Global existence of weak solutions to the FENE dumbbell model of polymeric flows

Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties. The proof uses many weak convergence techniques. In particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure. In addition, this quantity controls a rescaled defect measure of the gradient of the velocity.     

The Topological Gradient Method: From Optimal Design to Image Processing

The aim of this article is to review and extend the applications of the topological gradient to major image processing problems. We briefly review the topological gradient, and then present its application to the crack localization problem, which can be solved using the Dirichlet to Neumann approach. A very natural application of this technique in image processing is the inpainting problem, which can be solved by identifying the optimal location of the missing edges. Edge detection is of extreme importance, as edges convey essential information in a picture. A second natural application is then the image reconstruction. A class of image reconstruction problems is considered that includes restoration, demosaicing, segmentation and super-resolution. These problems are studied using a unified theoretical framework which is based on the topological gradient method. This tool is able to find the localization and orientation of the edges for blurred, low sampled, partially masked, noisy images. We review existing algorithms and propose new ones. The performance of our approach is compared with conventional image reconstruction processes.     

A multiobjective stochastic program for hospital bed planning

In this paper, we study hospital bed capacity management for a set of existing hospitals when the demand for beds is random. We propose a multiobjective stochastic program model to assign beds to hospital departments. We consider three objective functions to be minimized, which are the cost of creation and management of new beds and the number of nurses and physicians working in these hospitals, subject to demand satisfaction of three kinds of health-care specialities. A certainty equivalent program was derived based on a mixture between the chance constrained approach, the recourse approach and the goal programming approach. Empirical results using real data from 157 Tunisian national hospitals are reported.     

Some actinide complexes of pyridin-, pyrrol-, furan- and thiophen-aldazine Schiff bases

Actinide chloride complexes with pyridinaldazine (PAA), pyrrolaldazine (PyAA-H₂), furanaldazine (FAA), and thiophenaldazine (TAA): An(L)Cl_n·m-H₂O, where An = Th, UO₂; L = PAA, PyAA-H₂, FAA, TAA; n = 2, 4; m = 0, 2, 3, 5 (also, mononuclear with 2L, dinuclear and trinuclear complexes) have been prepared by the reaction of ThCl₄, UO₂Cl₂ or UO₂(Ac)₂·2H₂O with PAA, PyAA-H₂, FAA or TAA and characterized by spectral data, electrical conductance, thermal and elemental analysis.     

Molecular Conformation and Mobility of Polyamines Adsorbed on Silica Studied by Spin Labeling

Poly(ethyleneimine) and poly(4-vinylpyridine) chains adsorbed on Nucleosil silica have been randomly labeled with nitroxide free radicals. The EPR signal is very sensitive to the molecular Brownian motion of the segments and shows generally at least two different environments: trains adsorbed on the surface with a restricted mobility, and loops and tails protruding into the solution with a fast motion. The rotational correlation times and the relative fraction of each population are given as functions of the coverage achieved and of the specific surface area of the silica for the samples in contact with methanol and sometimes water. The overall picture is consistent with a diffuse layer for the PEI and a more compact one with some heterogeneities for the P4VP. Copyright 1999 Academic Press.     

Fixed point theorems for the sum of ( ws)-compact and asymptotically $${\Phi}$$-nonexpansive mappings

In this paper, we introduce the concept of an asymptotically \({\Phi}\)-nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically \({\Phi}\)-nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.