Existence and asymptotic stability of a viscoelastic wave equation with a delay

In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem

The Bresse system in thermoelasticity

In this paper, we consider the Bresse system coupled with the Fourier law of heat conduction. We prove that the decay rate of the solution is very slow. In fact, we show that the L²‐norm of the solution decays with the rate of (1 + t)^?1/12 similar to the one obtained for the Timoshenko system. In addition, we found that the wave speed of the first two equations still control the decay rate of the solution with respect to the regularity of the initial data. This seems to be the first result dealing with the behavior of the Cauchy problem in the Bresse–Fourier model. Copyright © 2014 John Wiley & Sons, Ltd.     

Shape Selectivity in Enol Thioether Synthesis Catalyzed by Zeolites

The competitive reaction catalyzed by solid acid catalyst between two cyclohexanones (1a) and (1b) with thiophenol (2) has been studied. No selectivity was observed with the lamellar montmorillonite in contrast with microporous aluminosilicates (zeolites) where shape selectivity was observed, in particularly when the zeolites were saturated by thiophenol (2) before a competitive reaction.     

Sulfur-capped cyclodextrins: a new class of cavitands with extroverted as well as introverted donor functionalities

Ansa-cyclodextrins were obtained in high yields by reaction of sodium sulfide with A,B-di- or A,B,D,E-tetramesylated alpha-CD precursors; the resulting thiocavitands are suitable for forming nanotubular molecules, as well as for hosting metal-organic fragments.     

Ultrafast extreme ultraviolet induced isomerization of acetylene cations

Ultrafast isomerization of acetylene cations ([HC=CH](+)) in the low-lying excited A(2)Σ(g)(+) state, populated by the absorption of extreme ultraviolet (XUV) photons (38 eV), has been observed at the Free Electron Laser in Hamburg, (FLASH). Recording coincident fragments C(+) + CH2(+) as a function of time between XUV-pump and -probe pulses, generated by a split-mirror device, we find an isomerization time of 52±15 fs in a kinetic energy release (KER) window of 5.8相似文献   

Idempotent et cohomologie de Hochschild

Any idempotent element e of an (associative) algebra T defines an algebra $A=eTe$ with unit e. We show that the morphism which compares their Hochschild cohomology algebras is a Gerstenhaber algebras morphism. Moreover, this morphism factorizes through the cohomological algebras of many triangular algebras. To cite this article: B. Bendiffalah, D. Guin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Global non‐existence of solutions of a class of wave equations with non‐linear damping and source terms

In this paper we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. We prove, under suitable conditions on α,β,m,p and for negative initial energy, a global non‐existence theorem. This improves a result by Yang (Math. Meth. Appl. Sci. 2002; 25 :825–833), who requires that the initial energy be sufficiently negative and relates the global non‐existence of solutions to the size of Ω. Copyright © 2004 John Wiley & Sons, Ltd.     

Cyclodextrin-based thiacavitands as building blocks for the construction of metallo-nanotubes

Two new cyclodextrin-based ligands with dual exo/endo binding domains were synthesised in high yields by reacting dimesylated or tetramesylated α-CD derivatives with sodium sulfide in either dimethylsulfoxyde or acetone/18-crown-6. The capping of adjacent glucose units was shown to be strongly favoured in both cases. Depending on the nature of the metal precursor being used, one of the synthesised thiacavitands forms either rigid nanotubular dimers or chelate complexes having receptor properties upon metal complexation.