Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.     

D.C.隶属函数模糊集及其应用(Ⅱ)--D.C.隶属函数模糊集的万能逼近性

本文是D．C．隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D．C．隶属函数模糊集，建立了D．C．隶属函数模糊集对模糊集的万有逼近性。探讨了D．C．隶属函数模糊集与模糊数之间的关系，给出了用D．C．隶属函数模糊集逼近模糊数的e-Cellina逼近形式，得到模糊数与D．C．函数之间的一个对应算子，指出了用模糊数表示D．C．函数的问题。     

Reservoir operations optimization via fuzzy criterion decision processes

In this paper, we propose the treatment of complex reservoir operation problems via our newly developed tool of fuzzy criterion decision processes. This novel approach has been shown to be a more flexible and useful analysis tool especially when it is desirable to incorporate an expert’s knowledge into the decision models. Additionally, it has been demonstrated that this form of decision models will usually result in an optimal solution, which guarantees the highest satisfactory degree. We provide a practical exemplification procedure for the models presented as well as an application example.     

负关联噪声驱动下单模激光的定态分析

研究了负关联的加法和乘法高斯白噪声驱动下单模激光损失模型的定态情况。文中推导了负关联情况下，定态时的激光场幅的几率分布，光强的平均值，光强的协方差以及光强的偏斜率。并和文献〔１，２〕中正关联时的定态分析作了比较，发现了有意义的新现象。     

用模糊综合评价值作为单纯形优化指标

本文介绍了一个模糊综合评价方法,讨论了模糊运算方法对运算结果即综合评价值的影响,并将模糊综合评价值用作单纯形优化指标。     

模糊正交法用于石墨炉探针原子化测定铋条件的研究

模糊正交法是通过把正交试验结果模糊化,然后用模糊数学的理论和方法来处理实验数据。与常规正交设计相比,能在同样实验工作量的情况下获得更多的信息。本文采用模糊正交法对元素Bi的测定条件进行优化,并将其同常规正交设计方差分析的结果进行了比较,并提出一个综合评价参数,对建立的分析方法进行了综合评价。     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

分子的模糊对称性

将模糊数学方法引入对分子对称点群的研究,建立描述具有不完整分子对称性的模糊点对称群(集合).建立具有模糊对称性分子轨道的模糊表示及其模糊特征标(模糊广义宇称).通过对典型的线状分子、平面分子以及非平面的立体分子等进行分析,展示了一个新的理论化学园地.初步探讨了具有模糊对称性的动态反应体系.从模糊对称性出发,探讨了分子轨道对称守恒原理的半定量特征.     

Limit of detection estimator for second-order bilinear calibration

A new approach is developed for estimating the limit of detection in second-order bilinear calibration with the generalized rank annihilation method (GRAM). The proposed estimator is based on recently derived expressions for prediction variance and bias. It follows the latest IUPAC recommendations in the sense that it concisely accounts for the probabilities of committing both types I and II errors, i.e. false positive and false negative declarations, respectively. The estimator has been extensively validated with simulated data, yielding promising results.