Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition

We establish gradient estimates for bounded solutions of semilinear parabolic equations, where the nonlinearity only satisfies one-sided quadratic upper growth assumptions, instead of the classical (two-sided) Bernstein's condition. This extends a recent work of Al. and Ar. Tersenov (Indiana Univ. Math. J. 50 (2001) 1899–1913), where results of this kind were obtained for radial solutions in a ball, by a different technique. To cite this article: J.-Ph. Bartier, Ph. Souplet, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Combined intra-intermolecular criss-cross cycloaddition of a new fluorinated unsymmetrical allenylazine with alkynes

The reaction of a new fluorinated unsymmetrical allenylazine with dimethyl acetylenedicarboxylate and phenylacetylene affords the combined intra-intermolecular criss-cross cycloaddition products, 2,3-disubstituted-1,10-diazatricyclo[5.2.1.0^4,10]deca-2,6-diene derivatives. The products contain three fused five-membered rings with two nitrogen atoms within an unsaturated heterocyclic system. The structures were assigned using 2D NMR correlations and in the case of the phenylacetylene adduct by X-ray structure analysis.     

Incremental evolution of induced anisotropy

The aim of this article is to define a model that describes the evolution of the yield surface during plasticity. We propose a modelisation that is completely different from the classical approach as far as conception is concerned. It consists of describing the yield surface evolution with the help of velocity. The yield function is not directly known but is obtained by integrating a differential law starting from an initial surface. A very simple evolution law is used; the complexity of the induced anisotropy is obtained by incremental accumulation.     

Study of a fiber-optic LAN with a distributed controller

In this paper the performance of a fiber-optic LAN with spread spectrum multiplexing is discussed from the viewpoint of transmission parameters. Two architectures are considered. The first concerns a structure with cascade-connected Y-type fiber-optic couplers. The second concerns an architecture with cascade-connected active optoelectronic repeater-coupler (ORCA) devices.     

Synthesis of new silylated sulfur-containing heterocycles through thionation of bis(acylsilanes)

The thionation of bis(acylsilanes) with spacers of variable size with hexamethyldisilathiane under cobalt(II) chloride or trimethylsilyl triflate catalysis affords 2,5-bis(trialkylsilyl)-thiophenes, 2,6-bis(trialkylsilyl)-4H-thiopyrans and 2,7-bis(trialkylsilyl)-4,5-dihydrothiepine generally along with a minor amount of the corresponding oxo analogue. The synthesis of both symmetrical and unsymmetrical bis(trialkylsilyl) derivatives was achieved.     

Convex Sobolev inequalities and spectral gap

This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006).