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Abstract: Let be an algebraically closed field of characteristic 0. In this paper, we prove the equivalence between stability and quasi-reductivity for parabolic subalgebras of exceptional Lie algebras. Therefore, and considering the results of [1], we give a positive answer to the assertion (ii) of the conjecture (5.6) in [11] for parabolic Lie algebras. [Copyright &y& Elsevier]

Abstract: In this paper we give a complete answer to the isotropy of an Albert bilinear form over the function field of a quadric in characteristic 2. As a consequence, we complete the classification of nongood bilinear forms of height and degree 2 given in Laghribi and Rehmann (2009) . [Copyright &y& Elsevier]

Abstract: In this paper, we prove the following result: let X be a complex manifold, hyperbolic for the Carathéodory distance and let U be an open set relatively compact in X. Then, there exists such that we get, for the Carathéodory infinitesimal metric, . We also get results concerning fixed points of holomorphic mappings from X to U. [Copyright &y& Elsevier]

Abstract: In this paper we define the notion of “graded algebra with symmetries”. This notion is a generalization of the extended differential forms. We prove that for a graded algebra with symmetries T, we associate a subalgebra which generalizes the noncommutative differential forms. Using this algebra , we can define the Hochschild and cyclic homologies, cup i-products and the Steenrod squares. [Copyright &y& Elsevier]

The sound quality improvement of a product at stage of its design is a concern of many firms. This design being made starting from tools based on numerical methods such as FEM, BEM or on semi-analytical methods, it is important that their predictions integrate the sound quality expected. The objective of this paper is to show the interest and the benefit of a perceptive step to the vibroacoustic system improvement. Specifically it is more a question of evaluating, through sound perception, the relevance of certain structural parameters and parameters of analysis, in order to refine the sound prediction. The studied system is a vibrating plate coupled to a cavity, in which acoustic pressures are measured, by taking into account variations related to the plate thickness, to the conditions of tightening at the edges of the plate and to the cavity sound absorption. The maximum frequency of analysis is also subjectively studied, by using listening tests of dissimilarity and preference based on the method of pair comparison. [ABSTRACT FROM AUTHOR]

This paper presents a new approach of robust multi-objective optimization and multilevel for design of complex mechanical structures. This optimization is on two levels: system and elements. The robust multi-objective problem on system-level to be solved is with four cost functions: on the one hand the minimization of the global mass and displacement. in a fixed point of mechanical structure to be studied, arid on the other hand the maximization of the robustness respectively of the mass and displacement whereas the robust multi-objective problem on the element-level is with two cost functions: minimization of the element mass and maximization of its robustness. Contrary to the existing formulations, this new approach takes into account uncertainties on the design parameters on the system-level and on the element-level. Moreover, it answers the task sharing commonly used in industry field. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the Weierstrass Preparation Theorem, we apply this effective result to binomial equations. We prove that the Artin function of a system of binomial equations is bounded by a doubly exponential function in general and that it is bounded by an affine function if the order of the approximated solutions is bounded. [Copyright &y& Elsevier]

Abstract: A bounded linear operator on a Hilbert space is said to be reflexive if the operators which leave invariant the invariant subspaces of T are wot-limits of polynomials in T. In this paper we give a necessary and sufficient condition for an extension of a subnormal operator by an algebraic one to be reflexive.We also give a formula for the reflexivity defect of such extensions. [Copyright &y& Elsevier]

Abstract: Recently, Q. Chen, C. Miao and Z. Zhang (2009) have proved that weak Leray solutions of the Navier–Stokes are unique in the class with . In this paper, we establish that this criterion remains true for . [Copyright &y& Elsevier]

Abstract: In this Note, we state a polynomial characterization of weakly invariant designs and show how to derive the construction of weakly invariant designs for the action of a compact group of matrices on an experimental domain, whose interior is not empty, from the construction of rotatable designs. As a consequence, it enables us to search for weakly invariant designs using techniques coming from computational commutative algebra and to benefit from the cumulated knowledge of rotatable designs which have been intensively studied since the seminal paper of Box and Hunter. To cite this article: F. Bertrand, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]

Abstract: The fundamental example of Gerstenhaber algebra is the space of polyvector fields on , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping algebra of a Gerstenhaber algebra . This structure gives us a definition of the Chevalley–Harrison cohomology operator for . We finally show the nontriviality of a Chevalley–Harrison cohomology group for a natural Gerstenhaber subalgebra in . [Copyright &y& Elsevier]

This paper presents the basic ideas and properties of elliptic functions and elliptic integrals as an expository essay. It explores some of their numerous consequences and includes applications to some problems such as the simple pendulum and the Euler rigid body motion. [ABSTRACT FROM AUTHOR]

This paper is the continuation of a precedent one (cf. [2]). We decompose a subclass of semi-simples nuclear algebras as direct sum of simples ideals and we give a Wedderburn decomposition for these algebras. [ABSTRACT FROM AUTHOR]

Abstract: Let Ω be an opened domain of with a boundary Γ. The problem numbered (1) in the text has a unique solution in , if , on a part of Γ the area S of which is different from zero and . ɛ is the damping of an elastic structure and ζ is the normalised acoustic impedance of the internal wall of the cavity. ɛ and are small parameters. Thanks to a proper modal expansion and a mean over a narrow band of wave number k, an integral relation between the trace of u on and g is built to the first order in and ɛ, using the residues theorem. It is not an equivalent equation to the problem, but just a step towards its resolution, which will be published in future papers. To cite this article: D. Brenot, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: Let T be a closed positive current of dimension p in and H an analytic subvariety of of dimension . We denote by the slice of T in H if it exists. We consider the functions on defined by and . The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong–Skoda 1981–1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125–162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43]. [Copyright &y& Elsevier]

This paper presents a numerical analysis of the interaction between shallow tunnelling and structure on surface. The analysis is done using the software Flac3D, based on three-dimensional finite differences. The TBM tunnel excavation is simplified and is taken into account by volume loss. First, a reference calculation without structure on surface is presented. A numerical model coupling ground mass and structure on surface is then used to study the soil-structure interaction. The structure is composed by columns and floors, founded on a raft. The material has elastic properties of a reinforced concrete. Results are analysed in term of ground displacement on surface. The last part presents the influence of the structure stiffness on soil displacements on surface. [ABSTRACT FROM AUTHOR]

Motivated by the superconductivity, we are interested in the fundamental state of the Schoro¨dinger operator with magnetic field. In this paper, we propose a numerical approach based on the finite elements method to determine the bottom of the spectrum of this operator in general domains. We improve the numerical results by using mesh-refinement techniques based on a posteriori error estimators developed elsewhere. We also look at the monotonicity of the bottom of the spectrum in an angular sector according to the angle to complement the theorical study of Bonnaillie (C. R. Acad. Sci. Paris, Ser. I 336 (2) (2003) 135–140). To cite this article: F. Alouges, V. Bonnaillie, C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]