13,067 research outputs found
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 -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 by a
noncommutative 3-dimensional nilmanifold. This yields the differential
calculus. We then compute the Jacobian of the ramified covering 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 -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
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