平面上的近似连续积分

近似连续Ｐｅｒｒｏｎ 积分首先由Ｂｕｒｋｉｌｌ提出,称之为ＡＰ积分,由于近似复盖具有划分性质,因而可以给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义． 但是,在平面上近似复盖是否具有划分性质还不知道． 本文给出了一种方法,用这种方法可以在平面上给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义而不需要证明划分的存在性．     

Logunov场方程解的非存在性与近似解

本文讨论了Ａ．Ａ．Ｌｏｇｕｎｏｖ相对引力论中的场方程，给出了一种形式的近似解，并且讨论了几种情形的解的非存在性。特别地，讨论了Ｒ（２＋１）中的情形．     

简单补偿随机规划的一种异步并行算法

本文利用凸规划的近似分解方法，给出了求解具有简单补偿随机规划问题的一种异步并行算法．     

一类双曲反问题的逼近算法及收敛性

该文考虑地球物理勘探中出现的间断特性阻抗的反演问题．利用样条插值理论，把无穷维空间上的反问题用有限维空间上的反问题来近似．利用半群理论，证明了近似反问题之解收敛于原反问题之解．据此可得到求解反问题的一种稳定的近似算法．     

固定合作规模网络的平均路径长度

本文提出了一种特殊的合作网络,称之为固定合作规模网络．我们重点研究了这类网络的平均路径长度,通过建立微分方程,得到平均路径长度的增加速度近似与网络规模的对数成正比．     

具有高阶分界线环的多项式微分系统的近似系统

利用Hamilton系统的挑动系统得到了构造具有高阶分界线环的多项式微分系统的近似系统的一种方法，并举出了具体例子．     

粗糙集的相似度量

在近似空间中,分别以集合的上下近似以及元素的隶属度定义了两个集合间的相似度度量,讨论了两种相似度的性质,并对两种相似度进行了比较．     

向量优化问题局部近似解的等价性

主要研究两种不同序关系下向量优化问题的近似解.一种是正锥序关系下的近似解,另一种是多面体锥序关系下的近似解.针对这两种序关系下向量优化问题的近似解,建立了局部近似最优解和μ阶严格局部近似最优解之间的等价关系,同时构建了这两种序关系下近似有效点集之间的等价关系.     

时滞惯性流形及近似时滞惯性流形族

时滞惯性流形是对耗散系统惯性流形、近似惯性流形的最新发展,它基于对 大小涡分量间相互作用更细致的观察,即改变了惯性流形和近似惯性流形方法中大小 涡分量间相互作用为瞬时行为的隐含假定,而认为这种作用与系统的历史相关的．本 文结出了一类耗散系统时滞惯性流形的存在性证明,由于其存在性不需要“谱间隔条 件”保证,因而时滞惯性流形是广泛存在的．随后我们引出了一类离散的时滞惯性流 形,并在此基础上构造了一种近似时滞惯性流形族,分别给出了它们近似时滞惯性流 形的误差估计,结果显示这种新方法为构造稳定和高精度的算法提供了可能．     

求解约束极小极大问题的一种K─S函数的近似迭代法

借助于极大熵方法和逼近法，给出了一种求解约束极小极大问题的K－S函数近似迭代法，同时讨论算法的有关收敛性．     

煤炭资源最佳开采时期研究

煤炭资源是一种不可再生资源,即耗竭性资源.现在的煤炭资源开采策略是一种掠夺式的开采,不仅浪费资源,而且会使我国的煤炭将来很难满足现代化建设的需要.为此,本文采用经济控制论模型试图探讨煤炭资源的最佳开采时期.     

一类与BB型对偶剖分相关的广义差分格式的L2模误差估计

广义差分法的研究涉及到对求解区域做某种剖分及相应的对偶剖分,对区域做三角形剖分时,最常用的对偶剖分是所谓的外心对偶剖分和重心对偶剖分[4][2],在计算流体中,还经常用到另一种对偶剖分即重心相联对偶剖分(BB型对偶剖分)[6]。[6]对一类椭圆     

On an identity for zeros of Bessel functions

In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the first kind, which in particular reduces to some other new identities. We also show that our method can be applied for the zeros of other special functions, like Struve functions of the first kind, and modified Bessel functions of the second kind.     

Indefinite integrals involving complete elliptic integrals of the third kind

A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected.     

Maximum Principle for Risk-Sensitive Stochastic Optimal Control Problem and Applications to Finance

This article is concerned with a risk-sensitive stochastic optimal control problem motivated by a kind of optimal portfolio choice problem in the financial market. The maximum principle for this kind of problem is obtained, which is similar in form to its risk-neutral counterpart. But the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter. This result is used to solve a kind of optimal portfolio choice problem and the optimal portfolio choice strategy is obtained. Computational results and figures explicitly illustrate the optimal solution and the sensitivity to the volatility rate parameter.     

Uniformly locally o-minimal structures and locally o-minimal structures admitting local definable cell decomposition

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which admits local definable cell decomposition.     

Galerkin方法的一种简单后处理过程

基于近似惯性流形思想,以流函数形式定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程为例,给出了一种简单的后处理Ｇａｌｅｒｋｉｎ方法。其主要思想是利用近似惯性流形概念和对真解的一种新的分解,构造高低频分量间的近似作用规律。文中证明了这种简单的后处理Ｇａｌｅｒｋｉｎ方法可以较小的代价获得较经典Ｇａｌｅｒｋｉｎ方法高得多的精度。     

L-统计量的Edgeworth展开和随机加权逼近

文［１］讨论了Ｌ－统计量的一种能达到Ｏ１√ｎ精确度的随机加权逼近,本文则给出了Ｌ－统计量的Ｅｄｇｅｗｏｒｔｈ展开和一种能达到ｏ１√ｎ精确性的新的随机加权逼近     

Boundary-value problems for a hyperbolic equation with nonlocal conditions of the I and II kind

In this paper we consider two initial-boundary value problems with nonlocal conditions. The main goal is to propose a method for proving the solvability of nonlocal problems with integral conditions of the first kind. The proposed method is based on the equivalence of a nonlocal problem with an integral condition of the first kind and a nonlocal problem with an integral condition of the second kind in a special form. We prove the unique existence of generalized solutions to both problems.     

Error bounds of the Galerkin method for singular integral equations of the second kind

For solving singular integral equations of the first kind Erdogan proposed a method of Galerkin type, and convergence was proved by Linz. In this paper we consider equations of the second kind, and it is found that the method converges also in this case. However, stronger conditions than for the first kind equations must be imposed. The computational aspect of the convergence problem is also considered.