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A permutation which shifts all elements of a set by a fixed offset, with the elements shifted off the end inserted back at the beginning. For a set with elements a_0, a_1, ...

A generalization by Kronecker of Kummer's theory of prime ideal factors. A divisor on a full subcategory C of mod(A) is an additive mapping chi on C with values in a ...

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

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 ...

Let G be a group and theta n permutation of G. Then theta is an orthomorphism of G if the self-mapping nu of G defined by nu(x)=x^(-1)theta(x) is also an permutation of G.

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

Given a polynomial in a single complex variable with complex coefficients p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, the reciprocal polynomial is defined by ...

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...

Let P=a_1x+a_2x^2+... be an almost unit in the integral domain of formal power series (with a_1!=0) and define P^k=sum_(n=k)^inftya_n^((k))x^n (1) for k=+/-1, +/-2, .... If ...