一类生化反应数学模型的分析

本文讨论了生化反应中一类可逆两分子饱和反应,它的数学模型可近似表达为应用常微分方程定性和稳定性的方法分析了参数的所有情况,得到了正初值的正半轨线的有界性、正平衡点的稳定性及极限环的存在唯一性等结论。     

Experimental Study of Effect of Medium Boundary on Light Distribution in Tissue Phantoms

An experimental method for investigating the effect of medium boundary on distributions of light in the biological tissue phantom intralipid is presented. Measurements of distributions of light in intralipid-10% suspensions at 633 nm are described, in which a narrow collimated beam is incident on the surface of the phantoms and into the different depths inside of the phantoms. The experimental results show that the effect of the boundary of the medium on the curves geometry of light distributions is trivial, but the effect on intensity of scattering light is obvious, the maximal relative change of the energy fluence reaches 53.8% and the position of the peak of the energy fluence curve has a shift of 1.1 mm in the reverse direction of incident light for the phantom with albedo a=0.998, and the effect of the boundary is decreased with the increase of the absorption coefficients of tissue phantoms. The experimental results were analysed by the diffusion theory. These studies will be helpful for further understandings of the relation between the boundary of biological tissue and the distribution of light in tissue.     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

求解极限环的谱展开法

提出了一种求解自治非线性常微分方程周期解的方法－谱展开法，它直接把解形式上写成Ｆｏｕｒｉｅｒ级数，其频率和各谐波成份待定，而将原非线性微分方程问题变换成求解相应的非线性代数方程组，还以ａｖｎ ｄｅｒ Ｐｏｌ方程和神经元群平均场方程为例对该方法进行说明和讨论。     

Helmholtz方程外边值问题的自然边界元法

本文利用Ｆｏｕｒｉｅｒ展开获得了圆外区域上的Ｈｅｌｍｈｏｌｔｚ方程边值问题的Ｐｏｉｓｓｏｎ积分公式和积分方程，并用Ｇａｌｅｒｋｉｎ法求积分方程的解，导出了刚度矩阵元素的计算公式，讨论了数值技术，给出了变分解的唯一性定理和近似解的误差估计。     

Bound States of the S-Wave Equation with Equal Scalar and Vector Standard Eckart Potential

A supersymmetric technique for the bound-state solutions of the s-wave Klein-Gordon equation with equal scalar and vector standard Eckart-type potential is proposed. Its exact solutions are obtained. Possible generalization of our approach is outlined.     

随机环境中多物种分枝随机游动

引进了随机环境中多物种分枝随机游动的一般模型.在分枝过程非灭绝的情况下,讨论了系统的状态分类,得到了系统暂留及强常返的充要条件是存在k个定义在整数集上的函数分别满足某种性质.最后给出了系统强暂留的充分条件.     

Mixed Elastico-Plasticity Problems with Partially Unknown Boundaries

In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed.     

BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u＂ = ｜u｜^p

In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.     

Blind equalization of underwater acoustic channelusing a combined constant modulus algorithm

A kind of Combined Constant Modulus Algorithm (CCMA) is presented to compensate the defects of the Constant Modulus Algorithm (CMA) and the Sign Error CMA (SECMA). And CCMA is applied to the equalization of the underwater acoustic channel (UWAC). Based on the decision of the equalizer‘s output, its iteration process switches between CMA and SECMA automatically. It is more robust than SECMA, and more computationally efficient than CMA. Therefore, it is very suitable for the recovery of the underwater data transmission. The performance of CCMA is proven by computer simulation for the equalization of the UWAC.