A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms

The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ω^ε. Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.     

Study of various parameters influencing the fixation of metallic ions Cu2+, Zn2+, and Ni2+ at the catalytic Amberlyst-15 resin in the presence of alcohols

The ionic exchange behavior of Zn²⁺, Ni²⁺, and Cu²⁺ metallic ions on Amberlyst-15 commercial resin was studied as a function of resin solution contact time, initial concentration of metallic ions, nature of the solvent, and the amount of resin. The metallic ions were studied in ternary mixtures using both column and batch experiments. In addition, water, methanol, ethanol, and propan-2-ol were used as solvents for dissolving metallic ions. It was found that the resin behavior depends on the solvent nature and the metallic ion concentration. The analysis of solutions by atomic absorption spectrometry revealed that the affinity of the resin for the studied metallic ions followed the sequence Cu²⁺ > Ni²⁺ > Zn²⁺ in the case of an aqueous medium. Furthermore, uptake increased with increasing amount of resin. A better uptake was observed in the case of the 75:25 % water/methanol compositions when the column technique was used. For the batch technique, we noted a better uptake using 100 % water. The uptake rate decreased with an increase in the number of carbons for the 50 % water–50 % alcohol solvents. The acid–base properties of Amberlyst-15 commercial resin were studied by 2-propanol decomposition test. Propene and acetone are the main expected products and it is believed that they are formed through dehydration or dehydrogenation reaction on acid and base sites, respectively.     

About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half‐space, of which the cross‐section is a local perturbation of a homogeneous half‐plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves propagating more rapidly than S‐waves. Thanks to the boundary of the deformed half‐plane and some reduced equations, these eventual eigenmodes must locally vanish. Adapting to our case a unique continuation principle for the elasticity system, we conclude that these eigenmodes vanish everywhere. Copyright © 2002 John Wiley & Sons, Ltd.     

Hermitean Matrix Ensembles and Orthogonal Polynomials

In this article, we investigate orthogonal polynomials associated with complex Hermitean matrix ensembles using the combination of the methods of Coulomb fluid (or potential theory), chain sequences, and Birkhoff–Trjitzinsky theory. We give a general formula for the largest eigenvalue of the N×N Jacobi matrices (which is equivalent to estimating the largest zero of a sequence of orthogonal polynomials) and the two-level correlation function for the α ensembles (α>0) introduced previously for α>1. In the case of 0<α<1, we give a natural representation for the weight function that is a special case of the general Nevanlinna parametrization. We also discuss Hermitean matrix ensembles associated with general indeterminate moment problems.     

Use of the Domain Derivative to Prove Symmetry Results in Partial Differential Equations

In this paper we present a different method for proving symmetry results in partial differential equations. The principal idea is to use the classical tool of shape optimization, namely, the differentiation with respect to the domain. The aim is to derive, from an optimality condition, information on the boundary of the domain.     

Ramanujan continued fractions via orthogonal polynomials

Some Ramanujan continued fractions are evaluated using asymptotics of polynomials orthogonal with respect to measures with absolutely continuous components.     

Condensations aryniques d'enolates de cetones—VI: Synthese de phenyl-2 cyclohexanones tricyclo[6,n,0,02,7]trienes-2,4,6 ols-1 diversement substitues

The condensation of benzyne in aprotic medium with the enolates of the 2,2,6-trimethyl, 3,3,5,5-tetramethyl, 4-4-dimethyl, 4-methyl, 4-t-butyl cyclohexanones as well as with those of α-tetralone and α-benzosuberone leads to the corresponding α-phenyl ketones and several tri and tetracyclic benzocyclobutenols.     

Ferrioxamine B analogues: targeting the FoxA uptake system in the pathogenic Yersinia enterocolitica

A series of ferrioxamine B analogues that target the bacterium Yersinia enterocolitica were prepared. These iron carriers are composed of three hydroxamate-containing monomeric units. Two identical monomers consist of N-hydroxy-3-aminopropionic acid coupled with beta-alanine, and a third unit at the amino terminal is composed of N-hydroxy-3-aminopropionic acid and one of the following amino acids: beta-alanine (1a), phenylalanine (1b), cyclohexylalanine (1c), or glycine (1d). Thermodynamic results for representatives of the analogues have shown a strong destabilization (3-4 orders of magnitude) of the ferric complexes with respect to ferrioxamine B, probably due to shorter spacers and a more strained structure around the metal center. No significant effect of the variations at the N-terminal has been observed on the stability of the ferric complexes. By contrast, using in vivo radioactive uptake experiments, we have found that these modifications have a substantial effect on the mechanism of iron(III) uptake in the pathogenic bacteria Yersinia enterocolitica. Analogues 1a and 1d were utilized by the ferrioxamine B uptake system (FoxA), while 1b and 1c either used different uptake systems or were transported to the microbial cell nonspecifically by diffusion via the cell membrane. Transport via the FoxA system was also confirmed by uptake experiments with the FoxA deficient strain of Yersinia enterocolitica. A fluorescent marker, attached to 1a in a way that did not interfere with its biological activity, provided additional means to monitor the uptake mechanism by fluorescence techniques. Of particular interest is the observation that 1a was utilized by the uptake system of ferrioxamine B in Yersinia enterocolitica (FoxA) but failed to use the ferrioxamine uptake route in Pseudomonas putida. Here, we present a case in which biomimetic siderophore analogues deliberately designed for a particular bacterium can distinguish between related uptake systems of different microorganisms.