关于P－局部群系的临界性问题

本文利用文献［１］定义的超中心，给出了户ｐ－局部群系临界性问题的结构。利用该结构将文献［２］的一些结果推广到一般的ｐ－局部群系式上，从而使Ｉｔ６定理［３］和Ｂｕｃｋｌｅｙ定理［３］成为本文定理２．２和定理２．３的特殊情况。本文还利用Ｓ－拟正规的概念［３］，将Ｉｔ６定理和Ｂｕｃｋｌｅｙ定理推广到一般的ｐ－局部群系上。     

集合函数多目标规划的拉格朗日型对偶定理

本文在［１］的基础上．给出了集合函数多目标规划的拉格朗日型弱对偶定理，严格对偶定理和逆对偶定理．     

随机样本长度经验过程的极限定理

本文得到以函数为指标的随机样本长度经验过程的泛函中心极限定理．给出一列随机元关于某概率分布混合的充分条件．把Billingsley~［2，定理4．5］的一定理推广到非可分距离空间，并举了两个例子说明这些结果的应用．     

关于Hermite-Fejer插值过程的平均收敛

文［１］讨论了某些非Ｗ－过程的插值算子的加权平均逼近的收敛性和收敛阶．如记Ｈｎ（ｆ；ｘ）为以第二类Ｃｈｅｂｙｓｈｅｖ多项式Ｕｎ（ｘ）的零点作为插值节点，区间［－１，１］上的函数ｆ（ｘ）的Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值算子，［１］中证得：定理Ａ当０＜ｐ...     

三谈牛顿恒等式及其应用

三谈牛顿恒等式及其应用刘初生（湖南娄底师专数学系４１７０００）文［１］、［２］介绍了牛顿恒等式及其在解题中的应用，作为续篇，本文再谈谈它的推广及在习题编拟方面的应用．定理１设ｘ１，ｘ２，…，ｘｎ是方程ｘｎ＋ａ１ｘｎ－１＋…＋ａｎ－１ｘ＋ａｎ＝０的ｎ个...     

S.N.Berns型三角插值多项式

1．引言由Faber定理［1］可知，以任何点组作为插值节点的函数g（t）的Lagrange三角插值多项式算子并非对每个连续的周期函数都能在全实轴上一致地收敛．为改善其收敛性，Bernstein在［2］中将Lagrange插值基函数作平均，得算子Zn—1其中为插值节点，为ragrange三角插值多项式的基函数．O．K。。在1969年t3］得到估计式／43＼／7T＼ig（t）一on（g，t）l三卜十三）w（；“）．＼7TZ八Th／他于1973年［4J将上面的估计式改进为19／7T＼ig（t）一Cn（g，t）155叫g，“）．“””’“””’”一QnV’n／［4］中还引进算子B。（g，t）＝＝…     

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．     

可列值随机变量序列的一个小偏差定理

本文得到了可列值随机变量序列的用不等式表示的强极限定理,即小偏差定理,包含了［１］的结果．［１］中研究的是相对于齐次Ｍａｒｋｏｖ 链的偏差,而本文允许非齐次的情形．     

关于多元多项式逼近的一些结果

本文首先用积分型线性正算子实现了C（［-π,π］m×［-α,α］k）上多元代数与三角多项式的混合逼近．进而，通过构造更具体的乘积核，还得到了C（［-π,π］m）上三角逼近的。维Rogosinski型逼近定理及Cr（［-1，1］k）上k维代数多项式逼近的Timan型定理．     

Hermite—Fejer插值于Lp下的收敛逼近阶

本文把文［1—3」等仅对P≤4给予证明的P．Erdos－Feldheim型定理给出了一个完整的证明，且把文［1］的结果作了改进．     

考虑货架存放期的经济批量排产问题的求解

在化工、造纸、制药、钢铁等工业生产中，一台设备或一条生产线可以生产多种产品的情况很常见。在生产中，如何安排各类产品的生产顺序以及生产数量显得十分重要。这类问题通常称作经济批量排产问题，这类问题是生产库存中的经典问题。本文研究的经济批量排产问题考虑了产品货架存放期因素，针对以往研究的不足，本文提出用批量变动方法求解该类问题，由计算结果显示，按照这种排产方法花费的成本要低于其他两种经济批量排产问题常用的方法。     

An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments

Recently, Chiu et al. (2012) [1] present an alternative optimization procedure to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. This inventory model was proposed by Chiu et al. (2011) [2]. Both papers do not consider the determining of the number of shipments. This paper determines both the optimal replenishment lot size and the optimal number of shipments jointly. The solution of this paper is better than the solutions of Chiu et al.  and .     

弧长约束下的二次样条插值

1 引言 具有约束的插值与逼近在曲线及曲面的设计中有重要的意义。目前已有很多有关保持单调性,凸性等性质的样条插值的结果。另一种很重要的约束就是保持曲面在某些区域上的面积,例如在汽车工业中,由于受实际因素的限制,性能的原因甚至是美学的原因,需要曲面满足在某些区域的有界性,特别在飞机的进气道的设计中,经常遇到如下问题:如何构造具有面积约束的插值曲面?这个问题在一元的情形即是保持弧长约束,它是由Wang &Damme首先提出来的,它可以用来解决旋转不变曲面的面积约束插值。Wang&Damme针对S_3~1(△)给出了插值的适定性及误差估计,但对S_2~1(△),因为其自由度最多是2,从而不能满足弧长约束。采用加细剖分的办法,使结点数增加,但让新增结点上的y值自由,这样就相应地增加了自由度,从而可用来解决这个问题。     

A note on “quality improvement and setup reduction in the joint economic lot size model”

In a recent paper, Affisco et al. [J.F. Affisco, M.J. Paknejad, F. Nasri, Quality improvement and setup reduction in the joint economic lot size model, European Journal of Operations Research 142 (2002) 497–508] propose a quality-adjusted joint economic lot size model that considers investments in quality improvement and setup cost reduction. In particular, they consider a single-vendor, single-buyer, deterministic demand economic lot-sizing problem, and they investigate the potential impact of economic investments in the vendor’s quality improvement and setup cost reduction efforts on the system-wide costs. However, the particular form of the investment function that they use to represent the cost of investments in quality improvement does not represent actual practice in many industries. Hence, in this note, we develop modified models for quality improvement and simultaneous quality improvement and setup cost reduction using a modified form of the investment function. Our fundamental results and conclusions are substantially different than those in Affisco et al. (2002).     

Cayley-Bacharach定理在沿平面代数曲线插值问题中的应用

1 引 言 本文是讨论关于沿平面代数曲线的Lagrange插值问题,该问题与在二维实平面R~2上的二元Lagrange插值有关.设n为非负整数并且e_n=1/2(n+1)(n_2).P_n代表所有全     

Reformulation by discretization: Application to economic lot sizing

In this paper we apply a discretization reformulation technique to the classical economic lot sizing problem. This reformulation yields the same LP bounds as the original model. We show, however, that by reducing adequately the coefficients of some variables, one obtains an enhanced reformulation whose LP relaxation solution is integer.     

A dynamic lot sizing model with exponential machine breakdowns

This paper addresses the dynamic lot sizing model with the assumption that the equipment is subject to stochastic breakdowns. We consider two different situations. First we assume that after a machine breakdown the setup is totally lost and new setup cost is incurred. Second we consider the situation in which the cost of resuming the production run after a failure might be substantially lower than the production setup cost. We show that under the first assumption the cost penalty for ignoring machine failures will be noticeably higher than in the classical lot sizing case with static demand. For the second case, two lot sizes per period are required, an ordinary lot size and a specific second (or resumption) lot size. If during the production of a future period demand the production quantity exceeds the second lot size, the production run will be resumed after a breakdown and terminated if the amount produced is less than this lot size. Considering the results of the static lot sizing case, one would expect a different policy. To find an optimum lot sizing decision for both cases a stochastic dynamic programming model is suggested.     

ACM元各向异性分析的Newton方法

本文将一维Lagrange插值多项式的Newton表达式推广到二维非标准的Hermite插值,给出著名板元-ACM元插值多项式的Newton表达式,由此给出ACM元对四阶和二阶椭圆问题的各向异性插值误差估计,为复杂单元的各向异性分析开辟了新的途径.     

Lagrange Interpolation on a Sphere

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔｎｂｅａｎｏｎｎｅｇａｔｉｖｅｉｎｔｅｇｅｒａｎｄＳ ={(ｘ ,ｙ ,ｚ)∈Ｒ3 |ｘ2 + ｙ2 +ｚ2 =1 }ｂｅｔｈｅｕｎｉｔｓｐｈｅｒｅｉｎＲ3 .Ｐ( 2 )ｎ ａｎｄＰ( 3 )ｎ ｄｅｎｏｔｅｔｈｅｓｐａｃｅｏｆａｌｌｂｉｖａｒｉａｔｅｐｏｌｙｎｏｍｉａｌｓｏｆｔｏｔａｌｄｅｇｒｅｅ≤ｎａｎｄｔｈｅｓｐａｃｅｏｆａｌｌｔｒｉｖａｒｉａｔｅｐｏｌｙｎｏｍｉａｌｓｏｆｔｏｔａｌｄｅｇｒｅｅ≤ｎｒｅｓｐｅｃｔｉｖｅｌｙ ,ｉ.ｅ .Ｐ( 2 )ｎ =∑0≤ｉ+ｊ≤ｎａｉｊｘｉｙｊ｜ａｉｊ ∈Ｒ ,Ｐ( 3 …     

An O(T log T) Algorithm for the Dynamic Lot Size Problem with Limited Storage and Linear Costs

In this paper the dynamic lot size problem with time varying storage capacities and linear costs is addressed. Like in the uncapacitated version, this problem can be formulated as a network flow problem. Considering the properties of the underlying network, we devise an O(T log T) greedy algorithm to obtain optimal policies and we report computational results for randomly generated problems.