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.     

Conformal capacities and conformally invariant functions on Riemannian manifolds

This paper develops the theory of conformal invariants initiated inJ. Differential Geom 8 (1973), 487–510 for a Riemannian manifoldM with dimensionn2. We construct and study four conformally invariant functions M, M, M, M resp. depending on 4, 3 or 2 points onM, defined as extremal capacities for condensers associated with those points. These functions have similarities with the classical invariants onS ⁿ ,R ⁿ orH ⁿ . Their properties, and especially their continuity, are efficient tools for solving some problems of conformal geometry in the large.     

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].     

Arsenite oxidation and arsenate determination by the molybdene blue method

Based on the similarity in properties of arsenate and phosphate, the colorimetric method using the molybdene blue complex was tested in order to determine low As(V) concentration in waters. The influence of complex formation time, daylight, temperature and competitive anions (silicate and sulphate) upon complex formation was determined. Optimal complex formation was reached in 1 h at 20±1 °C and was slightly favoured when developed in daylight. The formation rate declined with decreasing reaction temperature and no influence of any of the competitive anions tested (at concentrations usually found in natural waters of granitic areas) was noted. The detection limit of this method was 20 μg As(V) l⁻¹. This simple, fast and sensitive arsenic determination method is suitable for field analysis, especially for waters containing low levels of phosphate and organic matter. Through arsenate determination, this colorimetric method allowed the arsenite oxidation efficiency of five common industrial oxidants to be compared. H₂O₂ and MnO_2(s) were not considered as effective oxidants as a high excess was necessary to ensure As(III) oxidation. NaOCl and KMnO₄ were promising oxidants as they allowed complete arsenite oxidation with a small excess for NaOCl or even less than the electron stoichiometric ratio in the case of KMnO₄. FeCl₃ was the most effective oxidant among the reagents tested here.     

Complexes acetyleniques de titane(II). Reactivite vis-a-vis de l'hydrogene moleculaire: Une nouvelle approche du titanocene

¹³C NMR measurements were performed on [Re₃(μ-H)₃(CO)₁₀]^2? at various temperatures and field strengths. Selective decoupling allowed assignments of the carbonyl resonances. Spin-lattice relaxation time measurements indicated that two mechanisms, scalar coupling and chemical shielding anisotropy, contribute to the relaxation of carbon-13. Variable temperature experiments revealed that more than one mechanism is responsible for the fluxional behaviour.     

Synthesis of thienothiazocinoisoindolediones and thienothiazinoisoindolones from mercaptothiophenes and chloromethylphthalimide

2-Thienylthiomethylphthalimides 3a,b were synthesized by action of Chloromethylphthalimide on 2-or 3-mercaptothiophene. Reduction of 3a,b and Wittig reaction using carbethoxycarbonyltriphenyl-phosphorane gave the corresponding acetic acids 5a,b which cyclized under Friedel and Crafts conditions to lead the thienothiazocinoisoindolediones 6a,b. Thienothiazinoisoindolones 7a,b were obtained from hydroxyisoindolones derivatives 4a,b in acid conditions via an acyliminium ion.