Degeneracy in NLP and the development of results motivated by its presence

We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. Ideal nondegeneracy at a local minimizer is taken to mean satisfaction of second order sufficient conditions, linear independence and strict complimentary slackness. Following a brief exploration of the relationship of these conditions with the classical definition of nondegeneracy in linear programming, we recall a number of optimality and regularity conditions used to attempt to resolve degeneracy and survey results of Fiacco, McCormick, Robinson, Kojima, Gauvin and Janin, Shapiro, Kyparisis and Liu. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.Research supported by National Science Foundation Grant ECS 90-00560 and Grant N00014-89-J-1537 Office of Naval Research     

The Maximal Closed Classes of Unary Functions in p-Valued Logic

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group S_k, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.     

定位定量检测光电内窥系统

本文分析定位定量窥测系统设计中普遍存在的问题,提出一种检测方案,并预示窥测仪器的发展趋势。     

关于Fuzzy聚类分析及其在脊髓灰质炎中的应用

本文用Fuzzy数学的观点探讨了Fuzzy聚类分析，并通过对脊髓灰质炎病毒抗体水平的Fuzzy聚类分析，获得了良好的聚类效果，为该项问题的研究提供了科学依据。     

分布耦合系数对线性啁啾光栅色散的影响

本文从光栅反向耦合波方程出发,经相位共轭变换用Runge-Kuta-Gil方法对其数值求解。针对线性啁啾光栅耦合系数变化服从不同的分布,分析了各种分布对光栅反射谱特性和色散特性的影响。     

韧性金属裂纹尖端损伤区内应变场测量——数字散斑相关法应用

本文用数字散斑相关方法测量了五种不同幂硬化指数韧性金属材料(铝和铜),双边裂纹尖端细观区域内应变场.对所得结果用韧性损伤模型进行了分析.在此法中以金属自然表面结构为散斑场,不同加载状态的散斑场进行比较,得到相对变形与应变.图象之间相关性 C 是变形参数或是位移及其导数的泛函.使其相关性 C 取最大值的试凑变形即为其真实变形场.这一方法在细观测量中应用得到满意的结果.     

产生短间隔高精度纳秒激光双脉冲的实用电路

本文介绍了我们研制的“运动粒子瞬态激光全息测试仪”电子线路.该电路经严格的逻辑设计及计算,采用了10MHz时钟电路,并将1MHz的时钟信号巧妙地引入门控电路中,同时在技术上采用了行之有效的措施,消除了可能产生0.1μs的随机误差,时间间隔达到了(1～9)±0.1μs的精度,所输出的激光双脉冲能量接近,整机抗干抗能力强,一次性试验成功率高,可精确地测量雾化粒子场中的微粒的速度、形状、大小及其分布,收到了良好的使用效果.     

Wormhole solution in Bergmann-Wagoner scalar-tensor gravitational theory

We give a Euclidean wormhole solution in the vacuum Bergmann-Wagoner scalar-tensor gravitational theory. We show that this wormhole, unlike others, has complex charge and is a baby universe (half a wormhole).     

原子吸收光谱法测定铬基合金中钒

本文研究了用原子吸收光谱法，在笑气－乙炔火焰中，测定钒的最佳条件，不用任何分离手段，以铝盐做干扰抑制剂，消除铬，镍对测定钒的干扰，西方法用于铬基合金中钒的测定，方法简单准确，具有实用意义。