若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.     

The Existence and Global $p$-Exponential Stability of Periodic Solution for Stochastic BAM Neural Networks with Delays

In this paper, we consider a class of stochastic BAM neural networks with delays. By establishing new integral inequalities and using the properties of spectral radius of nonnegative matrix, some sufficient conditions for the existence and global $p$-exponential stability of periodic solution for stochastic BAM neural networks with delays are given. An example is provided to show the effectiveness of the theoretical results.     

多检测GPC/SEC技术在高分子表征中的应用Ⅳ.氘化高分子的溶液性质

采用体积排斥色谱法／ 示差折光指数／ 直角激光光散射／ 示差粘度三检测联用技术表征了氘化聚苯乙烯、聚苯乙烯和氘化聚苯乙烯－ 聚异戊二烯。结果表明,在θ条件下,虽然氘化聚苯乙烯的化学依赖性常数υＴ,ＤＰＳ比聚苯乙烯的化学依赖性常数υＴ,ＰＳ大,但２５ ℃时在四氢呋喃中,氘化聚苯乙烯的分子尺寸仍小于聚苯乙烯的分子尺寸。由于嵌段共聚物的淋洗体积随组成变化,所以用传统的ＳＥＣ／ＲＩ得不到准确的分子量。经比较膜渗透、小角激光光散射和基质辅助激光脱吸与离子化时间飞行质谱等的实验结果,证明体积排斥色谱法／ 示差折光指数／ 直角激光光散射／ 示差粘度三检测技术能准确地得到氘化二嵌段共聚物的分子量以及其它重要信息。     

Geometric Integration Methods that Preserve Lyapunov Functions

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function. AMS subject classification (2000) 65L05, 65L06, 65L20, 65P40     

自全国各地100多位理事Road Machinery Branch of China Highway and Transportation Society He

In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period τ, the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.     

几类特定边界值条件下的常微分方程特征值问题

在文献[1]的基础上,借助于图形分析方法,讨论了几类特定边界值条件下的特征值问题.同时,本文对文献[1]中的错误结论作出了更正.本文给出的方法对讨论非线性边值问题的可解性提供了一种新的途径.     

氯化钾水溶液微观结构的分子动力学模拟研究

氯化钾水溶液不同于氯化钠的,其在低温下只能形成无水盐和冰.现有研究表明在氯化钠水溶液中不仅存在着水分子连续分布的区域与离子团簇,而且这二者的物质组成也与该溶液所形成晶体的分别对应.为了探寻其他溶液中是否存在此类对应关系,并考察溶液的微观结构,本文采用分子动力学方法对氯化钾水溶液进行了研究,表明了该溶液的一些性质.氯化钾水溶液中K⁺-K⁺和Cl^--Cl^-径向分布函数的特征具有一致性,峰的最大值所对应的位置都分别相同,明显不同于氯化钠水溶液的.系列时刻下瞬态图像内O到其最近离子距离中最大值的统计结果表明氯化钾水溶液中存在着一定大小的水分子连续分布的区域,其平均尺寸至少为2.26 nm;瞬态图像中K⁺与其最近邻Cl^-之间的距离主要分布在0.28 nm～0.38 nm之间,占比约为97.4%;溶液中存在着较大和较小两类离子团簇,较大团簇的平均尺寸为1.73nm,平均离子数是25.0,其内部的离子与周围离子之间具有与氯化钾晶体类似的结构;这些结果表明氯化钾水溶液中也...     

Periodic solutions of a periodic stochastic human immunodeficiency virus model with distributed delay and cytotoxic T lymphocytes immune response

In this paper, a periodic stochastic human immunodeficiency virus (HIV) model with distributed delay and cytotoxic T lymphocytes (CTL) immune response is investigated. First, by It $ô$'s formula, we show that the solution with any positive initial value is global and positive. Then, by the stochastic comparison theorem, we obtain the sufficient conditions guaranteeing the existence and global attractivity of infection-free periodic solution. Furthermore, we discuss the existence of the infective periodic solution by Has'minskii theory. Finally, numerical examples are given to illustrate the results.