On the zeros of polynomials: An extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier B.V. All rights reserved.

Thermally activated exchange narrowing of the Gd3+ ESR fine structure in a single crystal of Ce1-xGdxFe4P12 (x approximate to 0.001) skutterudite

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stabilizing a class of time delay systems using the Hermite-Biehler theorem

In this paper we use the Hermite-Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. (C) 2003 Elsevier B.V. All rights reserved.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic tau decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic pi(+/-) - pi(0) mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be chi'(0) approximate to (50 MeV)(2). In addition, the fulfillment of the Crewther theorem is demonstrated.

Approximate analytical states of a polynomial potential: an example of symmetry restoration

An approximate analytical expression for the first two eigenvalues of the Schrodinger equation for the potential V(x) = Ax(4) + Bx(2) is achieved by using the Symanzik scaling symmetry. A kind of symmetry restoration when one of the potential parameters changes conveniently is observed. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

DIRAC CONFINEMENT BY A VARIATIONAL APPROACH

An analytical approximate method for the Dirac equation with confining power law scalar plus vector potentials, applicable to the problem of the relativistic quark confinement, is presented. The method consists in an improved version of a saddle-point variational approach and it is applied to the fundamental state of massless single quarks for some especial cases of physical interest. Our treatment emphasizes aspects such as the quantum-mechanical relativistic Virial theorem, the saddle-point character of the critical point of the expectation value of the total energy, as well as the Klein paradox and the behaviour of the saddle-point variational energies and wave functions.

Thermally stimulated depolarizations: Disclosing an approximate universality

This paper presents an approximate universality displayed by thermally stimulated depolarization currents ruled by stretched exponential relaxations when properly re-scaled. A visually perfect universality occurs especially when the energy and the heating rate are varied. It becomes somewhat poorer when the frequency factor or the stretched exponent changes. Empirical relations between the half widths and other pertinent parameters are given.

Approximate expression for the energy of a D-dimensional anharmonic oscillator

An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.