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https://en.wikipedia.org/wiki/Jacobi%20elliptic%20functions | In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi... |
https://en.wikipedia.org/wiki/CBA | CBA may refer to:
Maths and science
Casei Bifidus Acidophilus, a bacterium
Colicin, activity protein
Complete Boolean algebra, a concept from mathematics
Cytometric Bead Array, a bead-based immunoassay
Cell Based Assay, also a kind of immunoassay
4-Carboxybenzaldehyde, a byproduct in the industrial production o... |
https://en.wikipedia.org/wiki/Azuma%27s%20inequality | In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.
Suppose is a martingale (or super-martingale) and
almost surely. Then for all positive integers N and all positive reals ,
... |
https://en.wikipedia.org/wiki/Field%20norm | In mathematics, the (field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield.
Formal definition
Let K be a field and L a finite extension (and hence an algebraic extension) of K.
The field L is then a finite dimensional vector space over K.
Multiplication by... |
https://en.wikipedia.org/wiki/Jacobi | Jacobi may refer to:
People with the surname Jacobi
Mathematics:
Jacobi sum, a type of character sum
Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations
Jacobi eigenvalue algorithm, a method for calculating the eigenvalues and eigenvectors of a real symmetric ... |
https://en.wikipedia.org/wiki/Cube%20%28algebra%29 | In arithmetic and algebra, the cube of a number is its third power, that is, the result of multiplying three instances of together.
The cube of a number or any other mathematical expression is denoted by a superscript 3, for example or .
The cube is also the number multiplied by its square:
.
The cube function is ... |
https://en.wikipedia.org/wiki/Historiometry | Historiometry is the historical study of human progress or individual personal characteristics, using statistics to analyze references to geniuses, their statements, behavior and discoveries in relatively neutral texts. Historiometry combines techniques from cliometrics, which studies economic history and from psychome... |
https://en.wikipedia.org/wiki/1742%20in%20science | The year 1742 in science and technology involved some significant events.
Astronomy
January 14 – Death of Edmond Halley; James Bradley succeeds him as Astronomer Royal in Great Britain.
Mathematics
June – Christian Goldbach produces Goldbach's conjecture.
Colin Maclaurin publishes his Treatise on Fluxions in Great... |
https://en.wikipedia.org/wiki/J-invariant | In mathematics, Felix Klein's -invariant or function, regarded as a function of a complex variable , is a modular function of weight zero for defined on the upper half-plane of complex numbers. It is the unique such function which is holomorphic away from a simple pole at the cusp such that
Rational functions of ar... |
https://en.wikipedia.org/wiki/Linking%20number | In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. In Euclidean space, the linking number is always an integer, but may be positiv... |
https://en.wikipedia.org/wiki/Eric%20de%20Sturler | Eric de Sturler (born 15 January 1966, Groningen) is a Professor of Mathematics at Virginia Tech in Blacksburg, Virginia. He is on the editorial board of Applied Numerical Mathematics and the Open Applied Mathematics Journal.
Prof. de Sturler completed his Ph.D. under the direction of Henk van der Vorst at Technische ... |
https://en.wikipedia.org/wiki/Limit%20cycle | In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some no... |
https://en.wikipedia.org/wiki/Orthogonal%20functions | In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval:
The functions and are orthogonal when this integral is zero... |
https://en.wikipedia.org/wiki/Gambler%27s%20ruin | In statistics, gambler's ruin is the fact that a gambler playing a game with negative expected value will eventually go broke, regardless of their betting system.
The concept was initially stated: A persistent gambler who raises their bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce i... |
https://en.wikipedia.org/wiki/Parametrization%20%28geometry%29 | In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitizati... |
https://en.wikipedia.org/wiki/Glossary%20of%20order%20theory | This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be the following overview articles:
completeness properties of partial ord... |
https://en.wikipedia.org/wiki/127%20%28number%29 | 127 (one hundred [and] twenty-seven') is the natural number following 126 and preceding 128. It is also a prime number.
In mathematics
As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also the largest known Mersenne prime exponent for a Mersenne number, , which is also a Mersenne prime. It was ... |
https://en.wikipedia.org/wiki/Thoralf%20Skolem | Thoralf Albert Skolem (; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic and set theory.
Life
Although Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem attended secondary school in Kristiania (later renamed Oslo), passing the un... |
https://en.wikipedia.org/wiki/Exact%20functor | In mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations because they can be directly applied to presentations of objects. Much of the work in homological algebra is designed to cope with functors that ... |
https://en.wikipedia.org/wiki/Integral%20test%20for%20convergence | In mathematics, the integral test for convergence is a method used to test infinite series of monotonous terms for convergence. It was developed by Colin Maclaurin and Augustin-Louis Cauchy and is sometimes known as the Maclaurin–Cauchy test.
Statement of the test
Consider an integer and a function defined on the un... |
https://en.wikipedia.org/wiki/Michel%20Plancherel | Michel Plancherel (16 January 1885 – 4 March 1967) was a Swiss mathematician. He was born in Bussy (Fribourg, Switzerland) and obtained his Diplom in mathematics from the University of Fribourg and then his doctoral degree in 1907 with a thesis written under the supervision of Mathias Lerch. Plancherel was a professor ... |
https://en.wikipedia.org/wiki/Plancherel%20theorem | In mathematics, the Plancherel theorem (sometimes called the Parseval–Plancherel identity) is a result in harmonic analysis, proven by Michel Plancherel in 1910. It states that the integral of a function's squared modulus is equal to the integral of the squared modulus of its frequency spectrum. That is, if is a funct... |
https://en.wikipedia.org/wiki/Locally%20compact%20abelian%20group | In several mathematical areas, including harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group of integers (equipped with the discrete topology), or the real numbers or the circle (both with their u... |
https://en.wikipedia.org/wiki/Abstraction%20%28mathematics%29 | Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract de... |
https://en.wikipedia.org/wiki/Nine%20lemma | In mathematics, the nine lemma (or 3×3 lemma) is a statement about commutative diagrams and exact sequences valid in the category of groups and any abelian category. It states: if the diagram to the right is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as wel... |
https://en.wikipedia.org/wiki/1740%20in%20science | The year 1740 in science and technology involved some significant events.
Mathematics
Jean Paul de Gua de Malves publishes his work of analytic geometry, .
Metallurgy
Benjamin Huntsman develops the technique of crucible steel production at Handsworth, South Yorkshire, England.
Physics
Jacques-Barthélemy Micheli d... |
https://en.wikipedia.org/wiki/Category%20of%20abelian%20groups | In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category: indeed, every small abelian category can be embedded in Ab.
Properties
The zero object of Ab is the trivial group {0} which consists only of its neutral element.
The m... |
https://en.wikipedia.org/wiki/Quadratic%20field | In algebraic number theory, a quadratic field is an algebraic number field of degree two over , the rational numbers.
Every such quadratic field is some where is a (uniquely defined) square-free integer different from and . If , the corresponding quadratic field is called a real quadratic field, and, if , it is cal... |
https://en.wikipedia.org/wiki/Set | Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics
Mathematics
Set (mathematics), a collection of elements
Category of sets, the category whose objects and morphisms are sets and total functions, respectively
Electronics and computing
Set (abstract data type), a data type in computer scienc... |
https://en.wikipedia.org/wiki/Positive%20linear%20functional | In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space is a linear functional on so that for all positive elements that is it holds that
In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements. The signi... |
https://en.wikipedia.org/wiki/Positive%20operator%20%28Hilbert%20space%29 | In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator acting on an inner product space is called positive-semidefinite (or non-negative) if, for every , and , where is the domain of . Positive-semidefinite operators are denoted as . The operator... |
https://en.wikipedia.org/wiki/Extreme%20point | In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of In linear programming problems, an extreme point is also called vertex or corner point of
Definition
Throughout, it is assumed that is a real or complex... |
https://en.wikipedia.org/wiki/160%20%28number%29 | 160 (one hundred [and] sixty) is the natural number following 159 and preceding 161.
In mathematics
160 is the sum of the first 11 primes, as well as the sum of the cubes of the first three primes.
Given 160, the Mertens function returns 0. 160 is the smallest number n with exactly 12 solutions to the equation φ(x) =... |
https://en.wikipedia.org/wiki/170%20%28number%29 | 170 (one hundred [and] seventy) is the natural number following 169 and preceding 171.
In mathematics
170 is the smallest n for which φ(n) and σ(n) are both square (64 and 324 respectively). But 170 is never a solution for φ(x), making it a nontotient. Nor is it ever a solution to x - φ(x), making it a noncototient.
... |
https://en.wikipedia.org/wiki/180%20%28number%29 | 180 (one hundred [and] eighty) is the natural number following 179 and preceding 181.
In mathematics
180 is an abundant number, with its proper divisors summing up to 366. 180 is also a highly composite number, a positive integer with more divisors than any smaller positive integer. One of the consequences of 180 havi... |
https://en.wikipedia.org/wiki/190%20%28number%29 | 190 (one hundred [and] ninety) is the natural number following 189 and preceding 191.
In mathematics
190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after 1, 28, and 91) with that combination of properties. It is also a truncated square pyramid number.
Inte... |
https://en.wikipedia.org/wiki/Color%20theory | In the visual arts, color theory is the body of practical guidance for color mixing and the visual effects of a specific color combination. Color terminology based on the color wheel and its geometry separates colors into primary color, secondary color, and tertiary color. The understanding of color theory dates to ant... |
https://en.wikipedia.org/wiki/Lusser%27s%20law | Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser, and also known as Lusser's product law or the probability product law of series components, it states that the reliability of a series of components is equal to the product of the individual reliabilities of the comp... |
https://en.wikipedia.org/wiki/Von%20Neumann%20bicommutant%20theorem | In mathematics, specifically functional analysis, the von Neumann bicommutant theorem relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. In essence, it is a connection between the algebraic and topological sides of operator theory.
The formal stat... |
https://en.wikipedia.org/wiki/Bicommutant | In algebra, the bicommutant of a subset S of a semigroup (such as an algebra or a group) is the commutant of the commutant of that subset. It is also known as the double commutant or second commutant and is written .
The bicommutant is particularly useful in operator theory, due to the von Neumann double commutant the... |
https://en.wikipedia.org/wiki/Operator%20algebra | In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings.
The results obtained in the study of operator algebras are often phrased in algebraic terms, while the technique... |
https://en.wikipedia.org/wiki/Incomplete%20gamma%20function | In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals.
Their respective names stem from their integral definitions, which are defined similarly to the gamma function but with different or "incomp... |
https://en.wikipedia.org/wiki/Gaussian%20period | In mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of roots of unity. The periods permit explicit calculations in cyclotomic fields connected with Galois theory and with harmonic analysis (discrete Fourier transform). They are basic in the classical theory called cyclotomy. Closely... |
https://en.wikipedia.org/wiki/496%20%28number%29 | 496 (four hundred [and] ninety-six) is the natural number following 495 and preceding 497.
In mathematics
496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 31, 25 − 1, with 24 (25 − 1) yielding 496. Also relat... |
https://en.wikipedia.org/wiki/Kerr%20metric | The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact so... |
https://en.wikipedia.org/wiki/Second%20%28disambiguation%29 | A second is the base unit of time in the International System of Units (SI).
Second, Seconds or 2nd may also refer to:
Mathematics
2 (number), as an ordinal (also written as 2nd or 2d)
Second of arc, an angular measurement unit, of a degree
Seconds (angle), units of angular measurement
Music
Notes and interval... |
https://en.wikipedia.org/wiki/Sulfur%20hexafluoride | Sulfur hexafluoride or sulphur hexafluoride (British spelling) is an inorganic compound with the formula SF6. It is a colorless, odorless, non-flammable, and non-toxic gas. has an octahedral geometry, consisting of six fluorine atoms attached to a central sulfur atom. It is a hypervalent molecule.
Typical for a nonp... |
https://en.wikipedia.org/wiki/Galois%20extension | In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys th... |
https://en.wikipedia.org/wiki/Field%20trace | In mathematics, the field trace is a particular function defined with respect to a finite field extension L/K, which is a K-linear map from L onto K.
Definition
Let K be a field and L a finite extension (and hence an algebraic extension) of K. L can be viewed as a vector space over K. Multiplication by α, an element o... |
https://en.wikipedia.org/wiki/Pure%20mathematics | Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications.... |
https://en.wikipedia.org/wiki/Block%20matrix | In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or ... |
https://en.wikipedia.org/wiki/Spline%20%28mathematics%29 | In mathematics, a spline is a special function defined piecewise by polynomials.
In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
In the compute... |
https://en.wikipedia.org/wiki/153%20%28number%29 | 153 (one hundred [and] fifty-three) is the natural number following 152 and preceding 154.
In mathematics
The number 153 is associated with the geometric shape known as the Vesica Piscis or Mandorla. Archimedes, in his Measurement of a Circle, referred to this ratio (153/265), as constituting the "measure of the fish... |
https://en.wikipedia.org/wiki/Rotation%20%28disambiguation%29 | Rotation is a circular motion of a body about a center.
Rotation may also refer to:
Science, mathematics and computing
Rotation (anatomy)
Rotation (mathematics)
Rotation (medicine), medical student training
Rotation (physics), ratio between a given angle and a full turn of 2π radians
Bitwise rotation, a mathema... |
https://en.wikipedia.org/wiki/Conjugate%20element%20%28field%20theory%29 | In mathematics, in particular field theory, the conjugate elements or algebraic conjugates of an algebraic element , over a field extension , are the roots of the minimal polynomial of over . Conjugate elements are commonly called conjugates in contexts where this is not ambiguous. Normally itself is included in th... |
https://en.wikipedia.org/wiki/137%20%28number%29 | 137 (one hundred [and] thirty-seven) is the natural number following 136 and preceding 138.
Mathematics
the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime.
an Eisenstein prime with no imaginary part and a real part of the form .
the fourth Stern prime.
a ... |
https://en.wikipedia.org/wiki/1734%20in%20science | The year 1734 in science and technology involved some significant events.
Mathematics
George Berkeley publishes The Analyst, an empiricist critique of the foundations of infinitesimal calculus, influential in the development of mathematics.
Leonhard Euler introduces the integrating factor technique for solving first... |
https://en.wikipedia.org/wiki/1730%20in%20science | The year 1730 in science and technology involved some significant events.
Astronomy
The analemma is developed by the French astronomer Grandjean de Fouchy.
Mathematics
James Stirling publishes Methodus differentialis, sive tractatus de summatione et interpolatione serierum infinitarum.
Physics
The Reaumur scale i... |
https://en.wikipedia.org/wiki/Weak%20operator%20topology | In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space , such that the functional sending an operator to the complex number is continuous for any vectors and in the Hilbert space.
Explicitly, for an operator there is ba... |
https://en.wikipedia.org/wiki/Strong%20operator%20topology | In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced by the seminorms of the form , as x varies in H.
Equivalently, it is the coarsest topology such that, for each fixed x in H, ... |
https://en.wikipedia.org/wiki/Predual | In mathematics, the predual of an object D is an object P whose dual space is D.
For example, the predual of the space of bounded operators is the space of trace class operators, and the predual of the space L∞(R) of essentially bounded functions on R is the Banach space L1(R) of integrable functions.
Abstract algebr... |
https://en.wikipedia.org/wiki/Kimotsuki%20District%2C%20Kagoshima | is a district located in Kagoshima Prefecture, Japan.
As of the January 1, 2006 merger but with 2003 population statistics, the district has an estimated population of 46,943 and a density of 65.9 persons per km2. The total area is 712.55 km2.
Towns and villages
Higashikushira
Kimotsuki
Kinkō
Minamiōsumi
Mergers
On ... |
https://en.wikipedia.org/wiki/%C5%8Cshima%20District%2C%20Kagoshima | is a district located in Kagoshima Prefecture, Japan.
As of the March 20, 2006 merger but with 2003 population statistics, the district has an estimated population of 78,882 and a density of 84.4 persons per km2. The total area is 934.10 km2.
Towns and villages
Amagi
China
Isen
Kikai
Setouchi
Tatsugō
Tokunoshima
Wado... |
https://en.wikipedia.org/wiki/Ternary%20operation | In mathematics, a ternary operation is an n-ary operation with n = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A.
In computer science, a ternary operator is an operator that takes three arguments as input and returns one output.
Examples
The fun... |
https://en.wikipedia.org/wiki/Miyazaki%20District%2C%20Miyazaki | was a district located in Miyazaki Prefecture, Japan.
As of 2003 population statistics (but following the January 1, 2006 merger of the towns of Sadowara and Tano), the district had an estimated population of 28,937 and the density of 605.25 persons per km2. The total area was 47.81 km2.
Former towns and villages
Ki... |
https://en.wikipedia.org/wiki/Kitamorokata%20District%2C%20Miyazaki | is a district located in Miyazaki Prefecture, Japan.
As of the Miyakonojō merger (but with the population statistics as of October 2020), the district has an estimated population of 25,591 and a density of 232.6 persons per km2. The total area is 110.0 km2.
Towns and villages
Mimata
Mergers
On January 1, 2006 the ... |
https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner%20constant | In mathematics, the Ramanujan–Soldner constant (also called the Soldner constant) is a mathematical constant defined as the unique positive zero of the logarithmic integral function. It is named after Srinivasa Ramanujan and Johann Georg von Soldner.
Its value is approximately μ ≈ 1.45136923488338105028396848589202744... |
https://en.wikipedia.org/wiki/Dirichlet%27s%20unit%20theorem | In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of the group of units in the ring of algebraic integers of a number field . The regulator is a positive real number that determines how "dense" the units are.
The stateme... |
https://en.wikipedia.org/wiki/Nest%20algebra | In functional analysis, a branch of mathematics, nest algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by and have many interesting properties. They are non-selfadjoint algebras, are closed in the weak operator topology and ... |
https://en.wikipedia.org/wiki/Reflexive%20operator%20algebra | In functional analysis, a reflexive operator algebra A is an operator algebra that has enough invariant subspaces to characterize it. Formally, A is reflexive if it is equal to the algebra of bounded operators which leave invariant each subspace left invariant by every operator in A.
This should not be confused with a... |
https://en.wikipedia.org/wiki/Ring%20of%20integers | In mathematics, the ring of integers of an algebraic number field is the ring of all algebraic integers contained in . An algebraic integer is a root of a monic polynomial with integer coefficients: . This ring is often denoted by or . Since any integer belongs to and is an integral element of , the ring is always ... |
https://en.wikipedia.org/wiki/Invertible%20%28disambiguation%29 | Invertible may refer to
Mathematics
Invertible element
Invertible function
Invertible ideal
Invertible knot
Invertible jet
Invertible matrix
Invertible module
Invertible sheaf
Others
Invertible counterpoint
See also
Inverse (disambiguation) |
https://en.wikipedia.org/wiki/Ideal%20norm | In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an ideal in a less complicated ring. When the less complicated number ring is tak... |
https://en.wikipedia.org/wiki/Fractional%20ideal | In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where frac... |
https://en.wikipedia.org/wiki/Derived%20set | A derived set may refer to:
Derived set (mathematics), a construction in point-set topology
Derived row, a concept in musical set theory |
https://en.wikipedia.org/wiki/Conservative%20vector%20field | In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not change the value of the line integral. Path independence of the line integr... |
https://en.wikipedia.org/wiki/Errors%20and%20residuals | In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value... |
https://en.wikipedia.org/wiki/Laplacian%20vector%20field | In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is described by the following differential equations:
From the vector calculus identity it follows that
that is, that the field v satisfies Laplace's equation.
However... |
https://en.wikipedia.org/wiki/Poincar%C3%A9%20half-plane%20model | In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H , together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.
Equivalently the Poincaré half-plane model is sometimes described as a complex plane where the imaginary part... |
https://en.wikipedia.org/wiki/Vanish%20at%20infinity | In mathematics, a function is said to vanish at infinity if its values approach 0 as the input grows without bounds. There are two different ways to define this with one definition applying to functions defined on normed vector spaces and the other applying to functions defined on locally compact spaces.
Aside from th... |
https://en.wikipedia.org/wiki/Standard%20basis | In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs of real numbers, the standard basis ... |
https://en.wikipedia.org/wiki/1714%20in%20science | The year 1714 in science and technology involved some significant events.
Mathematics
March – Roger Cotes publishes Logometrica in the Philosophical Transactions of the Royal Society. He provides the first proof of what is now known as Euler's formula and constructs the logarithmic spiral.
May – Brook Taylor publish... |
https://en.wikipedia.org/wiki/1713%20in%20science | The year 1713 in science and technology involved some significant events.
Astronomy
John Rowley of London produces an orrery to a commission by Charles Boyle, 4th Earl of Orrery.
Mathematics
September 9 – Nicolas Bernoulli first describes the St. Petersburg paradox in a letter to Pierre Raymond de Montmort.
Novemb... |
https://en.wikipedia.org/wiki/1711%20in%20science | The year 1711 in science and technology involved some significant events.
Biology
Luigi Ferdinando Marsigli shows that coral is an animal rather than a plant as previously thought.
Mathematics
Giovanni Ceva publishes De Re Nummeraria (Concerning Money Matters), one of the first books on mathematical economics.
Joh... |
https://en.wikipedia.org/wiki/Harmonic%20divisor%20number | In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are
1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 .
Harmonic divisor numbers were introduced by Øystein Ore, who showed that every per... |
https://en.wikipedia.org/wiki/Inscribed%20angle | In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.
Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.... |
https://en.wikipedia.org/wiki/144%20%28number%29 | 144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.
In mathematics
144 is the square of 12. It is also the twelfth Fibonacci number, following 89 and preceding 233, and the only Fibonacci number (other than 0, and 1) to also be a square. 144 is... |
https://en.wikipedia.org/wiki/Metric%20signature | In mathematics, the signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix of the metric tensor with res... |
https://en.wikipedia.org/wiki/Space%20group | In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219... |
https://en.wikipedia.org/wiki/555%20%28number%29 | 555 (five hundred [and] fifty-five) is the natural number following 554 and preceding 556.
In mathematics
555 is a sphenic number. In base 10, it is a repdigit, and because it is divisible by the sum of its digits, it is a Harshad number. It is also a Harshad number in binary, base 11, base 13 and hexadecimal.
It is... |
https://en.wikipedia.org/wiki/Antiholomorphic%20function | In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions.
A function of the complex variable z defined on an open set in the complex plane is said to be antiholomorphic if its derivative with respect to exists... |
https://en.wikipedia.org/wiki/Y-intercept | In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.... |
https://en.wikipedia.org/wiki/NCD | NCD may refer to:
Language
Nemine contradicente (or N.C.D.), for 'with no one speaking against'
Non-convergent discourse, an asymmetricly bilingual conversation
Mathematics
Normalized compression distance, in statistics and information theory
Nearly completely decomposable Markov chain, in probability theory
Medicin... |
https://en.wikipedia.org/wiki/Sperner%27s%20lemma | In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring (described below) of a triangulation of an simplex contains a cell whose vertices all have different colors.
The init... |
https://en.wikipedia.org/wiki/Probabilistic%20proposition | A probabilistic proposition is a proposition with a measured probability of being true for an arbitrary person at an arbitrary time. They may be contrasted with deterministic propositions, which assert that something is certain with no element of chance. Probabilistic proportions may be either categorical or conditiona... |
https://en.wikipedia.org/wiki/Sallen%E2%80%93Key%20topology | The Sallen–Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity. It is a degenerate form of a voltage-controlled voltage-source (VCVS) filter topology. It was introduced by R. P. Sallen and E. L. Key of MIT Lincoln Laboratory in 1955... |
https://en.wikipedia.org/wiki/Flow | Flow may refer to:
Science and technology
Fluid flow, the motion of a gas or liquid
Flow (geomorphology), a type of mass wasting or slope movement in geomorphology
Flow (mathematics), a group action of the real numbers on a set
Flow (psychology), a mental state of being fully immersed and focused
Flow, a spacecra... |
https://en.wikipedia.org/wiki/1644%20in%20science | The year 1644 AD in science and technology involved some significant events.
Mathematics
The Basel problem is posed by Pietro Mengoli, and will puzzle mathematicians until solved by Leonhard Euler in 1735.
Technology
Jacob van Eyck collaborates with the bellfounding duo Pieter and François Hemony to create the firs... |
https://en.wikipedia.org/wiki/1679%20in%20science | The year 1679 in science and technology involved some significant events.
Botany
Establishment of Hortus Botanicus (Amsterdam).
Mathematics
Samuel Morland publishes The Doctrine of Interest, both Simple & Compound, probably the first tables produced with the aid of a calculating machine.
Medicine
Great Plague of ... |
https://en.wikipedia.org/wiki/1677%20in%20science | The year 1677 in science and technology involved some significant events.
Astronomy
Publication of the first English star atlas, John Seller's Atlas Coelestis.
Mathematics
Publication of Cocker's Arithmetick: Being a Plain and Familiar Method Suitable to the Meanest Capacity for the Full Understanding of That Incom... |
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