混合序列加权和的强收敛性

本文给出混合序列加权和的强收敛性的一些充分条件，这些结论推广和改进了文［１］定理３，文［２］定理３；文［３］定理４．１５以及文［４］定理４．     

多裂纹圆柱弯曲问题的奇异积分

本文在文［１］的基础上，利用文［２］给出的无裂纹柱体弯曲问题的通解，求得了多裂纹圆柱横力弯曲应力函数及横截面剪应力的奇异积分表达式。本文方法借助数值积分表达式￣［３］，极易在微机上实现，可以完全类似文［１］所做的那样进行数值计算．     

几类特殊测地块的构造(英)

本文给出了一种构造给定直径d和围长g的测地块的方法．它是文［1］中构造法的推广，解决了文［1］中待研究的几个问题．同时，对文［1］中的一个错误进行了修正．     

谈欧氏空间中的变换和线性变换

谈欧氏空间中的变换和线性变换彭明海彭学梅（湖南省吉首大学４１６０００）文［３］推广了文［１］、文［２］的全部定理，本文不仅推广了文［３］的全部定理，而且得出新的结果．同时，论证也较简捷．今介绍给同行参考．定理１σ和τ是欧氏空间Ｖ的两个变换，φ是Ｖ的线...     

也谈对数大小的比较

也谈对数大小的比较万兴灿（湖北省宜昌市第一中学４４３０００）探究文［１］、［２］、［３］获益非浅，对比言之，文［３］方法从形式到实质仍是文［２］的方法．本文倾向文［１］处理方法，加以推广，则可较全面、简捷地解决对数大小的比较．定理１设１＜ａ＜ｂ，ｍ＞...     

r─循环矩阵的逆

本文给出了ｒ─循环矩阵的求逆公式，推广了文［１］，［２］的结论．     

Vandermonde行列式的一个推广及其在初等数学中的应用

Ｖａｎｄｅｒｍｏｎｄｅ行列式的一个推广及其在初等数学中的应用肖振纲（湖南岳阳师专４１４０００）文［１］，［２］先后利用复变函数中的留数定理讨论了初等数学中的Ｉ．Ｊ．Ｍａｔｒｉｘ定理的两个推广，文［３］则用初等方法讨论了所述两个推广的关系，本文首先给出...     

再谈欧氏空间的变换和线性变换

文［３］推广了文［１］～［２］中的全部定理,文［４］又推广了文［３］的全部定理,本文推广了文［４］的全部定理,指出了文［４］中的一个错误论断,并给出了线性变换的一个等价条件．为简便,文中的Ｖ表示欧氏空间,ＶＶ表示Ｖ的所有变换的集合,Ｌ（Ｖ）表示Ｖ的所...     

关于一类自由作业机器排序问题

文章研究文［１］中提出的加工时间依赖于机器的自由作业排序问题。Ｍ．Ｄｏｒｏｒ在［１］中提出了一个算法（算法３．４）。最近，Ａ．Ｊ．Ｖａｋｈａｒｉａ、Ｂ．Ｃａｔａｙ［２］及项思明、唐国春［３］均指出Ｍ．Ｄｏｒｏｒ的算法不是最优的。项思明和唐国春提出对这类问题在机器连续加工情形下的一种求解方法，即将排序问题化成指派问题。本文对这种解法作了简化，并回答文［３］中提出的几个问题。     

试卷质量的灰色综合评判

李文革．试卷质量的灰色综合评判．数理统计与管理，１９９７，１６（４），４２～４５．本文运用灰色综合评判评价了文［１］中的七套试卷，得到了与文［１］不同的结果，但本文的结果更符合客观实际。     

An exact parallel method for a bi-objective permutation flowshop problem

In this paper, we propose a parallel exact method to solve bi-objective combinatorial optimization problems. This method has been inspired by the two-phase method which is a very general scheme to optimally solve bi-objective combinatorial optimization problems. Here, we first show that applying such a method to a particular problem allows improvements. Secondly, we propose a parallel model to speed up the search. Experiments have been carried out on a bi-objective permutation flowshop problem for which we also propose a new lower bound.     

Some non-interior path-following methods based on a scaled central path for linear complementarity problems

In this paper we present some non-interior path-following methods for linear complementarity problems. Instead of using the standard central path we use a scaled central path. Based on this new central path, we first give a feasible non-interior path-following method for linear complementarity problems. And then we extend it to an infeasible method. After proving the boundedness of the neighborhood, we prove the convergence of our method. Another point we should present is that we prove the local quadratic convergence of feasible method without the assumption of strict complementarity at the solution.     

A novel numerical method and its convergence for nonlinear delay Volterra integro-differential equations

In this paper, we suggest a convergent numerical method for solving nonlinear delay Volterra integro-differential equations. First, we convert the problem into a continuous-time optimization problem and then use a shifted pseudospectral method to discrete the problem. Having solved the last problem, we can achieve the pointwise and continuous approximate solutions for the main delay Volterra integro-differential equations. Here, we analyze the convergence of the method and solve some numerical examples to show the efficiency of the method.     

Performance of two-disk partition data allocations

In this paper, we present a method, called the partition data allocation method, to allocate a set of data into a multi-disk system. Using the partition data allocation method, we shall show that, in a two-disk system, the performance is influenced by how we disperse similar data onto different disks.     

Convergence of quasi-Newton method with new inexact line search

Quasi-Newton method is a well-known effective method for solving optimization problems. Since it is a line search method, which needs a line search procedure after determining a search direction at each iteration, we must decide a line search rule to choose a step size along a search direction. In this paper, we propose a new inexact line search rule for quasi-Newton method and establish some global convergent results of this method. These results are useful in designing new quasi-Newton methods. Moreover, we analyze the convergence rate of quasi-Newton method with the new line search rule.     

一种新的迭代收敛阶数的证明与推广

迭代方法是求解非线性方程近似根的重要方法.本文基于隐函数存在定理,提出了一种新的迭代方法收敛性和收敛阶数的证明方法,并分别对牛顿(Newton)和柯西(Cauchy)迭代方法迭代收敛性和收敛阶数进行了证明.最后,利用本文提出的证明方法,证明了基于三次泰勒(Taylor)展式构成的迭代格式是收敛的,收敛阶数至少为4,并提出猜想,基于n次泰勒展式构成的迭代格式是收敛的,收敛阶数至少为(n+1).     

Scenario decomposition of risk-averse multistage stochastic programming problems

For a risk-averse multistage stochastic optimization problem with a finite scenario tree, we introduce a new scenario decomposition method and we prove its convergence. The main idea of the method is to construct a family of risk-neutral approximations of the problem. The method is applied to a risk-averse inventory and assembly problem. In addition, we develop a partially regularized bundle method for nonsmooth optimization.     

On the Convergence of the Brent Method

1.IntroductionItiswellknownthattheBrentmethodforsolvingsystemsofnonlinearequati0nsistosolvethefo1lowingsystem:bymaldnguseoftheorthogonaltriangulaxfaCtoriz8tion.SupP0sethatwehaveanaPprokimationx(k)tox*,asoluti0nof(1.1).Thenthek-thiterativeprocedurecanbedescribedasfollows[1]:wherehk/Oisthedifferencestepcorrespondingtotheindexk(wewilldiscussthechoicesofhkinSecti0n4)-Constructanorthogonalmatrix(usuallybytheHouseholdtransf0rmation)Step4.Ifj相似文献   

Risk-averse dynamic programming for Markov decision processes

We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming equations and a value iteration method. For the infinite horizon problem we develop a risk-averse policy iteration method and we prove its convergence. We also propose a version of the Newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence. Finally, we discuss relations to min–max Markov decision models.     

一种求解非线性互补问题的方法及其收敛性

本文将Newton方法和外梯度方法相结合,提出了一种求解非线性互补问题的方法,证明了此方法的全局收敛性和超线性收敛性,在适当的条件下给出了一个有限终止结果。数值实验表明,此方法是有效的。