用WENO方法求解双曲型守恒律方程组的初(边)值问题

本文用WENO算法解决双曲型守恒律方程组初（边值）问题．给出一种满足熵条件、Sδ熵条件和边界熵条件的WENO算法．通过这个算法就能得到守恒律方程组的数值解，数值解和理论解是非常吻合的．     

解线性约束优化问题的新锥模型信赖域3法

本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法．论文采用零空间技术消除了新锥模型子问题中的线性等式约束，用折线法求解转换后的子问题，并给出了解线性等式约束优化问题的信赖域方法．论文提出并证明了该方法的全局收敛性，并给出了该方法解线性等式约束优化问题的数值实验．理论和数值实验结果表明新锥模型信赖域方法是有效的，这给出了用新锥模型进一步研究非线性优化的基础．     

Cahn-Hilliard方程的拟谱逼近

该文讨论用Ｌｅｇｅｎｄｒｅ拟谱方法数值求解非线性Ｃａｈｎ Ｈｉｌｌｉａｒｄ方程的Ｄｉｒｉｃｈｌｅｔ问题．建立了其半离散和全离散逼近格式，它们保持原问题能量耗散的性质．证明了离散解的存在唯一性，并给出了最佳误差估计．数值实验也证实了我们的结果．     

层流管流入口压力突然升高引起的水力瞬变的理论分析

研究了层流状态下管道入口压力突然升高引起的水力瞬变过程,建立了瞬态压力分布的偏微分方程和初边值条件,用分离变量法求得了压力的理论解．根据压力和流量间的约束关系,得到了关于流量的偏微分方程和初边值条件,用分离变量求得了瞬变过程流量分布理论解．最后,用特征线法(MOC)对该问题进行了数值求解,理论解和数值解吻合很好．     

非定常 N-S 方程的非线性 Galerkin 算法及其误差估计

本文给出了二维非定常N-S方程的三种数值格式,其中空间变量用谱非线性Galerkin算法进行离散,时间变量用有限差分离散,并研究了这些格式数值解的逼近精度．最后,给出了部分数值计算结果．     

GM（1，1）模型的样条插值函数的残差拟合

本文用样条函数对GM(1，1)模型的残差序列进行插值拟合，然后作用于二阶线性微分方程，并以此修正原模型，得到一种新的预测模型的数值解．     

信赖域子问题使用重新开始策略的共轭梯度法

给出了用共轭梯度法解信赖域子问题的重新开始策略，并证明了方法的收敛性，数值结果表明该策略可以大大提高算法的收敛速度．     

复合材料稳态热传导问题多尺度计算的一个数学模型

本文给出小周期复合材料稳态热传导问题的一种多尺度渐近展开方法，区别于传统方法中一次项和二次项系数都用解Hper^1（Q）周期边值问题得到，新展式构造时一次项系数仍通过解关于单胞Hper^1（Q）周期边值问题求得，而二次项系数用齐次边值问题求得，所构造渐近解属于H^1（n）．对光滑凸区域Ω，渐近解在H^1（Ω）空间仍具有较好的收敛性．优点为数值方法求解时，解一个齐次边界问题要比解一个Hper^1（Q）周期边值问题简单．     

一维单个守恒律的一类二阶、几乎熵耗散的格式

本文考虑一维单个守恒律方程，对其设计了一个基于熵耗散的非线性守恒型差分格式．本格式的数值流函数是Lax-Freidrichs格式和Lax-Wendroff格式数值流函数的凸组合，凸组合中的系数是由考虑耗散熵来决定的．这样在解的光滑区域内，格式几乎、甚至完全是Lax-Wendroff格式，而在解的间断处，格式几乎、甚至完全是Lax—Freidrichs格式．从而消除了间断附近的非物理振荡，实现了计算的非线性稳定性．理论分析表明本格式在解的非极值点处是二阶精度的，而在解的极值点处至少有一阶精度．数值试验表明格式是有效的．     

相互屏蔽的M＼D＼2排队系统优化

用多目标规划方法研究相互屏蔽的M\D＼2排队系统，得到关于系统优化的若干定理及其规划模型，在给定参数条件下得到了模型的数值解．     

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.     

Design of sliding mode controller for a class of fractional-order chaotic systems

In this paper, a sliding mode control law is designed to control chaos in a class of fractional-order chaotic systems. A class of unknown fractional-order systems is introduced. Based on the sliding mode control method, the states of the fractional-order system have been stabled, even if the system with uncertainty is in the presence of external disturbance. In addition, chaos control is implemented in the fractional-order Chen system, the fractional-order Lorenz system, and the same to the fractional-order financial system by utilizing this method. Effectiveness of the proposed control scheme is illustrated through numerical simulations.     

REDUCIBILITY OF REVERSIBLE SYSTEM WITH SMALL PERTURBATION

Reversible system following Hamiltonian system turns out to be another type of equation which has aroused wide interest in recent years. One open problem is whether the celebrated KAM theory and Nekhoroshev method can be extended to reversible system. As showed in [5], there exist KAM tori in reversible system. In this paper, we give a preliminary discussion on whether there is Nekhoroshev type result in reversible system. In particular, we try to apply this method to the reducibility of a type of common reversible system.     

Topological analysis of an integrable system related to the rolling of a ball on a sphere

A new integrable system describing the rolling of a rigid body with a spherical cavity on a spherical base is considered. Previously the authors found the separation of variables for this system on the zero level set of a linear (in angular velocity) first integral, whereas in the general case it is not possible to separate the variables. In this paper we show that the foliation into invariant tori in this problem is equivalent to the corresponding foliation in the Clebsch integrable system in rigid body dynamics (for which no real separation of variables has been found either). In particular, a fixed point of focus type is possible for this system, which can serve as a topological obstacle to the real separation of variables.     

Control of nonlinear systems on Poincaré section via quasi-sliding mode method

The order of some dynamical systems can be reduced by finding a good Poincaré section for them. In such a case the problem of controlling the main continuous system, can be reduced into controlling the discrete Poincaré map of the system which is usually nonlinear. In this paper, this idea is implemented for a simple nonlinear system. A quasi-sliding mode controller is used to stabilize the unstable fixed point of the discrete system and the control signal obtained, is applied to the main continuous system, where a corresponding limit cycle is observed. The process happens to be useful in understanding the necessary conditions for the existence of periodic responses in the system.     

A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set

It is known that the whole space can be a Li–Yorke scrambled set in a compact dynamical system, but this does not hold for distributional chaos. In this paper we construct a noncompact weekly mixing dynamical system, and prove that the whole space is a transitive extremal distributionally scrambled set in this system.     

Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response

In this paper, we discuss a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if the white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results.     

A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.     

关于图的导出森林独立系统

本文研究图的导出森林独立系统.在这个独立系统中,独立集是指导出子图不含圈的点子集.文中证明了图G的导出森林独立系统是拟阵当且仅当G是块森林.文中同时给出了在强弦图上求最大导出森林的多项式算法.     

On a Stochastic Survival Model for a System Under Randomly Variable Environment

In many cases, the survival probability of a system depends not only on the intrinsic characteristic of the system itself but also on the randomly variable external environment under which the system is being operated. In this paper we study a stochastic survival model for a system under random shock process which affects the survival of the system in a complicated way. The lifetime distribution of the system is derived, and the effect of environmental factors on the failure process of the system is also investigated.