Some extensions of the class of convex bodies

We introduce and study a new class of \eps-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how \eps-convex bodies connect with some classical results of Convex Geometry, as Helly theorem, and find applications to geometric tomography. We introduce the notion of a circular projection and investigate the problem of determination of \eps-convex bodies by their projection-type images. The results generalize corresponding stability theorems by H. Groemer

Ordering of droplets and light scattering in polymer dispersed liquid crystal films

We study the effects of droplet ordering in initial optical transmittance through polymer dispersed liquid crystal (PDLC) films prepared in the presence of an electrical field. The experimental data are interpreted by using a theoretical approach to light scattering in PDLC films that explicitly relates optical transmittance and the order parameters characterizing both the orientational structures inside bipolar droplets and orientational distribution of the droplets. The theory relies on the Rayleigh-Gans approximation and uses the Percus-Yevick approximation to take into account the effects due to droplet positional correlations.Comment: revtex4, 18 pages, 8 figure

Nonsmooth analysis of doubly nonlinear evolution equations

In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional,for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.Comment: 45 page

Big Domains Are Novel Ca2+-Binding Modules: Evidences from Big Domains of Leptospira Immunoglobulin-Like (Lig) Proteins

binds to a Big domains, which would provide a novel functional role of the proteins containing Big fold. with dissociation constants of 2–4 µM. Lig A9 and Lig A10 domains fold well with moderate thermal stability, have β-sheet conformation and form homodimers. Fluorescence spectra of Big domains show a specific doublet (at 317 and 330 nm), probably due to Trp interaction with a Phe residue. Equilibrium unfolding of selected Big domains is similar and follows a two-state model, suggesting the similarity in their fold. binding

Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments

This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fr\'echet means of distributions on metric spaces, such as manifolds and stratified spaces, have played an important role in this endeavor. Apart from theoretical issues of uniqueness of the Fr\'echet minimizer and the asymptotic distribution of the sample Fr\'echet mean under uniqueness, applications to image analysis are highlighted. In addition, nonparametric Bayes theory is brought to bear on the problems of density estimation and classification on manifolds