Moduli space and structure of noncommutative 3-spheres

We analyse the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and prove a general algebraic result which considerably refines the classical homomorphism from a quadratic algebra to a cross-product algebra associated to the characteristic variety and lands in a richer cross-product. It allows to control the $C^\ast$-norm on involutive quadratic algebras and to construct the differential calculus in the desired generality. The moduli space of noncommutative 3-spheres is identified with equivalence classes of pairs of points in a symmetric spaceof unitary unimodular symmetric matrices. The scaling foliation of the moduli space is identified to the gradient flow of the character of a virtual representation of SO(6). Its generic orbits are connected components of real parts of elliptic curves which form a net of biquadratic curves with 8 points in common. We show that generically these curves are the same as the characteristic variety of the associated quadratic algebra. We then apply the general theory of central quadratic forms to show that the noncommutative 3-spheres admit a natural ramified covering $\pi$ by a noncommutative 3-dimensional nilmanifold. This yields the differential calculus. We then compute the Jacobian of the ramified covering $\pi$ by pairing the direct image of the fundamental class of the noncommutative 3--dimensional nilmanifold with the Chern character of the defining unitary and obtain the answer as the product of a period (of an elliptic integral) by a rational function...Comment: 50 pages. References adde

The Moderating Effect of Job Characteristics on Managers' Reactions to Career Plateau

This study analyzes the impact of career plateau and job characteristics on people's attitudes or behaviors, but it also extends the traditional field of research on career plateau by taking into account the influence of factors linked to job characteristics on the relationship between career plateau and work-related attitudes. Our results show that subjective career plateau, job enrichment potential, role ambiguity and participation in decision making are related to various individual attitudes and behaviors. The impact of career plateau on these variables varies according to job enrichment potential, participation in decision making and role ambiguity. Although these direct and moderating effects are only significant for some of the facets of job satisfaction and behavior, it appears that these job characteristics can contribute to limit the negative consequences associated with career plateau. Cette recherche analyse l'impact du plateau de carrière et des caractéristiques de l'emploi sur les attitudes et les comportements,0501s aussi élargie les recherches traditionnelles sur le plateau de carrière en prenant en compte l'influence des facteurs liés aux caractéristiques des emplois sur la relation entre le plateau de carrière et les attitudes reliées au travail. Nos résultats montrent que le plateau subjectif , le potentiel d'enrichissement du travail, l'ambiguité de rôle et la participation à la prise de décisions sont reliés aux diverses attitudes et comportements. L'impact du plateau de carrière sur ces attitudes est modéré par le potentiel d'enrichissement de l'emploi, la participation à la prise de décision et l'ambiguité de rôle. Quoi que les effets directs et modérateurs sont significatifs pour seulement quelques facettes de la satisfaction au travail, il apparaît que ces caractéristiques de l'emploi peuvent contribuer à limiter les conséquences négatives associées au plateau de carrière.Career plateau, role ambiguity, job enrichment, participation in decision making, job satisfaction, Plateau de carrière, ambiguïté de rôle, enrichissement de l'emploi, participation à la prise de décision, satisfaction de l'emploi

Non-classical field state stabilization in a cavity by reservoir engineering

We propose an engineered reservoir inducing the relaxation of a cavity field towards non-classical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity interaction is first dispersive, then resonant, then dispersive again. The reservoir pointer states are those produced by an effective Kerr Hamiltonian acting on a coherent field. We thereby stabilize squeezed states and quantum superpositions of multiple coherent components in a cavity having a finite damping time. This robust method could be implemented in state-of-the-art experiments and lead to interesting insights into mesoscopic quantum state superpositions and into their protection against decoherence.Comment: submitted to Phys.Rev.Let

Unbounded symmetric operators in KK-homology and the Baum-Connes Conjecture

Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac operator on the circle and for the Dolbeault operator on closed surfaces. Two proofs are provided, one using topology and the other one, surprisingly involved, sticking to analysis, on the basis of the previous result. As a second application, we construct, in a purely analytical language, various homomorphisms linking the homology of a group in low degree, the K-homology of its classifying space and the analytic K-theory of its C^*-algebra, in close connection with the Baum-Connes assembly map. For groups classified by a 2-complex, this allows to reformulate the Baum-Connes Conjecture.Comment: 42 pages, 3 figure

Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov-Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics.Comment: 15 page

A Symbolic Transformation Language and its Application to a Multiscale Method

The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of geometries combining thin and periodic structures with the possibility of multiple nested scales. In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple package for rule-based programming, rewriting strategies and their combination with standard Maple code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.Comment: 36 page