仅有x-分量耦合的非恒同Lorenz系统的渐近同步

考虑外部耦合格式为n×x阶实对称不可约,行和为零且对角线以外的元素非正的矩阵,内部耦合格式为仅有x-分量参与耦合的非恒同Lorenz格点系统的渐近同步.运用Lyapunov稳定性理论讨论系统解的一致有界耗散性.并在此基础上采用Cauchy-Schwaxz不等式证明当耦合强度足够大时仅有x-分量参与耦合的非恒同Lorenz格点系统的解出现渐近同步,即系统解的任意两个对应分量的差在时间趋向于无穷时是一个小的有界量.     

n维耦合振子格点系统的同步性

本文通过在相空间中引入新范数的方法研究了Dirichlet,Neumann,周期三个不同边界条件下带有周期外力的n维二阶耦合振子格点系统的同步性.在Dirichlet边界条件下,如果系统非线性项的一阶偏导数有界,则当耦合系数足够大时,系统是有界耗散的并且任意两个解之间是同步的.在Neumann与周期边界条件下,如果不同子系统的外力之间的差和不同子系统的非线性项之间的差都比较小,并且系统是有界耗散的,则当耦合系数足够大时,系统任意一个解的任意两个分量之间是渐近同步的.这两种情况下,当耦合系数c_1→+∞,c_2→+∞时,系统任意一个解的任意两个分量之间是同步的.     

非恒同耦合系统的同步

在过去的几十年,由于同步在通信、光学、神经生物网络等不同领域的广泛应用,使得耦合动力系统的同步行为吸引了很多的注意.除了关于周期信号的经典同步概念,还引入了许多新的同步的类型:如混沌同步,相同步,广义同步等等.利用不变流形理论讨论非恒同耦合系统的同步.     

具结构阻尼的耦合梁方程组在非线性边界条件下的吸引子

研究了具有转动惯量和结构阻尼的耦合梁方程组在非线性边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性,其次证明了系统存在有界吸收集和半群的渐近光滑性,最后得到了全局吸引子的存在.     

一类高阶非线性中立型微分方程的振动性

本文研究以下n阶非线性中立型微分方程有界解的振动性和渐近性,得出(1)仅有振动解的几个充分条件。     

一类耦合梁方程组在非线性边界条件下解的长时间动力行为（英文）

本文研究一类具有强阻尼项的耦合梁方程组在非线性边界条件下的长时间动力行为,首先利用一些常用不等式和先验估计证明该系统存在唯一的整体解,其次通过证明系统存在有界吸收集和半群的渐近光滑性得到整体吸引子的存在性.     

具有非线性热源项的耦合杆系统

主要以经典的算子半群理论为依据,研究了一类具有非线性热效应的耦合杆系统的长时间行为.首先在齐次边界条件和初始条件下,证明了系统解的存在唯一性;其次通过渐近先验估计,证明了系统有界吸收集的存在性;最后利用算子半群的分解技巧,得到了系统全局吸引子的存在性.     

具有双记忆项的热弹耦合梁方程的整体吸引子

研究了具有双记忆项的非线性热弹耦合梁方程,利用已知的研究结果给出解的适定性定理,其次通过先验估计并结合常用不等式证明系统存在有界吸收集,且利用标准方法验证半群的渐近紧性,得到整体吸引子的存在性.     

N个异结构混沌系统的环链耦合同步

提出了一种通过环链耦合实现N个异结构混沌系统同步的方法.以New系统、Chen系统、Lü系统、Lorenz系统和Rssler系统作为典型的例子,验证了这种同步控制方法的有效性.利用Liapunov稳定性定理,构造控制器的具体形式,并确定了耦合系数的取值范围.仿真模拟结果表明,在控制器的作用下,选择适当的耦合系数值,可以同时使N个异结构混沌系统达到完全同步.     

三个耦合的非扩散Lorenz系统的全局混沌同步

以Lyapunov稳定性理论和矩阵论为基础,针对非扩散Lorenz系统,提出了一种三个耦合的恒等系统的全局混沌同步方案.该方案的关键是耦合参数的选取.通过选择适当的耦合参数,使得三个系统的状态变量达到同步,并利用Mathematic软件进行数值仿真.理论分析和仿真结果都表明了该方法的有效性.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the dependence of the growth rate on the length of the defining relator

Let { } be a sequence of finitely presented groups with generating setA={a1, …, am}, and letRk be the symmetrized set of words over the alphabetA∪A−1 obtained from the defining words and their inverses by all cyclic shifts. We shall assume that the words inRk are cyclically irreducible, and their lengths tend to ∞ ask increases. In the paper, it is proved that ifRk satisfies the small cancellation conditionC'(1/6) and the number of relators increases not very rapidly with increasingk, then the growth rate ψ(Gk) tends to 2m−1 ask→∞. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 611–617, April, 1999.