Nonlinear Correlations of Protein Sequences and Symmetries of Their Structures

We investigate the nonlinear correlations of protein sequences by using the nonlinear prediction method developed in nonlinear dynamical theory. It is found that a lot of protein sequences show strong nonlinear correlations and have deterministic structures. Further investigations show that the strong nonlinear correlations of these protein sequences are due to the symmetries of their tertiary structures. Furthermore, the correlation lengths of the sequences are related to the degrees of the symmetries. These results support the duplication mechanism of protein evolution and also reveal one aspect how amino acid sequences encode their spatial structures.     

病毒感染群体动力学模型分析

本文构建并讨论了一类病毒感染的群体动力学模型,得到了模型存在轨道稳定周 期解的充分条件,较好地解释了在病毒持续感染者体内观察到的病毒载量波动现象.     

高维电报方程的对称周期解

讨论n维电报方程的对称周期解．利用Schauder不动点定理，在非共振条件下给出了一个存在性定理．     

浅议数列“周期”的应用

众所周知，数列是一种特殊的函数，函数的性质在数列中的应用是一个很普通的问题，函数中有周期问题，所以数列中也必然有“周期”问题，有些数列问题，表面上看与“周期”无关，但实际上隐藏着周期性，一旦揭示了其周期性，该问题便迎刃而解，下面举数例说明数列周期的应用．     

高维系统周期解的共振分支

本文利用Liapunov－Schmidt方法获得了高维自治系统在共振情况下决定周期解个数的分支函数，并通过计算分支函数的主项，分析分支函数的零点，研究了具两对共轭特征根的四维系统多个周期解的共振分支问题．     

仓库容量有限条件下的一类存贮管理模型

建立了一类仓库容量有限条件下存贮管理决策模型 ,给出最优存贮策略 .     

线性递归序列模q

设{u_k}_k≥0为一个线性递归序列．序列{u_k(mod q)}_(k≥0)是周期的,很多人都对其周期有过研究．本文应用二次数域中理想的理论,较完全地刻面了二次线性递归序列模q的周期长度,所获结果加强并推广了Engstrom及Wall的结论．     

用线性插值法求单摆运动周期的近似解

利用线性插值的方法,提出了一个任意摆角条件下的单摆运动周期的近似公式.并利用Mathematica软件将该公式与精确解进行了比较,还与其他近似公式进行了对比.结果表明,该公式的近似程度相当好.     

Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition

In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.     

非自治时滞微分方程的正周期解

By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.