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A set of algebraic invariants for a quantic such that any invariant of the quantic is expressible as a polynomial in members of the set. Gordan (1868) proved the existence of ...

A algebraic loop L is a generalized Bol loop if for all elements x, y, and z of L, ((xy)z)alpha(y)=x((yz)alpha(y)) for some map alpha:L->L. As the name suggests, these are ...

Let f be an entire function of finite order lambda and {a_j} the zeros of f, listed with multiplicity, then the rank p of f is defined as the least positive integer such that ...

Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

A simplicial complex is a space with a triangulation. Formally, a simplicial complex K in R^n is a collection of simplices in R^n such that 1. Every face of a simplex of K is ...

Let m_1, m_2, ..., m_n be distinct primitive elements of a two-dimensional lattice M such that det(m_i,m_(i+1))>0 for i=1, ..., n-1. Each collection Gamma={m_1,m_2,...,m_n} ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

The vertex set of a graph is simply a set of all vertices of the graph. The cardinality of the vertex set for a given graph g is known as the vertex count of g. The vertex ...