The nonlinear problem of two membranes

The problem of finding the position of two membranes, one constrained by the other, attached to rigid supports, subjected to external forces, is considered. It is proved existence of solution, if we assume a compatibility condition relating the mean curvature of the boundary of the set where the problem is defined and the given data. It is also proved the W^{2,p} regularity of the solution for P greater or equal to 1.Fundação para a Ciência e a Tecnologia (FCT

Variational problems with non-constant gradient constraints

This paper studies existence, uniqueness, continuous dependence on the given data and the asymptotic behavior of the solution of an evolutive variational inequality with non-constant gradient constraint and homogeneous Dirichlet boundary condition. With assumptions on the given data, we prove existence of solution for a variational inequality with two obstacles, a Lagrange multiplier problem and an equation with gradient constraint. Equivalence of these problems with the variational inequality with gradient constraint is proved. An example of non-equivalence among these problems is given in order to show the necessity of the assumptions

The inhibitory activity of synthetic compounds and ions against transporters of multi-drug resistant bacteria

RESUMO: Sessenta e três derivados de hidantoína foram utilizados para avaliar possíveis efeitos de modulação na actividade das bombas de efluxo (BE) na Salmonella NCTC 13349 utilizando um método fluorimétrico semi-automático. Nenhum dos compostos apresentaram actividade anti-bacteriana até concentrações de 240 mg/L. Entre todos os compostos, SZ-7 demonstrou possuir propriedades de modulação de effluxo na presença de glucose. Para testar esta actividade, estirpes de Salmonella resistentes à ciprofloxacina, induzidas a elevados níveis de resistência com sobre-expressão de BE, foram expostas ao SZ-7. Este derivado afectou a susceptibilidade das estirpes à ciprofloxacina. Uma vez que os 63 compostos estudados apresentaram pouco efeito inibitório /cumulativo, apesar de serem conhecidos pelos seus efeitos moduladores de BE-dependentes de iões em eucariotas, foi questionado o papel dos iões na regulação de BE bacterianas, que poderão influenciar a eficácia de novos compostos. Para este estudo, utilizamos a Escherichia coli AG100 como modelo, devido ao extenso conhecimento no que respeita a estrutura e actividade das BE. Devido à importância de iões de cálcio (Ca2+) nos canais de transporte membranar e na actividade de ATPases, a sua actividade na modulação do efluxo foi investigada. De resultados anteriormente obtidos concluiu-se que a pH 5 o efluxo é independente de energia metabólica; contudo, a pH 8 é absolutamente dependente, sendo que o Ca2+ é indispensável para manter a actividade das ATPases bacterianas. A acumulação/effluxo de EtBr pela E. coli AG100 foi determinada na presença/ausência de Ca2+, clorpromazina (inibidor de ligação de Ca2+ a proteínas), e ácido etilenodiamino tetra-acético (quelante de Ca2+). Acumulação/effluxo aumentou a pH 8, contudo o Ca2+ reverte estes efeitos evidenciando a sua importância no funcionamento das BE bacterianas. Em resumo este trabalho colocou em evidência que muitos aspectos bioquímicos e bioenergéticos devem ser tomados em consideração no estudo da resistência bacteriana mediada por BE.------- ABSTRACT: Sixty-three hydantoin derivatives were evaluated for their modulating effects on efflux pump (EP) activity of Salmonella NCTC 13349 utilizing a semi-automatic fluorometric method. None of the compounds presented antibacterial activities at concentrations as high as 240 mg/L. Among all compounds, SZ-7 showed possible efflux modulating activity in the presence of glucose, indicative of a potential EP inhibitor. To verify its potential effects, ciprofloxacin-resistant Salmonella strains, induced to high level resistance with over-expressing EPs, were exposed to SZ-7. This derivative affected the susceptibility of the ciprofloxacin-resistant strains. Since the 63 compounds studied had very low inhibitory/accumulative effects, even though their known for being efficient in modulating ion-driven eukaryotic EPs, we questioned whether ions had a leading role in regulating bacterial EPs, influencing the effectiveness of new compounds. For this study we used Escherichia coli AG100 as a model, due to the extensive knowledge on its EPs structure and activity. Owing the importance of calcium ions (Ca2+) for membrane transport channels and activity of ATPases, the role of Ca2+ was investigated. From previous results we concluded that at pH 5 efflux is independent of metabolic energy; however, at pH 8 it is entirely dependent of metabolic energy and the Ca2+ ions are essential to maintain the activity of bacterial ATPases. Accumulation and efflux of ethidium bromide (EtBr) by E. coli AG100 was determined in the presence and absence of Ca2+, chlorpromazine (inhibitor of Ca2+-binding to proteins), and ethylenediaminetetraacetic acid (Ca2+ chelator). Accumulation of EtBr increased at pH 8; however Ca2+ reversed these effects providing information as to the importance of this ion in the regulation of bacterial EP systems. Overall this work puts in evidence that many biochemical and bioenergetic aspects related to the strains physiology need to be taken into consideration in bacterial drug resistance mediated by EPs

A two obstacles coupled problem

We consider a system of an evolutionary variational inequality of two obstacles type, depending on the temperature, coupled with the heat equation. We prove existence of solution of this system and we present examples that motivated this work. In particular, with additional assumptions on the data, we prove that solutions of this problem are also solutions of a similar problem where the convex set is of gradient constraint type (that depends on the temperature), improving a previous result.This research was partially supported by CMAT - Centro de Matemática da Universidade do Minho, financed by the Strategic Project PEst-OE/MAT/UI0013/2014

Convergence of convex sets with gradient constraint

Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação (POCTI), União Europeia (UE). Fundo Europeu de Desenvolvimento Regional - (Portugal/FEDER-EU)

A diffusion problem with gradient constraint depending on the temperature

We consider a system of a variational inequality with gradient constraint depending on the temperature, coupled with the heat equation. We prove existence of solution of this system by approximating it by a system of equations and using a fixed point argument.Fundação para a Ciência e a Tecnologia (FCT) - Pluriannual Funding Program, projecto UT-Austin/MAT/0035/2008.Centro de Matemática da Universidade do Minh