A Necklace of Wulff Shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density.AMS subject classification: 60K35, 60K37, 82B24, 82B41     

拓扑线性空间中的Drop定理和Phelps引理以及Ekeland变分原理

将Phelps引理,Ekland变分原理,Pareto有效性定理推广到拓扑线性空间,同时证明了这三个定理与郑喜印证明的拓扑线性空间中的Drop定理彼此等价.     

Acoustic analysis of voice in multiple sclerosis patients

The objective is to investigate the presence of dysphonic symptoms in multiple sclerosis (MS) patients and to compare quantitative acoustic parameters in multiple sclerosis patients and normal individuals. The method of study was an 8-month controlled cross-sectional that was carried out with 106 individuals (30 MS, 76 controls). Both groups included males and females from 20 to 55 years. Exclusion criteria were prior vocal disorder, laryngeal microsurgery, recent endotracheal intubation, tumors, laryngeal, lung or mediastinal metastases, respiratory disease, and other associated neurological diagnoses. For dysphonic symptoms (qualitative variables), associations were assessed using Mantel-Haenszel's chi2 test, with Yates correction or the Fisher exact test when necessary. Statistical significance was set at p< or =0.05. Dysphonia was observed in 70% of MS individuals versus 33% of controls (p=0.01). Association was found between MS and dysphonia (OR: 2.2, CI 95%: 1.13-4.25). Fundamental frequency was higher among MS patients (p=0.01). Fundamental frequency deviation was significantly higher in MS women (but not men) than controls (p=0.00). Jitter was higher in MS men than in all other groups (p=0.00). Results suggest that evaluation and treatment of MS patients should be revised, evaluating voice alterations in relation to other signs. MS seems to intensify gender effect on fundamental frequency deviation, noise, and jitter, with MS women presenting fewer voice variations than men.     

Recent Emission Channeling Studies in Wide Band Gap Semiconductors

We present results of recent emission channeling experiments on the lattice location of implanted Fe and rare earths in wurtzite GaN and ZnO. In both cases the majority of implanted atoms are found on substitutional cation sites. The root mean square displacements from the ideal substitutional Ga and Zn sites are given and the stability of the Fe and rare earth lattice location against thermal annealing is discussed.     

Random Flights in Higher Spaces

We consider in this paper random flights in ℝ ^d performed by a particle changing direction of motion at Poisson times. Directions are uniformly distributed on hyperspheres S ₁ ^d . We obtain the conditional characteristic function of the position of the particle after n changes of direction. From this characteristic function we extract the conditional distributions in terms of (n+1)−fold integrals of products of Bessel functions. These integrals can be worked out in simple terms for spaces of dimension d=2 and d=4. In these two cases also the unconditional distribution is determined in explicit form. Some distributions connected with random flights in ℝ³ are discussed and in some special cases are analyzed in full detail. We point out that a strict connection between these types of motions with infinite directions and the equation of damped waves holds only for d=2. Related motions with random velocity in spaces of lower dimension are analyzed and their distributions derived.     

Stopping criteria for inner iterations in inexact potential reduction methods: a computational study

We focus on the use of adaptive stopping criteria in iterative methods for KKT systems that arise in Potential Reduction methods for quadratic programming. The aim of these criteria is to relate the accuracy in the solution of the KKT system to the quality of the current iterate, to get computational efficiency. We analyze a stopping criterion deriving from the convergence theory of inexact Potential Reduction methods and investigate the possibility of relaxing it in order to reduce as much as possible the overall computational cost. We also devise computational strategies to face a possible slowdown of convergence when an insufficient accuracy is required.