Estimates for the Sobolev trace constant with critical exponent and applications

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow \|u\|^p_{W^{1,p}(\Omega)} that are independent of $\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.Comment: 22 pages, submitte

Aspects mécaniques du VIVITRON : l'ossature

Les principaux aspects mécaniques du VIVITRON sont abordés à travers la description de l'ossature et du réservoir. Les résultats du calcul des efforts dans l'ossature sont reportés

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

LSD1 cooperates with CTIP2 to promote HIV-1 transcriptional silencing

Microglial cells are the main HIV-1 targets in the central nervous system (CNS) and constitute an important reservoir of latently infected cells. Establishment and persistence of these reservoirs rely on the chromatin structure of the integrated proviruses. We have previously demonstrated that the cellular cofactor CTIP2 forces heterochromatin formation and HIV-1 gene silencing by recruiting HDAC and HMT activities at the integrated viral promoter. In the present work, we report that the histone demethylase LSD1 represses HIV-1 transcription and viral expression in a synergistic manner with CTIP2. We show that recruitment of LSD1 at the HIV-1 proximal promoter is associated with both H3K4me3 and H3K9me3 epigenetic marks. Finally, our data suggest that LSD1-induced H3K4 trimethylation is linked to hSET1 recruitment at the integrated provirus

Changes in neuronal activation patterns in response to androgen deprivation therapy: a pilot study

<p>Abstract</p> <p>Background</p> <p>A common treatment option for men with prostate cancer is androgen deprivation therapy (ADT). However, men undergoing ADT may experience physical side effects, changes in quality of life and sometimes psychiatric and cognitive side effects.</p> <p>Methods</p> <p>In this study, hormone naïve patients without evidence of metastases with a rising PSA were treated with nine months of ADT. Functional magnetic resonance imaging (fMRI) of the brain during three visuospatial tasks was performed at baseline prior to treatment and after nine months of ADT in five subjects. Seven healthy control patients, underwent neuroimaging at the same time intervals.</p> <p>Results</p> <p>ADT patients showed reduced, task-related BOLD-fMRI activation during treatment that was not observed in control subjects. Reduction in activation in right parietal-occipital regions from baseline was observed during recall of the spatial location of objects and mental rotation.</p> <p>Conclusions</p> <p>Findings, while preliminary, suggest that ADT reduces task-related neural activation in brain regions that are involved in mental rotation and accurate recall of spatial information.</p

An Exploratory Study into the Factors Impeding Ethical Consumption

Although consumers are increasingly engaged with ethical factors when forming opinions about products and making purchase decisions, recent studies have highlighted significant differences between consumers’ intentions to consume ethically, and their actual purchase behaviour. This article contributes to an understanding of this “ethical purchasing gap” through a review of existing literature, and the inductive analysis of focus group discussions. A model is suggested which includes exogenous variables such as moral maturity and age which have been well covered in the literature, together with further impeding factors identified from the focus group discussions. For some consumers, inertia in purchasing behaviour was such that the decision-making process was devoid of ethical considerations. Several manifested their ethical views through post-purchase dissonance and retrospective feelings of guilt. Others displayed a reluctance to consume ethically due to personal constraints, a perceived negative impact on image or quality, or an outright negation of responsibility. Those who expressed a desire to consume ethically often seemed deterred by cynicism, which caused them to question the impact they, as an individual, could achieve. These findings enhance the understanding of ethical consumption decisions and provide a platform for future research in this area

Smooth attractors of finite dimension for von Karman evolutions with nonlinear frictional damping localized in a boundary layer

In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the long-time behavior of nonlinear plates has been a topic of recent interest. Since the von Karman plate system is of "hyperbolic type" with critical nonlinearity (noncompact with respect to the phase space), this latter topic is particularly challenging in the case of geometrically constrained and nonlinear damping. In this paper we first show the existence of a compact global attractor for finite-energy solutions, and we then prove that the attractor is both smooth and finite dimensional. Thus, the hyperbolic-like flow is stabilized asymptotically to a smooth and finite dimensional set. Key terms: dynamical systems, long-time behavior, global attractors, nonlinear plates, nonlinear damping, localized dampin

Using a virtual environment to assess cognition in the elderly

YesEarly diagnosis of Alzheimer’s disease (AD) is essential if treatments are to be administered at an earlier point in time before neurons degenerate to a stage beyond repair. In order for early detection to occur tools used to detect the disorder must be sensitive to the earliest of cognitive impairments. Virtual reality (VR) technology offers opportunities to provide products which attempt to mimic daily life situations, as much as is possible, within the computational environment. This may be useful for the detection of cognitive difficulties. We develop a virtual simulation designed to assess visuospatial memory in order to investigate cognitive function in a group of healthy elderly participants and those with a mild cognitive impairment. Participants were required to guide themselves along a virtual path to reach a virtual destination which they were required to remember. The preliminary results indicate that this virtual simulation has the potential to be used for detection of early AD since significant correlations of scores on the virtual environment with existing neuropsychological tests were found. Furthermore, the test discriminated between healthy elderly participants and those with a mild cognitive impairment (MCI)

How do we get there? Effects of cognitive aging on route memory

© 2017 The Author(s) Research into the effects of cognitive aging on route navigation usually focuses on differences in learning performance. In contrast, we investigated age-related differences in route knowledge after successful route learning. One young and two groups of older adults categorized using different cut-off scores on the Montreal Cognitive Assessment (MoCA), were trained until they could correctly recall short routes. During the test phase, they were asked to recall the sequence in which landmarks were encountered (Landmark Sequence Task), the sequence of turns (Direction Sequence Task), the direction of turn at each landmark (Landmark Direction Task), and to identify the learned routes from a map perspective (Perspective Taking Task). Comparing the young participant group with the older group that scored high on the MoCA, we found effects of typical aging in learning performance and in the Direction Sequence Task. Comparing the two older groups, we found effects of early signs of atypical aging in the Landmark Direction and the Perspective Taking Tasks. We found no differences between groups in the Landmark Sequence Task. Given that participants were able to recall routes after training, these results suggest that typical and early signs of atypical aging result in differential memory deficits for aspects of route knowledge