Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains II. The limiting problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The contribution of different androgen receptor domains to receptor dimerization and signaling

The androgen receptor (AR) is a ligand-activated transcription factor of the nuclear receptor superfamily that plays a critical role in male physiology and pathology. Activated by binding of the native androgens testosterone and 5-dihydrotestosterone, the AR regulates transcription of genes involved in the development and maintenance of male phenotype and male reproductive function as well as other tissues such as bone and muscle. Deregulation of AR signaling can cause a diverse range of clinical conditions, including the X-linked androgen insensitivity syndrome, a form of motor neuron disease known as Kennedy’s disease, and male infertility. In addition, there is now compelling evidence that the AR is involved in all stages of prostate tumorigenesis including initiation, progression, and treatment resistance. To better understand the role of AR signaling in the pathogenesis of these conditions, it is important to have a comprehensive understanding of the key determinants of AR structure and function. Binding of androgens to the AR induces receptor dimerization, facilitating DNA binding and the recruitment of cofactors and transcriptional machinery to regulate expression of target genes. Various models of dimerization have been described for the AR, the most well characterized interaction being DNA-binding domain- mediated dimerization, which is essential for the AR to bind DNA and regulate transcription. Additional AR interactions with potential to contribute to receptor dimerization include the intermolecular interaction between the AR amino terminal domain and ligand-binding domain known as the N-terminal/C-terminal interaction, and ligand-binding domain dimerization. In this review, we discuss each form of dimerization utilized by the AR to achieve transcriptional competence and highlight that dimerization through multiple domains is necessary for optimal AR signaling.

Domains of rural social work practice

Even though there is substantial agreement about the nature of rural contexts, practice principles, and factors influencing practice we still do not have a framework for organising this knowledge in a way that can directly inform the practitioner in their day-to-day work. In this paper, we introduce the concepts 'practice domains', 'domain location', and 'domain alignment' that, taken together, provide such a framework. We suggest that each practitioner works within a number of practice domains. A domain is a discourse about practice comprising narratives about how a social worker should practise and which factors they should take most account of in their practice decision making. Each practitioner, and each practice process, can be located somewhere within each domain (domain location) and also situated amongst domains according to their relative alignment with each of them (domain alignment). In this paper, we present this framework and show how it is useful for practitioners in understanding practice, identifying factors influencing it, and making practice decisions in immediate, concrete situations.

A general procedure for the derivation of principal domains of higher-order spectra

A general procedure to determine the principal domain (i.e., nonredundant region of computation) of any higher-order spectrum is presented, using the bispectrum as an example. The procedure is then applied to derive the principal domain of the trispectrum of a real-valued, stationary time series. These results are easily extended to compute the principal domains of other higher-order spectra

The influence of deprivation domains on malnutrition risk in outpatients with chronic obstructive pulmonary disease

Deprivation assessed using the Index of Multiple Deprivation (IMD) has been shown to be an independent risk factor for both malnutrition and mortality in outpatients with chronic obstructive pulmonary disease (COPD) (Collins et al., 2010a, b). IMD consists of a range of different deprivation domains, although it is unclear which ones are most closely linked to malnutrition. The aim of the current study was to investigate whether the relationship between malnutrition and deprivation was a general one, affecting all domains in a consistent manner, or specific, affecting only certain domains.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.