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.

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.

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.

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom-Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed. (C) 2011 Elsevier B.V. All rights reserved.

Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method. Journal of the Operational Research Society (2012) 63, 183-200. doi: 10.1057/jors.2011.6 Published online 17 August 2011

Gender differences in drinking patterns and alcohol-related problems in a community sample in Sao Paulo, Brazil

OBJECTIVE: To investigate drinking patterns and gender differences in alcohol-related problems in a Brazilian population, with an emphasis on the frequency of heavy drinking. METHODS: A cross-sectional study was conducted with a probability adult household sample (n = 1,464) in the city of Sao Paulo, Brazil. Alcohol intake and ICD-10 psychopathology diagnoses were assessed with the Composite International Diagnostic Interview 1.1. The analyses focused on the prevalence and determinants of 12-month non-heavy drinking, heavy episodic drinking (4-5 drinks per occasion), and heavy and frequent drinking (heavy drinking at least 3 times/week), as well as associated alcohol-related problems according to drinking patterns and gender. RESULTS: Nearly 22% (32.4% women, 8.7% men) of the subjects were lifetime abstainers, 60.3% were non-heavy drinkers, and 17.5% reported heavy drinking in a 12-month period (26.3% men, 10.9% women). Subjects with the highest frequency of heavy drinking reported the most problems. Among subjects who did not engage in heavy drinking, men reported more problems than did women. A gender convergence in the amount of problems was observed when considering heavy drinking patterns. Heavy and frequent drinkers were twice as likely as abstainers to present lifetime depressive disorders. Lifetime nicotine dependence was associated with all drinking patterns. Heavy and frequent drinking was not restricted to young ages. CONCLUSIONS: Heavy and frequent episodic drinking was strongly associated with problems in a community sample from the largest city in Latin America. Prevention policies should target this drinking pattern, independent of age or gender. These findings warrant continued research on risky drinking behavior, particularly among persistent heavy drinkers at the non-dependent level.

SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS

Via variational methods, we study multiplicity of solutions for the problem {-Delta u = lambda b(x)vertical bar u vertical bar(q-2)u + au + g(x, u) in Omega, u - 0 on partial derivative Omega, where a simple example for g( x, u) is |u|(p-2)u; here a, lambda are real parameters, 1 < q < 2 < p <= 2* and b(x) is a function in a suitable space L-sigma. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any lambda > 0, and a total of five nontrivial solutions are obtained when lambda is small and a >= lambda(1). Note that this type of results are valid even in the critical case.

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Non-inflammatory destructive periodontal disease: a clinical, microbiological, immunological and genetic investigation

Periodontitis comprises a group of multifactorial diseases in which periodontopathogens accumulate in dental plaque and trigger host chronic inflammatory and immune responses against periodontal structures, which are determinant to the disease outcome. Although unusual cases of non-inflammatory destructive periodontal disease (NIDPD) are described, their pathogenesis remains unknown. A unique NIDPD case was investigated by clinical, microbiological, immunological and genetic tools. The patient, a non-smoking dental surgeon with excessive oral hygiene practice, presented a generalized bone resorption and tooth mobility, but not gingival inflammation or occlusion problems. No hematological, immunological or endocrine alterations were found. No periodontopathogens (A. actinomycetemcomitans, P. gingivalis, F. nucleatum and T. denticola) or viruses (HCMV, EBV-1 and HSV-1) were detected, along with levels of IL-1 beta and TNF-alpha in GCF compatible with healthy tissues. Conversely ALP, ACP and RANKL GCF levels were similar to diseased periodontal sites. Genetic investigation demonstrated that the patient carried some SNPs, as well HLA-DR4 (*0404) and HLA-B27 alleles, considered risk factors for bone loss. Then, a less vigorous and diminished frequency of toothbrushing was recommended to the patient, resulting in the arrest of alveolar bone loss, associated with the return of ALP, ACP and RANKL in GCF to normality levels. In conclusion, the unusual case presented here is compatible with the previous description of NIDPD, and the results that a possible combination of excessive force and frequency of mechanical stimulation with a potentially bone loss prone genotype could result in the alveolar bone loss seen in NIDPD.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

Gender differences in drinking patterns and alcohol-related problems in a community sample in São Paulo, Brazil

OBJECTIVE: To investigate drinking patterns and gender differences in alcohol-related problems in a Brazilian population, with an emphasis on the frequency of heavy drinking. METHODS: A cross-sectional study was conducted with a probability adult household sample (n = 1,464) in the city of São Paulo, Brazil. Alcohol intake and ICD-10 psychopathology diagnoses were assessed with the Composite International Diagnostic Interview 1.1. The analyses focused on the prevalence and determinants of 12-month nonheavy drinking, heavy episodic drinking (4-5 drinks per occasion), and heavy and frequent drinking (heavy drinking at least 3 times/week), as well as associated alcohol-related problems according to drinking patterns and gender. RESULTS: Nearly 22% (32.4% women, 8.7% men) of the subjects were lifetime abstainers, 60.3% were non-heavy drinkers, and 17.5% reported heavy drinking in a 12-month period (26.3% men, 10.9% women). Subjects with the highest frequency of heavy drinking reported the most problems. Among subjects who did not engage in heavy drinking, men reported more problems than did women. A gender convergence in the amount of problems was observed when considering heavy drinking patterns. Heavy and frequent drinkers were twice as likely as abstainers to present lifetime depressive disorders. Lifetime nicotine dependence was associated with all drinking patterns. Heavy and frequent drinking was not restricted to young ages. CONCLUSIONS: Heavy and frequent episodic drinking was strongly associated with problems in a community sample from the largest city in Latin America. Prevention policies should target this drinking pattern, independent of age or gender. These findings warrant continued research on risky drinking behavior, particularly among persistent heavy drinkers at the non-dependent level.