SELF-CONSISTENT SOLUTION OF THE SCHWINGER-DYSON EQUATIONS FOR THE NUCLEON AND MESON PROPAGATORS

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

A W-matrix methodology for solving sparse network equations on multiprocessor computers

This paper describes a methodology for solving efficiently the sparse network equations on multiprocessor computers. The methodology is based on the matrix inverse factors (W-matrix) approach to the direct solution phase of A(x) = b systems. A partitioning scheme of W-matrix , based on the leaf-nodes of the factorization path tree, is proposed. The methodology allows the performance of all the updating operations on vector b in parallel, within each partition, using a row-oriented processing. The approach takes advantage of the processing power of the individual processors. Performance results are presented and discussed.

DISSIPATIVE BOUSSINESQ SYSTEM OF EQUATIONS IN THE BENARD-MARANGONI PHENOMENON

By using the long-wavelength approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a Benard-Marangoni system is obtained. It includes nonlinearity, dispersion, and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained.

On some classes of exactly-solvable Klein-Gordon equations

In this work we discuss some exactly solvable Klein-Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials. (c) 2005 Elsevier B.V. All rights reserved.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

On dichotomic maps for non autonomous discrete equations

A new procedure is given for the study of stability and asymptotic stability of the null solution of the non autonomous discrete equations by the method of dichotomic maps, which it includes Liapunov's Method asa special case. Examples are given to illustrate the application of the method.

On the periodic solutions of the static, spherically symmetric Einstein-Yang-Mills equations

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

Applicability of the equations of Freundlich and Langmuir to the adsorption of the azo dye procion scarlet on paramorphic colonies of Neurospora crassa.

Experiments on the adsorption of Procion Scarlet MX-G by normal hyphae and by paramorphic colonies of Neurospora crassa were performed at pH 2.5, 4.5 and 6.5 at 30 degrees C. The measured adsorption isotherms were evaluated by the Freundlich and Langmuir equations. The removal of dye was most effective at pH 2.5 and more dye was adsorbed per unit mass of cells in the paramorphic cultures than in the normal hyphae. The statistical tests showed Langmuir's equation to give a better fit to the adsorption data.