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In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V×W, that is closed in the Zariski topology. In set theory, a subset of a Cartesian product of two sets is called a binary relation or correspondence; thus, a correspondence here is a relation that is defined by algebraic equations.
The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...
The Dold–Kan correspondence between the category sAb of simplicial abelian groups and the category () of nonnegatively graded chain complexes can be constructed explicitly through a pair of functors [1] pg 149 so that these functors form an equivalence of categories. The first functor is the normalized chain complex functor
Throughout this article, capital letters (such as ,,,,, and ) will denote sets. On the left hand side of an identity, typically, will be the leftmost set, will be the middle set, and; will be the rightmost set.
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...