Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

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.

Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Existence and stability of new nanoreactors: Highly swollen hexagonal liquid crystals

We report the preparation of direct hexagonal liquid crystals, constituted of oil-swollen cylinders arranged on a triangular lattice in water. The volume ratio of oil over water, rho, can be as large as 3.8. From the lattice parameter measured by small-angle X-ray scattering, we show that all the oil is indeed incorporated into the cylinders, thus allowing the diameter of the cylinders to be controlled over one decade range, provided that the ionic strength of the aqueous medium and rho are varied concomitantly. These hexagonal swollen liquid crystals (SLCs) have been first reported with sodium dodecyl sulfate as anionic surfactant, cyclohexane as solvent, 1-pentanol as co-surfactant, and sodium chloride as salt (Ramos, L.; Fabre, P. Langmuir 1997, 13, 13). The stability of these liquid crystals is investigated when the pH of the aqueous medium or the chemical nature of the components (salt and surfactant) is changed. We demonstrate that the range of stability is quite extended, rendering swollen hexagonal phases potentially useful for the fabrication of nanomaterials. As illustrations, we finally show that gelation of inorganic particles in the continuous aqueous medium of a SLC and polymerization within the oil-swollen cylinders of a SLC can be conducted without disrupting the hexagonal order of the system.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Effects of ginger (Zingiber officinale Roscoe) on DNA damage and development of urothelial tumors in a mouse bladder carcinogenesis model

Extracts of the spice ginger (Zingiber officinale Roscoe) are rich in gingerols and shogaols, which exhibit antioxidant, anti-inflammatory, antifungal, anti mycobacterial, and anticarcinogenic proprieties. The present study evaluated the chemoprotective effects of a ginger extract on the DNA damage and the development of bladder cancer induced by N-butyl-N-(4-hydroxibutyl) nitrosamine (BBN)/N-methyl-N-nitrosourea (MNU) in male Swiss mice. Groups G1-G3 were given 0.05% BBN in drinking water for 18 weeks and four i.p. injections of 30 mg/kg body weight MNU at 1, 3, 10, and 18 weeks. Group G4 and G5 received only the BBN or MNU treatments, respectively, and groups G6 and G7 were not treated with BBN or MNU. Additionally, Groups G2, G3, and G6 were fed diets containing 1, 2, and 2% ginger extract, respectively, while Groups G1, G4, G5, and G7 were fed basal diet. Samples of peripheral blood were collected during the experiment for genotoxicity analysis; blood collected 4 hr after each MNU dose was used for the analysis of DNA damage with the Comet assay (assay performed on leukocytes from all groups), while reficulocytes collected 24 hr after the last MNU treatment of Groups G5-G7 were used for the micronucleus assay. At the end of the experiment, the urinary bladder was removed, fixed, and prepared for histopathological, cell proliferation, and apoptosis evaluations. Ginger by itself was not genotoxic, and it did not alter the DNA damage levels induced by the BBN/MNU treatment during the course of the exposure. The incidence and multiplicity of simple and nodular hyperplasia and transitional cell carcinoma (TCC) were increased by the BBN/MNU treatment, but dietary ginger had no significant effect on these responses. However, in Group G2 (BBN/MNU/2% ginger-treated group), there was an increased incidence of Grade 2 TCC. The results suggest that ginger extract does not inhibit the development of BBN-induced mouse bladder tumors.

Stability, characterization and functionality of proton conducting NiO-BaCe0.85-xNbxY0.15O3-delta cermet anodes for IT-SOFC application

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

A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Método das aproximações sucessivas e aplicações

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Introdução às equações diferenciais ordinárias e aplicações: Ana Claudia Chinchio. -

Pós-graduação em Matemática Universitária - IGCE

Absolute continuity and existence of solutions to dynamic inclusions in time scales

We provide some properties for absolutely continuous functions in time scales. Then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question. We also introduce the so called Euler solution to dynamical systems in time scales and prove its existence. A combination of the existence of Euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty, compact, convex and has closed graph. © 2012 Springer-Verlag.

Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.