Regularity of the optimal shape for the first eigenvalue of the Laplacian with volume and inclusion constraints

We consider the well-known following shape optimization problem: $$\lambda_1(\Omega^*)=\min_{\stackrel{|\Omega|=a} {\Omega\subset{D}}} \lambda_1(\Omega),$$ where $\lambda_1$ denotes the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary condition, and $D$ is an open bounded set (a box). It is well-known that the solution of this problem is the ball of volume $a$ if such a ball exists in the box $D$ (Faber-Krahn's theorem). In this paper, we prove regularity properties of the boundary of the optimal shapes $\Omega^*$ in any case and in any dimension. Full regularity is obtained in dimension 2

Schéma de niveaux de 223Ra. I. Rayonnements γ émis dans la désintégration 227Th → 223Ra

Les transitions γ dans 223Ra ont été étudiées à l'aide de diodes Ge-Li en faisant appel à différents procédés de purification et de mesure afin de minimiser l'importance des six descendants radioactifs. A peu près 180 transitions parmi celles observées ont pu être placées dans le schéma de niveaux

Schéma de niveaux de 223Ra II. Spectre d'électrons de conversion interne émis dans la désintégration 227Th → 223Ra

Cet article expose l'ensemble de nos études sur les quelques 300 raies de conversion du spectre d'électrons émis dans la désintégration 227 Th → 223Ra : étude par spectrométrie à focalisation semi-circulaire et à double focalisation, ce qui a permis de fixer toutes les intensités en valeur absolue par désintégration α et de fournir un grand nombre de multipolarités

Reductions and special parts of closures

We provide an axiomatic framework for working with a wide variety of closure operations on ideals and submodules in commutative algebra, including notions of reduction, independence, spread, and special parts of closures. This framework is applied to tight, Frobenius, and integral closures. Applications are given to evolutions and special Brian\c{c}on-Skoda theorems.Comment: to appear in Journal of Algebra (This version corrects some typos

Impact of cancer occurrence on health-related quality of life: A longitudinal pre-post assessment

BACKGROUND: Investigations focusing and implementing on the impact of cancer on health-related quality of life (HRQoL) by the way of a mean comparison between cancer patients and subjects from the general population, are scarce and usually cross-sectional. Longitudinal application of HRQoL instruments to a general, initially healthy population allows for change to be assessed as an event occurs, rather than afterwards. The objective of the present study was to investigate the impact of new cancer on HRQoL. METHODS: The 36-item Short Form (SF-36) and 12-item General Health Questionnaire (GHQ-12) were applied to the French SU.VI.MAX cohort in 1996 and 1998. A controlled longitudinal study was used to determine the impact on HRQoL of newly diagnosed cancer: 84 patients with cancer that occurred between the 2 HRQoL measures were compared with 420 age- and sex-matched cancer-free controls. RESULTS: Initial HRQoL level was similar in the two groups. A new cancer had a particularly marked effect on the SF-36 Physical functioning, Role-physical and General health dimensions (more than 6.6-point difference in change in HRQoL evolution on a 0–100 scale). The Bodily pain and Vitality dimensions were less severely affected (difference in change varying from 4.4 to 6.3 points), and there was no effect on either the GHQ-12 score or the SF-36 Mental health, Role-emotional and Social functioning dimensions. CONCLUSIONS: The negative impact of cancer on the lives of patients was assessed in terms of HRQoL. The aspects most likely to be affected were those with a physical component, and general health perceptions. These results can thus help quantify the impact of a new cancer on HRQoL evolution and potentially facilitate early intervention by identifying the most affected HRQoL domains

E-Learning and North-South collaboration: the experience of two public health schools in France and Benin

Introduction: Distance learning (e-learning) can facilitate access to training. Yet few public health E-learning experiments have been reported; institutes in developing countries experience difficulties in establishing on-line curricula, while developed countries struggle with adapting existing curricula to realities on the ground. In 2005, two schools of public health, one in France and one in Benin, began collaborating through contact sessions organised for Nancy University distance-learning students. This experience gave rise to a partnership aimed at developing training materials for e-Learning for African students. The distance-learning public health course at Nancy teaches public health professionals through a module entitled "Health and Development." The module is specifically tailored for professionals from developing countries. To promote student-teacher exchanges, clarify content and supervise dissertations, contact sessions are organized in centres proximate and accessible to African students. The Benin Institute's main feature is residential team learning; distance-learning courses are currently being prepared. Outcome: The two collaborating institutions have developed a joint distance-learning module geared toward developing countries. The collaboration provides for the development, diffusion, and joint delivery of teaching modules featuring issues that are familiar to African staff, gives the French Institute credibility in assessing research work produced, and enables modules on specific African issues and approaches to be put online. Lessons learned: While E-learning is a viable educational option for public health professionals, periodic contact can be advantageous. Our analysis showed that the benefit of the collaboration between the two institutions is mutual; the French Institute extends its geographical, cultural and contextual reach and expands its pool of teaching staff. The Benin Institute benefits from the technical partnership and expertise, which allow it to offer distance learning for Africa-specific contexts and applications

The {\L}ojasiewicz exponent of a set of weighted homogeneous ideals

We give an expression for the {\L}ojasiewicz exponent of a set of ideals which are pieces of a weighted homogeneous filtration. We also study the application of this formula to the computation of the {\L}ojasiewicz exponent of the gradient of a semi-weighted homogeneous function (\C^n,0)\to (\C,0) with an isolated singularity at the origin.Comment: 15 page