A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

A uniqueness theorem for the determination of sources in the Germain–Lagrange plate equation

We prove a uniqueness result related to the Germain–Lagrange dynamic plate differential equation. We consider the equation {∂2u∂t2+△2u=g⊗f,in ]0,+∞)×R2,u(0)=0,∂u∂t(0)=0, where uu stands for the transverse displacement, ff is a distribution compactly supported in space, and g∈Lloc1([0,+∞)) is a function of time such that g(0)≠0g(0)≠0 and there is a T0>0T0>0 such that g∈C1[0,T0[g∈C1[0,T0[. We prove that the knowledge of uu over an arbitrary open set of the plate for any interval of time ]0,T[]0,T[, 0

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2D

A direct reconstruction algorithm for complex conductivities in W-2,W-infinity(Omega), where Omega is a bounded, simply connected Lipschitz domain in R-2, is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107-19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Measure functional differential equations and functional dynamic equations on time scales

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

Hybrid heuristic-waterfilling game theory approach in MC-CDMA resource allocation

This paper discusses the power allocation with fixed rate constraint problem in multi-carrier code division multiple access (MC-CDMA) networks, that has been solved through game theoretic perspective by the use of an iterative water-filling algorithm (IWFA). The problem is analyzed under various interference density configurations, and its reliability is studied in terms of solution existence and uniqueness. Moreover, numerical results reveal the approach shortcoming, thus a new method combining swarm intelligence and IWFA is proposed to make practicable the use of game theoretic approaches in realistic MC-CDMA systems scenarios. The contribution of this paper is twofold: (i) provide a complete analysis for the existence and uniqueness of the game solution, from simple to more realist and complex interference scenarios; (ii) propose a hybrid power allocation optimization method combining swarm intelligence, game theory and IWFA. To corroborate the effectiveness of the proposed method, an outage probability analysis in realistic interference scenarios, and a complexity comparison with the classical IWFA are presented. (C) 2011 Elsevier B.V. All rights reserved.

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

Minimal Landau background gauge on the lattice

We present the first numerical implementation of the minimal Landau background gauge for Yang-Mills theory on the lattice. Our approach is a simple generalization of the usual minimal Landau gauge and is formulated for the general SU(N) gauge group. We also report on preliminary tests of the method in the four-dimensional SU(2) case, using different background fields. Our tests show that the convergence of the numerical minimization process is comparable to the case of a null background. The uniqueness of the minimizing functional employed is briefly discussed.

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.

Auditory and communicative abilities in the auditory neuropathy spectrum disorder and mutation in the Otoferlin gene: clinical cases study

This study had the aim to investigate the auditory and communicative abilities of children diagnosed with Auditory Neuropathy Spectrum Disorder due to mutation in the Otoferlin gene. It is a descriptive and qualitative study in which two siblings with this diagnosis were assessed. The procedures conducted were: speech perception tests for children with profound hearing loss, and assessment of communication abilities using the Behavioral Observation Protocol. Because they were siblings, the subjects in the study shared family and communicative context. However, they developed different communication abilities, especially regarding the use of oral language. The study showed that the Auditory Neuropathy Spectrum Disorder is a heterogeneous condition in all its aspects, and it is not possible to make generalizations or assume that cases with similar clinical features will develop similar auditory and communicative abilities, even when they are siblings. It is concluded that the acquisition of communicative abilities involves subjective factors, which should be investigated based on the uniqueness of each case.

O Recuo Brutalista

Em conformidade com a dúvida de seu título, o difundido livro The New Brutalism: Ethic or Aesthetic? de Reyner Banham não é possível explicar o Brutalismo como manifestação artística coesa, dotada de consistência e reprodutibilidade formal. A citação de arquitetos famosos, porém divergentes, parece associar e comparar obras ásperas com a pretensão de reerguer uma arquitetura moderna considerada ascética, monótona e insuficiente e gera um teoricismo da aparência crua e do moralismo dos objetos. Discurso que oculta, ou desvia a atenção do retorno artístico à sublimidade e construção artesanal. O Brutalismo é aceito como evolução natural dos estágios modernos anteriores e sanciona artefatos toscos, pesados e inacabados como se fossem filiados ao processo moderno desinfestado. Esconde contradições e disfarça seu rompimento com o moderno para prolongar a expressão Movimento moderno. Mas o objeto claro, econômico e preciso é repudiado pelo consumidor e, por ser pouco representativo, o artista faz sua maquiagem com episódios contrastantes e monumentais na informalidade das cidades espontâneas. No entanto, parece possível suspender a noção positiva e corretiva do Brutalismo para entendê-lo como um recuo artístico vulgarizador que despreza aperfeiçoamento e afronta a atitude moderna com banalização conceptiva, exagero, figuralidade, musculação estrutural, grandeza tectônica, rudimento e rudeza. Assim, moralismo, retorno rústico e originalidade desqualificam a expressão International Style entendida como a culminação da arquitetura moderna do pós-guerra, ao depreciá-la como decadente, como produto imobiliário, comercial e corporativo a serviço do capital. Essa interpretação desvela uma crítica anti-industrial, portanto antimodernista e diversa da pós-modernidade, porém contestadora e realista para fornecer imagens à cultura e aos insensíveis à estrutura da forma moderna. Diverso da pós-modernidade pela dependência ao moderno e ausência de apelo popular. Tornada insignificante a configuração oportuna do artefato, o arquiteto tenta reter sua notabilidade artística, ou o prestígio que parece enfraquecer na aparência símile da especificação de catálogo, no rigor modular. Indispõe-se e repudia componentes, Standards e acabamentos impessoais da indústria da construção para insistir em autoria e inspiração, mas repete cacoetes estilísticos de época e o inexplicável uso intensivo de concreto bruto e aparente para sentir-se engajado e atualizado. Porém, é necessário distinguir obras de aparência severa concebidas pela atitude moderna mais autêntica das de concreto aparente em tipos ou configurações aberrantes. Para avançar na discussão do Brutalismo propõe-se entender este fenômeno com a substituição do juízo estético moderno de sentido visual postulado por Immanuel Kant (1724-1804) por um sentimento estético fácil e relacionado com a sensação da empatia, com a Einfühlung de Robert Vischer (1847-1933). Na época da cultura de massas, admite-se o rebaixamento das exigências no artefato e a adaptação brutalista com a transfiguração dos processos de arquitetura moderna. Assim, a forma é substituída pela figura ou pelo resumo material; a estrutura formal subjacente pelo ritmo e exposição da estrutura física; o reconhecimento visual pelo entusiasmo psicológico ou pelo impulso dionisíaco; a concepção substituída pelo partido, ou, ainda, pelo conceito; a sistematização e a ordem pela moldagem e a organização; a abstração e síntese pela originalidade e essencialidade, o sentido construtivo pela honestidade material; a identidade das partes pela fundição ou pela unicidade objetal e a residência pela cabana primitiva.