Based on the upper-triangular Hessenberg forms for descriptor linear systems and a method for right coprime factorization of descriptor linear systems using matrix elementary transformations, a simple, neat and numerically stable iterative formula for right coprime factorization of a regular singleinput descriptor linear system is proposed. This iterative formula gives directly the coefficients...

Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(G) is called degree coprime G if for every v∈V-D, there exist vertex u∈D such that uv∈E(G) and (deg u,deg v)=1. The minimum cardinality the domination number denoted by γ_cp (G). non-coprime v)≠1. γ_ncp We obtain some graphs.

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records. 1. The polynomial selection method of Montgomery and Murphy In this section we brief...

In this paper, rate distortion performance of nested sampling and coprime sampling is studied. It is shown that with the increasing of distortion, the data rate decreases. With these two sparse sampling algorithms, the data rate is proved to be much less than that without sparse sampling. With the increasing of sampling spacings, the data rate decreases at certain distortion, which is because w...

Periodical cicadas are known for their unusually long life cycle for insects and their prime periodicity of either 13 or 17 years. One of the explanations for the prime periodicity is that the prime periods are selected to prevent cicadas from resonating with predators with submultiple periods. This paper considers this hypothesis by investigating a population model for periodical predator and ...

In this paper, it is shown that a linear uncertain system described by a certain L 1 multiplicative or relative perturbation in its coprime factors that are not necessarily normalized, is the same as the one described by a gap or-gap metric ball. Hence all the stability robustness results for gap or-gap metric uncertainty carry over to this type of coprime factor perturbation. Uncertain systems...

The unexpected link which is the topic of this article was remarked on by Atiyah himself and his collaborator Raoul Bott in their fundamental 1983 paper [AB83] on the Yang-Mills equations over Riemann surfaces. In this paper Atiyah and Bott used ideas coming from Yang-Mills theory and equivariant Morse theory to derive inductive formulae for the Betti numbers of the moduli spaces M(n, d) of sta...