Perturbed eigenvalues of polyharmonic operators in domains with small holes

We study singular perturbations of eigenvalues of the polyharmonic operator on bounded domains under removal of small interior compact sets. We consider both homogeneous Dirichlet and Navier conditions on the external boundary, while we impose homogeneous Dirichlet conditions on the boundary of the removed set. To this aim, we develop a notion of capacity which is suitable for our higher-order context, and which permits to obtain a description of the asymptotic behaviour of perturbed simple eigenvalues in terms of a capacity of the removed set, in dependence of the respective normalized eigenfunction. Then, in the particular case of a subset which is scaling to a point, we apply a blow-up analysis to detect the precise convergence rate, which turns out to depend on the order of vanishing of the eigenfunction. In this respect, an important role is played by Hardy-Rellich inequalities in order to identify the appropriate functional space containing the limiting profile. Remarkably, for the biharmonic operator this turns out to be the same, regardless of the boundary conditions prescribed on the exterior boundary

Targeting RAGE prevents muscle wasting and prolongs survival in cancer cachexia

Background: Cachexia, a multifactorial syndrome affecting more than 50% of patients with advanced cancer and responsible for ~20% of cancer-associated deaths, is still a poorly understood process without a standard cure available. Skeletal muscle atrophy caused by systemic inflammation is a major clinical feature of cachexia, leading to weight loss, dampening patients' quality of life, and reducing patients' response to anticancer therapy. RAGE (receptor for advanced glycation end-products) is a multiligand receptor of the immunoglobulin superfamily and a mediator of muscle regeneration, inflammation, and cancer. Methods: By using murine models consisting in the injection of colon 26 murine adenocarcinoma (C26-ADK) or Lewis lung carcinoma (LLC) cells in BALB/c and C57BL/6 or Ager−/− (RAGE-null) mice, respectively, we investigated the involvement of RAGE signalling in the main features of cancer cachexia, including the inflammatory state. In vitro experiments were performed using myotubes derived from C2C12 myoblasts or primary myoblasts isolated from C57BL/6 wild type and Ager−/− mice treated with the RAGE ligand, S100B (S100 calcium-binding protein B), TNF (tumor necrosis factor)α±IFN (interferon) γ, and tumour cell- or masses-conditioned media to analyse hallmarks of muscle atrophy. Finally, muscles of wild type and Ager−/− mice were injected with TNFα/IFNγ or S100B in a tumour-free environment. Results: We demonstrate that RAGE is determinant to activate signalling pathways leading to muscle protein degradation in the presence of proinflammatory cytokines and/or tumour-derived cachexia-inducing factors. We identify the RAGE ligand, S100B, as a novel factor able to induce muscle atrophy per se via a p38 MAPK (p38 mitogen-activated protein kinase)/myogenin axis and STAT3 (signal transducer and activator of transcription 3)-dependent MyoD (myoblast determination protein 1) degradation. Lastly, we found that in cancer conditions, an increase in serum levels of tumour-derived S100B and HMGB1 (high mobility group box 1) occurs leading to chronic activation/overexpression of RAGE, which induces hallmarks of cancer cachexia (i.e. muscle wasting, systemic inflammation, and release of tumour-derived pro-cachectic factors). Absence of RAGE in mice translates into reduced serum levels of cachexia-inducing factors, delayed loss of muscle mass and strength, reduced tumour progression, and increased survival. Conclusions: RAGE is a molecular determinant in inducing the hallmarks of cancer cachexia, and molecular targeting of RAGE might represent a therapeutic strategy to prevent or counteract the cachectic syndrome

Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case

We study the nonlinear Schrodinger equation for the s-fractional p-Laplacian strongly coupled with the Poisson equation in dimension two and with p =2s, which is the limiting case for the embedding of the fractional Sobolev space Ws,p(R2). We prove existence of solutions by means of a variational approximating procedure for an auxiliary Choquard equation in which the uniformly approximated sign-changing logarithmic kernel competes with the exponential nonlinearity. Qualitative properties of solutions such as symmetry and decay are also established by exploiting a suitable moving planes technique

Lógica fuzzy aplicada à gerência de distribuição de carga em um grid de computadores.

Os avanços tecnológicos têm levado a um aumento no volume de dados científicos disponíveis, seja por meio da coleta feita por diferentes senso- res, como por modelos matemáticos que geram inúmeras saídas distintas. Especialmente nas pesquisas em mudanças climáticas, os especialistas têm que lidar com esse grande volume de dados, o que extrapola a capacidade do ser humano de cálculo e análise. Desta forma, o apoio computacional se torna fundamental para alavancar as pesquisas em diferentes áreas. Em busca de uma solução economicamente viável e ecologicamente correta para este problema, e que ainda pudesse ser compartilhada por diversos projetos na empresa, a equipe do projeto SCAF adotou a computação em grade

Recodificando o aplicativo móvel Agritempo a partir de requisitos identificados no processo de validação.

A redefinição de código de aplicativos é de suma importância para que sejam atendidas efetivamente as necessidades do público-alvo. A utilização desta prática propõe revisar, corrigir e/ou adicionar recursos no projeto com base nos dados identificados após as etapas de validação realizadas com futuros usuários, durante o processo de desenvolvimento de software. A revisão de código normalmente é feita após a apresentação de um protótipo aos stakeholders, gerando um relatório contendo os principais pontos a serem revisados. O processo utilizado na validação do aplicativo Agritempo tinha por objetivo a melhoria do aplicativo de forma geral para atender à demanda das diferentes classes de usuários, tornando simples a experiência destes

Redesign participativo do aplicativo móvel Agritempo: a importância da interação usuário-desenvolvedor.

Este trabalho apresenta o impacto da aplicação do DCU no processo de desenvolvimento de um aplicativo móvel para o produtor agrícola por meio de uma validação colaborativa

A quasilinear transmission problem with application to Maxwell equations with a divergence-free D-field

Maxwell equations in the absence of free charges require initial data with a divergence-free displacement field D. In materials in which the dependence D=D(E) is nonlinear the quasilinear problem 07 c5D(E)=0 is hence to be solved. In many applications, e.g. in the modelling of wave packets, an approximative asymptotic ansatz of the electric field E is used, which satisfies this divergence condition at t=0 only up to a small residual. We search then for a small correction of the ansatz to enforce 07 c5D(E)=0 at t=0 and choose this correction in the form of a gradient field. In the usual case of a power type nonlinearity in D(E) this leads to the sum of the Laplace and p-Laplace operators. We also allow for the medium to consist of two different materials so that a transmission problem across an interface is produced. We prove the existence of the correction term for a general class of nonlinearities and provide regularity estimates for its derivatives, independent of the L2-norm of the original ansatz. In this way, when applied to the wave packet setting, the correction term is indeed asymptotically smaller than the original ansatz. We also provide numerical experiments to support our analysis