Eine rasche Bestimmung des Fetts?ure- und Alkaligehaltes in Seifen

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Free energy in spin-flip processes is non-increasing

In this paper, we propose a new and shorter proof of the following fact: in a spin-flip process on {–1, +1} ^S , whereS is a countable set, the free energy is non-increasing.Free energy is a well defined functional only for invariant measures under a convenient group of bijections ofS. We formalize this with the notion ofB-ameanability ofS. This frame contains the usual example ofZ ^d under translations but also many nice lattices that are not groups under groups of isometries.For invariant measures, except Gibbs ones, the free energy is strictly decreasing. Among invariant measures, the only stationary measures for the spin-flip process are therefore Gibbs measures. From this result we also deduce an ergodic theorem.The first result on this subject was obtained by Holley [1] for a finite range potential on and some extension by Higuchi, Shiga [2].     

Gaussian approximation of exponential type orbitals based on B functions

This work gives new, highly accurate optimized gaussian series expansions for the B functions used in molecular quantum mechanics. These functions are generally chosen because of their compact Fourier transform, following Shavitt. The inverse Laplace transform in the square root of the variable is used for Gauss quadrature in this work. Two procedures for obtaining accurate gaussian expansions have been compared for the required extended precision arithmetic. The first is based on Gaussian quadratures and the second on direct optimization. Both use the Maple computer algebra system. Numerical results are tabulated and compared with previous work. Special cases are found to agree before pushing the optimization technique further. The optimal gaussian expansions of B functions obtained in this work are available for reference. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Mesures de Gibbs invariantes et mesures d'equilibre

We are interested here in the characterization on a symbolic space, of invariant Gibbs measures as equilibrium measures. The first result in this topic was obtained by Lanford and Ruelle (see for example [6]).This problem involves different objects that can all be defined by using the only amenability of the translation group and the only continuity of the local specification. We therefore tried to state our theorems in this general frame. Among the elements of our proof, there is the use of the information gain introduced by H. Föllmer [1] and some arguments similar to those of C.J. Preston in [5]. But the amenability techniques that we widely develop in [2], [4] and [7] are decisive tools for getting the result.The corresponding problem for subshifts is not considered in the present paper so symbolic spaces are product spaces.     

Einen Beitrag zur chemischen Erkennung von blauen Farben auf Garnen und Geweben

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On a random variable associated with excursions in an M/M/∞ system

We show in this paper how the theory of continued fractions can be used to invert the Laplace transform of a transient characteristic associated with excursions in an M/M/∞ system with unit service rate and input intensity u. The characteristic under consideration is the area V swept under the occupation process of an M/M/∞ queue during an excursion period above a given threshold C. The Laplace transform V ^⋆ of this random variable has been established in earlier studies and can be expressed as a ratio of Tricomi functions. In this paper, we first establish the continued fraction representation of V ^⋆, which allows us to obtain an alternative expression of the Laplace transform in terms of Kummer functions. It then turns out that the continued fraction considered is the even part of a Stieltjes (S) fraction, which provides information on the location of the poles of V ^⋆. It appears that the Laplace transform has simple poles on the real negative axis. Taking benefit of the fact that the spectrum is compact and that the numerical values of the Laplace transform can easily be computed by means of the continued fraction, we finally use a classical Laplace transform inversion technique to numerically compute the survivor probability distribution function x➙ℙ{V > fx} of the random variable V, which exhibits an exponential decay only for very large values of the argument x when the ratio u/C is sufficiently smaller than one. This revised version was published online in June 2006 with corrections to the Cover Date.     

Die Untersuchung der Oele des Handels

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On the area swept under the occupation process of an M/M/1 queue in a busy period

We compute in this paper the distribution of the area swept under the occupation process of an M/M/1 queue during a busy period. For this purpose, we use the expression of the Laplace transform of the random variable established in earlier studies as a fraction of Bessel functions. To get information on the poles and the residues of , we take benefit of the fact that this function can be represented by a continued fraction. We then show that this continued fraction is the even part of an S fraction and we identify its successive denominators by means of Lommel polynomials. This allows us to numerically evaluate the poles and the residues. Numerical evidence shows that the poles are very close to the numbers as . This motivated us to formulate some conjectures, which lead to the derivation of the asymptotic behaviour of the poles and the residues. This is finally used to derive the asymptotic behaviour of the probability survivor function . The outstanding property of the random variable is that the poles accumulate at 0 and its tail does not exhibit a nice exponential decay but a decay of the form for some positive constants c and , which indicates that the random variable has a Weibull-like tail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Zur Erkennung verschiedener Faserstoffe in Geweben und Gespinnsten

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Groupes pavables et principe variationnel

Sans résumé