一类超二次自治哈密顿系统的周期解

结合Maslov指标理论，利用环绕定理证明了一类超二次自治哈密顿系统的周期解的存在性，而这类哈密顿系统所对应的作用泛函可能不满足Palais—Smale条件．     

三维非线性临界解析动态方程的局部渐近稳定性

考察了三维非线性临界动态方程Z.=f(Z),f(0)=0,Df(0)=A,σ(A)={±ω.i,0},ω>0的局部渐近稳定性.首先在非奇异线性坐标变换和时间尺度变换下,将其化成标准形式.之后,运用形式级数法的思想,在f(Z)是解析的假设下,研究了三维自由动态方程Z.=f(Z)的李雅普诺夫V函数的构造问题,给出了确定李雅普诺夫V函数的方法,并得到了判别三维解析动态方程局部渐近稳定的一组充分条件.     

An aperiodic phenomenon of the unscented Kalman filter in filtering noisy chaotic signals

A non-periodic oscillatory behavior of the unscented Kalman filter (UKF) when used to filter noisy contaminated chaotic signals is reported. We show both theoretically and experimentally that the gain of the UKF may not converge or diverge but oscillate aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the UKF converge to zero. However, when the system being considered is chaotic, the Kalman gain either converges to a fixed point with a magnitude larger than zero or oscillates aperiodically.     

最大度为9和10时边染色临界图的下界

关于Vizing边染色临界图边数下界的猜想,到目前为止,△≤5的情况已经得到证明,在传统Fiorini不等式方法证明边染色临界图下界的基础上,借鉴了文献[1]的思想,得到了新的关于最大度是9和10的边染色临界图的下界:△=9时,m≥33/10 n;△=10时,m≥43/12 n.     

Impulsive Control and Synchronization of a Critical Chaotic System

This paper investigates the impulsive control and synchronization of a chaotic system, which is a particular case of the so-called generalized Lorenz canonical form （GLCF） with r τ -1 Based on the impulsive control method, some new criteria are obtained to guarantee the impulsively controlled chaotic system and error system to be globally asymptotically stable at origin. Moreover, to be some simulation results are included to visualize the effectiveness and feasibility of the proposed method.     

Rapid growth cost in ＂all-fish＂ growth hormone gene transsenic carp： Reduced critical swimming speed

Evidence has accumulated that there is a trade-off between benefits and costs associated with rapid growth. A trade-off between growth rates and critical swimming speed （Uc,t） had been also reported to be common in teleost fish. We hypothesize that growth acceleration in the F3 generation of ＂all-fish＂ growth hormone gene （GH） transgenic common carp （Cyprinus carpio L.） would reduce the swimming abilities. Growth and swimming performance between transgenic fish and non-transgenic controls were compared. The results showed that transgenic fish had a mean body weight 1.4--1.9-fold heavier, and a mean specific growth rate （SGR） value 6%-10% higher than the controls. Transgenic fish, however, had a mean absolute Ucr, （cm/s） value 22% or mean relative Ucrit （BL/s） value 24% lower than the controls. It suggested that fast-growing ＂all-fish＂ GH-transgenic carp were inferior swimmers. It is also supported that there was a trade-off between growth rates and swimming performance, i.e. faster-growing individuals had lower critical swimming speed.     

计算转子系统固有频率的有限元法之改进

在采用有限元法计算转子系统的固有频率时,通常把转子系统化为刚性圆盘、轴段、和轴承座等单元,先计算出各单元的运动方程,然后把各单元组合起来形成系统的运动方程。文章把刚性圆盘和弹性轴段视为同一单元处理,其结果计算更为准确、编程更为简单。同时文章也给出了计算转子系统临界频率的一种较好方法。     

整体传递矩阵法的Riccati变换

研究了多转子系统的Riccati变换问题，导出了多转子系统各种具体单元的Riccati变换公式以及Riccati变换中逆矩阵的计算公式，给出了数值算例。研究表明，尽管整体传递矩阵取系统的状态向量作为传递向量，增加了自由度，但计算工作量基本上没有增加。     

串联加工网络关键路径的计算与扰动分析

文献[5]在极大代数上线性系统描述的框架下，通过关键路径研究了DEDS参数扰动对系统的影响，关键路径的计算是其核心问题，本文讨论了串联加工网络的路径的性质，在偏序科上运用动态规划的最优原理研究了DEDS的关键路径的计算问题，并给出了详细的算法。在此基础上，给出了扰动分析的新方法。     

简谐势阱中弱相互作用玻色气体的临界温度及基态粒子占据率

应用局域密度近似法（LDA）对简谐势约束下的非理想玻色气体发生玻色－爱因斯坦凝聚（BEC）时的临界温度作出计算，进而讨论了弱相互作用对临界温度及基态粒子占据率的影响。这些研究将有助于对BEC这种新物态性质的进一步了解。