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:

     

Reduced Minimum Modulus Preserving in Banach Space

Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].      

New estimates for the Laplacian,the div–curl,and related Hodge systems

We establish new estimates for the Laplacian, the div–curl system, and more general Hodge systems in arbitrary dimension, with an application to minimizers of the Ginzburg–Landau energy. To cite this article: J. Bourgain, H. Brezis, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Intersubband transport in quantum wells in strong magnetic fields mediated by single- and two-electron scattering

We show theoretically that in quantum wells subjected to a strong magnetic field the intersubband current peaks at magnetic field values, which reveal the underlying specific intersubband scattering mechanism. We have designed and grown a superlattice structure in which such current oscillations are clearly visible, and in which the transition from the purely single-electron to the mixed single- and two-electron scattering regimes can be observed by tuning the applied voltage bias. The measurements were conducted in ultrahigh magnetic fields (up to 45 T) to obtain the full spectrum of the current oscillations.