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.     

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].     

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     

1,3,5-Trisubstituted hexahy drotriazines as mannich reagents. I. Preparation of secondary aminomethyl sulfide hydrochlorides

1,3,5-Trisubstituted hexahy drotriazines react with hydrogen chloride in the presence of anhydrous solvents to form useful intermediates for the introduction of the RNHCH₂- group into compounds which undergo the Mannich reaction. The effectiveness of the new aminomethyl-ating agent has been demonstrated by the preparation of secondary aminomethyl sulfide hydro-chlorides.     

Interactions électriques dans les phases mésomorphes des systèmes amphiphile-eau: Rôle de la teneur en eau,de la longueur de la chaîne paraffinique,de la nature du cation,et de la température

Summary Using X-ray diffraction techniques, we have determined the specific surface of polar groups in the two structures observed for binary soap-water systems in the mesomorphic state: the cylindrical structure and the lamellar one.This parameter depends upon the temperature, the nature of the polar group, the type of structure of the system and the quantity of water present in the mixture. It is, on the contrary, independent of the length of the paraffin chain of the soap. This result suggests that the role of the electrical state of the aqueous regions is by far the most important.

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Zusammenfassung Mit Hilfe der Röntgenstrahlen-Diffraktion wurde die spezifische Fläche polarer Gruppen der zwei wichtigsten Strukturen der binären Seifen/Wasser-Systeme im mesomorphen Zustand bestimmt: die zylindrische und die lamellare Struktur.Diese Größe ist von der Temperatur, der Natur der polaren Gruppen, der Struktur des Systems und des Wassergehaltes der Mischung abhängig. Die spezifische Fläche ist jedoch von der Länge der Seifen-Paraffin-Kette unabhängig. Der elektrische Zustand des wässerigen Teiles scheint also sehr wichtig zu sein.

     

Studies on the 4-benzoylpyridine-3-carboxamide entity as a fragment model of the Isoniazid-NAD adduct

An ortho-metallation-electrophilic substitution sequence was employed as a key step to build the 4-benzoylpyridine framework. It was found that 4-benzoylpyridine-3-carboxamide and an N-pyridyl alkylated derivative both exist in a unique cyclized hemiamidal structure, not in the usually expected keto-amide open form. These structures represent fragment models of the Isoniazid-NAD adducts involved in the mechanism of action of the antituberculous drug Isoniazid.     

Palladium-catalyzed synthesis of substituted cyclopentadienes and indenes from allylic esters

Various mono- and di-substituted cyclopentadienes have been prepared by palladium-catalyzed alkylation of allylic esters with cyclopentadienide and t-butyl-cyclopentadienide anions. The same procedure has been applied to the preparation of substituted indenes.