Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation
In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the formula, and Faulhaber's formula for the sum of powers is an immediate consequence.
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional.
In mathematics, a surjective function (also known as surjection, or onto function ) is a function f such that every element y can be mapped from some element x such that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y.
In abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial splits, i.e., decomposes into linear factors.
In numerical analysis, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for numerical integration based on evaluating the integrand at equally spaced points. They are named after Isaac Newton and Roger Cotes.
The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not.
There are quite a few ALGOL60 translators in existence which have been designed to handle recursion and non-local references properly, and I thought perhaps a little test-program may be of value. Hence I have written the following simple routine, which may separate the man-compilers from the boy-compilers.
In mathematics, a symmetric polynomial is a polynomial P(X1, X2, …, Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally, P is a symmetric polynomial if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), …, Xσ(n)) = P(X1, X2, …, Xn).
In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum of an objective function . The other approach is trust region.
In 1893 Giuseppe Lauricella defined and studied four hypergeometric series FA, FB, FC, FD of three variables. They are :
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823. A publication was not delivered before 1874 by Seidel.
In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method, used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced this method in 1926. Its early form was known to Seki Kōwa and was found for rectification of the circle, i.e. the calculation of π. It is most useful for accelerating the convergence of a sequence that is converging linearly.
In computer vision a camera matrix or (camera) projection matrix is a matrix which describes the mapping of a pinhole camera from 3D points in the world to 2D points in an image.
In the context of combinatorial mathematics, stars and bars is a graphical aid for deriving certain combinatorial theorems. It was popularized by William Feller in his classic book on probability. It can be used to solve many simple counting problems, such as how many ways there are to put n indistinguishable balls into k distinguishable bins.
BMW X may refer to the following BMW crossovers, SAVs, and SACs:
In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 dimensional projective space studied by Wolf Barth and Isidro Nieto (1994) that is the Hessian of the Segre cubic.
Symbolic circuit analysis is a formal technique of circuit analysis to calculate the behaviour or characteristic of an electric/electronic circuit with the independent variables, the dependent variables, and the circuit elements represented by symbols.
In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let ρ be its rank function, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality
The Benning Road Line, designated Route X1, X3 is a weekday peak hour only bus route operated by the Washington Metropolitan Area Transit Authority between Minnesota Avenue station of the Orange Line of the Washington Metro and Foggy Bottom–GWU station of the Orange, Blue, and Silver Lines of the Washington Metro (X1) or Duke Ellington Bridge in Adams Morgan (X3). The line operates every 10–31 minutes during weekday peak hours in the peak direction only. X1 trips are roughly 41 minutes while X3 trips are roughly 45 minutes. All service along the X1 and X3 lines is currently suspended.
