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.     

Stereoelectronic Aspects of the Anomeric Effect in Fluoromethylamine

High-level ab initio calculations have been made for fluoromethylamine to study structural and energetic effects of the relative orientation of the N lone pair to the C? F bond. The anti-conformer (N lone pair anti-planar to the C? F bond) corresponds to the global energy minimum. It has the longest C? F distance, the shortest C? N distance, and is 7.5 kcal·mol^?1 more stable than the related perpendicular conformation (lone pair perpendicular to the C? F bond). The syn-conformation also shows hallmarks of the anomeric effect: long C? F bond, short C? N bond, and energetic stability when allowance is made for the two pairs of eclipsed hydrogens. The transition state for N inversion is close to the syn-structure; rotation about the C? N bond is strongly coupled with this inversion process. Small bond distance changes of ca. 0.02 Å between parallel and perpendicular conformations are associated with dissociation energy differences of ca. 30 kcal·mol^?1. Various criteria for assessing the strength of the anomeric effect are discussed.     

Synthesis, optical and electroanalytical characterizations of a thiacalix[4](N-phenylazacrown-5)ether-BODIPY ionophore

Novel fluorogenic 1,3-alt thiacalix[4](N-phenylazacrown-5)ether ionophore has been synthesized by conjugation of the N-phenyl group with borondipyrromethene (BODIPY) fluorophore moiety. The ionophore exhibits pronounced off-on type fluorescent responses to some transition metal ions, in particular to Cu²⁺. In a PVC membrane electrode, distinct Ag⁺ selectivity was observed in potentiometric transduction.     

Microdeformation behavior in nanotemplated epoxy thermosets: A study with in situ tensile deformation technique in transmission electron microscopy

Microdeformation behavior in nanostructured block copolymer‐toughened epoxy resins, or templated epoxy thermosets, was studied using an in situ tensile deformation technique performed directly in a transmission electron microscope. The observed microdeformation modes were found to correlate well with the macroscopic mechanical properties of the materials. In the order of decreasing macroscopic fracture toughness, the microdeformation modes were observed to change from large uniform plastic deformation over an extensive area, to localized plastic deformation bands, to little plastic deformation observed in the most brittle material. A similar trend was also observed when samples of the same material were tested at different temperatures, reflecting changes in the deformation mechanism as a function of temperature. Structural defects were observed in nanotoughening phases when plastic deformation was observed. The implication of the observed microdeformation modes to the macroscopic toughening mechanisms is discussed in the context of the micromorphology of the nanometer sized toughening phases and parameters of the epoxy matrix chemistry such as bromination, molecular weight, and interfacial miscibility. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 393–406, 2009     

Numerical simulations of droplet formation in a cross‐junction microchannel by the lattice Boltzmann method

An immiscible liquid–liquid multiphase flow in a cross‐junction microchannel was numerically studied using the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing surface tension force based on the continuum surface force (CSF) method. Recoloring step was replaced by the anti‐diffusion scheme in the mixed region to reduce the side‐effect and control the thickness of the interface. The present method was tested by the simulation of a static bubble. Laplace's law and spurious velocities were examined. The results show that our model is more advantageous for simulations of immiscible fluids than the existing immiscible lattice BGK models. Computational results of multiphase flow in a cross‐junction microchannel were obtained and analyzed based on dimensionless numbers. It is found that the flow pattern is decided mostly by the capillary number at a small inlet flux. However, at the same capillary number, a large inlet flux will lead to much smaller droplet generation. For this case, the flow is determined by both the capillary number and the Weber number. Copyright © 2007 John Wiley & Sons, Ltd.     

汽车保险的广义泊松过程模型

本文针对汽车保险中多车辆相撞事故的理赔建立起广义泊松过程模型,利用概率母泛函给出了其理赔总量在(0,t]内的均值与方差,并基于鞅分析方法证明了其破产概率的Lundberg不等式.