Resumo em Inglês:

There are given sufficient conditions for the asymptotic stability of the zero solution of equation (1.1) with p = 0 and the boundedness of all solutions of the same equation (1.1), with p <FONT FACE=Symbol>¹</FONT> 0.

Resumo em Inglês:

This paper pursues the study carried out by the authors in Stability and Hopf bifurcation in the Watt governor system [14], focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system, as presented in Pontryagin's book Ordinary Differential Equations, [13]. Here are studied the codimension two and three Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, illustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found a region in the space of parameters where an attracting periodic orbit coexists with an attracting equilibrium.

Resumo em Inglês:

In this work, a stationary Stokes flow with thermal effects is studied both mathematically and numerically. First, existence, uniqueness and regularity of the weak solution of the problem are established. Next, finite element approximation to the problem, based on a fixed point algorithm, is proposed. Then, an error estimate between continuous solution and discrete one is obtained. Finally, some numerical tests are presented to confirm the theoretical results.

Resumo em Inglês:

This paper deals with the modelling of injection moulding processes taking into account the deformability of the preform and the polymerisation of the resin. The coupled flow-deformation problem in the infiltrated and dry region is formulated with the corresponding boundary conditions and with the proper evolution equations determining the motion of the boundaries. An approximated analytical discussion is performed to obtain some estimates on the infiltration velocity, helping in identifying a window of applicability in the parameters space (i.e., the mouldability diagram), which fits well with the numerical simulations.

Resumo em Inglês:

In this article, we propose to model the inverse of a given matrix as the state of a proper first order matrix differential equation. The inverse can correspond to a finite value of the independent variable or can be reached as a steady state. In both cases we derive corresponding dynamical systems and establish stability and convergence results. The application of a numerical time marching scheme is then proposed to compute an approximation of the inverse. The study of the underlying schemes can be done by using tools of numerical analysis instead of linear algebra techniques only. With our approach, we recover some known schemes but also introduce new ones. We derive in addition a masked dynamical system for computing sparse inverse approximations. Finally we give numerical results that illustrate the validity of our approach.

Resumo em Inglês:

We discuss the convergence of line search methods for minimization. We explain how Newton's method and the BFGS method can fail even if the restrictions of the objective function to the search lines are strictly convex functions, the level sets of the objective functions are compact, the line searches are exact and the Wolfe conditions are satisfied. This explanation illustrates a new way to combine general mathematical concepts and symbolic computation to analyze the convergence of line search methods. It also illustrate the limitations of the asymptotic analysis of the iterates of nonlinear programming algorithms.