Michael Gil’ Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel Correspondence should be addressed to Michael Gil’, [email protected] Received 20 March 2012; Accepted 28 May 2012 Academic Editor: Andrei Volodin Copyright q 2012 Michael Gil’. This is an open access article distributed under the Creative Commons Attribution License, which permit...

We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on an algebraic relationship between proper parametrizations of a same curve, which leads to a triangular polynomial system that can be solved in a very fast way; in particular, curves parametrized by polynomials of ...

A graph is called (generically) rigid in Rd if, for any choice of sufficiently generic edge lengths, it can be embedded in Rd in a finite number of distinct ways, modulo rigid transformations. Here we deal with the problem of determining the maximum number of planar Euclidean embeddings as a function of the number of the vertices. We obtain polynomial systems which totally capture the structure...

Scalar linear time-varying systems are addressed. In particular, a new factorization method for the associated scalar polynomial system differential operator is presented. It differs from the classical results due to Cauchy and Floquet, in that it is based upon successive Riccati transformations of the Frobenius companion system matrix. As a consequence, the factorization is obtained in terms o...

When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {Pn(x)}∞n=0, we consider a point masses perturbation τ of σ given by τ := σ+ λ ∑m l=1 ∑ml k=0((−1) ulk/k!)δ (x− cl), where λ, ulk, and cl are constants with ci = cj for i = j. That is, τ is a generalized Uvarov transform of σ satisfying A(x)τ = A(x)σ, where A(x) = ∏m l=1(x− cl) l. We find necessary and suff...

In this work, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve the limit cycle problem for a general Liénard polynomial systemwith an arbitrary (but finite) number of singular points. © 2012 Elsevier Ltd. All rights reserved.

We classify generic systems of polynomial equations with a single solution, or, equivalently, collections of lattice polytopes of minimal positive mixed volume. As a byproduct, this classification provides an algorithm to evaluate the single solution of such a system.

Polynomial equations with perturbed coefficients arise in several areas of engineering sciences, for instance, in automatic control theory, dynamical systems, optimization and in control theory. For such equations, it is necessary to study their roots and to establish a priori estimates to define regions containing such roots. Attending to the fact that these equations can be seen as algebraic ...

Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...