模糊数学在企业创新能力评定中的应用

建立了企业创新的系统结构图,并利用模糊综合评价法建立了一个对企业创新能力进行评定的三级模糊综合评判的数学模型,采用层次分析法更加合理的确定了权重的分配,通过实例说明了该模型的使用方法,得到了更有效的结果.     

基于贝叶斯序贯方法的微波效应实验设计

提出了一种基于贝叶斯验后概率的序贯检验方法,建立了检验的判别准则,给出了判别准则临界值的计算方法。在给定截尾实验次数的条件下,提出了一种截尾方案,建立了截尾判断方法。将其用于解决验证效应物在微波作用下失效概率达到给定水平的微波效应实验设计问题,给出了相应的实验方案和所需样本量的估计。最后,通过实例对上述方法的应用过程进行了说明,并和现有方法进行了分析比较。     

基于热成像仪从能量视角辨观化学反应*

“能量”是学生认识化学变化的重要维度,本实验借助手持红外热成像仪“看到”化学反应中的能量变化。在实验中通过拍摄等量的不同酸溶液与氢氧化钠溶液混合反应时的热成像图,从“温度”高低间接反映出热量变化,从宏观的能量变化建立模型,推理微观的成键、断键等过程,探究酸碱中和反应过程的放热以及弱酸电离过程的吸热,并培养学生的证据推理能力和科学探究意识。     

AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS

In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.     

Łukasiewicz Tribes are Absolutely Sequentially Closed Bold Algebras

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets.     

Penalty functions,Newton's method,and quadratic programming

In this paper, the search directions computed by two versions of the sequential quadratic programming (SQP) algorithm are compared with that computed by attempting to minimize a quadratic penalty function by Newton's method, and it is shown that the differences are attributable to ignoring certain terms in the equation for the Newton correction. Since the effect of ignoring these terms may be to make the resultant direction a poor descent direction for the quadratic penalty function, it is argued that the latter is an inappropriate merit function for use with SQP. A method is then suggested by which these terms may be included without losing the benefits gained from the use of the orthogonal transformations derived from the constraints Jacobian.The authors wish to thank A. R. Conn and N. I. M. Gould for spirited discussions which took place when the second author spent some time at Waterloo, Ontario, Canada; they also thank L. C. W. Dixon for the clarifications that he suggested to the penultimate draft of this paper.     

A Bahadur efficiency comparison between one and two sample rank statistics and their sequential rank statistic analogues

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424–436) and Lombard (1981, South African Statist. J.15 129–152), even though the two families of statistics (those based on full ranks and those based on sequential ranks) have the same Pitman efficiency against local alternatives. In the process, general results on large deviation probabilities and laws of large numbers for statistics based on sequential ranks are obtained.     

关于一类连续最优控制问题的一种可实现的离散方法

本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。     

Quantum-chemical study of the interface formed by carboxylic species on TiO<Subscript>2</Subscript> nanoparticles. 1. Nanoparticle surface

The current paper presents results of a quantum-chemical study of the surface structure of nanoparticles of both rutile and anatase crystallographic modifications. Different stages of the surface relaxation are discussed. Water adsorption is considered. The calculations were performed in the spd-basis by using semi-empirical quantum-chemical codes, both sequential and parallel. The results are mainly addressed to the study of the interface formed by titania nanoparticles and a set of carboxylated species, namely, benzoic, bi-isonicotinic acids as well as tris-(2,2′-dcbipyridine) Fe(II) complex placed on the surface of either rutile or anatase polymorphs.This revised version was published online in August 2005 with a corrected issue number.