Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

PHA(MCL) biosynthesis systems in Pseudomonas aeruginosa and Pseudomonas putida strains show differences on monomer specificities

The production of PHA from plant oils by Pseudomonas species soil isolated from a sugarcane crop was evaluated. Out of 22 bacterial strains three were able to use efficiently plant oils to grow and to accumulate PHA. Pseudomonas putida and Pseudomonas aeruginosa strains produced PHA presenting differences on monomer composition compatible with variability on monomer specificity of their PHA biosynthesis system. The molar fraction of 3-hydroxydodecanoate detected in the PHA was linearly correlated to the oleic acid supplied. A non-linear relationship between the molar fractions of 3-hydroxy-6-dodecenoate (3HDd Delta(6)) detected in PHA and the linoleic acid supplied was observed, compatible with saturation in the biosynthesis system capability to channel intermediate of P-oxidation to PHA synthesis. Although P. putida showed a higher 3HDd Delta(6) yield from linoleic acid when compared to P. aeruginosa, in both species it was less than 10% of the maximum theoretical value. These results contribute to the knowledge about the biosynthesis of PHA with a controlled composition from plant oils allowing in the future establishing the production of these polyesters as tailor-made polymers. (C) 2009 Elsevier B.V. All rights reserved.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.