Asymptotic stability of semigroups associated with linear weak dissipative systems with memory

We study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations. We show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution. In the case of the lack of exponential decay, we find the polynomial rate of decay of the solution. Some examples are given.     

Shape preservation regions for six-dimensional spaces

We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables, two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order that the space has shape preserving representations for curves. We describe the shape preserving regions for both families. To our friend Mariano Gasca on occasion of his 60th birthday Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

On the concentration and determination of plutonium in natural waters by adsorption on MnO2 filters

A new method of analysis of the efficiency of four filters of MnO₂ in series which takes into account the reactions induced in plutonium by the sorbent is described. The system of differential equations describing the behaviour of plutonium in water as it passes through the filters is solved and the parameters of the filters are determined for a best fitting of the solutions corresponding to the experimental uncertainties. The method is checked by numerical simulation and then applied to water solutions with a known plutonium concentration and to some experimental results given by other authors. In all occassions the results are consistent with the possibility of determining the contents of plutonium in sea and continental waters with uncertainties of the order of 10%.     

Improvement of the properties of polyarylate reinforced with liquid crystalline polymers

Blends of polyarylate of bisphenol A, PAr, with two commercial main chain liquid crystalline polymers, Vectra A950 and Vectra B950, are studied. From dynamic viscoelastic measurements it is deduced that both systems (PAr/Vectra A950 and PAr/Vectra B950) are immiscible and scanning electron microscopy (SEM) micrographs show the presence of spherical domains of the liquid crystalline polymer when PAr constitutes the matrix. Extrusion capillary measurements reveal that, under conditions of temperature and shear rate similar to those of processing, the viscosity is reduced to approximately 10% of its value when the content of liquid crystalline polymer is only 20%. This great improvement of the rheological properties is observed in both PAr/Vectra A950 and PAr/Vectra B950 blends. The effect of draw ratio on Young's modulus for different compositions is also analyzed, pointing out the reinforcing action of both liquid crystalline polymers on polyarylate: for instance, 20% of Vectra B950 in the blend gives rise to a 700% increase of the modulus of fibres prepared at a draw ratio of 50. SEM of the extrudates reveals that the spherical domains are elongated at the entrance of the capillary giving rise to a microfibrillar morphology which is related to the excellent rheological and mechanical properties of the blends.     

Lattices contained in planar orders are planar

The covering graph of a lattice which is contained in an ordered set with a planar covering graph is itself planar.Presented by R. W. Quackenbush.     

Local solution for the Kadomtsev-Petviashvili equation with periodic conditions

In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u _t +u _xxx +uu _x ) _x −u _yy =0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based upon the application of singular perturbation techniques.     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.