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Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

A group action G×Omega->Omega might preserve a special kind of partition of Omega called a system of blocks. A block is a subset Delta of Omega such that for any group ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

Cauchy's functional equation is the equation f(x+y)=f(x)+f(y). It was proved by Cauchy in 1821 that the only continuous solutions of this functional equation from R into R ...

A copositive matrix is a real n×n square matrix A=(a_(ij)) that makes the corresponding quadratic form f(x)=x^(T)Ax nonnegative for all nonnegative n-vectors x. Copositive ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...