Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations

In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Measure functional differential equations and functional dynamic equations on time scales

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

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.

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier Inc. All rights reserved.

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Metal biosorption onto dry biomass of Arthrospira (Spirulina) platensis and Chlorella vulgaris: Multi-metal systems

Binary and ternary systems of Ni2+, Zn2+, and Pb2+ were investigated at initial metal concentrations of 0.5, 1.0 and 2.0 mM as competitive adsorbates using Arthrospira platensis and Chlorella vulgaris as biosorbents. The experimental results were evaluated in terms of equilibrium sorption capacity and metal removal efficiency and fitted to the multi-component Langmuir and Freundlich isotherms. The pseudo second order model of Ho and McKay described well the adsorption kinetics, and the FT-IR spectroscopy confirmed metal binding to both biomasses. Ni2+ and Zn2+ interference on Pb2+ sorption was lower than the contrary, likely due to biosorbent preference to Pb. In general, the higher the total initial metal concentration, the lower the adsorption capacity. The results of this study demonstrated that dry biomass of C. vulgaris behaved as better biosorbent than A. platensis and suggest its use as an effective alternative sorbent for metal removal from wastewater. (C) 2012 Elsevier B.V. All rights reserved.

On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R-0 obtained from both approaches are compared, showing good agreement. (C) 2012 Elsevier B.V. All rights reserved.

On a new class of abstract integral equations and applications

In this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations. (C) 2012 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.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

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.