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.

GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

LOSS of EXPONENTIAL STABILITY FOR A THERMOELASTIC SYSTEM WITH MEMORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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

PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

LOWER SEMICONTINUITY of PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

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

Transmission problem for waves with frictional damping April 22, 2007

In this paper we consider the transmission problem, in one space dimension, for linear dissipative waves with frictional damping. We study the wave propagation in a medium with a component with attrition and another simply elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size. ©2007 Texas State University.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Titanium in Dentistry: Historical development, state of the art and future perspectives

Titanium is a metallic element known by several attractive characteristics, such as biocompatibility, excellent corrosion resistance and high mechanical resistance. It is widely used in Dentistry, with high success rates, providing a favorable biological response when in contact with live tissues. Therefore, the objective of this study was to describe the different uses of titanium in Dentistry, reviewing its historical development and discoursing about its state of art and future perspective of its utilization. A search in the MEDLINE/PubMed database was performed using the terms 'titanium', 'dentistry' and 'implants'. The title and abstract of articles were read, and after this first screening 20 articles were selected and their full-texts were downloaded. Additional text books and manual search of reference lists within selected articles were included. Correlated literature showed that titanium is the most used metal in Implantology for manufacturing osseointegrated implants and their systems, with a totally consolidated utilization. Moreover, titanium can be also employed in prosthodontics to obtain frameworks. However, problems related to its machining, casting, welding and ceramic application for dental prosthesis are still limiting its use. In Endodontics, titanium has been used in association to nickel for manufacturing rotatory instruments, providing a higher resistance to deformation. However, although the different possibilities of using titanium in modern Dentistry, its use for prostheses frameworks still needs technological improvements in order to surpass its limitations. © 2012 Indian Prosthodontic Society.

Lack of association between ABO histo-blood groups, secretor and non-secretor phenotypes, and anti-Toxoplasma gondii antibodies among pregnant women from the northwestern region of São Paulo State, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Historical land-cover/use in different slope and riparian buffer zones in watersheds of the state of São Paulo, Brazil

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

Strategic planning for dairy cattle: SWOT analysis applied to a property of a farmers' association in Dracena, São Paulo state, Brazil

The sector of milk production in Brazil is very heterogeneous (high-tech in large scale X family properties). This study aimed to develop a diagnostic as a basis for a strategic plan to face the challenges inherent in operating a dairy farm in property of a farmers' association in Dracena, São Paulo, Brazil. It was observed that the association needs a more efficient guidance in the marketing, production and finance areas, not to compromise the search for new markets and continued growth in activity.