Bimodules de Kasparov non bornés équivariants pour les groupoïdes topologiques localement compacts

We study the unbounded KK-theory of S. Baaj and P. Julg in the equivariant framework concerning the action of locally compact groups and groupoids, and give some geometrical examples. To cite this article: F. Pierrot, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Invariant measures for the horocycle flow on periodic hyperbolic surfaces

We classify the ergodic invariant Radon measures for the horocycle flow on geometrically infinite regular covers of compact hyperbolic surfaces. The method is to establish a bijection between these measures and the positive minimal eigenfunctions of the Laplacian of the surface. Two consequences arise: if the group of deck transformations G is of polynomial growth, then these measures are classified by the homomorphisms from G ₀ to ℝ where G ₀ ≤ G is a nilpotent subgroup of finite index; if the group is of exponential growth, then there may be more than one Radon measure which is invariant under the geodesic flow and the horocycle flow. We also treat regular covers of finite volume surfaces. The first author was supported by NSF grant 0500630. The second author was supported by NSF grant 0400687.     

Crystal structure of 3,3-dichloro-N-p-methoxyphenyl-4-(2-phenylstryl)-2-azetidinone.

3,3-Dichloro-N-p-methoxyphenyl-4-(2-phenylstryl)-2-azetidinone (C22H15Cl2NO2) was studied by X-Ray analysis, which indicated a monoclinic space group, P2(1)/c, with a = 9.619(5), b = 13.879(4), c = 14.161(5)A, beta = 100.16(3)degrees, V = 1860.8(13)A3, Z = 4, Dc = 1.414 g cm(-3), micro(Mo Kalpha) = 0.366 mm(-1) and F000 = 816. The structure was solved by direct methods and refined to R = 0.041 for 4026 reflections [I > 2sigma(I). The beta-lactam ring (2-azetidinone) has antimicrobial affects. The substituents of the methoxyphenyl and phenyl substituents do not change the activity property of the beta-lactam ring, and the activity properties depend on the planarity of the beta-lactam ring.     

First results for the measurement of double-electron capture of 106Cd in the experiment TGV II

Present status of the experiment TGV II which is devoted to the measurement of double-beta decay of ¹⁰⁶Cd is given. The low background spectrometer TGV II is installed in the Modane Underground Laboratory and has been running from February 2005 with approx 10 grams of ¹⁰⁶Cd enriched at 75%. After an analysis of 3736 hours of experimental data the new improved half-life limit for 2νEC/EC decay of ¹⁰⁶Cd (0 _g.s. ⁺ → 0 _g.s. ⁺ ) is given as T ₁ ^2/2ν > 4.8 × 10¹⁹ years (90% CL). The search for 2νEC/EC decay of ¹⁰⁶Cd to the excited states of ¹⁰⁶Pd allows to determine the limits of the half-lives T ₁ ^2/2ν (0 _g.s. ⁺ → 2 ₁ ⁺ ) > 3.9 × 10¹⁹ years (90% CL) and T ₁ ^2/2ν (0 _g.s. ⁺ → 0 ₁ ⁺ ) > 5.8 × 10¹⁹ years (90% CL). Presented by I. Štekl at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Tunneling as a Classical Escape Rate Induced by the Vacuum Zero-point Radiation

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results.     

An approach for obtaining the intensity of the radiation transmitted through a scatterer

Monte Carlo simulation was applied to the investigation of intensity of the radiation transmitted through a scatterer. Simulations consisted of a pencil beam of monoenergetic photons with energies from 50 keV to 10 meV incident on water, aluminium, iron, copper, tin and lead slabs. We determined the scattered radiation and the scatter fractions recorded in the detector plane. An empirical formula, which is a function of the physical parameters scatterer thickness, the linear attenuation coefficient, and the atomic number was obtained for intensity of radiation transmitted through a scatterer. This work was supported by the Scientific and Technical Research Council of Turkey (TUBITAK) [TBAG-2032 (101T053)].     

Expanding models with a varying cosmological term and bulk stress

The effect of a varying cosmological term and a dissipative bulk stress on the evolution of a homogeneous and isotropic universe is investigated. In the cases of interest neither analytical nor qualitative analysis is feasible and so we study these numerically only. Our work extends that of Calvão et al. to bulk stresses not considered in their analysis.     

A Shadowing Theorem for ordinary differential equations

A new notion of shadowing of a pseudo orbit, an approximate solution, of an autonomous system of ordinary differential equations by an associated nearby true orbit is introduced. Then a general theorem which guarantees the existence of shadowing of pseudo orbits in compact hyperbolic sets is proved.Supported in part by the Air Force.Supported in part by NSF grant DMS 9201951.