Structure and evolution of strange attractors in non-elastic triangular billiards

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter λ is varied. For λ∈(0,1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of λ gaps arise in the Cantor structure. For λ close to 1, the attractor splits into three transitive components, whose basins of attraction have fractal boundaries.     

Asymmetric Nucleophilic Monofluorobenzylation of Carbonyl Compounds: Synthesis of Enantiopure vic‐Fluorohydrins and α‐Fluorobenzylketones

Asymmetric nucleophilic monofluoroalkylation of a broad range of aldehydes with an α‐fluoro‐γ‐sulfinylbenzyl carbanion takes place with complete control of the facial selectivity at the carbanion and good to high anti‐diastereoselectivity to give easily separable mixtures of two optically pure 1,2‐fluorohydrin derivatives (up to 24:1 anti/syn). Separation and removal of the p‐tolylsulfinyl group with tBuLi provides enantiomerically pure anti‐1,2‐disubstituted‐1,2‐fluorohydrins, whereas α‐fluorobenzylketones can be obtained by desulfinylation of the mixture followed by pyridinium chlorochromate oxidation (one‐pot process).     

Optical properties of single wall carbon nanotubes dispersed in biopolymers

In this paper we report the optical studies of single wall carbon nanotubes dispersed in biomaterials. We have obtained very stable suspensions of SWNTs, which allowed us to get good photoluminescence signal from the individually dispersed nanotubes. These new hybrid systems may find some applications in bionanocomposites with photoluminescence properties and in biosensors. Furthermore, the dispersion of carbon nanotubes in these biocompatible materials is important for evaluating the toxicity of either isolated or lightly bundled single wall carbon nanotubes.     

Lithium storage mechanisms and effect of partial cobalt substitution in manganese carbonate electrodes

A promising group of inorganic salts recently emerged for the negative electrode of advanced lithium-ion batteries. Manganese carbonate combines low weight and significant lithium storage properties. Electron paramagnetic resonance (EPR) and magnetic measurements are used to study the environment of manganese ions during cycling in lithium test cells. To observe reversible lithium storage into manganese carbonate, preparation by a reverse micelles method is used. The resulting nanostructuration favors a capacitive lithium storage mechanism in manganese carbonate with good rate performance. Partial substitution of cobalt by manganese improves cycling efficiency at high rates.     

Measuring velocity fields in wind tunnels with holographic interferometry

This paper investigates the feasibility of using holographic interferometry in wind tunnel flows for measuring velocity fields rather than density or temperature fields. First results were obtained in a vortex street behind a cylinder at Re=190(U _∞=0.7 m/s). The light scattered from an illuminated fluid plane was holographically recorded twice with the same reference beam. Using a time interval of 10 μs, local fluid displacements smaller than a few microns were recorded. The holographic plate was placed in front and as close as possible to the fluid plane. The interferograms obtained from the hologram reconstruction give information about one velocity component, at 45° with the illuminated plane. The alignment of the cylinder axis with this 45° direction provided definite confirmation about the vortex street having a non-negligible axial velocity. The constant velocity fluid region has proven to be very useful for quantifying the velocity information contained in the interferogram. Received: 8 November 1999/Accepted: 14 March 2000     

On the finite element method for elliptic problems with degenerate and singular coefficients

We consider Dirichlet boundary value problems for second order elliptic equations over polygonal domains. The coefficients of the equations under consideration degenerate at an inner point of the domain, or behave singularly in the neighborhood of that point. This behavior may cause singularities in the solution. The solvability of the problems is proved in weighted Sobolev spaces, and their approximation by finite elements is studied. This study includes regularity results, graded meshes, and inverse estimates. Applications of the theory to some problems appearing in quantum mechanics are given. Numerical results are provided which illustrate the theory and confirm the predicted rates of convergence of the finite element approximations for quasi-uniform meshes.

     

Determination of the strange quark content of the nucleon from a next-to-leading-order QCD analysis of neutrino charm production

We present the first next-to-leading-order QCD analysis of neutrino charm production, using a sample of 6090 ^– and -induced opposite-sign dimuon events observed in the CCFR detector at the Fermilab Tevatron. We find that the nucleon strange quark content is suppressed with respect to the non-strange sea quarks by a factor =0.477 _–0.053 ^+0.063 , where the error includes statistical, systematic and QCD scale uncertainties. In contrast to previous leading order analyses, we find that the strange seax-dependence is similar to that of the non-strange sea, and that the measured charm quark mass,m _c =1.70±0.19 GeV/c², is larger and consistent with that determined in other processes. Further analysis finds that the difference inx-distributions betweenxs(x) and is small. A measurement of the Cabibbo-Kobayashi-Maskawa matrix element |V _cd |=0.232 _–0.020 ^+0.018 is also presented.     

Graphs with at most one crossing

The crossing number of a graph $G$ is the least number of crossings over all possible drawings of $G$. We present a structural characterization of graphs with crossing number one.     

Preparation of Benzylidene Barbituric Acids Promoted by Infrared Irradiation in Absence of Solvent

Several benzaldehydes were condensed with barbituric acid under infrared irradiation, in absence of solvent, affording the corresponding 5-benzylidene barbituric acids.