Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra

Hom-Lie algebra (superalgebra) structure appeared naturally in q-deformations, based on σ-derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of α ^k -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted osp(1, 2) superalgebra and q-deformed Witt superalgebra.     

Multiple positive solutions of the one-dimensional p-Laplacian

In this work we investigate the existence of positive solutions of the p-Laplacian, using the quadrature method. We prove the existence of multiple solutions of the one-dimensional p-Laplacian for α?0, and determine their exact number for α=0.     

Coactions on Hochschild homology of Hopf-Galois extensions and their coinvariants

Let B⊆A be an H-Galois extension, where H is a Hopf algebra over a field K. If M is a Hopf bimodule then , the Hochschild homology of A with coefficients in M, is a right comodule over the coalgebra C_H=H/[H,H]. Given an injective left C_H-comodule V, our aim is to understand the relationship between and . The roots of this problem can be found in Lorenz (1994) [15], where and are shown to be isomorphic for any centrally G-Galois extension. To approach the above mentioned problem, in the case when A is a faithfully flat B-module and H satisfies some technical conditions, we construct a spectral sequence

     

Well-posedness and general decay for Moore–Gibson–Thompson equation in viscoelasticity with delay term

Ricerche di Matematica - The problem of Moore–Gibson–Thompson equation with infinite memory and time delay terms is considered. Under suitable Lyapunov functionals with an appropriate...     

Comparative Baeyer-Villiger oxidation of cyclohexanone on Fe-pillared clays and iron tetrasulfophthalocyanine covalently supported on silica

The Baeyer-Villiger oxidation of cyclohexanone to caprolactone has been investigated at room temperature over AlFe-pillared clays, using oxygen as oxidant in the presence of benzaldehyde. A nearly complete conversion is observed with a selectivity into caprolactone above 80%. The observation of an induction period in the kinetics, of high activity of the non-pillared clay, and the detection of Fe traces in the reaction medium, suggest a process involving homogenous catalysis. The reaction is indeed catalysed in homogeneous phase by a few ppm of Fe. By contrast, iron phthalocyanine covalently supported on silica appears as a true heterogeneous catalyst, giving a selectivity above 95% to caprolactone at 61% conversion.     

Approximation numérique d'un problème de membrane non linéaire

We study numerically the deformations of a nonlinearly elastic membrane. We consider the nonlinear membrane model obtained by Le Dret and Raoult using Γ-convergence. In this model, membrane deformations minimize a highly nonquadratic energy. We consider a conforming finite element approximation of the problem and use a nonlinear conjugate gradient algorithm to minimize the discrete energy. To cite this article: N. Kerdid et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Structural and nanomechanical properties of porous silicon: Cheap substrate for CMOS process industry

The surface topology of porous silicon (PSi) is a relevant parameter that decides the compatibility of such substrate with CMOS process. Using standard resistivity (1–10 Ω·cm) of Si substrate to fabricate PSi-S is a low cost solution for the industry. In this paper, through an atomic force microscopy (AFM) analysis, the root mean square (RMS) roughness, the power spectral density and the correlation length were determined for different PSi layers. Furthermore, the measured hardness, Young's modulus, and stress have been made for different thicknesses of PSi: 5, 10, 50, and 200 μm. The obtained results demonstrated that very interesting properties have been achieved with the 50 μm-thick PSi-S layer with a maximum porosity around 65%, a surface roughness less than 1 nm and a hardness value of (~1 GPa). The realized results encourage the utilization the PSi-based substrate into the industry process and thus the development of a Systems-on-Chip (SoC).     

Production of Graphite During the Extinguishing Arc with New SF6 Alternative Gases

Most high voltage circuit breakers in operation use SF₆ as the arc interruption medium because of its high dielectric strength and good arc interruption properties. However SF₆ also displays a high global warming potential which motivates the investigation of possible alternatives such as CO₂–Novec?4710 and N₂–Novec?5110 mixtures proposed by different HVCB manufacturers. CB power test comparison between pure CO₂ and CO₂–Novec?4710 mixture shows that the latter created a large amount of graphite and reduced CB performances after several current breaking shots. Using Gibbs free energy method, a theoretical study has been conducted on SF₆ replacement candidates listed above. Aiming to understand graphite formation, several parameters impact were discussed: carrier gas such as CO₂ and N₂, pressure and O₂ initial mixture proportions. The study focuses on graphite condensation temperature and graphite production amount evolutions in respect to the study parameters as well as in respect to CB inter-contacts space condition in terms of pressure and temperature at current-zero. It has been shown that a high percentage of CO₂ in the mixture reduces graphite condensation temperature by 2600 K while adding N₂ do not make such an impact. Pressure increases graphite condensation temperature and O₂ reduces it. The amount of graphite produced is pressure independent but decreases with the increase of O₂ proportion in the initial mixture. It has been shown that adding a sufficient O₂ amount can prevent graphite production at all.

     

Reactivity of N-substituted alkenylidene hydrazinecarbothioamides toward tetracyanoethylene,an efficient synthesis stereoselective 1,3-thiazole compounds

Research on Chemical Intermediates - The reaction between N-substituted alkenylidene hydrazinecarbothioamides and two molar amounts of tetracyanoethylene (TCNE) in anhydrous THF at room temperature...     

Synthesis and characterization of highly ordered mesoporous nanomaterials Al-MCM-41 and Al-SBA-15 from bentonite as efficient catalysts for the production of biodiesel MELA and EELA

Research on Chemical Intermediates - Low-cost Al-MCM-41 and Al-SBA-15 mesoporous materials are successfully synthesized from bentonite as silicon and aluminum sources instead of laboratory reagents...