关于二台机器自由作业的总流程问题

二台机器自由作业的总流程问题是NP困难问题．当加工时间仅依赖于机器时，该问题尚未被解决．本文对于机器均不允许空闲的约束条件下的上述问题，给出了显式解，即最优时间表的构造形式，从而改进了文献中的结果．此外，本文还对允许空闲的上述问题，作了一些讨论，指出了Vakharia和Catay一文（1997）中算法的错误．     

弹性接触问题及线性有限元逼近

1．引言及预备知识最早研究简化了的弹性接触的数学问题（称为单边问题）应属A．Signorini（1933年）．到70年代初，G．Fichera（1972）[4]及G．Duvaut和J．L．Lions（1972）问对此类问题有进一步的研究，建立了问题的解的存在性，正则性以及唯一性．R．Glowinski等的专著[5]中讨论了问题的数值逼近（也可见问中所列文献）．特别应提到捷克数学家J．Ne6as，1．HlavA6ek等所进行的工作（见［7］及其中的文献）以及Kikuchi和Oden［9］，从数学问题的形成到与之等价的变分问题解的存在性，以及有限元逼近的收敛性和误差估计都有研究．本…     

以凸包为工具求解组合几何题

组合几何诞生于20世纪中叶．是用组合数学的成果来解决几何学中的问题．主要研究几何图形的拓扑性质和有限制条件的欧几里德性质．组合几何以其内容丰富．题目新颖，难度有层次而在竞赛数学中异军突起．分类是一种重要的数学思想方法，它分化了问题的难度．对每一子问题而言，原来问题中的不确定因素变成了确定因素(因为附加了已知条件)，     

区间参数结构振动问题的矩阵摄动法

当结构的参数具有不确定性时，结构的固有频率也将具有某种程度的不确定性．本文讨论了区间参数结构的振动问题，将区间参数结构的特征值问题归结为两个不同的特征值问题来求解．提出了求解区间参数结构振动问题的矩阵摄动方法．数值运算结果表明，本文所提出方法具有运算量小，结果精度高等优点．     

锥优化模型在Robust桁架拓扑设计实例中的应用

本文讨论Robust桁架拓扑设计(TTD)问题，即桁架结构设计问题，使其在固定重量的情况下，具有最佳的承载能力．本文陈述了几种应用锥优化解Robust TTD问题的方法，并简介了锥优化最新的领域．同时，本文给出了一个单负荷的线性模型和一个多负荷的半正定优化模型以及Robust TTD问题．文中所有的模型均有例证．例证显示通过应用对偶性这些模型的规模能被充分的减小．     

评析

问题153，154来稿较少，暂不评析． 问题 155 该问题共收稿7篇，均认为问题提出者的结论是正确的，可加以逻辑证明．来稿中，江苏省徐州高级中学沈家书、浙江省杭州市长河高级中学许鑫娟给出了与选登1相同的证明，湖北省武汉市黄陂一中高二（17）班喻超同学也参与了对该问题的讨论．     

多目标运输问题的Fnzzy线性规划解法

经典运输问题是一类特殊的单目标线性规划问题，可用表上作业法或单纯形法求其最优解［１］．近年来，许多学者研究了多目标运输问题，提出了相应的求解算法［６－９］．本文应用Ｆｕｚｚｙ线性规划的方法，给出了多目标运输问题的又一求解算法．     

二维椭圆型方程反问题中优化算法的比较

近年来，决定椭圆型方程系数反问题在地磁、地球物理、冶金和生物等实际问题上有着广泛的应用．本文讨论了二维的决定椭圆型方程系数反问题的数值求解方法．由误差平方和最小原则，这个反问题可化为一个变分问题，并进一步离散化为一个最优化问题，其目标函数依赖于要决定的方程系数．本文着重考察非线性共轭梯度法在此最优化问题数值计算中的表现，并与拟牛顿法作为对比．为了提高算法的效率我们适当选择加快收敛速度的预处理矩阵．同时还考察了线搜索方法的不同对优化算法的影响．数值实验的结果表明，非线性共轭梯度法在这类大规模优化问题中相对于拟牛顿法更有效．     

被相交裂纹消弱且含圆形孔洞的弹性平面问题

该文讨论了被相交裂消弱且含圆形孔洞的弹性平面问题．对此问题，文中利用复变函数理论并结合分拆函数法，把问题化为人们极为熟悉的Ｒｉｅｍａｎｎ这值问题的求解．由此，文中给出问题的封闭形式解．     

具有年龄结构和迁移的非线性种群的最优生育控制

对一类非线性种群模型，以生育率为控制变量，研究最小代价一规模问题和最小代价一偏差问题．证明了最优控制的存在唯一性，给出了一阶最优性条件，讨论了最优反馈的合成．所得结论推广了文献中的一个结果．     

信息不对称约束下用水许可证拍卖制度设计

用水许可证制度是实施水资源统一管理的重要措施之一。行政配置中配置主体之间存在信息不对称，导致配置效率低，也存在“寻租”的可能。本文首先分析了信息不对称约束下的取用水许可证配置效率问题，然后引入拍卖理论，建立了信息不对称约束下的取用水许可证拍卖模型。属于多物品拍卖问题，本文给出了最优拍卖制度设计，实现取水许可证的高效配置，为取用水许可证的高效配置市场化方式提供借鉴作用。     

A hybrid method to evaluate pure endowment policies: Crédit Agricole and ERGO Index linked policies

An empirical method to evaluate pure endowment policies is proposed. The financial component of the policies is described using the time dependent Black Scholes model and making a suitable choice for its time dependent parameter functions. Specifically, the integral of the time dependent risk free interest rate is modeled using an extension of the Nelson and Siegel yield curve (see Dielbold and Li, 2006). The time dependent volatility is expressed using two different models. One of these is based on an extension of the Nelson and Siegel model (Dielbold and Li, 2006), while the other assumes that the volatility is a piecewise function with respect to the time variable. The demographic component is modeled using a generalization of the geometric Brownian mean reverting Gompertz model while an asymptotic formula for survival probability is derived when the mortality risk volatility is small. The method has been tested on two policies. In these the risk free interest rate parameters are calibrated using the one-month, three-month, six-month, one-year, three-year and five-year US treasury constant maturity yields and the parameters of the volatility are calibrated using the VSTOXX volatility indices. The choice of the data employed in the calibration depends on the policy to be evaluated. The performance of the method is established comparing the observed values of the policies with the values obtained using this method.     

Reliability analysis of Polytube industry using supplementary variable technique

The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the sub-systems are variable. The mathematical equations are derived using Chapman-Kolmogorov differential equations which are formed using mnemonic rule from the transition diagram of Polytube manufacturing plant. The system of partial differential equations obtained has been solved using Lagrange’s method and reliability of the system for the various choices of constant transition rates is solved numerically using Runge-Kutta fourth order. A sensitive analysis of subsystem is finally carried out to improve overall availability.     

关于漏失数据弥补的几点意见

漏失数据的弥补,通常采用使误差项的平方和达到最小的原则来确定,这样弥补的数据,有时会出现负值等异常情况.本文提出采用相邻小区的平均值来代替漏失数据,或用回归分析的方法分析试验结果,同样能得到最小二乘法相一致的结论,但不会出现负值.     

Content-based image retrieval using visually significant point features

This paper presents a new image retrieval scheme using visually significant point features. The clusters of points around significant curvature regions (high, medium, and weak type) are extracted using a fuzzy set theoretic approach. Some invariant color features are computed from these points to evaluate the similarity between images. A set of relevant and non-redundant features is selected using the mutual information based minimum redundancy-maximum relevance framework. The relative importance of each feature is evaluated using a fuzzy entropy based measure, which is computed from the sets of retrieved images marked relevant and irrelevant by the users. The performance of the system is evaluated using different sets of examples from a general purpose image database. The robustness of the system is also shown when the images undergo different transformations.     

Modified Maximum Likelihood Estimators Based on Ranked Set Samples

The maximum livelihood estimator (MLE) using a ranked set sample (RSS) usually has no closed expression because the maximum likelihood equation involves both hazard and inverse hazard functions, and may no longer be efficient when the judgment ranking is imperfect. In this paper, we consider a modified MLE (MMLE) using RSS for general parameters, which has the same expression as the MLE using a simple random sample (SRS), except that the SRS in the MLE is replaced by the RSS. The results show that, for the location parameter, the MMLE is always more efficient than the MLE using SRS, and for the scale parameter, the MMLE is at least as efficient as the MLE using SRS, when the same sample size is used. Under the perfect judgment ranking, numerical examples also show that the MMLE has good efficiency relative to the MLE based on RSS. When the judgment error is present, we conduct simulations to show that the MMLE is more robust than the MLE using RSS.     

扁柱面网壳的非线性动力学行为

用连续化法建立了正三角形网格的三向单层扁柱面网壳的非线性动力学方程和协调方程．在两对边简支条件下用分离变量函数法给出扁柱面网壳的横向位移．由协调方程求出张力,通过Galerkin作用得到了一个含二次、三次的非线性动力学微分方程．通过求Floquet指数讨论平衡点邻域的稳定性,用复变函数留数理论求出Melnikov函数,可得到该动力学系统发生混沌运动的临界条件．通过数值计算模拟和Poincaré映射也证明了混沌运动存在．     

ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

Alternating direction finite element (ADFE) scheme for d-dimensional nonlin-ear system of parabolic integro-differential equations is studied. By using a local approxi-mation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is sim-plified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coeffi-cients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence proper-ties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2 norm space estimates and O((△t)2) estim     

Robust tensor completion using transformed tensor singular value decomposition

In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal‐to‐noise ratio than that by using Fourier transform and other robust tensor completion methods.     

求解约束优化问题的一种算法的改进

针对用遗传算法求解约束优化问题时,初始种群产生的方法进行了研究,提出了初始种群产生的一种新方法.实验证明,该方法较直接利用随机数产生初始种群的方法,具有更快的运算速度.