Generalized nonuniform dichotomies and local stable manifolds

We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.Comment: 18 pages. New version with minor corrections and an additional theorem and an additional exampl

Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

A ara romana de Vila Velha de Mourão

Volta a estudar-se, do ponto de vista epigráfico, a ara romana, que fora encontrada, em reaproveitamento, na parede norte da igreja da Vila Velha de Mourão (distrito de Évora, Conventus Pacensis). A novidade prende-se com a nova interpretação dada à 1ª linha da epígrafe: D(iis) D(eabus) O(mnibus) S(acrum)

Physics with nonperturbative quantum gravity: radiation from a quantum black hole

We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a definitely non-thermal spectrum. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area, computed using the loop representation of quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov spectrum, but --effectively-- a Hawking's thermal spectrum. The Bekenstein-Mukhanov result is therefore likely to be an artefact of the naive ansatz, rather than a robust result. The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.Comment: 4 pages, latex-revtex, no figure

Thermodynamic formalism for contracting Lorenz flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ for the contracting Lorenz flow and for $t$ in an interval containing $[0,1]$. We also analyse the Lyapunov spectrum of the flow in terms of the pressure

What Factors Determine the Levels of Physical Activity after Cardiac Rehabilitation Program?

introdução: Os Programas de Reabilitação Cardíaca ganharam enorme relevância na prevenção de doenças cardiovasculares constituindo um desafio assegurar a prática de exercício físico regular durante e após o fim do programa supervisionado. O objetivo deste trabalho foi determinar os fatores que influenciam os hábitos de atividade física 12 meses após um Programa de Reabilitação Cardíaca.Material e Métodos: Estudo prospetivo abrangendo 580 doentes com cardiopatia isquémica consecutivamente orientados para Programas de Reabilitação Cardíaca na Unidade de Reabilitação Cardiovascular do Centro Hospitalar do Porto, entre Janeiro de 2008 e Junho de 2011. Avaliaram-se os níveis de atividade física através do International Physical Activity Questionnaire realizado no início do programa, aos 3 e 12 meses depois. Foram testados como potenciais determinantes dos hábitos de atividade física a longo prazo: idade; sexo; fatores de risco modificáveis; capacidade funcional (alcançada em prova de esforço); análises laboratoriais (HbA1c, perfil lipídico, Proteína C Reativa e Peptideo Natriurético Cerebral). Realizou-se análise de regressão linear para identificar os preditores significativos e encontrar o melhor ajuste do modelo.Resultados: A idade avançada, género feminino, a capacidade funcional, níveis de atividade física baixos previamente ao Programa de Reabilitação Cardíaca e uma fraca evolução do International Physical Activity Questionnaire durante o programa foram os melhores preditores univariáveis de uma evolução menos favorável do International Physical Activity Questionnaire nos 12 meses de follow-up. A análise de regressão linear multivariável concluiu que o melhor modelo explicativo incluía: idade, género, evolução do IPAQ no programa (R2 ajust = 0,318; f = 60,62; p < 0,001).Conclusão: A identificação de subgrupos de doentes com menor tendência à prática de atividade física permite desenvolver estratégias individualizadas, maximizando o potencial terapêutico e preventivo dos Programas de Reabilitação Cardíaca

Spectrum of Charged Black Holes - The Big Fix Mechanism Revisited

Following an earlier suggestion of the authors(gr-qc/9607030), we use some basic properties of Euclidean black hole thermodynamics and the quantum mechanics of systems with periodic phase space coordinate to derive the discrete two-parameter area spectrum of generic charged spherically symmetric black holes in any dimension. For the Reissner-Nordstrom black hole we get $A/4G\hbar=\pi(2n+p+1)$, where the integer p=0,1,2,.. gives the charge spectrum, with $Q=\pm\sqrt{\hbar p}$. The quantity $\pi(2n+1)$, n=0,1,... gives a measure of the excess of the mass/energy over the critical minimum (i.e. extremal) value allowed for a given fixed charge Q. The classical critical bound cannot be saturated due to vacuum fluctuations of the horizon, so that generically extremal black holes do not appear in the physical spectrum. Consistency also requires the black hole charge to be an integer multiple of any fundamental elementary particle charge: $Q= \pm me$, m=0,1,2,.... As a by-product this yields a relation between the fine structure constant and integer parameters of the black hole -- a kind of the Coleman big fix mechanism induced by black holes. In four dimensions, this relationship is $e^2/\hbar=p/m^2$ and requires the fine structure constant to be a rational number. Finally, we prove that the horizon area is an adiabatic invariant, as has been conjectured previously.Comment: 21 pages, Latex. 1 Section, 1 Figure added. To appear in Class. and Quant. Gravit

Vaccine-elicited memory CD4+ T cell expansion is impaired in the lungs during tuberculosis

Immunological memory is the key biological process that makes vaccines possible. Although tuberculosis vaccines elicit protective immunity in animals, few provide durable protection. To understand why protection is transient, we evaluated the ability of memory CD4+ T cells to expand, differentiate, and control Mycobacterium tuberculosis. Both naive and memory CD4+ T cells initially proliferated exponentially, and the accumulation of memory T cells in the lung correlated with early bacterial control. However, later during infection, memory CD4+ T cell proliferation was curtailed and no protection was observed. We show that memory CD4+ T cells are first activated in the LN and their recruitment to the lung attenuates bacterial growth. However, their interaction with Mtb-infected macrophages does not promote continued proliferation. We conclude that a lack of sustained expansion by memory-derived T cells in the lung limits the durability of their protection, linking their slower expansion with transient protection in vaccinated mice