辛变换与辛差分格式

由于数学方法在经典力学理论研究中的广泛应用,人们对于经典力学系统的内在性质的理解更加深刻,因而,在数值方法上力求模拟经典力学系统的内在守恒性质.经典力学系统的统一描述——Hamilton力学系统的数学理论体系,为探求经典力学系统的数值方法的对称与守恒奠定了坚实的基础.基于Hamilton力学系统的对称与守恒性质,[3]中提出了保持Hamilton能量守恒的差分格式,[4]中对一类Hamilton方程给出了     

关于相对紧性质的研究

利用有限交性质的集族及网的性质描述了相对紧性质,给出了相对紧性质的两个等价结果.     

Banach空间的（LP）性质

本文给出了(L_p)性质的定义,并就具有该性质的Banach空间进行了讨论,给出了这一性质的对偶性质,证明了若 X 与 X~* 均具(L_p)性性,则 X 是自反的。     

迭代函数系统的强跟踪性质

给出了迭代函数系统(IFS(F))的强跟踪性质的概念并且研究了它的相关性质.结合经典动力系统的相关方法,首先证明了一致压缩的迭代函数系统都有强跟踪性质,从而给出了具有强跟踪性质的相关例子;另外也证明了两个IFS(F)的强跟踪性质在拓扑共轭的条件下是保持不变的;最后我们得到了:如果IFS(F)有小距离扩张性,则它是开的当且仅当它具有强跟踪性质.     

Rudin性质与拟Z-连续Domain

对一般子集系统 Z,引入了 Rudin性质,给出了它的映射式刻划,作为拟连续偏序集和Z-连续偏序集的公共推广,引入了拟Z-连续Domain的概念,讨论了拟Z-连续Domain的基本性质,特别地,给出了 Rudin性质及其映射式刻划在拟 Z-连续Domain方面的若干应用,将关于拟连续偏序集的主要结果推广至了拟 Z-连续 Domain情形。     

Rudin性质与拟Z-连续Domain

对一般子集系统Z,引入了Rudin性质,给出了它的映射式刻划.作为拟连续偏序集和Z-连续偏序集的公共推广,引入了拟Z-连续Domain的概念,讨论了拟Z-连续Domain的基本性质,特别地,给出了Rudin性质及其映射式刻划在拟Z-连续Domain方面的若干应用,将关于拟连续偏序集的主要结果推广至了拟Z-连续Domain情形.     

关于圆锥曲线与等比数列的一个性质的补充

文[1]给出了圆锥曲线与等比数列的一个性质． 作为文[1]的补充，本文再给出三个类似的结论．     

常微分方程周期脉冲控制问题的均方turnpike性质

本文研究了一类常微分方程的最优控制问题,其中控制以脉冲的形式周期地施加到系统中.首先,给出了该问题及其参考控制问题的最大值原理.其次,在控制系统能控的假设条件下,证明了系统的能观性不等式.最后,利用最大值原理以及能观性不等式,获得了两个最优控制问题的最优状态和最优控制在时间足够长时的收敛关系—均方turnpike性质.     

对三角形的一个性质的再探究

文[1]提出了三角形的一个“性质”并给出了证明，文[2]又给出了“性质1”并且也给出了证明．受它们的启发，本文也将有关性质进一步探究推广．     

函数的次微分性质

本文给出了函数的Fenchel次微分、Frechet次微分,Hadamard次微分,Gateaux次微分的一些重要性质,并对函数的性质尤其是凸性给出其次微分刻画。     

RISK-BASED MULTIATTRIBUTE DECISION-MAKING IN PROPERTY AND WATERSHED MANAGEMENT

ABSTRACT. Determining best management systems for properties and evaluating their sustainability at the watershed scale are useful and important aspects of integrated watershed management. Multiattribute decision-making (MADM) is very useful for modeling the selection of best management systems for properties in a watershed. This paper reviews four MADM approaches including utility theory, surrogate worth tradeoff, free iterative search and stochastic dominance with respect to a function (SDWF). Emphasis is on determining how the first three methods could be used to determine the best (most preferred) combinations of attributes and associated management systems for a property. An application of the expected utility method with risk neutral preferences is presented in which farmer's preferences for five attributes are used to rank five farming systems for an agricultural watershed in Missouri. A framework is presented for assessing the sustainability of the best management systems for all properties in a watershed and the cost-effectiveness of policies for enhancing sustainable resource management at the watershed scale.     

半线性椭圆型方程组正解的对称性和单调性

该文讨论了扇型区域上一类半线性椭圆型方程组混合边值问题正解的对称性和单调性．所得结果是文献［1］－［14］的一个推广．     

Stability Concepts in Topological Dynamics by Nonstandard Methods

It is known that it is not possible to introduce C⁰ -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rⁿ. Classically these amount to considering the space of all systems on a given subset of Rⁿ as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.     

对称不定系统的一类预处理子的注记

由于对称正定系统已有很多有效的求解方法,因此将对称的、或者非对称的不定系统转化为对称正定系统就成为解决这类问题的方法之一构造了一类简洁有效的预处理子,将对称不定系统转化为对称正定型,研究了所得预处理系统的谱性质,估计了其谱条件数,推广了现有结论.     

The Basis Properties of Some Systems of Exponential Functions,Cosines, and Sines

We consider some systems of exponential functions, cosines, and sines with complex-valued coefficients and establish a necessary and sufficient condition for completeness and minimality of these systems in Lebesgue spaces.     

Matrix polynomials and the index problem for elliptic systems

The main new results of this paper concern the formulation of algebraic conditions for the Fredholm property of elliptic systems of P.D.E.'s with boundary values, which are equivalent to the Lopatinskii condition. The Lopatinskii condition is reformulated in a new algebraic form (based on matrix polynomials) which is then used to study the existence of homotopies of elliptic boundary value problems. The paper also contains an exposition of the relevant parts of the theory of matrix polynomials and the theory of elliptic systems of P.D.E.'s.

     

一类弱非线性方程组的Picard-MHSS迭代方法

修正的Hermite/反Hermite分裂(MHSS)迭代方法是一类求解大型稀疏复对称线性代数方程组的无条件收敛的迭代算法.基于非线性代数方程组的特殊结构和性质,我们选取Picard迭代为外迭代方法,MHSS迭代作为内迭代方法,构造了求解大型稀疏弱非线性代数方程组的Picard-MHSS和非线性MHSS-like方法.这两类方法的优点是不需要在每次迭代时均精确计算和存储Jacobi矩阵,仅需要在迭代过程中求解两个常系数实对称正定子线性方程组.除此之外,在一定条件下,给出了两类方法的局部收敛性定理.数值结果证明了这两类方法是可行、有效和稳健的.     

The Basis Properties of Power Systems in L p

We consider power systems with complex-valued coeficients. We establish a necessary and suficient condition for completeness and minimality and also a necessary condition for the basis property of these systems in Lebesgue spaces.     

The Asymptotic Property of Solutions to a Class of Integrodifferential Equations

The asymptotic property of solutions to a class of integrodifferential systems containing a small parameter singularly is studied.     

基于超循环理论的组织循环系统及其性能评价

企业同生物体一样,健康和能源是其生存的基本条件.企业中表现为良好的经营能力和持续不断的资源.这至少依赖于两个循环系统来完成:新陈代谢循环系统和资源平衡循环系统.这两个循环系统之间还具有一定的协同关系.二者失去平衡,同样会导致企业的失败.新陈代谢循环、资源平衡循环以及其它一些支持循环的协同运转构成了一个完整的组织循环系统.从企业的生存入手,对企业的循环系统的构成和要素进行研究.在此基础上,研究组织循环性能的评价方法,包括平衡性、鲁棒性和平滑性三个方面.