Complexity and computability of solutions to linear programming systems

Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal centered-cutoff algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By model approximation, both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral constraint contraction algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the imposed problem ignorance of past complexity research is deleterious to research progress on computability or efficiency of computation.This research was partly supported by Project NR047-071, ONR Contract N00014-80-C-0242, and Project NR047-021, ONR Contract N00014-75-C-0569, with the Center for Cybernetic Studies, The University of Texas at Austin.     

基于织物电极的心电监测系统

为解决传统动态心电监测存在的一些问题,例如粘性心电电极刺激皮肤、信噪比随使用时间延长而下降、动态心电图仪缺乏实时分析能力等,研制了一种可穿戴心电异常检测系统。制作了有导电织物材料心电电极的穿戴衣,设计了心电信号采集装置,提出了基于分析R-R间期和QRS波群波形的异常心电波形检测算法,在PDA（Personal Digital Assistant）平台上实现了基于该算法的异常心电信号识别软件。通过实际测试,验证了本系统的有效性和可靠性。     

基于心态指标的区间灰数关联度模型

针对已有的灰色关联度模型仅适用于实数序列而不能应用于区间灰数序列的情况,通过引入决策者心态指标,将区间灰数序列转化为决策者心态指标序列,并且当决策者的心态指标确定时,心态指标序列就转化为实数序列,于是通过对体现决策者心态的实数序列建立灰色关联度模型,得到了反映出决策者心态的灰色关联度,从而构建了基于心态指标的区间灰数关联度模型。决策者处于不同心态时,可以通过调整其心态计算灰关联度,从而使建立的关联度模型更加符合实际。最后,通过计算实例说明了模型的可行性。     

混杂纤维对高性能混凝土拉压比的影响

为研究低掺量钢-聚丙烯混杂纤维对高性能混凝土拉压比的影响,采用正交试验法设计了18组混杂纤维高性能混凝土试件及1组普通高性能混凝土对比试件,通过标准试验方法进行立方体抗压强度和劈裂抗拉强度试验,试验中考虑的因素主要是钢纤维的特征参数(类型、体积率、长径比)和聚丙烯纤维体积率.分析各因素对高性能混凝土拉压比的影响,结果表明:混杂纤维高性能混凝土具有明显延性破坏特征,而普通高性能混凝土表现为脆性破坏,混杂纤维的掺入使高性能混凝土的拉压比最大提高了26.2%,平均提高了9.9%.在影响高性能混凝土拉压比的四个因素中,钢纤维类型的影响最大,其次是聚丙烯纤维的体积率,影响最小的是钢纤维长径比.高性能混凝土中掺入适量钢-聚丙烯混杂纤维后,拉压比显著提高,韧性得到明显改善.     

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.     

DCT- and DST-based splitting methods for Toeplitz systems

New splitting iterative methods for Toeplitz systems are proposed by means of recently developed matrix splittings based on discrete sine and cosine transforms due to Kailath and Olshevsky [Displacement structure approach to discrete-trigonometric transform-based preconditioners of G. Strang type and of T. Chan type, SIAM J. Matrix Anal. Appl. 26 (2005), pp. 706–734]. Theoretical analysis shows that new splitting iterative methods converge to the unique solution of a symmetric Toeplitz linear system. Moreover, an upper bound of the contraction factor of our new splitting iterations is derived. Numerical examples are reported to illustrate the effectiveness of new splitting iterative methods.     

区间线性规划的最优解

该文指出了前人定义的区间线性规划最优解所在区间存在的问题,用反例说明其不足之处,给出了求任一介于区间线性规划问题任一最优值对应最优解的算法。     

两种情形下威布尔分布置信下限的确定

采用样本空间排序法,讨论了在Ⅰ型区间删失数据情形下和定时截尾情形下的数据服从威布尔分布时的可靠度置信下限问题,其中威布尔分布的形状参数是在某有限区间内.对给定的置信水平和任意大小的样本,给出了威布尔分布下可靠度置信下限的确定方法.