珠算与笔算对比分析及在数学教学中的运用研究

在对笔算和珠算进行对比分析以前,我们首先要搞清楚一些基本概念和基本知识,否则就会出现不知所云和莫名其妙的情况。进行对比分析就要求二者处在同一起跑线上,否则就没有可比性。一、几个基本概念（一）教学的定义     

Testing for the Absence of Random Effects in a Two-way Nested Design with Mixed Effects Model: A Nonparametric Approach

Two-way nested design with mixed effects model arises in many practical situations. In the classical analysis of variance set-up, a test for the absence of the random effects is obtained under the assumption that the random effects and the errors are normally distributed. The present paper avoids this assumption and provides an asymptotically distribution-free test procedure for the above problem. The asymptotic null distribution of the test statistic is obtained. Actual implementation of the test is straight forward given the prior information on quantiles of the intra-block differences of observations. In the absence of such information, working test procedures are proposed. The performances of these tests are compared with the classical analysis of variance test through simulations. The tests are then illustrated by some real data sets.     

Strict (ε, δ)-Subdifferentials and Extremality Conditions

A new abstract definition of extremality is introduced extending traditional extremality notions in optimization problems. The set of points satisfying the new definition includes points not necessarily optimal in the usual sense but nevertheless having some extremal properties. Necessary and sufficient extremality conditions are derived. Contrary to usual notions of extremality the new one is stable relative to small deformations of the data.     

Controllability of Nonsmooth Discrete Systems with Delay

This paper is concerned with a study of local controllability to discrete inclusions with delay. The sufficient conditions for relative and complete local controllability are obtained on the base of using Mordukhovich's nonsmooth constructions.     

正态定限（Orthant）概率

本文采用不同以往的方法;对正态定限（Ｏｒｔｈａｎｔ）概率积分施行线性变换与极坐标变换;得到了一个新的递推公式,使积分重数至少降低了３重;并推导了四维正态定限概率的表达式,这对进行数值计算是十分有意义的．     

短样本多指标动态经济数据变点的一种识别方法

本文研究了多指标动态经济数据的变点问题,使用多元分析的方法,给出了在样本长度较短情况下识别变点的一种方法,并用这种方法分析了国民经济统计中的一个实际例子。     

L-模糊正规子群之间的对应定理

群G的一个L-模糊正规子群A的陪集做成的群G／A与群G的一个商群是自然同构的。如果f：G→G’是群的满同态，则G’的L-模糊正规子群做成的群与G的在f的核上取定值的L-模糊正规子群做成的群之间存在一个保序的双射。     

A result of shepp

A simple direct proof is given of a result due to L. Shepp that a certain function of two independent normal random variables with zero means and possibly unequal variances is itself normal.     

Normal Multiresolution Approximation of Curves

A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular, we show that these properties critically depend on the underlying subdivision scheme and that, in general, the convergence of normal multiresolution approximations equals the convergence of the underlying subdivision scheme.