Stochastic partial differential equations with singular terminal condition

In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the generator. Then we study the case where the terminal data is singular, in the sense that it can be equal to +$\infty$ on a set of positive measure. In this setting we show that there exists a minimal solution, both for the BDSDE and for the SPDE. Note that solution of the SPDE means weak solution in the Sobolev sense

Cathodoluminescence investigations of GaAs thin layers

AbstractIn this work, we report the theoretical results of cathodoluminescence (CL) for GaAs layer. The simulation of the CL excitation and intensity is developed using 2-D model based on the electron beam energy dissipation and taking into account the effects of carrier diffusion, internal absorption and the recombination process in the semiconductors.We have investigated the influence of the electron beam conditions (energy, current and beam diameter) and some physical parameters (absorption coefficient, gap energy) on the CL intensity. Results allow us particularly to predict the intensity evolution and shift of CL peak emitted near the fundamental energy gap as a function of the electron beam current and energy. A comparative study between simulated and experimental CL spectra at low temperature is realized

Addison's disease symptoms - a cross sectional study in urban South Africa

BACKGROUND: Addison's disease is a potentially life-threatening disorder, and prompt diagnosis, and introduction of steroid replacement has resulted in near normal life-expectancy. There are limited data describing the clinical presentation of Addison's disease in South Africa. It is hypothesised that patients may present in advanced state of ill-health, compared to Western countries. Patients A national database of patients was compiled from primary care, referral centres and private practices. 148 patients were enrolled (97 white, 34 mixed ancestry, 5 Asian and 12 black). METHODS: Demographic and clinical data were elicited using questionnaires. Biochemical data were obtained from folder reviews and laboratory archived results. RESULTS: The majority of the cohort was women (62%). The median and inter-quartile age range (IQR) of patients at enrolment was 46.0 (32.0-61.0) years, with a wide range from 2.8-88.0 years. The median and IQR age at initial diagnosis was 34.0 (20.0-45.0) years (range 0.02-77.0) years, indicating that at the time of enrolment, the patients, on average, were diagnosed with Addison's disease 12 years previously. Hyperpigmentation was observed in 76%, nausea and vomiting occurred in more than 40%, and weight loss was noted in 25%. Loss of consciousness as a presenting feature was recorded in 20 %. with a 95% confidence interval [CI] of (14-28%) and shock occurred in 5% CI (1.5-8.5%). Case-finding was recorded at 3.1 per million. CONCLUSIONS: The usual constellation of hyperpigmentation, nausea, vomiting and weight loss suggests Addison's disease, but a significant proportion present with an advanced state of ill-health and Addisonian crises. A lower prevalence rate, compared to Western countries is suggested