Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Lower-semicontinuity and optimization of convex functionals

The result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b],X) of the regulated functions in [a, b], that is, the functions f : [a, 6] → X that have only descontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we introduce a convex functional Lβf(x) of Nemytskii type, and we present conditions for its lower-semicontinuity. As consequence, Weierstrass Theorem garantees (under compacity conditions) the existence of solution to the problem min{Lβf(x)}. © 2009 Academic Publications.

The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Semigrupos de operadores lineares aplicados às equações diferenciais parciais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Existência de soluções quase automórficas para equações diferenciais abstratas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Soluções quase periódicas para equações diferenciais funcionais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Domínios de potências fracionárias de operadores matriciais segundo Lasiecka-Triggiani

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Soluções quase automórficas para equações diferenciais abstratas de segunda ordem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Free electromagnetic field in Riemannian space-time via DKP theory

We study the massless Duffin-Kemmer-Petiau (DKP) equation in Riemannian space-times, particularly the massless spin 1 sector which reproduces the free Maxwell's equations.

The Effects of Subarachnoid Administration of Preservative-Free S(+)-Ketamine on Spinal Cord and Meninges in Dogs

BACKGROUND: The N-methyl-D-aspartate receptor antagonist ketamine and its active enantiomer, S(+)-ketamine, have been injected in the epidural and subarachnoid spaces to treat acute postoperative pain and relieve neuropathic pain syndrome. In this study we evaluated the effects of a single dose of preservative-free S(+)-ketamine, in doses usually used in clinical practice, in the spinal cord and meninges of dogs.METHODS: Under anesthesia (IV etomidate (2 mg/kg) and fentanyl (0.005 mg/kg), 16 dogs (6 to 15 kg) were randomized to receive a lumbar intrathecal injection (L5/6) of saline solution of 0.9% (control group) or S(+)-ketamine 1 mg/kg(-1) (ketamine group). All doses were administered in a volume of 1 mL over a 10-second interval. Accordingly, injection solution ranged from 0.6% to 1.5%. After 21 days of clinical observation, the animals were killed; spinal cord, cauda equine root, and meninges were removed for histological examination with light microscopy. Tissues were examined for demyelination (Masson trichrome), neuronal death (hematoxylin and eosin) and astrocyte activation (glial fibrillary acidic protein).RESULTS: No clinical or histological alterations of spinal tissue or meninges were found in animals from either control or ketamine groups.CONCLUSION: A single intrathecal injection of preservative-free S(+)-ketamine, at 1 mg/kg-1 dosage, over a concentration range of 6 to 15 mg/mL injected in the subarachnoid space in a single puncture, did not produce histological alterations in this experimental model. (Anesth Analg 2012;114:450-55)

An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

PP-wave light-cone free string field theory at finite temperature

In this paper, a real-time formulation of light-cone pp-wave string field theory at finite temperature is presented. This is achieved by developing the thermo field dynamics (TFD) formalism in a second quantized string scenario. The equilibrium thermodynamic quantities for a pp-wave ideal string gas are derived directly from expectation values on the second quantized string thermal vacuum. Also, we derive the real-time thermal pp-wave closed string propagator. In the flat space limit it is shown that this propagator can be written in terms of Theta functions, exactly as the zero temperature one. At the end, we show how superstrings interactions can be introduced, making this approach suitable to study the BMN dictionary at finite temperature.

A simple action for a free fractional spin particle

By studying classical realizations of the sl(2, R-fraktur sign) algebra in a two dimensional phase space (q,π), we have derived a continuous family of new actions for free fractional spin particles in 2 + 1 dimensions. For the case of light-like spin vector (SμSμ = 0), the action is remarkably simple. We show the appearence of the Zitterbewegung in the solutions of the equations of motion, and relate the actions to others in the literature at classical level. © 1997 Elsevier Science B.V.