Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Highly polarized dithiafulvenes: synthesis and nonlinear optical properties

Push-pull dithiafulvenes with reduced bond length alternation (BLA) and high optical nonlinearities have been prepared. The interplay between the proaromaticity of the donor and the structural and optical properties of these merocyanines is discussed. The donor ability of dithiafulvenes can reach that of ferrocene or dialkylaminophenyl groups.     

Aberrations theory of a time dependent magnetic field lens

We analyze new forms of aberrations affecting a time dependent magnetic field lens recently proposed. The lens consist of an axially symmetric ellipsoidal solenoid producing a spatially uniform but time pulsating homogeneous field. The dynamics of electrons emitted by some object and injected into this coil shows that this system is capable of focusing a parallel beam or produce images free of geometrical aberrations. The cardinal elements of this lens change periodically in positions and therefore to obtain a stationary image it is necessary to employ a chopped electron beam. Two forms of aberrations originate from the finite duration of the electron pulse and the energy dispersion of the incoming beam (chromatic aberration). Their image degradation effects are quite similar and result from recording different axially displaced images at some fixed stationary plane. We show how, by adjusting the parameters characterizing the magnetic pulse and introducing small apertures that increase the depth of focus, their effects can be reduced or in some cases eliminated. Other forms of instrumental aberrations characteristic of this time dependent magnetic field lens are briefly discussed.     

Quantum optical predictions inQ representation for Bell's type experiments

Using the Q representation, we study the disagreement between quantum optical formalism and local realism and we show that the phenomenon of enhancement, first revealed by the local realist analysis, could receive a simple explanation if we use this particular version of the quantum formalism. Nevertheless, some fundamental difficulties remain.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).