Tavis-Cummings模型中两纠缠原子纠缠的演化特性

研究了两个纠缠的两能级原子与单模粒子数场进行相互作用系统中两原子的纠缠演化.结果表明：两个原子之间的纠缠呈现出周期性的演化特性，初始两原子的状态、原子之间的偶极相互作用和粒子数场对腔中两个原子的纠缠有着显著的影响.发现适当选择原子的初态，两原子会永远处于最大纠缠态. 关键词： 量子纠缠 偶极-偶极相互作用 部分转置矩阵负本征值 纠缠原子     

Boundary Crossing for the Difference of Two Ordinary or Compound Poisson Processes

We consider the lower boundary crossing problem for the difference of two independent compound Poisson processes. This problem arises in the busy period analysis of single-server queueing models with work removals. The Laplace transform of the crossing time is derived as the unique solution of an integral equation and is shown to be given by a Neumann series. In the case of ±1 jumps, corresponding to queues with deterministic service times and work removals, we obtain explicit results and an approximation useful for numerical purposes. We also treat upper boundaries and two-sided stopping times, which allows to derive the conditional distribution of the maximum workload up to time t, given the busy period is longer than t.     

Study of a new novel process for preparing and co-stretching PTFE membrane and its properties

A new idea regarding improvement of the elastic recovery property of a PTFE/PU compound membrane through a co-stretching process was put forward. The experimental results show that the PTFE/PU membrane has great elastic recovery owing to PU. When the longitudinally stretching ratio of PTFE is 200%, the traverse stretching ratio is 850%, and the thickness of PU is 0.03 mm. When the longitudinally and traverse elastic recovery of PTFE/PU is 82.1% and 88.6%, respectively, the porosity is 78.0%, mean pore size is 0.382 μm, and the water vapour permeability is 9330 g/24 h m². It has been used for the SARS protective clothing in China.     

Oscillation and Nonoscillation of Neutral Differential Equations with Positive and Negative Coefficients

In this paper, oscillattion and nonoscillation criteria are established for neutral differential equations with positive and negative coefficients. Our criteria improve and extend many results known in the literature.     

一个新的稳定性判据

本文得到了一个常系数线性差分方程组零解渐近稳定的新判据。     

Gas permeability and permselectivity of polyimides with large aromatic rings

Polyimides with large aromatic rings were prepared from 3,6-diaminocarbazole (CDA), N-ethyl-3,6-diaminocarbazole (ECDA), 2,7-diaminofluorene (DAF), 2,7-diaminofluorenon (DAFO), and dimethyl-3,7-diaminodibenzothiophene-5,5-dioxide (DDBT) with 2-bis(2,4-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) and 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA). Their physical properties, including gas permeability and permselectivity, were investigated in comparison with those of the related polyimides from 1,3-phenylenediamine (mPD). Glass transition temperatures of the polyimides with large aromatic rings were much higher than those of the mPD-based polyimides as a result of increased rigidity of the former polymer chains. With changing diamine from mPD to the large aromatic diamines, charge transfer (CT) interaction between the moieties of acid anhydride and diamine seems to be enhanced, judging from the red shift of absorption edge of the polyimide films and the red shift of CT excitation band of the 6FDA-based polyimides in solution. Fraction of free space (V_F) was a little smaller for the polyimides with large aromatic rings except DDBT than for the mPD-based polyimides, probably because of enhancement in polymer chain-chain interactions as a result of the increased CT interaction. The DDBT-based polyimides had large V_F than the mPD-based polyimides because of the nonplanar structure of neighboring dibenzothiophene-5,5-dioxide and imide rings. For the 6FDA-based polyimides, permeability coefficients to H₂, O₂, N₂, CO₂, and CH₄ were in the order, DAFO < mPD ～ DAF < CDA < ECDA < DDBT. As for the membrane performance for H₂/CH₄, CO₂/CH₄, and O₂/N₂ systems, it is significant to change diamine from mPD to DDBT or CDA, but not to DAF or DAFO. The DDBT-based polyimides were excellent for H₂/CH₄ and CO₂/CH₄ separations. © 1995 John Wiley & Sons, Inc.     

Nevanlinna-Pick interpolation: Pick matrices have bounded number of negative eigenvalues

The Nevanlinna-Pick interpolation problem is studied in the class of functions defined on the unit disk without a discrete set, with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. It is shown, in particular, that the degenerate problem always has a unique solution, not necessarily meromorphic. A related extension problem to a maximal function in the class is also studied.

     

Polymerization of [o-n-(perfluorohexyl)phenyl]acetylene and polymer properties

Synthesis, properties, and membrane-separation functions of a novel fluorine-containing poly(phenylacetylene) were examined. The monomer used was [o-n-(perfluorohexyl)phe-nyl]acetylene, which has a rigid rod-like ortho-substituent. Polymers, whose intrinsic vis-cosities ([η]) were ca. 0.4–2.2 dL/g, were obtained in high yields with various W and Mo catalysts. The MoCl₅–Ph₃Sb catalyst achieved the highest [η] of 2.25 dL/g corresponding to an M_w over one million. The polymer was a brown solid soluble only in F -containing solvents such as m-(CF₃)₂C₆H₄. The oxygen permeability coefficient of the polymer mem-brane was 90 barrers, which is the second highest among those of ortho-substituted poly(phenylacetylenes). In the pervaporation of an ethanol–water mixture, the poly-mer membrane showed ethanol permselectivity [α(EtOH/H₂O) = 1.7]. © 1995 John Wiley & Sons, Inc.     

Structure/permeability relationships of polyimides with branched or extended diamine moieties

Mean permeability coefficients for CO₂, O₂, N₂, and CH₄ in seven types of 6FDA polyimides with branched or extended diamine moieties were determined at 35.0°C (95.0°F) and at pressures up to 10.5 atm (155 psia). In addition, solubility coefficients for CO₂, O₂, N₂, and CH₄ in six of these polyimides were determined at 35.0°C and at 6.8 atm (100 psia). Mean diffusion coefficients for the six gas/polyimide systems were calculated from the permeability and solubility data. The relationships between the chemical structure of the polyimides, some of their physical properties (glass transition temperature, mean interchain spacing, specific free volume), and their gas permeability, diffusivity, and solubility behavior are discussed. The 6FDA polyimides studied here exhibit a considerably lower selectivity for the CO₂/CH₄ and O₂/N₂ gas pairs than 6FDA polyimides with short and stiff aromatic diamines with comparable CO₂ and O₂ permeabilities. © 1993 John Wiley & Sons, Inc.     

Molecular Precursor Role in the Synthesis of ZrMVI2O8, MVI = Mo,W: Isolation and Properties of Zr3Mo8O24(OiPr)12(iPrOH)4

The studies of zirconium isopropoxide solvate, Zr(OiPr)4·iPrOH(I), interaction with molybdenum oxoisopropoxide in different solvents (HOiPr, hexane) revealed I to be the only isolable crystalline product in alcohol. In hexane I crystallized from Zr-rich solutions (up to Zr : Mo = 1 : 2 ratio). From the solutions with Zr : Mo = 1 : 2 ratio repeatedly dried in vacuo and subsequently redissolved in hexane, the crystallization of Zr3Mo8O24(OiPr)12(iPrOH)4(II) occurred slowly with 12% yield. II can be recrystallized from hexane, but is destroyed by iPrOH which causes the formation of I. Thermal decomposition of II in air at 800°C (2 h) gives a single phase ZrMo2O8(III). Hydrolysis studies of hexane solutions, prepared in a manner analogous to those, from which II was obtained, showed that single-phase samples of III could be obtained when a thin layer of solution was left for hydrolysis and evaporation of solvent in a moist air and then annealed at 800°C (2 h). The same kind annealing of a xerogel, obtained by hydrolysis with water solutions in iPrOH and subsequent drying at 100°C gave a complex mixture of phases where III was not even the major component. No Zr-W complex was isolable under analogous conditions. From the xerogel, obtained by hydrolysis with H2O/iPrOH, ZrO2 and WO3 crystallized separately on heating. Only traces of ZrW2O8(IV) were obtained along with individual oxides when 1% water in ether was applied for hydrolysis. Molecular precursor is therefore crucial for obtaining III, IV.