混合序列部分和的强大数定律

设{Xn，n≥1）是ρ^-混合序列．利用随机变量的截尾方法和ρ^-混合序列的三级数定理这一工具研究了ρ^-混合序列的性质。得到了矩条件下ρ^-混合序列的—类强极限定理和强大数定律。并给出了一些简单应用。推广了若干经典的强大数定律．     

Fuzzy Bayesian system reliability assessment based on exponential distribution

The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called “Resolution Identity” in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO).     

随机狄里克莱级数在收敛右半平面上的增长性和值分布

本文利用随机变量序列的强大数定律 ,研究了随机变量序列 {Xn}在独立 (可不同分布 )情形下的性质 ,并得到当随机狄里克莱级数 ∑∞n =1anXne-λns 满足(ⅰ )limn ∞nλn =D <∞ ;(ⅱ ) limn ∞ln｜an｜λn =0 等条件时的增长性以及值分布 .     

Optimally conditioned scaled ABS algorithms for linear systems

Using a strict bound of Spedicato to the condition number of bordered positive-definite matrices, we show that the scaling parameter in the ABS class for linear systems can always be chosen so that the bound of a certain update matrix is globally minimized. Moreover, if the scaling parameter is so chosen at every iteration, then the condition number itself is globally minimized. The resulting class of optimally conditioned algorithms contains as a special case the class of optimally stable algorithms in the sense of Broyden.This work was done in the framework of research supported by MPI, Rome, Italy, 60% Program.     

The Distribution of Condition Numbers of Rational Data of Bounded Bit Length

We prove that rational data of bounded input length are uniformly distributed (in the classical sense of H. Weyl, in [42]) with respect to the probability distribution of condition numbers of numerical analysis. We deal both with condition numbers of linear algebra and with condition numbers for systems of multivariate polynomial equations. For instance, we prove that for a randomly chosen n\times n rational matrix M of bit length O(n ⁴ log n) + log w , the condition number k(M) satisfies k(M) ≤ w n ^5/2 with probability at least 1-2w ^-1 . Similar estimates are established for the condition number μ_ norm of M. Shub and S. Smale when applied to systems of multivariate homogeneous polynomial equations of bounded input length. Finally, we apply these techniques to estimate the probability distribution of the precision (number of bits of the denominator) required to write approximate zeros of systems of multivariate polynomial equations of bounded input length. March 7, 2001. Final version received: June 7, 2001.     

双随机狄里克莱级数收敛性

该文研究特点是;用强大数定律,中心极限定理研究随机系数{a_n}部分和及随机指数λ_n极限性质, 研究结果是;(i)在易满足条件下,(ii)在a_n独立同分布,方差存在条件下;(iii)在{a_n}独立,Ea_n=0,及附加适当条件下,得出收敛横坐标σ_c简洁公式。     

Recent trends in random number and random vector generation

A survey of recent work in the areas of uniform pseudorandom number and uniform pseudorandom vector generation is presented. The emphasis is on methods for which a detailed theory is available. A progress report on the construction of quasirandom points for efficient multidimensional numerical integration is also given.     

扭环粘正n棱柱外侧面数的确定

本文给出了一个确定扭环粘正 n棱柱外侧面数的简洁且具有一般性的结论 ,它可以看成是麦比乌斯带在一定意义下的推广 .对该棱柱的其它性质也进行了讨论 .     

Approximation Numbers of Identity Operators between Symmetric Sequence Spaces

We prove asymptotic formulas for the behavior of approximation quantities of identity operators between symmetric sequence spaces. These formulas extend recent results of Defant, Masty o, and Michels for identities l_pⁿF_n with an n-dimensional symmetric normed space F_n with p-concavity conditions on F_n and 1p2. We consider the general case of identities E_nF_n with weak assumptions on the asymptotic behavior of the fundamental sequences of the n-dimensional symmetric spaces E_n and F_n. We give applications to Lorentz and Orlicz sequence spaces, again considerably generalizing results of Pietsch, Defant, Masty o, and Michels.     

Sensitivity of sample values not generated by inversion

The perturbation generation rule of Suri (Ref. 1) is extended to cases where random variables are not generated by inversion. Conditions are given for the use of other methods. Infinitesimal perturbation analysis is shown to be compatible with common random number techniques in cases where finite-difference approximations are not.This work was supported by the National Science Foundation, Grants Nos. ECS-82-13680 and CDR-85-001-08.