Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

On laplace integrals and transfer operators in large dimension: Examples in the nonconvex case

This Letter gives detailed proofs concerning the analysis of the pair correlations for a nonconvex model. Using the transfer matrix approach, the problem is reduced to the analysis of the spectral properties of this transfer operator. Although the problem is similar to the semiclassical study of the Kac operator presented in a paper with M. Brunaud, which was devoted to the study of exp-(v/2) exp h ² exp-(v/2) for h small, new features appear for the model exp-(v/2h) exp h exp-(v/2h). Our principal results concern the splitting of this operator between the two largest eigenvalues. We give an upper and a lower bound for this splitting in the semi-classical regime. As a corollary, we get good control of the decay of the pair correlation. Some of the results were announced in a previous paper. Related WKB constructions will be developed in a later paper.Inspired by papers by M. Kac [15, 16].     

Recherches sur la structure électronique de composés soufrés (méthode L.C.A.O. améliorée)

Improved L.C.A.O. method primitively built for conjugated molecules holding only atoms of second row in the periodic classification is extended to molecules holding atoms of the third row. The application is done for thiophen, thioketones, SO₂ and SO₃. d orbitals are not introduced in this study. Discussion about results shows that d orbitals must be introduced when the sulphur atom is strongly positively charged like in sulphur oxides.     

Anderson localization for multi-dimensional systems at large disorder or large energy

We prove that discrete Schrödinger operators on ^d with a random-potential have almost-surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy. This is the first proof of localization for multi-dimensional Anderson models.Groupe de recherche 048 du CNRS     

Significance of oligomerization reactions in the transesterification of dimethyl terephthalate with ethylene glycol

Experimental investigations dealing with and mathematical models proposed for the kinetics of the transesterification of dimethyl terephthalate with ethylene glycol were critically reviewed. The models were found to be inadequate, while the investigations were found to be entirely lacking in information about the significance of oligomerization reactions. The significance of these reactions was deduced to be negligible by carrying out an analysis of the kinetics of possible ester interchange and transesterification reactions by use of data on methanol reported in the reviewed literature. This analysis was made possible by the application of numerical quadrature routines in testing the assumed models by the integral method.