Hajek—Renyi不等式的推广及其应用

对Hajek-Renyi不等式进行了推广，利用推广的不等式给出了随机变量序列绝对平均意义下的强大数定律的一个条件．     

Lower bound for the convergence rate of nonstationary Jacobi-like iteration

Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix A is an H-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with 〈A〉 as the coefficient matrix, where 〈A〉 is a comparison matrix of A.     

基于SPA的双枝模糊决策分析

将集对理论(SPA)与双枝模糊决策理论相结合,用集对分析的方法研究进行双枝模糊决策的方法,分别对双枝模糊决策因素域和双枝模糊决策的上枝、下枝和双枝进行了集对分析,给出了用SPA进行双枝模糊决策的性质,同时讨论了双枝模糊决策的动态分析方法,以及双枝模糊决策度强弱态势预测的方法,从而为双枝模糊决策理论的研究提供了新的视角和方法,为双枝模糊决策的应用提供了更方便的工具和更强的理论支持。     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Pearson-χ~2距离的若干性质

本文对数理统计中常用的 Pearson- χ2距离的分析特性进行了讨论 ,得到了这一距离的一些解析性质 ,最后我们还给出了几个常用距离的关系 .     

Fermi, Majorana and the Statistical Model of Atoms

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.     

Dimethylamino-substituted 7H-Benzo[de]pyrazolo[5,1-a]isoquinolin-7-ones and Their Behavior under Vilsmeier-Haack Conditions

The behavior of dimethylamino-substituted 7H-benzo[de]pyrazolo[5,1-a]isoquinoline-7-ones, synthesized for the first time, under conditions of the Vilsmeier-Haack reaction. It has been shown that, on heating with POCl₃ and DMF, they are converted by electrophilic substitution at the position ortho to the dimethylamino group, followed by cyclization of the iminium adduct to a quinazolinium salt. When an acetyl group is present, the Arnold reaction, leading to the formation of a chloroaryl, accompanies the heterocyclization. The rates and proportion of the reaction products depend on the position of the dimethyl groups relative to the pyrazole ring.