, a point in a convex set which does not lie in any open line segment joining two points in the set
Maxima and minima, extremes on a mathematical function
Science
Extremophile, an organism which thrives in or requires "extreme"
Extremes on Earth... |
https://en.wikipedia.org/wiki/Spin%20tensor | In mathematics, mathematical physics, and theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in
general relativity and special relativity, as well as quantum mechanics, relativistic quantum mechanics, and quantum field th... |
https://en.wikipedia.org/wiki/Subfactor | In the theory of von Neumann algebras, a subfactor of a factor is a subalgebra that is a factor and contains . The theory of subfactors led to the discovery of the
Jones polynomial in knot theory.
Index of a subfactor
Usually is taken to be a factor of type , so that it has a finite trace.
In this case every Hilbe... |
https://en.wikipedia.org/wiki/Arunas%20Rudvalis | Arunas Rudvalis (born June 8, 1945) is an Emeritus Professor of Mathematics at the University of Massachusetts Amherst. He is best known for the Rudvalis group.
Rudvalis went to the Harvey Mudd College and received his Ph.D. degree in Dartmouth College under direction of Ernst Snapper.
External links
Arunas Rudvalis... |
https://en.wikipedia.org/wiki/Ergodic%20flow | In mathematics, ergodic flows occur in geometry, through the geodesic and horocycle flows of closed hyperbolic surfaces. Both of these examples have been understood in terms of the theory of unitary representations of locally compact groups: if Γ is the fundamental group of a closed surface, regarded as a discrete subg... |
https://en.wikipedia.org/wiki/Rigidity%20theory | Rigidity theory may refer to
Study of the concept of rigidity (mathematics)
Mathematical theory of structural rigidity
Rigidity theory (physics), or topological constraints theory, describes or predicts the mechanical properties of glass |
https://en.wikipedia.org/wiki/Mostow%20rigidity%20theorem | In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group and hence unique. The theorem was proven for closed manifo... |
https://en.wikipedia.org/wiki/Lefschetz%20pencil | In mathematics, a Lefschetz pencil is a construction in algebraic geometry considered by Solomon Lefschetz, used to analyse the algebraic topology of an algebraic variety V.
Description
A pencil is a particular kind of linear system of divisors on V, namely a one-parameter family, parametrised by the projective line.... |
https://en.wikipedia.org/wiki/Rational%20mapping | In mathematics, in particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties. This article uses the convention that varieties are irreducible.
Definition
Formal definition
Formally, a rational map between two varieties is an equivalen... |
https://en.wikipedia.org/wiki/Complex%20dimension | In mathematics, complex dimension usually refers to the dimension of a complex manifold or a complex algebraic variety. These are spaces in which the local neighborhoods of points (or of non-singular points in the case of a variety) are modeled on a Cartesian product of the form for some , and the complex dimension is... |
https://en.wikipedia.org/wiki/Constant%20sheaf | In mathematics, the constant sheaf on a topological space associated to a set is a sheaf of sets on whose stalks are all equal to . It is denoted by or . The constant presheaf with value is the presheaf that assigns to each open subset of the value , and all of whose restriction maps are the identity map . The c... |
https://en.wikipedia.org/wiki/Function%20field | Function field may refer to:
Function field of an algebraic variety
Function field (scheme theory)
Algebraic function field
Function field sieve
Function field analogy |
https://en.wikipedia.org/wiki/Function%20field%20of%20an%20algebraic%20variety | In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebra... |
https://en.wikipedia.org/wiki/Noetherian%20scheme | In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets , noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus, a scheme is noetherian if and only if it is locally noetherian and quasi-compact. As wit... |
https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Bendixson%20theorem | In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
Theorem
Given a differentiable real dynamical system defined on an open subset of the plane, every non-empty compact ω-limit set of an orbit, whic... |
https://en.wikipedia.org/wiki/Mixed%20boundary%20condition | In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary v... |
https://en.wikipedia.org/wiki/Port%20Saunders | Port Saunders is a community of 674 located in Newfoundland and Labrador, Canada.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Port Saunders had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a popul... |
https://en.wikipedia.org/wiki/Monomial%20representation | In the mathematical fields of representation theory and group theory, a linear representation (rho) of a group is a monomial representation if there is a finite-index subgroup and a one-dimensional linear representation of , such that is equivalent to the induced representation .
Alternatively, one may define it ... |
https://en.wikipedia.org/wiki/Schwartz%E2%80%93Zippel%20lemma | In mathematics, the Schwartz–Zippel lemma (also called the DeMillo–Lipton–Schwartz–Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determining whether a given multivariate polynomial is the
0-polynomial (or identically equal to 0). It was discovered independent... |
https://en.wikipedia.org/wiki/Paul%20Sally | Paul Joseph Sally, Jr. (January 29, 1933 – December 30, 2013) was a professor of mathematics at the University of Chicago, where he was the director of undergraduate studies for 30 years. His research areas were p-adic analysis and representation theory.
He created several programs to improve the preparation of school... |
https://en.wikipedia.org/wiki/Lawrence%20C.%20Evans | Lawrence Craig Evans (born November 1, 1949) is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
His research is in the field of nonlinear partial differential equations, primarily elliptic equations. In 2004, he shared the Leroy P. Steele Prize for Seminal Contribution... |
https://en.wikipedia.org/wiki/Topple%20rate | Topple rate is measure of how often the leading companies in a particular industry changes. It is defined as the probability that a firm in the industry, already in the top 20% in revenue, will drop out of this revenue leadership position within the next five years. The topple rate is one method of measuring overall co... |
https://en.wikipedia.org/wiki/George%20Alfred%20Barnard | George Alfred Barnard (23 September 1915 – 9 August 2002) was a British statistician known particularly for his work on the foundations of statistics and on quality control.
Early life and education
George Barnard was born in Walthamstow, London. His father was a cabinet maker and his mother had been a domestic servan... |
https://en.wikipedia.org/wiki/Madhava%20of%20Sangamagrama | Mādhava of Sangamagrāma (Mādhavan) () was an Indian mathematician and astronomer who is considered as the founder of the Kerala school of astronomy and mathematics. One of the greatest mathematician-astronomers of the Late Middle Ages, Madhava made pioneering contributions to the study of infinite series, calculus, tri... |
https://en.wikipedia.org/wiki/Jye%E1%B9%A3%E1%B9%ADhadeva | Jyeṣṭhadeva (Malayalam: ജ്യേഷ്ഠദേവൻ) () was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama (). He is best known as the author of Yuktibhāṣā, a commentary in Malayalam of Tantrasamgraha by Nilakantha Somayaji (1444–1544). In Yuktibhāṣā, Jyeṣṭhadeva had gi... |
https://en.wikipedia.org/wiki/East%20Wales | East Wales () is either a ITL 3 statistical region of Wales or generally a region encompassing the easternmost parts of the country.
Usage
The UK Office for National Statistics has as its highest level sub-division, East Wales, covering the whole east side of the country. It is defined as Powys, Flintshire and Wrexham... |
https://en.wikipedia.org/wiki/Circle%20bundle | In mathematics, a circle bundle is a fiber bundle where the fiber is the circle .
Oriented circle bundles are also known as principal U(1)-bundles, or equivalently, as principal SO(2)-bundles. In physics, circle bundles are the natural geometric setting for electromagnetism. A circle bundle is a special case of a sphe... |
https://en.wikipedia.org/wiki/Y-homeomorphism | In mathematics, the y-homeomorphism, or crosscap slide, is a special type of auto-homeomorphism in non-orientable surfaces.
It can be constructed by sliding a Möbius band included on the surface
around an essential 1-sided closed curve until the original position; thus it is necessary that the surfaces have genus gre... |
https://en.wikipedia.org/wiki/Weaire%E2%80%93Phelan%20structure | In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum sur... |
https://en.wikipedia.org/wiki/Andr%C3%A9%20Hunebelle | André Hunebelle (1 September 1896 – 27 November 1985) was a French maître verrier (master glassmaker) and film director.
Master Glass Artist
After attending polytechnic school for mathematics, he became a decorator, a designer, and then a master glass maker in the mid-1920s (first recorded exhibition PARIS 1927 includ... |
https://en.wikipedia.org/wiki/Brun%27s%20theorem | In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant, usually denoted by B2 . Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sie... |
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