Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

Limit sets and the Poincare-Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincare-Bendixson Theorem for impulsive semidynamical systems. (C) 2008 Elsevier Inc. All rights reserved.

A transformational language for mutant description

Mutation testing has been used to assess the quality of test case suites by analyzing the ability in distinguishing the artifact under testing from a set of alternative artifacts, the so-called mutants. The mutants are generated from the artifact under testing by applying a set of mutant operators, which produce artifacts with simple syntactical differences. The mutant operators are usually based on typical errors that occur during the software development and can be related to a fault model. In this paper, we propose a language-named MuDeL (MUtant DEfinition Language)-for the definition of mutant operators, aiming not only at automating the mutant generation, but also at providing precision and formality to the operator definition. The proposed language is based on concepts from transformational and logical programming paradigms, as well as from context-free grammar theory. Denotational semantics formal framework is employed to define the semantics of the MuDeL language. We also describe a system-named mudelgen-developed to support the use of this language. An executable representation of the denotational semantics of the language is used to check the correctness of the implementation of mudelgen. At the very end, a mutant generator module is produced, which can be incorporated into a specific mutant tool/environment. (C) 2008 Elsevier Ltd. All rights reserved.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Generating segmented meshes from textured color images

This paper presents a new framework for generating triangular meshes from textured color images. The proposed framework combines a texture classification technique, called W-operator, with Imesh, a method originally conceived to generate simplicial meshes from gray scale images. An extension of W-operators to handle textured color images is proposed, which employs a combination of RGB and HSV channels and Sequential Floating Forward Search guided by mean conditional entropy criterion to extract features from the training data. The W-operator is built into the local error estimation used by Imesh to choose the mesh vertices. Furthermore, the W-operator also enables to assign a label to the triangles during the mesh construction, thus allowing to obtain a segmented mesh at the end of the process. The presented results show that the combination of W-operators with Imesh gives rise to a texture classification-based triangle mesh generation framework that outperforms pixel based methods. Crown Copyright (C) 2009 Published by Elsevier Inc. 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.

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Screening the Schistosoma mansoni transcriptome for genes differentially expressed in the schistosomulum stage in search for vaccine candidates

Schistosomiasis affects more than 200 million people worldwide; another 600 million are at risk of infection. The schistosomulum stage is believed to be the target of protective immunity in the attenuated cercaria vaccine model. In an attempt to identify genes up-regulated in the schistosomulum stage in relation to cercaria, we explored the Schistosoma mansoni transcriptome by looking at the relative frequency of reads in EST libraries from both stages. The 400 genes potentially up-regulated in schistosomula were analyzed as to their Gene Ontology categorization, and we have focused on those encoding-predicted proteins with no similarity to proteins of other organisms, assuming they could be parasite-specific proteins important for survival in the host. Up-regulation in schistosomulum relative to cercaria was validated with real-time reverse transcription polymerase chain reaction (RT-PCR) for five out of nine selected genes (56%). We tested their protective potential in mice through immunization with DNA vaccines followed by a parasite challenge. Worm burden reductions of 16-17% were observed for one of them, indicating its protective potential. Our results demonstrate the value and caveats of using stage-associated frequency of ESTs as an indication of differential expression coupled to DNA vaccine screening in the identification of novel proteins to be further investigated as potential vaccine candidates.

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators {A(t) : t is an element of 1}. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of solutions for second order partial neutral functional differential equations

We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

Differential regulation of PGC-1 alpha expression in rat liver and skeletal muscle in response to voluntary running

Background: The beneficial actions of exercise training on lipid, glucose and energy metabolism and insulin sensitivity appear to be in part mediated by PGC-1 alpha. Previous studies have shown that spontaneously exercised rats show at rest enhanced responsiveness to exogenous insulin, lower plasma insulin levels and increased skeletal muscle insulin sensitivity. This study was initiated to examine the functional interaction between exercise-induced modulation of skeletal muscle and liver PGC-1 alpha protein expression, whole body insulin sensitivity, and circulating FFA levels as a measure of whole body fatty acid (lipid) metabolism. Methods: Two groups of male Wistar rats (2 Mo of age, 188.82 +/- 2.77 g BW) were used in this study. One group consisted of control rats placed in standard laboratory cages. Exercising rats were housed individually in cages equipped with running wheels and allowed to run at their own pace for 5 weeks. At the end of exercise training, insulin sensitivity was evaluated by comparing steady-state plasma glucose (SSPG) concentrations at constant plasma insulin levels attained during the continuous infusion of glucose and insulin to each experimental group. Subsequently, soleus and plantaris muscle and liver samples were collected and quantified for PGC-1 alpha protein expression by Western blotting. Collected blood samples were analyzed for glucose, insulin and FFA concentrations. Results: Rats housed in the exercise wheel cages demonstrated almost linear increases in running activity with advancing time reaching to maximum value around 4 weeks. On an average, the rats ran a mean (Mean +/- SE) of 4.102 +/- 0.747 km/day and consumed significantly more food as compared to sedentary controls (P < 0.001) in order to meet their increased caloric requirement. Mean plasma insulin (P < 0.001) and FFA (P < 0.006) concentrations were lower in the exercise-trained rats as compared to sedentary controls. Mean steady state plasma insulin (SSPI) and glucose (SSPG) concentrations were not significantly different in sedentary control rats as compared to exercise-trained animals. Plantaris PGC-1 alpha protein expression increased significantly from a 1.11 +/- 0.12 in the sedentary rats to 1.74 +/- 0.09 in exercising rats (P < 0.001). However, exercise had no effect on PGC-1 alpha protein content in either soleus muscle or liver tissue. These results indicate that exercise training selectively up regulates the PGC-1 alpha protein expression in high-oxidative fast skeletal muscle type such as plantaris muscle. Conclusion: These data suggest that PGC-1 alpha most likely plays a restricted role in exercise-mediated improvements in insulin resistance (sensitivity) and lowering of circulating FFA levels.