Arrangement transformation approach to state-to-state quantum reactive scattering H + DH→DH + H, HH + D

Arrangement transformation approach (ATA) for doing state-to-state quantum reactive scattering calculations of atom-diatom systems is given. The state-to-state results of H + DH on ISTH potential energy surface are presented, and it can be deduced from the results that the ATA method can be used for the system with more than three atoms. Project supported by the National Natural Science Foundation of China (Grant No. 19774038) and Shandong Science Foundation (Grant No. Y96A08012).     

一个素变数的Diophantine不等式

设１＜Ｃ＜１３／１２．本文证明了存在Ｎ（Ｃ）＞０使得对任意实数Ｎ＞Ｎ（Ｃ），下面的不等式｜＋＋　－Ｎ｜＜Ｎ－　　　　）ｌｏｇｓＮ有素数解ｐ１，ｐ２，ｐ３，其中ｓ＝２（１５）．     

Bifurcation of nonlinear problems modeling flows through porous media

This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary value problems. This work is supported in part by NSF of Shandong Province and NNSF of China     

涉及导函数的亚纯函数的唯一性

本文研究亚纯函数f与f＇具有两个公共值时的Frank问题,证明了若f与f＇以0为CM公共值,以有穷非零复数b为IM公共值,则f=f＇或f=2b/1-ce-2z,其中c为任一有穷非零复数.     

OSCILLATIONS OF SOLUTION FOR A CLASS OF HIGHER-ORDER NEUTRAL DIFFERENTIAL EQUATION

In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.     

期望和残差收益估计不可靠的鲁棒模型

投资优化问题的最优策略会随着输入参数的扰动而出现敏感的变化,针对投资优化问题中出现的随机变量的参数估计不可靠的情况,本文引入不确定集合描述随机收益的有关矩信息,提出了投资优化问题的一个鲁棒性模型,并采用数学规划的理论和方法,给出了该模型的最优策略和有效前沿的解析表示。本方法能够为采用保守策略的、对不确定性厌恶的投资者提供一种最优的投资策略。     

PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.     

Quasi-C-Ehresmann Semigroups and Their Subclasses

We introduce the concept of a quasi-C-Ehresmann semigroup. Some special quasi-C-Ehresmann semigroups will be considered. We will show that the quasi-C-Ehresmann semigroups are special U-semiabundant semigroups and orthodox U-liberal semigroups, which have been recently studied by several authors. Some characterization theorems of this new class of semigroups are obtained. Many results of quasi-C-semigroups in the literature can be extended to quasi-C-Ehresmann Semigroups.     

Polymer-mediated and ultrasound-assisted crystallization of ropivacaine: Crystal growth and morphology modulation

The objective of this research was to modify the crystal shape and size of poorly water-soluble drug ropivacaine, and to reveal the effects of polymeric additive and ultrasound on crystal nucleation and growth. Ropivacaine often grow as needle-like crystals extended along the a-axis and the shape was hardly controllable by altering solvent types and operating conditions for the crystallization process. We found that ropivacaine crystallized as block-like crystals when polyvinylpyrrolidone (PVP) was used. The control over crystal morphology by the additive was related to crystallization temperature, solute concentration, additive concentration, and molecular weight. SEM and AFM analyses were performed providing insights into crystal growth pattern and cavities on the surface induced by the polymeric additive. In ultrasound-assisted crystallization, the impacts of ultrasonic time, ultrasonic power, and additive concentration were investigated. The particles precipitated at extended ultrasonic time exhibited plate-like crystals with shorter aspect ratio. Combined use of polymeric additive and ultrasound led to rice-shaped crystals, which the average particle size was further decreased. The induction time measurement and single crystal growth experiments were carried out. The results suggested that PVP worked as strong nucleation and growth inhibitor. Molecular dynamics simulation was performed to explore the action mechanism of the polymer. The interaction energies between PVP and crystal faces were calculated, and mobility of the additive with different chain length in crystal-solution system was evaluated by mean square displacement. Based on the study, a possible mechanism for the morphological evolution of ropivacaine crystals assisted by PVP and ultrasound was proposed.