NUMBER THEORETIC METHODS IN APPLIED STATISTICS (Ⅱ)

In this paper, the authors give some applications of F-uniformly distributedsequences, which are suggested in their previous paper under the same title, in experimen-tal design, experiments with mixtures, geometric probability and simulation.     

Irrationality of Power Series for Various Number Theoretic Functions

We study formal power series whose coefficients are taken to be a variety of number theoretic functions, such as the Euler, Möbius and divisor functions. We show that these power series are irrational over [X], and we obtain lower bounds on the precision of their rational approximations.     

Inverse Functions of Number Theoretic Functions (II)

In this paper^[1] we defined the weak and the strong left inverse functions of f and the weak and the strong right inverse functions of f.In the present paper we shall give their definitions by means of the primitive recursion or the limited minimal or maximal operator. The principal results are:     

一个数论函数和它的均值的计算

设 p是一个素数 ,n是任意正整数 ,函数α(n ,p)表示 p在n !标准分解式中的指数 ,本文给出了函数α(n ,p)的均值 ∑n相似文献   

关于一个新数论函数的混合均值

Let p and q be two distinct primes,epq(n) denotes the largest exponent of power pq which divides n.In this paper,we study the mean value properties of function epq(n), and give some hybrid mean value formulas for epq(n) and Dirichlet divisor function d(n).     

数域上的模糊模式识别方法

本文首先指出了现有的模糊模式识别方法「１」的局限性，进而，构造了一种具有数域特点的贴近度公式。文中列举的若干算例表明新理论在数域上明显地优于传统方法，证明本文所提方法是非常合理的。     

概率统计类课程多维立体教学的实践与认识

针对概率统计类课程不同于其它确定性数学的特点,作者从教学内容及教学方法两个方面进行了探索与实践.在教学内容上,强调点面结合,拓展一些现代的与本学科密切有关的面上知识.在教学方法上,强调多维立体教学方式,即结合多媒体课件,案例教学,软件演示,实验教学,实现以教师为主导,学生为主体的主客体相结合的教学思想,以期达到使学生受益最大化的目标.     

Operator Theoretic Methods for the Eigenvalue Counting Function in Spectral Gaps

Using the notion of spectral flow, we suggest a simple approach to various asymptotic problems involving eigenvalues in the gaps of the essential spectrum of self-adjoint operators. Our approach employs some elements of the theory of the spectral shift function. Using this approach, we provide generalisations and streamlined proofs of two results in this area already existing in the literature. We also give a new proof of the generalised Birman–Schwinger principle. Submitted: March 10, 2009. Accepted: April 22, 2009.     

数学方法在安全预警系统中的应用

利用矿区测井数据,基于再生核理论,构造了再生核神经网络,并将再生核神经网络的计算问题转化为求解线性方程组的问题.利用一种改进的中心线法重构采煤工作面,这种方法重构的曲面是连续的,与实际地质情况相符合,为地质情况的综合解释提供了新的依据.     

概率统计课程教学方法的几点体会

通过教学实践与理论思考,并结合目前大学生的特点,对概率论与数理统计课程的教学方法阐述四点看法.主张在教学中引人历史典故,引进多媒体辅助教学,将教学与数学建模活动相结合,运用案例教学法以培养学生分析问题和解决问题的能力.