带泊松跳跃的几何布朗运动的经济模型

本文讨论了带泊松过程的几何布朗运动的经济模型,在收益函数R(x)=ax2-b的情形下,利用伊藤公式,求得平均收益的最优解.     

含硫醚链节的透明聚酰胺酸的合成及表征

合成了一种具有耐高温、氧化稳定性及透明性的聚硫醚酰胺酸，并对各步中间产物进行了基本表征。讨论了温度对硫醚二酐形成的影响。     

一类具有三参数的奇摄动方程

本文用非标准分析作为工具研究一类具有三参数的奇摄动方程，指出参数和轨线的关系，给出了方程存在极限环的条件。     

On the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids

Abstract We analyze mathematical models governing planar flow of chemical reaction from unburnt gasesto burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction aresignificant. These models can be then formulated as the Navier-Stokes equations for exothermically reactingcompressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, andlarge-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations withconstant adiabatic exponent γ and specific heat C_v. Our approach for the existence and regularity is to combinethe difference approximation techniques with the energy methods, total variation estimates, and weak conver-gence argumeots to deal with large jump discontinuities; and for large-time behavior is an a posteriori argumentdirectly from the weak form of the equations. The approach and ideas we develop here can be applied to solvinga more complicated model where γ     

超高光束质量研究

提出了边界波具有π跃变性质的假说，作为惠更斯—菲涅耳原理的补充。根据该假说，在腔外和腔内实现了一系列新光束。重要的是，实现了等效光束质量因子小于１的新光束ＣＯ２激光器。这可看作是可控非线性自聚焦的结果。     

基于跳跃波动率的未定权益定价模型

讨论了具有随机波动率的未定权益定价问题,建立了两状态波动率的股票价格行为模型,在股票价格过程是连续过程、跳风险不可定价的假设下,推导出未定权益的定价公式.     

On Stability and Stabilizability of Singular Stochastic Systems with Delays

This paper deals with the class of continuous-time singular linear systems with Markovian jump parameters and time delays. Sufficient conditions on the stochastic stability and stochastic stabilizability are developed. A design algorithm for a state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse free, and stochastically stable is proposed in terms of the solutions to linear matrix inequalities. The research of this author was supported by NSERC Grant RGPIN36444-02. The research of this author was supported by the Program for a New Century of Excellent Talents in the Universities and by the Foundation for the Authors of National Excellent Doctoral Dissertations of P. R. China, Grant 200240. The research of this author was supported by HKU Grant RGC 7029/05P.     

POSITIVE SOLUTIONS FOR p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES

The three-point boundary value problems of p-Laplacian dynamic equations on time scales are investigated. By using Krasnosel＇skii＇s fixed-point theorem and fixed-point index theorem, criteria are achieved for the existence of at least one, two or 2n positive solutions. Furthermore, some examples are included to illustrate the main theorems.     

Smolukhovsky problem for electrons in a metal

We find an analytic solution of the Smolukhovsky problem of the temperature and electric potential jumps in a metal under the action of the temperature gradient normal to the surface. We take the character of the electron energy accommodation on the surface into account. We find the analytic expressions for the electric field generated by heat processes, for the temperature distribution, and for the electric potential.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 93–111, January, 2005.     

双调制步进扫描红外光谱技术用于聚氨酯薄膜动态拉伸实验

将步进扫描多调制傅里叶红外光谱技术用于聚氨酯薄膜动态拉伸的流变光谱性质研究。讨论了步进扫描干涉仪的工作原理、包括相调制在内的多调制频率与数字采集实验设置及数字信号处理方法。得到聚氨酯薄膜在100Hz频率、1.0λ振幅的相调制作用下，相对于5Hz拉伸频率的同相位（In-phase)和正交相位（Quadrature)的红外吸收光谱。