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Let A=a_(ij) be a matrix with positive coefficients so that a_(ij)>0 for all i,j=1, 2, ..., n, then A has a positive eigenvalue lambda_0, and all its eigenvalues lie on the ...

Let C_(L,M) be a Padé approximant. Then C_((L+1)/M)S_((L-1)/M)-C_(L/(M+1))S_(L/(M+1)) = C_(L/M)S_(L/M) (1) C_(L/(M+1))S_((L+1)/M)-C_((L+1)/M)S_(L/(M+1)) = ...

A frustum (unfortunately commonly misspelled "frustrum") is that portion of a solid which lies between two parallel planes cutting the solid. Degenerate cases are obtained ...

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

A full angle, also called a complete angle, round angle, or perigon, is an angle equal to 2pi radians =360 degrees corresponding to the central angle of an entire circle. ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...

A finite extension K=Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ...

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

A functional graph is a directed graph in which each vertex has outdegree one, and can therefore be specified by a function mapping {1,...,n} onto itself. Functional graphs ...

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.