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We prove global existence of solutions to the continuous nonhomogeneous Smoluchowski equation for coagulation rates satisfying a more general structure condition than the Galkin–Tupchiev monotony hypothesis considered in (Ph. Laurençot, S. Mischler, Arch. Rational Mech. Anal. 162 (1) (2002) 45–99). The Smoluchowski coagulation rate fulfils this condition as well as some rates which vanish on the diagonal. Under the condition of positivity of the coagulation rate outside of the diagonal we prove that solutions tend to 0 in the large time asymptotic. These results depend on a new estimate from below for the dissipation rate of the Lp-norm, p>1. To cite this article: S. Mischler, M. Rodriguez Ricard, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
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Thermal properties of benzoic acids carrying one or two semiperfluorinated alkoxy tails on the aromatic core have been investigated in binary mixtures with the non-liquid crystalline bidirectional trans-1,2-bis(4-pyridyl)ethylene. The hydrogen bonded complexes built from the complementary molecular species show a significantly enhanced mesophase stability compared with the fluorinated acids in their pure states. The mesophase morphologies of the complexes are governed mainly by the number of the partially fluorinated chains grafted to the acid component. Mixed systems comprising the one-chain acids exhibit a smectic C phase followed by a smectic A phase at more elevated temperatures. Incorporation of a second semiperfluorinated chain into the acid leads to the formation of columnar mesophases. These columnar phases of the H-bonded complexes should represent ribbon phases resulting from the collapse of the smectic layers. 相似文献
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Microarrays are a popular technology to study genes that are differentially expressed between two conditions. In this Note, we propose an iterative procedure to determine the biggest subset of non-differentially expressed genes. We prove a pseudo Markov relationship that allows practical computations. We obtain explicit expressions for FDR and the level of the proposed test at each step. To cite this article: A. Bar-Hen, S. Robin, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
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In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0 F 1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0 F 1functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( r F s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP2properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866). 相似文献