Measurement of the branching fraction of Gamma(4S) --> B0B0

We report the first measurement of the branching fraction f(00) for Gamma(4S) --> B(0)B(0). The data sample consists of 81.7 fb(-1) collected at the Gamma(4S) resonance with the BABAR detector at the SLAC PEP-II asymmetric-energy e(+)e(-) storage ring. Using partial reconstruction of the decay B(0) --> D(*+) l(-)nu(l) in which only the charged lepton and the soft pion from the decay D(*+) --> D(0)pi(+) are reconstructed, we obtain f(00) = 0.487 +/- 0.010(stat) +/- 0.008(syst). Our result does not depend on the branching fractions of B(0) --> D(*+)l(-)nu(l) and D(*+) --> D(0)pi(+) decays, on the ratio of the charged and neutral B meson lifetimes, nor on the assumption of isospin symmetry.     

Twist-grain-boundary structure in the B4 phase of a bent-core molecular system identified by second harmonic generation circular dichroism measurement

Second harmonic generation circular dichroism (SHG CD) measurements are performed on the B4 phase of a bent-core molecular system. Numerical analysis of SHG CD incorporating magnetic-dipole as well as electric-dipole interaction shows that the B4 phase is in a twist-grain-boundary structure with the helical axis along the bent direction of the molecules. The result is extremely important in the sense that achiral molecules are spontaneously optically resolved, i.e., deracemization, the chiral domains of which give rise to huge chiral nonlinear optical effect.     

Kato's inequality when Δu is a measure

We extend the classical version of Kato's inequality in order to allow functions u∈L¹_loc such that Δu is a Radon measure. This inequality has been recently applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation ?Δu+g(u)=μ, where μ is a measure and $\text{g}\text{:}\text{R}\text{→}\text{R}$ is a nondecreasing continuous function. To cite this article: H. Brezis, A.C. Ponce, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

New Deformation of Para-Bose Statistics

We propose commutation relations for a single mode -deformed para-Bose oscillator. In this new deformation of para-Bose statistics the distribution function has the same form as in the para-Bose statistics. Furthermore, we show analogies between the coherent states of -deformed and q-deformed para-Bose statistics.     

A novel synthesis of 5-functionalized oxazolidin-2-ones from enantiomerically pure 2-substituted N-[(R)-(+)-alpha-methylbenzyl]aziridines

5-Funtionalized enantiomerically pure oxazolidin-2-ones were prepared in one pot from commercially available chiral aziridines bearing an electron-withdrawing group at C-2 with retention of the configuration in high yields by regioselective aziridine ring-opening followed by intramolecular cyclization.     

L stability estimate for a one-dimensional Boltzmann equation with inelastic collisions

In this paper, we study the L¹ stability of a one-dimensional Boltzmann equation on the line with inelastic collisions in Rend. Sem. Mat. Fis. Milano 67 (1997) 169-179. Under the suitable assumptions on the initial data, we construct a nonlinear functional which measures L¹ distance between two mild solutions, and is nonincreasing in time t. Using the time-decay estimate of , we show that mild solutions are L¹-stable:

     

Theoretical study on structure of boron nitride fullerenes

We propose the parameters of the Stillinger-Weber potential for hexagonal boron nitride (BN) structures. For the reliability of these parameters, the structural property of BN fullerenes is investigated. The stability of BN fullerenes increases with increasing the number of atoms, due to the reduction of the curvature effect of BN fullerenes. The structures of the relative stable fullerenes are B₁₆N₁₆, B₁₈N₁₈, B₂₂N₂₂, B₂₅N₂₅, and B₂₈N₂₈.     

Crystal Structure and Spectroscopic Properties of Bis[trans‐dichlorobis(2,2‐dimethylpropane‐1,3‐diamine)chromium(III)] Tetrachlorozincate

The structure of trans‐[Cr(Me₂tn)₂Cl₂]₂ZnCl₄ (Me₂tn = 2,2‐dimethylpropane‐1,3‐diamine) was determined by a single‐crystal X‐ray diffraction study at 173 K. The analysis reveals that there are three crystallographically independent chromium(III) complex cations in the title compound. The chromium(III) atoms are coordinated by four nitrogen atoms of Me₂tn and two chlorine atoms in a trans arrangement, displaying a distorted octahedral geometry. The two six‐membered chelate rings in three complex cations are oriented in an anti chair–chair conformation with respect to each other. The Cr–N and Cr–Cl bond lengths average 2.0862(2) and 2.3112(6) Å, respectively. The ZnCl₄^2– have slightly distorted tetrahedral arrangement with Zn–Cl lengths and the Cl–Zn–Cl angles are influenced by hydrogen bonding. The resolved absorption maxima in the electronic d–d spectrum were fitted with a secular determinant for a quartet energy state of the d³ configuration in a tetragonal field. It is confirmed that the nitrogen atoms of the Me₂tn ligand are strong σ donors, but the chloro ligands have weak σ‐ and π donor properties toward the chromium(III) ion.     

Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide

This work is a continuation of [1]. We give a space-time variational formula to the problem of the scattered acoutic wave by a hard body, using the double layer retarded potential technique. New schemes are constructed from this variationnal formula, for which we prove the stability and errors estimates.     

Angle criteria for frame sequences and frames containing a Riesz basis

We obtain a condition implying that the union of two frame sequences is also a frame sequence. Christensen found a condition for this in terms of orthogonal projections. We phrase our condition by use of the angle between closed subspaces. Also a lower bound formula is obtained. We then apply the results to find conditions for a frame containing a Riesz basis to be a Riesz frame.