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https://en.wikipedia.org/wiki/Descartes%27%20theorem | In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who st... |
https://en.wikipedia.org/wiki/Medical%20astrology | Medical astrology (traditionally known as iatromathematics) is an ancient applied branch of astrology based mostly on melothesia (Gr. μελοθεσία), the association of various parts of the body, diseases, and drugs with the nature of the sun, moon, planets, and the twelve astrological signs. The underlying basis for medic... |
https://en.wikipedia.org/wiki/Similarity | Similarity may refer to:
In mathematics and computing
Similarity (geometry), the property of sharing the same shape
Matrix similarity, a relation between matrices
Similarity measure, a function that quantifies the similarity of two objects
Cosine similarity, which uses the angle between vectors
String metric, als... |
https://en.wikipedia.org/wiki/Companion%20matrix | In linear algebra, the Frobenius companion matrix of the monic polynomial
is the square matrix defined as
Some authors use the transpose of this matrix, , which is more convenient for some purposes such as linear recurrence relations (see below).
is defined from the coefficients of , while the characteristic poly... |
https://en.wikipedia.org/wiki/Seki%20Takakazu | , also known as , was a Japanese mathematician and author of the Edo period.
Seki laid foundations for the subsequent development of Japanese mathematics, known as wasan. He has been described as "Japan's Newton".
He created a new algebraic notation system and, motivated by astronomical computations, did work on infi... |
https://en.wikipedia.org/wiki/Ankeny%E2%80%93Artin%E2%80%93Chowla%20congruence | In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is
with integers t and u, it expresses in another form
for any prime number... |
https://en.wikipedia.org/wiki/List%20of%20municipalities%20of%20Sweden%20by%20wealth | This is a list of the municipalities of Sweden by average net wealth of its inhabitants in 2007 according to Statistics Sweden.
References
Municipalities, wealth
Municipalities, wealth
Sweden, Municipalities, wealth |
https://en.wikipedia.org/wiki/Hyperreal | Hyperreal may refer to:
Hyperreal numbers, an extension of the real numbers in mathematics that are used in non-standard analysis
Hyperreal.org, a rave culture website based in San Francisco, US
Hyperreality, a term used in semiotics and postmodern philosophy
Hyperrealism (visual arts), a school of painting
Hyper... |
https://en.wikipedia.org/wiki/Spectral%20graph%20theory | In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix.
The adjacency matrix of a simple undirected graph is a real symmetric ... |
https://en.wikipedia.org/wiki/List%20of%20multivariable%20calculus%20topics | This is a list of multivariable calculus topics. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics.
Closed and exact differential forms
Contact (mathematics)
Contour integral
Contour line
Critical point (mathematics)
Curl (mathematics)
Current (mathematics)
Curvatu... |
https://en.wikipedia.org/wiki/Chebotarev%27s%20density%20theorem | Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns... |
https://en.wikipedia.org/wiki/List%20of%20commutative%20algebra%20topics | Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ... |
https://en.wikipedia.org/wiki/Prediction%20interval | In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.
Prediction intervals are used in both f... |
https://en.wikipedia.org/wiki/Equation%20solving | In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution... |
https://en.wikipedia.org/wiki/Complex%20multiplication | In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer l... |
https://en.wikipedia.org/wiki/Quillen%E2%80%93Suslin%20theorem | The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between free modules and projective modules over polynomial rings. In the geometric setting it is a statement about the triviality of vector bundles on affine space.
The theo... |
https://en.wikipedia.org/wiki/Reduced%20ring | In ring theory, a branch of mathematics, a ring is called a reduced ring if it has no non-zero nilpotent elements. Equivalently, a ring is reduced if it has no non-zero elements with square zero, that is, x2 = 0 implies x = 0. A commutative algebra over a commutative ring is called a reduced algebra if its underlying ... |
https://en.wikipedia.org/wiki/Duality%20%28projective%20geometry%29 | In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language () and the other a more functional approach thr... |
https://en.wikipedia.org/wiki/Subobject | In category theory, a branch of mathematics, a subobject is, roughly speaking, an object that sits inside another object in the same category. The notion is a generalization of concepts such as subsets from set theory, subgroups from group theory, and subspaces from topology. Since the detailed structure of objects i... |
https://en.wikipedia.org/wiki/Frattini%20subgroup | In mathematics, particularly in group theory, the Frattini subgroup of a group is the intersection of all maximal subgroups of . For the case that has no maximal subgroups, for example the trivial group {e} or a Prüfer group, it is defined by . It is analogous to the Jacobson radical in the theory of rings, and intu... |
https://en.wikipedia.org/wiki/Poincar%C3%A9%20duality | In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then the kth cohomology group of M is isomorphic to the th ho... |
https://en.wikipedia.org/wiki/Random%20field | In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as ). That is, it is a function that takes on a random value at each point (or some other domain). It is also sometimes thought of as a synonym for a stochastic process with some restriction... |
https://en.wikipedia.org/wiki/Category%20of%20preordered%20sets | In mathematics, the category Ord has preordered sets as objects and order-preserving functions as morphisms. This is a category because the composition of two order-preserving functions is order preserving and the identity map is order preserving.
The monomorphisms in Ord are the injective order-preserving functions.
... |
https://en.wikipedia.org/wiki/Champernowne%20constant | In mathematics, the Champernowne constant is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933.
For base 10, the number is defined by concatenating representations of successi... |
https://en.wikipedia.org/wiki/Stoneham%20number | In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G. Stoneham (1920–1996). For coprime numbers b, c > 1, the Stoneham number αb,c is defined as
It was shown by Stoneham in 1973 that αb,c is b-normal whenever c is an odd prime and b is a primitive root of c2. In... |
https://en.wikipedia.org/wiki/Public%20health%20journal | A public health journal is a scientific journal devoted to the field of public health, including epidemiology, biostatistics, and health care (including medicine, nursing and related fields). Public health journals, like most scientific journals, are peer-reviewed. Public health journals are commonly published by healt... |
https://en.wikipedia.org/wiki/Alexandrov%20topology | In topology, an Alexandrov topology is a topology in which the intersection of every family of open sets is open. It is an axiom of topology that the intersection of every finite family of open sets is open; in Alexandrov topologies the finite restriction is dropped.
A set together with an Alexandrov topology is known... |
https://en.wikipedia.org/wiki/Borel%20regular%20measure | In mathematics, an outer measure μ on n-dimensional Euclidean space Rn is called a Borel regular measure if the following two conditions hold:
Every Borel set B ⊆ Rn is μ-measurable in the sense of Carathéodory's criterion: for every A ⊆ Rn,
For every set A ⊆ Rn there exists a Borel set B ⊆ Rn such that A ⊆ B and ... |
https://en.wikipedia.org/wiki/Artinian%20module | In mathematics, specifically abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules. They are for modules what Artinian rings are for rings, and a ring is Artinian if and only if it is an Artinian module over itself (with left or right multiplication). ... |
https://en.wikipedia.org/wiki/Square%20pyramidal%20number | In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming r... |
https://en.wikipedia.org/wiki/Specialization%20%28pre%29order | In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the ... |
https://en.wikipedia.org/wiki/Binomial%20%28polynomial%29 | In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of a sparse polynomial after the monomials.
Definition
A binomial is a polynomial which is the sum of two monomials. A binomial in a single indeterminate (also known as a univariate binomial) can b... |
https://en.wikipedia.org/wiki/Krull%27s%20principal%20ideal%20theorem | In commutative algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a commutative Noetherian ring. The theorem is sometimes referred to by its German name, Krulls Hauptidealsatz (from ("Principal") + + ("theorem")).
Precisely, if R ... |
https://en.wikipedia.org/wiki/Noetherian%20module | In abstract algebra, a Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially ordered by inclusion.
Historically, Hilbert was the first mathematician to work with the properties of finitely generated submodules. He proved an important theorem kn... |
https://en.wikipedia.org/wiki/Information%20content | In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable. It can be thought of as an alternative way of expressing probability, much like odds or log-odds, but which has par... |
https://en.wikipedia.org/wiki/Locus%20%28mathematics%29 | In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
The set of the points that satisfy some property is often called the locus of a point ... |
https://en.wikipedia.org/wiki/Flat%20morphism | In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e.,
is a flat map for all P in X. A map of rings is called flat if it is a homomorphism that makes B a flat A-m... |
https://en.wikipedia.org/wiki/Flat%20map | In differential geometry, flat map is a mapping that converts vectors into corresponding 1-forms, given a non-degenerate (0,2)-tensor.
See also
Flat morphism
Sharp map, the mapping that converts 1-forms into corresponding vectors
bind, another name for flatMap in functional programming
Differential geometry |
https://en.wikipedia.org/wiki/Coaxial | In geometry, coaxial means that several three-dimensional linear or planar forms share a common axis. The two-dimensional analog is concentric.
Common examples:
A coaxial cable is a three-dimensional linear structure. It has a wire conductor in the centre (D), a circumferential outer conductor (B), and an insulating ... |
https://en.wikipedia.org/wiki/Logistic%20distribution | In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurto... |
https://en.wikipedia.org/wiki/Florian%20Cajori | Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics.
Biography
Florian Cajori was born in Zillis, Switzerland, as the son of Georg Cajori and Catherine Camenisch. He attended schools first in Zillis and later in Chur. In 1875, Florian Cajori emigrated to the Unite... |
https://en.wikipedia.org/wiki/Happy%20number | In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because , and . On the other hand, 4 is not a happy number because the sequence starting with and eventually reaches , the number that started the sequence, ... |
https://en.wikipedia.org/wiki/Heinz%20Hopf | Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of topology and geometry.
Early life and education
Hopf was born in Gräbschen, German Empire (now , part of Wrocław, Poland), the son of Elizabeth (née Kirchner) and Wilhelm Hopf. His father was born Jewish and converted to... |
https://en.wikipedia.org/wiki/Rankit | In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing.
Example
This is perhaps most readily understood by m... |
https://en.wikipedia.org/wiki/Normal%20probability%20plot | The normal probability plot is a graphical technique to identify substantive departures from normality. This includes identifying outliers, skewness, kurtosis, a need for transformations, and mixtures. Normal probability plots are made of raw data, residuals from model fits, and estimated parameters.
In a normal p... |
https://en.wikipedia.org/wiki/Eugenio%20Beltrami | Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of cons... |
https://en.wikipedia.org/wiki/Spectral%20space | In mathematics, a spectral space is a topological space that is homeomorphic to the spectrum of a commutative ring. It is sometimes also called a coherent space because of the connection to coherent topos.
Definition
Let X be a topological space and let K(X) be the set of all
compact open subsets of X. Then X is sai... |
https://en.wikipedia.org/wiki/Carl%20Hindenburg | Carl Friedrich Hindenburg (13 July 1741 – 17 March 1808) was a German mathematician born in Dresden. His work centered mostly on combinatorics and probability.
Education
Hindenburg did not attend school but was educated at home by a private tutor as arranged by his merchant father. He went to the University of Leipzig... |
https://en.wikipedia.org/wiki/Bicategory | In mathematics, a bicategory (or a weak 2-category) is a concept in category theory used to extend the notion of category to handle the cases where the composition of morphisms is not (strictly) associative, but only associative up to an isomorphism. The notion was introduced in 1967 by Jean Bénabou.
Bicategories may ... |
https://en.wikipedia.org/wiki/Recurrence%20plot | In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for each moment in time, the times at which the state of a dynamical system returns to the previous state at ,
i.e., when the phase space trajectory visits roughly the same area in the phase space as at time . In other words, it is a... |
https://en.wikipedia.org/wiki/Central%20Statistics%20Office%20%28Ireland%29 | The Central Statistics Office (CSO; ) is the statistical agency responsible for the gathering of "information relating to economic, social and general activities and conditions" in Ireland, in particular the census which is held every five years. The office is answerable to the Taoiseach and has its main offices in Cor... |
https://en.wikipedia.org/wiki/Extrapolation | In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a ... |
https://en.wikipedia.org/wiki/126%20%28number%29 | 126 (one hundred [and] twenty-six) is the natural number following 125 and preceding 127.
In mathematics
As the binomial coefficient , 126 is a central binomial coefficient, and in Pascal's Triangle, it is a pentatope number. 126 is a sum of two cubes, and since 125 + 1 is σ3(5), 126 is the fifth value of the sum of c... |
https://en.wikipedia.org/wiki/List%20of%20districts%20in%20Northern%20Ireland%20%28pre-2015%29 | This is a list of the former local government districts in Northern Ireland showing statistics for population, population density and area. The figures are from the 2011 Census.
These districts officially dissolved on 1 April 2015 when they were merged into eleven larger districts, statistics for which are listed at L... |
https://en.wikipedia.org/wiki/Feuerbach%20point | In the geometry of triangles, the incircle and nine-point circle of a triangle are internally tangent to each other at the Feuerbach point of the triangle. The Feuerbach point is a triangle center, meaning that its definition does not depend on the placement and scale of the triangle. It is listed as X(11) in Clark Kim... |
https://en.wikipedia.org/wiki/The%20Calculus%20Affair | The Calculus Affair () is the eighteenth volume of The Adventures of Tintin, the comics series by the Belgian cartoonist Hergé. It was serialised weekly in Belgium's Tintin magazine from December 1954 to February 1956 before being published in a single volume by Casterman in 1956. The story follows the attempts of the ... |
https://en.wikipedia.org/wiki/Bound | Bound or bounds may refer to:
Mathematics
Bound variable
Upper and lower bounds, observed limits of mathematical functions
Physics
Bound state, a particle that has a tendency to remain localized in one or more regions of space
Geography
Bound Brook (Raritan River), a tributary of the Raritan River in New Jersey
B... |
https://en.wikipedia.org/wiki/Welch%27s%20method | Welch's method, named after Peter D. Welch, is an approach for spectral density estimation.
It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.
The method is based on the concept of using periodogram spectrum estimates, which are the result of conv... |
https://en.wikipedia.org/wiki/Braid%20group | In mathematics, the braid group on strands (denoted ), also known as the Artin braid group, is the group whose elements are equivalence classes of -braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see ). Example applications of braid groups include knot theory, where any knot ma... |
https://en.wikipedia.org/wiki/Prime%20geodesic | In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic, i.e. a geodesic which is a closed curve that traces out its image exactly once. Such geodesics are called prime geodesics because, among other things, they obey an asymptotic distribution law similar to the prime number theorem.
T... |
https://en.wikipedia.org/wiki/Composition%20%28combinatorics%29 | In mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same partition of that number. Every integer has finitel... |
https://en.wikipedia.org/wiki/Thomas%20E.%20Kurtz | Thomas Eugene Kurtz (born February 22, 1928) is a retired Dartmouth professor of mathematics and computer scientist, who along with his colleague John G. Kemeny set in motion the then revolutionary concept of making computers as freely available to college students as library books were, by implementing the concept of ... |
https://en.wikipedia.org/wiki/United%20Kingdom%20Mathematics%20Trust | The United Kingdom Mathematics Trust (UKMT) is a charity founded in 1996 to help with the education of children in mathematics within the UK.
History
The national mathematics competitions existed prior to the formation of the UKMT, but the foundation of the UKMT in the summer of 1996 enabled them to be run collectivel... |
https://en.wikipedia.org/wiki/Royal%20Statistical%20Society | The Royal Statistical Society (RSS) is an established statistical society. It has three main roles: a British learned society for statistics, a professional body for statisticians and a charity which promotes statistics for the public good.
History
The society was founded in 1834 as the Statistical Society of London... |
https://en.wikipedia.org/wiki/Oval%20%28disambiguation%29 | An oval is a curve resembling an egg or an ellipse.
Oval, The Oval, or variations may also refer to:
Mathematics
Cassini oval
Oval (projective plane)
Places
Singapore
The Oval, Singapore, a road within Seletar Aerospace Park off Seletar Aerospace Drive
United Kingdom
Oval, London, a district in South London
Unite... |
https://en.wikipedia.org/wiki/Subsequential%20limit | In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every subsequential limit is a cluster point, but not conversely. In first-countable spaces, the two concepts coincide.
In a topological space, if every subsequence has a subsequential limit to the same point, then the original seque... |
https://en.wikipedia.org/wiki/Nonholonomic%20system | A nonholonomic system in physics and mathematics is a physical system whose state depends on the path taken in order to achieve it. Such a system is described by a set of parameters subject to differential constraints and non-linear constraints, such that when the system evolves along a path in its parameter space (the... |
https://en.wikipedia.org/wiki/Ferryland | Ferryland is a town in Newfoundland and Labrador on the Avalon Peninsula. According to the 2021 Statistics Canada census, its population is 371.
Seventeenth century settlement
Ferryland was originally established as a station for migratory fishermen in the late 16th century but had earlier been used by the French, Sp... |
https://en.wikipedia.org/wiki/Density%20estimation | In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the dat... |
https://en.wikipedia.org/wiki/P-value | In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothes... |
https://en.wikipedia.org/wiki/Schwarzian%20derivative | In mathematics, the Schwarzian derivative is an operator similar to the derivative which is invariant under Möbius transformations. Thus, it occurs in the theory of the complex projective line, and in particular, in the theory of modular forms and hypergeometric functions. It plays an important role in the theory of un... |
https://en.wikipedia.org/wiki/Mean-field%20theory | In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic tha... |
https://en.wikipedia.org/wiki/Paul%20L%C3%A9vy%20%28mathematician%29 | Paul Pierre Lévy (15 September 1886 – 15 December 1971) was a French mathematician who was active especially in probability theory, introducing fundamental concepts such as local time, stable distributions and characteristic functions. Lévy processes, Lévy flights, Lévy measures, Lévy's constant, the Lévy distribut... |
https://en.wikipedia.org/wiki/Graph%20%28abstract%20data%20type%29 | In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics.
A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points), together with a set of u... |
https://en.wikipedia.org/wiki/Level%20set | In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is:
When the number of independent variables is two, a level set is called a level curve, also known as contour line or isoline; so a level curve is the set of all real-value... |
https://en.wikipedia.org/wiki/Kim%20Maltman | Kim Maltman (born 1951) is a Canadian poet and physicist who lives in Toronto, Ontario. He is a professor of applied mathematics at York University and pursues research in theoretical nuclear/particle physics. He is serving as a judge for the 2019 Griffin Poetry Prize.
Works
The Country of the Mapmakers (1977),
The... |
https://en.wikipedia.org/wiki/Brillouin%20zone | In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries... |
https://en.wikipedia.org/wiki/128%20%28number%29 | 128 (one hundred [and] twenty-eight) is the natural number following 127 and preceding 129.
In mathematics
128 is the seventh power of 2. It is the largest number which cannot be expressed as the sum of any number of distinct squares. However, it is divisible by the total number of its divisors, making it a refactorab... |
https://en.wikipedia.org/wiki/175%20%28number%29 | 175 (one hundred [and] seventy-five) is the natural number following 174 and preceding 176.
In mathematics
Raising the decimal digits of 175 to the powers of successive integers produces 175 back again:
175 is a figurate number for a rhombic dodecahedron, the difference of two consecutive fourth powers: It is also ... |
https://en.wikipedia.org/wiki/Higher-order%20logic | In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less we... |
https://en.wikipedia.org/wiki/Excitatory%20synapse | An excitatory synapse is a synapse in which an action potential in a presynaptic neuron increases the probability of an action potential occurring in a postsynaptic cell. Neurons form networks through which nerve impulses travels, each neuron often making numerous connections with other cells of neurons. These electri... |
https://en.wikipedia.org/wiki/Torus-based%20cryptography | Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003 in the form of a public key algorithm by the name of CEILIDH. It improves on conventional cryptosystems by re... |
https://en.wikipedia.org/wiki/369%20%28number%29 | Three hundred sixty-nine is the natural number following three hundred sixty-eight and preceding three hundred seventy.
In mathematics
369 is the magic constant of the 9 × 9 magic square and the n-Queens Problem for n = 9.
There are 369 free octominoes (polyominoes of order 8).
369 is a Ruth-Aaron Pair with 370. Th... |
https://en.wikipedia.org/wiki/Global%20optimization | Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of... |
https://en.wikipedia.org/wiki/BSGS | The initialism BSGS has two meanings, both related to group theory in mathematics:
Baby-step giant-step, an algorithm for solving the discrete logarithm problem
The combination of a base and strong generating set (SGS) for a permutation group |
https://en.wikipedia.org/wiki/Baby-step%20giant-step | In group theory, a branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite abelian group by Daniel Shanks. The discrete log problem is of fundamental importance to the area of public key cryptography.
Many of the most com... |
https://en.wikipedia.org/wiki/Look-and-say%20sequence | In mathematics, the look-and-say sequence is the sequence of integers beginning as follows:
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... .
To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups o... |
https://en.wikipedia.org/wiki/Speak%20%26%20Math | The Speak & Math (or Speak & Maths in some countries) was a popular electronic toy created by Texas Instruments in . Speak & Math was one of a three-part talking educational toy series that also included Speak & Spell and Speak & Read. The Speak & Math was sold worldwide. It was advertised as a tool for helping young c... |
https://en.wikipedia.org/wiki/Catalan%20solid | In mathematics, a Catalan solid, or Archimedean dual, is a polyhedron that is dual to an Archimedean solid. There are 13 Catalan solids. They are named for the Belgian mathematician Eugène Catalan, who first described them in 1865.
The Catalan solids are all convex. They are face-transitive but not vertex-transitive. ... |
https://en.wikipedia.org/wiki/Bernard%20Fr%C3%A9nicle%20de%20Bessy | Bernard Frénicle de Bessy (c. 1604 – 1674), was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for , a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magi... |
https://en.wikipedia.org/wiki/Symbolic%20method | In mathematics, the symbolic method in invariant theory is an algorithm developed by Arthur Cayley, Siegfried Heinrich Aronhold, Alfred Clebsch, and Paul Gordan in the 19th century for computing invariants of algebraic forms. It is based on treating the form as if it were a power of a degree one form, which correspond... |
https://en.wikipedia.org/wiki/Jean-Marie%20Souriau | Jean-Marie Souriau (3 June 1922, Paris – 15 March 2012, Aix-en-Provence) was a French mathematician. He was one of the pioneers of modern symplectic geometry.
Education and career
Souriau started studying mathematics in 1942 at École Normale Supérieure in Paris. In 1946 he was a research fellow of CNRS and an enginee... |
https://en.wikipedia.org/wiki/Tilting | Tilting may refer to:
Tilt (camera), a cinematographic technique
Tilting at windmills, an English idiom
Tilting theory, an algebra theory
Exponential tilting, a probability distribution shifting technique
Tilting three-wheeler, a vehicle which leans when cornering while keeping all of its three wheels on the grou... |
https://en.wikipedia.org/wiki/Quasi-arithmetic%20mean | In mathematics and statistics, the quasi-arithmetic mean or generalised f-mean or Kolmogorov-Nagumo-de Finetti mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function . It is also called Kolmogorov mean after Soviet mathematician Andrey Kolmogorov. It i... |
https://en.wikipedia.org/wiki/Jakob%20Steiner | Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry.
Life
Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards studied at Heidelberg. Then, he went to Berlin, earning a livelihood there, as in ... |
https://en.wikipedia.org/wiki/Lexicographic%20order | In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set.
There are several variants and generalizations of the... |
https://en.wikipedia.org/wiki/Riemann%E2%80%93Liouville%20integral | In mathematics, the Riemann–Liouville integral associates with a real function another function of the same kind for each value of the parameter . The integral is a manner of generalization of the repeated antiderivative of in the sense that for positive integer values of , is an iterated antiderivative of of orde... |
https://en.wikipedia.org/wiki/Vedic%20Mathematics | Vedic Mathematics is a book written by the Indian monk Bharati Krishna Tirtha, and first published in 1965. It contains a list of mathematical techniques, which were falsely claimed to have been retrieved from the Vedas and to contain advanced mathematical knowledge.
Krishna Tirtha failed to produce the sources, and s... |
https://en.wikipedia.org/wiki/Solution%20set | In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
For example, for a set of polynomials over a ring ,
the solution set is the subset of on which the polynomials all vanish (evaluate to 0), formally
The feasible region of a constrained optimization problem is ... |
https://en.wikipedia.org/wiki/Weakly%20harmonic%20function | In mathematics, a function is weakly harmonic in a domain if
for all with compact support in and continuous second derivatives, where Δ is the Laplacian. This is the same notion as a weak derivative, however, a function can have a weak derivative and not be differentiable. In this case, we have the somewhat sur... |
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