关于ρ-混合序列对数律的收敛速度

本文研究了ρ-混合序列对数律的收敛速度，在较弱的矩条件下得到了与独立同分布实随机变量类似的结果，并获得了ρ－混合序列满意对数律的一个充分性结果；讨论了ρ－混合序列重对数律的收敛速度的问题，得到了一个重对数律的充分性条件。     

关于可交换随机变量序列的重对数律

本文讨论了可交换随机变量序列{Xn:n≥1}的重对数律。     

更新过程的叠对数律

本文利用独立同分布随机变量序列部分和的叠对数律收敛速度结果,在一定条件下,研究了一般更新过程的叠对致律及其收敛速度。     

相伴的高斯随机变量序列的一个强不变原理

本文利用鞅的Skorohod表示, 在序列是高斯的且序列的协方差系数以幂指数速度递减的条件下,证明了相伴高斯随机变量序列的一个强不变原理\bd 作为推论得到了相伴高斯随机变量序列的重对数律和钟重对数律     

正则和函数的强极限及应用

研究了随机变量序列正则和函数的重对数律,作为应用,给出了正的随机变量序列部分和乘积的重对数律.同时,还获得了独立随机变量阵列相应的单对数律结果.     

关于独立场合重对数律的收敛速度

本文证明(1)收敛的一些充要条件,并给出重对数律收(?)速度的一种描述.全文假定随机变量序列{X_n,n≥1}独立,但不必同分布,EX_j=0,EX_j~2=σ_j~2,     

不同分布WOD随机变量序列的重对数律

在一个独立随机变量序列的重对数律的基础上,获得了一个不同分布WOD随机变量序列的重对数定理,定理的证明基于一个Kolmogorov型指数不等式.     

NA随机变量序列的最大部分和不等式及有界重对数律

本文给出了NA随机变量序列关于最大部分和的概率不等式及矩不等式,并获得了NA随机变量序列的Teicher型和Egorov型有界重对数律等.     

泛函型重对数律的收敛速度

泛函型重对数律的收敛速度王启应（南京大学）设｛Ｘ＿ｎ，ｎ≥１｝为ｉ．ｉ．ｄ．随机变量序列为定义在［１，∞）上的实函数。近年来，级数的收敛性问题，引起了众多学者的兴趣。作为一个研究方向，１９６８年，Ｄａｖｌ５￣［１］指出：上述级数的收敛除需要一定矩条件...     

广义线性模型中拟极大似然估计的强相合性及收敛速度

在广义线性模型(GLM)因变量有正确表述的假定及其他一些光滑性条件之下, 证明以概率1当样本量n充分大时, 广义线性模型的拟似然方程有一解, 且可求出该解收敛于真值的速度, 在一个重要的特例中, 该速度同于独立同分布随机变量序列部分和的重对数律所确定的速度, 故而不能改进.     

Call for nominations for 1994 elections

Mathematical Programming -     

Continuity Adjustment for Control Charts for Attributes

A unified approach is proposed for making a continuity adjustment on some control charts for attributes, e.g., np-chart and c-chart. through adding a uniform (0,1) random observation to the conventional sample statistic (e.g., npi and ci). The adjusted sample statistic then has a continuous distribution. Consequently, given any Type I risk a (the probability that the sample statistic is on or beyond the control limits), control charts achieving the exact value of a can be readily constructed. Guidelines are given for when to use the continuity adjustment control chart, the conventional Shewhart control chart (with ±3 standard deviations control limits), and the control chart based on the exact distribution of the sample statistic before adjustment.     

Algorithms for Computing Characters for Symmetric Spaces

Symmetric spaces or more general symmetric k-varieties can be defined as the homogeneous spaces G _k /K _k , where G is a reductive algebraic group defined over a field k of characteristic not 2, K the fixed point group of an involution θ of G and G _k resp. K _k the sets k-rational points of G resp. K. These symmetric spaces have a fine structure of root systems, characters, Weyl groups etc., similar to the underlying algebraic group G. The relationship between the fine structure of the symmetric space and the group plays an important role in the study of these symmetric spaces and their applications. To develop a computer algebra package for symmetric spaces one needs explicit formulas expressing the fine structure of the symmetric space and group in terms of each other. In this paper we consider the case that k is algebraically closed and give explicit algorithmic formulas for expressing the characters of the weight lattice of the symmetric space in terms of the characters of the weight lattice of the group. These algorithms can easily be implemented in a computer algebra package. The root system of the symmetric space can be described as the image of the root system of the group under a projection π derived from an involution θ on . This implies that . Using these formulas for the characters of each of these lattices we show that in fact . A.G. Helminck is partially supported by N.S.F. Grant DMS-0532140.     

多产品公司创建平台邀请竞争对手进行联合销售的策略研究

由于资金分配或生产规模的限制,多产品公司的某类产品与专门销售此类产品的专业产品公司相比,会有一定的不足.以两个产品公司为对象,研究了两个竞争性公司的联合销售模式,即多产品公司投资建设平台,邀请销售单一产品的专业公司在平台上共同销售某类产品.运用主从博弈建立联合销售的基础模型,探讨不同销售模式下的相关投资,并利用数值计算进行决策分析.研究表明,通过创建平台进行联合销售,一方面,消除了消费者的额外购物成本;另一方面,在平台进行联合销售使得两个公司由单纯的竞争关系转化为相互补充,不仅能够吸引更多有不同产品需求的客户,而且能够在一定程度上提高两个产品公司的利润.     

Criterion for complete determinacy for concave-convexlike games

Translated from Matematicheskie Zametki, Vol. 49, No. 3, pp. 73–76, March, 1991.     

Existence results for Hughes' model for pedestrian flows

In this paper we prove two global existence results for Hughes' model for pedestrian flows under assumptions that ensure that the traces of the solutions along the turning curve are zero for all positive times.     

Graphical Diagnostics for Markov Models for Categorical Data

Markov models are widely used as a method for describing categorical data that exhibit stationary and nonstationary autocorrelation. However, diagnostic methods are a largely overlooked topic for Markov models. We introduce two types of residuals for this purpose: one for assessing the length of runs between state changes, and the other for assessing the frequency with which the process moves from any given state to the other states. Methods for calculating the sampling distribution of both types of residuals are presented, enabling objective interpretation through graphical summaries. The graphical summaries are formed using a modification of the probability integral transformation that is applicable for discrete data. Residuals from simulated datasets are presented to demonstrate when the model is, and is not, adequate for the data. The two types of residuals are used to highlight inadequacies of a model posed for real data on seabed fauna from the marine environment.

Supplemental materials, including an R-package RMC with functions to perform the diagnostic measures on the class of models considered in this article, are at the journal’s website. The R-package is also available at CRAN.     

Christoffel-type functions for -orthogonal polynomials for Freud weights

This paper gives upper and lower bounds of the Christoffel-type functions , for the m-orthogonal polynomials for a Freud weight W=e^-Q, which are given as follows. Let a_n=a_n(Q) be the nth Mhaskar–Rahmanov–Saff number, φ_n(x)=max{n^-2/3,1-|x|/a_n}, and d>0. Assume that QC(R) is even, , and for some A,B>1

Then for xR

and for |x|a_n(1+dn^-2/3)