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A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

Let (Omega)_(ij) be the resistance distance matrix of a connected graph G on n nodes. Then Foster's theorems state that sum_((i,j) in E(G)))Omega_(ij)=n-1, where E(g) is the ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

The second-order ordinary differential equation (1-x^2)y^('')-2(mu+1)xy^'+(nu-mu)(nu+mu+1)y=0 (1) sometimes called the hyperspherical differential equation (Iyanaga and ...

A generalized eigenvector for an n×n matrix A is a vector v for which (A-lambdaI)^kv=0 for some positive integer k in Z^+. Here, I denotes the n×n identity matrix. The ...

A generalization of the equation whose solution is desired in Fermat's last theorem x^n+y^n=z^n to x^n+y^n=cz^n for x, y, z, and c positive constants, with trivial solutions ...

A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...