SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Comparison of different delivery systems of DNA vaccination for the induction of protection against tuberculosis in mice and guinea pigs

The great challenges for researchers working in the field of vaccinology are optimizing DNA vaccines for use in humans or large animals and creating effective single-dose vaccines using appropriated controlled delivery systems. Plasmid DNA encoding the heat-shock protein 65 (hsp65) (DNAhsp65) has been shown to induce protective and therapeutic immune responses in a murine model of tuberculosis (TB). Despite the success of naked DNAhsp65-based vaccine to protect mice against TB, it requires multiple doses of high amounts of DNA for effective immunization. In order to optimize this DNA vaccine and simplify the vaccination schedule, we coencapsulated DNAhsp65 and the adjuvant trehalose dimycolate (TDM) into biodegradable poly (DL-lactide-co-glycolide) (PLGA) microspheres for a single dose administration. Moreover, a single-shot prime-boost vaccine formulation based on a mixture of two different PLGA microspheres, presenting faster and slower release of, respectively, DNAhsp65 and the recombinant hsp65 protein was also developed. These formulations were tested in mice as well as in guinea pigs by comparison with the efficacy and toxicity induced by the naked DNA preparation or BCG. The single-shot prime-boost formulation clearly presented good efficacy and diminished lung pathology in both mice and guinea pigs.

The effects of long-term endurance training on the immune and endocrine systems of elderly men: the role of cytokines and anabolic hormones

Abstract Background a decline in immune and endocrine function occurs with aging. The main purpose of this study was to investigate the impact of long-term endurance training on the immune and endocrine system of elderly men. The possible interaction between these systems was also analysed. Results elderly runners showed a significantly higher T cell proliferative response and IL-2 production than sedentary elderly controls. IL-2 production was similar to that in young adults. Their serum IL-6 levels were significantly lower than their sedentary peers. They also showed significantly lower IL-3 production in comparison to sedentary elderly subjects but similar to the youngs. Anabolic hormone levels did not differ between elderly groups and no clear correlation was found between hormones and cytokine levels. Conclusion highly conditioned elderly men seem to have relatively better preserved immune system than the sedentary elderly men. Long-term endurance training has the potential to decelerate the age-related decline in immune function but not the deterioration in endocrine function.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Psychophysical analysis of contrast processing segregated into magnocellular and parvocellular systems in asymptomatic carriers of 11778 Leber`s hereditary optic neuropathy

We examined achromatic contrast discrimination in asymptomatic carriers of 11778 Leber`s hereditary optic neuropathy (LHON 18 controls) and 18 age-match were also tested. To evaluate magnocellular (MC) and Parvocellular (PC) contrast discrimination, we used a version of Pokorny and Smith`s (1997) Pulsed/steady-pedestal paradigms (PPP/SPP) thought to be detected via PC and MC pathways, respectively. A luminance pedestal (four 1 degrees x 1 degrees squares) was presented on a 12 cd/m(2) surround. The luminance of one of the squares (trial square, TS) was randomly incremented for either 17 or 133 ms. Observers had to detect the TS, in a forced-choice task, at each duration, for three pedestal levels: 7, 12, 19 cd/m(2). In the SPP, the pedestal was fixed, and the TS was modulated. For the PPP, all four pedestal squares pulsed for 17 or 133 ms, and the TS was simultaneously incremented or decremented. We found that contrast discrimination thresholds of LHON carriers were significantly higher than controls` in the condition with the highest luminance of both paradigms, implying impaired contrast processing with no evidence of differential sensitivity losses between the two systems. Carriers` thresholds manifested significantly longer temporal integration than controls in the SPP, consistent with slowed MC responses. The SPP and PPP paradigms can identify contrast and temporal processing deficits in asymptomatic LHON carriers, and thus provide an additional tool for early detection and characterization of the disease.

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

MATHEMATICAL ANALYSIS OF MAXIMUM POWER GENERATED BY PHOTOVOLTAIC SYSTEMS AND FITTING CURVES FOR STANDARD TEST CONDITIONS

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Periodic averaging theorems for various types of equations

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.