关于方程xy+yz+zx=n的正整数解

本文在广义Ｒｉｅｍａｎｎ猜想成立的条件下证明了：当且仅当正整数ｎ＝１，２，４，６，１０，１８，２２，３０，４２，５８，７０，７８，１０２，１３０，１９０，２１０，３３０，４６２时，方程ｘｙ＋ｙｚ＋ｚｘ＝ｎ无正整数解（ｘ，ｙ，ｚ）．     

齐民友先生谈数学教育改革──在PMN全国会议上的讲话(摘要)

这个会非常重要，我很高兴，主动来参加这个会．近年在国内，关于教育方面的种种问题都在考虑，不仅在中国，在美国也一样，例如在加州围绕教学改革，打了一场"数学之战"，最近这一年我与华中师大路刚同志谈的较多，无锡的徐沥泉老师，试着把数学方法论用于数学教学，做了很好的工作，数学教学问题的研究，郁很大的发展，英藉匈牙利人拉卡托斯，通过研究多面体的欧拉公式，以此为素材，为案例，搞助探论（heuristic，康宏逵先生的译法是准确的，有人译为探索法，亦可，译成"启发法"就在些勉强了），起初在一个杂志登出来，后来他的学生把它…     

关于丢番图方程x^2±2^m=y^n

本文证明了：方程ｘ２＋２ｍ＝ｙｎ，ｘ，ｙ，ｍ，ｎ∈Ｎ，ｇｃｄ（ｘ，ｙ）＝１，ｎ＞２仅有有限多组解（ｘ，ｙ，ｍ，ｎ），而且当（ｘ，ｙ，ｍ，ｎ）≠（５，３，１，３），（１１，５，２，３），（７，３，５，４）时，ｎ是适合ｎ≡７（ｍｏｄ８）以及２３≤ｎ＜８．５·１０６的奇素数，ｍａｘ（ｘ，ｙ，ｍ）＜Ｃ１；方程ｘ２－２ｍ＝ｙｎ，ｘ，ｙ，ｍ，ｎ∈Ｎ，ｇｃｄ（ｘ，ｙ）＝１，ｙ＞１；ｎ＞２仅有有限多组解（ｘ，ｙ，ｍ，ｎ），而且这些解都满足ｎ＜２·１０９炉以及ｍａｘ（ｘ，ｙ，ｍ）＜Ｃ２，这里Ｃ１，Ｃ２是可有效计算的绝对常数．     

关于折线的一个猜想的证明

文[1]中，王方汉老师有如下猜想：当n为形如4m－1（mEN）的素数时，生成数列凡一l＝（1，2，…，牛／，M，…，2，l）所确定的数列B，，具有遍历性．也就是说，设数列凡1＝（r，12，…，r。－l），h为正整数，B。＝（hi，bZ，…，b。），1＝hi＜bZ＜…＜b。且均为整数，设凡；与B。之间有如下映射关系：。。。。，；；＝（1，2，…，宁，宁，…，2，1）且n为形如4m－1的素数时，数列B。各项被n除的余数恰是0，1，2，…，n－1的一个全排列．显然，数列B。＝（hi，bZ，…，b。）各项被n除的余数恰是0，1，2，…，n一且的一个全排列等价于…     

多面体k级中线的几个性质

全文约定：用Ω表示三维欧氏空间的多面体，其顶点集为{A1，A2，…，An}，重心为G，令{A1，A2，…，An}={A’1,A’2，…，A’n}，由Ω的任意k个顶点A’1，A’2，…，A’k组成的多面体为Ωjk，其重心为Gjk，由Ω的剩余n-k个顶点A’k＋1，A＇k＋2，…，A’n所组成的多面体为Ωjk，其重心为Gjk（j=1，2，…，Cn^k）．     

关于C~∞-字的幂是C~∞-字的条件(Ⅰ)

本文证明了关于Ｃ∞－字的导数的下列重要结果：对任意Ｃ∞－字ｗ，若ｗ２是Ｃ∞－字，则对任意的自然数ｋ，一定存在ｕ∈Σ使得Ｄｋ（ｗ２）＝Ｄｋ（ｗ）ｕＤｋ（ｗ），其中Σ＝｛Λ，１，２，１２，２１，１１，２２，１１２，２１１，２２１，１２２，１２１，２１２，１１２１，１２１１，１２１２，２１２１，２１１２，１２２１，１１２２，２２１１，１１２１１｝．这个结果对彻底解决沈传龙与黄允宝（１９９４）提出的对任意Ｃ∞－字ｗ都有ｗ３不是Ｃ∞－字的猜想将起关键作用     

一个随机偏差定理

设{Xn，n≥0}是可列非齐次马尔可夫链，Sn（i0，i1，…，im-1，ω）表示m元状态序组（i0，i1，…，im-1）在序列（X0，X1，…，Xm-1），（X1，X2，…，Xm），…，（Xn-1，Xn，…，Xn＋m-2）中出现的次数.本文给出了关于Sn（i0，i1，…，im-1，ω）的一个对任意可列非齐次马尔可夫链普遍成立的随机偏差定理，即用不等式表示的一个强极限定理.     

读者来信

多年来，本刊录用的每一篇文章，都是先致信作者，通知稿件录用，并要求回信说明文章是否他投，大多数作者回信都会如实说明情况，但是，最近发现有些作者并未说真话，导致文章在多家杂志先后登出，造成了恶劣影响．这种影响是多方面的，首先，这是对作者自身诚信的一种否定；其二，这是对审稿人劳动的不尊重；其三，杂志的版面有限，这种行为直接剥夺了其他作者展现自己成果的机会；其四，这种行为严重影响了杂志的声誉，一些热心的读者通过电话，电子邮件和信件等形式指出这种现象，并列出了这些作者的名单和发表文章的题目，强烈谴责这种行为，在此，我们向这些关心和支持杂志的读者表示感谢，此前，为了保护作者的积极性，并未进行公开批评，针对当前这种现象呈增多之势，本着保护其他作者积极性、维护杂志声誉的想法，对于今后出现一稿多投的作者，我们将公开批评，列出作者姓名和发表文章题目，以正视听，下面摘登了朱永厂老师的一封来信．     

基于巴斯卡数据成败型元件串联系统可靠性经典精确置信限

设Ａ为由Ｋ个相互独立的成败型元件组成的串联系统，第ｉ个元件的可靠性ｐｉ，ｐｉ未知，ｉ＝１，２，…，Ｋ．设对第ｉ个元件，对于给定的ｍｉ，有ｎｉ个巴斯卡试验数据：Ｘｉ１，Ｘｉ２，…，Ｘｉｎｉ，其中Ｘｉｊ表示对第ｉ个元件进行试验，试验进行到ｍｉ次成功时所需要的试验次数ｊ＝１，２，…，ｎｉ，ｉ＝１，２，…，Ｋ．记Ｔｉ＝Ｘｉ１＋Ｘｉ２＋…＋Ｘｉｎｉ，ｉ＝１，２，…，ｋ．本文研究基于统计量（Ｔ１，Ｔ２，…，Ｔｋ）求串联系统Ａ的可靠性经典精确最优置信下限．     

关于广义Thue－Mahler方程的解数

设ａ，ｂ是非零整数，ｐ１，…，ｐｒ是不同的素数，Ｐ＝｛±｜ｍ１，…，ｍｒ是非负整数｝．设Ｋ是ｎ（ｎ≥３）次代数数域，α１，…，αｍ∈ｋ（１＜ｍ＜ｎ），△（α１，…，αｍ）是α１，…，αｍ的判别式，ｆ（ｘ１，…，ｘｍ）＝αＮｋ／Ｑ（α１ｘ１＋…＋αｍｘｍ）∈ｚ［ｘ１，…，ｘｍ］．本文证明了：当ｆ（ｘ１，…，ｘｍ）非退化且Ｐｉ△（α１，…，αｍ）（ｉ＝１，…，ｒ）时，方程ｆ（ｘ１，…，ｘｍ）＝ｂｙ，ｘ１，…，ｘｍ∈ｚ，ｇｃｄ（ｘ１，…，ｘｍ）＝１，ｙ∈Ｐ至多有（４Ｓｄ２）（Ｓｄ）组解（ｘ１，…，ｘｍ，ｙ），其中ｄ＝ｎ！，Ｓ＝ｒ＋ω是ｂ的不同素因数的个数，ｈＡ是Ｋ的类数．     

The impact of preventive activities on the economics of production systems: Modeling and application

In this paper, the impact of preventive activities on the economics of production systems has been discussed. A defective production system has been used to evaluate the financial return of a system with and without preventive activity. A mathematical model has been developed to simulate the situation. A practical case in the automotive industry has been used to verify the model. According to this research, it has been found that preventive activities will affect the return of the production system, and the effect depends on the cost of the action that has been taken.     

On One method for the numerical solution of a system of parabolic equations

An algorithm for the numerical solution of a system of two parabolic equations of a special form has been presented, and its stability has been proved. Estimates of the numerical solutions obtained have been made. Conditions guaranteeing the applicability of the sweep method are determined, and the time step at which the iterative method has the inner convergence has been estimated. An example of the application of the algorithm in soil science has been presented.     

Fuzzy periodic review system with fuzzy random variable demand

In this paper, a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously. A model has been developed with customer demand assumed to be a fuzzy random variable. The lead-time has been assumed to be a constant. The lead-time demand and the lead-time plus one period’s demand have also been assumed to be fuzzy random variables. A methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized. A numerical example has been presented to illustrate the model.     

Dirichlet Problem for a Fractional-Order Ordinary Differential Equation with Retarded Argument

A solution of the Dirichlet problem for a fractional-order ordinary differential equation has been found. Green’s function has been constructed for the problem concerned. The problem solution has been written in terms of Green’s function. A theorem on the existence and uniqueness of a solution of the posed problem has been proved, and a condition for its unique solvability has been derived. It is shown that the condition of solvability may only be violated a finite number of times.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

A nonlinear model for footings on granular bed–stone column reinforced earth beds

In the present study, an attempt has been made to model and analyze a combined footing supporting column, which is to be constructed on very soft soil. In view of small bearing capacity and very large deflections, foundations are constructed after improving the original ground. Here, the ground has been improved by providing the stone columns in the soft soil and on top of this improved ground; a granular fill layer has been placed just below the footing. The footing has been modeled as a beam having finite flexural rigidity. Granular fill layer, soft soil and stone columns have been represented by Pasternak shear layer, Kelvin–Voigt body and the Winkler springs, respectively. Nonlinear behavior of these has been considered by means of hyperbolic constitutive relationships. Governing differential equations for response of the system have been derived and presented in non-dimensional form. These equations have been solved using appropriate boundary conditions by means of an iterative Gauss Elimination technique.     

供应链营销渠道体系的研究

从供应链管理协调、优化的角度出发,探讨营销渠道的建设.以移动通讯行业为背景,提出了渠道协同应用的多目标规划模型,探讨了模型求解的方法,并以某移动分公司的数掘进行了算例分析.     

矩阵LU分解定理的简单证明及其数值实现

用简单的方法证明了矩阵LU分解定理,讨论了定理的推广以及定理相应的数值实现,并对《数值分析》课程教学方法改革进行了思考.     

Solvent extraction studies of indium

Solvent extraction of indium from malonic acid medium by Primene JM-T has been studied. The extraction has been studied as a function of pH and concentrations of malonic acid and sodium malonate. The nature of the acid-amine complex has been established by chemical analysis and by the application of the method of Hogfeldt and Fredlund. The equilibrium constant for the reaction has also been calculated. The nature of the indium complexes getting extracted has also been discussed.     

病态线性方程组的判定方法

针对用条件数来衡量方程组的性态将随阶数增大而变得异常困难这一问题,分析了病态线性方程组产生的原因,提出了一种判定方法,探讨了对一定精度要求的解的可允许扰动的数量级,实例证明了这种方法的有效性.