Foliations on 3-manifolds which are the classifying space of themselves

We classify the closed foliated 3-manifolds M, with codimension one foliations of nonexponential growth and which are homotopy equivalent to their classifying space B. Then we construct arbitrarily large manifolds with foliations with of any growth type and satisfying ₁(M) = ₁(B).*Partially supported by CAPES and CNRS     

Determination of the top Baum-Bott number via classical intersection theory

We determine geometrically the number , associated to a smooth m-dimensional projective variety V^m, invariant by a one-dimensional holomorphic foliation of ⁿ , using polar divisors associated to the foliation and Bézouts theorem.     

Almost summing mappings

We introduce a general definition of almost p-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost p-summing multilinear mappings coincides with the whole space of continuous multilinear mappings. Received: 17 June 2002     

Structure of the isovector dipole resonance in neutron-rich <Superscript>60</Superscript><Emphasis Type="Italic">Ca</Emphasis> nuclei and direct decay from pygmy resonance

The structure of the isovector dipole resonance in neutron-rich calcium isotope, ⁶⁰Ca, has been investigated by implementing a careful treatment of the differences of neutron and proton radii in the continuum random phase approximation (RPA). The calculations have taken into account the current estimates of the neutron skin. The estimates of the escape widths for direct neutron decay from the pygmy-dipole resonance (PDR) were shown rather wide, implicating a strong coupling to the continuum. The width of the giant-dipole resonance (GDR) was evaluated, bringing on a detailed discussion about its microscopic structure.Received: 22 September 2003, Revised: 9 February 2004, Published online: 7 September 2004PACS: 21.10.Pc Single-particle levels and strength functions - 21.60.-n Nuclear structure models and methods - 24.30.Cz Giant resonances - 24.30.Gd Other resonances     

Microscopic theory of dipole-exchange spin waves in magnetic multilayers

A microscopic model is employed to calculate the spectrum of dipole-exchange spin waves in multilayers in which thin ferromagnetic films are separated by non-magnetic spacers. Two configurations are considered: in one the films have magnetizations parallel to each other, in the other the magnetizations are antiparallel. The calculations extend a previous microscopic formalism that allows the calculation of the dipole-exchange spin wave spectrum in thin films. The results show the splitting of the frequency bands and the mode mixing caused by the dipolar interaction between the films as a function of spacer thickness.Received: 26 May 2004, Published online: 12 August 2004PACS: 75.30.Ds Spin waves - 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) - 75.70.-i Magnetic properties of thin films, surfaces, and interfaces     

Trap loss rate for heteronuclear cold collisions in two species magneto-optical trap

In this paper we review the present status on heteronuclear trap loss rate ( ) for alkali mixtures held in a magneto-optical trap (Na-K, Na-Rb, Na-Cs, K-Rb, Rb-Cs, Li-Cs). The intensity dependence of the for the mixture Cs-K is also presented for the first time in this report. The measurement techniques and a semiclassical model, considering both excited-ground and doubly excited channels, are reviewed. The comparison between the model and the experimental results indicates that radiative escape may be the dominant loss process for heteronuclear cold collisions. The obtained values for the crossed species trap loss indicate possibilities of future experiments involving such mixtures in a two species condensate.Received: 19 January 2004, Published online: 11 May 2004PACS: 32.80.Pj Optical cooling of atoms; trapping - 33.80.Ps Optical cooling of molecules; trapping - 34.50.Rk Laser-modified scattering and reactions     

Elastic and total cross-sections for electron scattering by acetylene in the intermediate energy range

We present a joint theoretical-experimental study on electron scattering by C₂H₂ in the intermediate energy range. We report calculated elastic differential, integral, and momentum-transfer as well as total (elastic + inelastic) and absorption cross-sections at impact energies ranging from 10 to 500 eV. Also, experimental absolute elastic cross-sections are reported in the (50-500)-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics. The iterative Schwinger variational method, combined with the distorted-wave approximation, is used to solve the scattering equations. Experimentally, the angular distributions of the scattered electrons are converted to absolute cross-sections using the relative flow technique. The comparison of our calculated with our measured results, as well as with other experimental and theoretical data available in the literature, is encouraging.Received: 26 August 2004, Published online: 5 October 2004PACS: 34.80.Bm Elastic scattering of electrons by atoms and molecules     

Spatially Periodic Solutions in Relativistic Isentropic Gas Dynamics

We consider the initial value problem, with periodic initial data, for the Euler equations in relativistic isentropic gas dynamics, for ideal polytropic gases which obey a constitutive equation, relating pressure p and density , p=², with 1, 0<<c, where c is the speed of light. Global existence of periodic entropy solutions for initial data sufficiently close to a constant state follows from a celebrated result of Glimm and Lax (1970). We prove that given any periodic initial data of locally bounded total variation, satisfying the physical restrictions ||v₀||<c, where v is the gas velocity, there exists a globally defined spatially periodic entropy solution for the Cauchy problem, if 1<₀, for some ₀>1, depending on the initial bounds. The solution decays in L_loc¹ to its mean value as t.     

Optimal Covering of Plane Domains by Circles Via Hyperbolic Smoothing

We consider the problem of optimally covering plane domains by a given number of circles. The mathematical modeling of this problem leads to a min–max–min formulation which, in addition to its intrinsic multi-level nature, has the significant characteristic of being non-differentiable. In order to overcome these difficulties, we have developed a smoothing strategy using a special class C^∞ smoothing function. The final solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original problem. The use of this technique, called Hyperbolic Smoothing, allows the main difficulties presented by the original problem to be overcome. A simplified algorithm containing only the essential of the method is presented. For the purpose of illustrating both the actual working and the potentialities of the method, a set of computational results is presented.