Based on the Bezout approach we propose a simple algorithm to determine gcd of two polynomials that don't need division, like Euclidean algorithm, or determinant calculations, Sylvester matrix algorithm. The needs only n steps for degree n. Formal manipulations give discriminant resultant any without needing division calculation.

a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

The task of determining the approximate greatest common divisor (GCD) of more than two univariate polynomials with inexact coefficients can be formulated as computing for a given Bezout matrix a new Bezout matrix of lower rank whose entries are near the corresponding entries of that input matrix. We present an algorithm based on a version of structured nonlinear total least squares (SNTLS) meth...

Indeed, in [3] they showed that, if one of the invariant circles of f is missing, then for some p and q with gcd(p; q) = 1 the map must have a periodic orbit of type (p; q) which is not a Birkhoff orbit. On the other hand, Boyland showed in [2] that a twistmap with a non Birkhoff periodic orbit of type (p; q) (gcd(p; q) = 1 must have positive topological entropy, which clearly implies the theorem.

In this paper is considered the preservation of properties of the ring of coefficients R to the rings R[x] and R [[x]], where R[x] denotes the polynomials ring and R [[x]] is the power series ring. This study is carry out in the context of finite conductor rings; in particular, properties like GCD, G − GCD, coherence, quasi coherence and finite conductor are analized.

BACKGROUND A rare complication of diverticulosis of the colon is giant colonic diverticula (GCD). The condition was first described in English literature in 1953. METHODS A Medline search was undertaken for English, French and German language articles on 'giant colonic diverticula'. RESULTS A total of 135 patients were identified, presenting with a total of 155 GCD. With a complication rate...

We handle a problem to assign the starting offsets of a collision-free schedule in a certain form called a well-formed gcd notation. Each activity in an activity set recurs with its own period. If more than one activity occurs at the same time slot, it is a collision. If a schedule can be constructed as a well-formed gcd notation, the schedule is known to be collision-free. In this paper, we in...