The order of operation can be exchanged with integral operation and derivation operation,then the concepts of almost everywhere convergence and everywhere convergence are introduced.
函数列{xn}的收敛性,说明:函数列的收敛域一般是定义域的子集;函数列虽然不一致收敛,但其极限函数可以是连续的;极限运算也可以与积分运算交换运算及求导运算交换运算的次序,并由此引出了函数列一致收敛与几乎处处收敛的概念,论述了叶果洛夫(Егоров)定理的建立与证明思路,充分说明了函数列{xn}在分析数学中的作用,诠释了数学概念、抽象与简单的辩证关系。
To make sure under what circumstances everywhere converge can be converted into uniform convergence,a typical counter-case has to be analysed.
在分析数学中一致收敛的重要性及几乎处处收敛不一定能够一致收敛。
With the aid of the geometry method,this paper presents the estimated values of the convergent reminders of certain important convergent sequences.
对某些重要的收敛序列,借助几何直观方法估计了它们的收敛余项。
In general,the convergent sequence and bounded set are concepts only in topological spaces.
收敛序列和有界集一般是拓扑空间中的概念 ,文章首先引入序列收敛 C和 L* -空间 (给出某种序列收敛关系的向量空间 ) ,然后在其中定义有界集 。
Main results are:① every implication open(closed)ball with radius not less then the norm of the heart point is an MP-filter;② every convergent sequence has unique limit;③ every convergent sequence is a Cauchy sequence;④ if a Cauchy sequence {xn} has a subsequence which converges to a point x,then {xn} converges to x too.
证明了:①每一半径不小于球心范数的蕴涵开(闭)球都是MP滤子;②每个收敛序列都有唯一的极限;③每个收敛序列都是Cauchy列;④如果一个Cauchy列{xn}的某个子列收敛于点x,则该Cauchy列本身也收敛于点x。
Proof of Levi Theorem on Almost Everywhere Convergence;
几乎处处收敛时Levi定理的证明
Almost Sure Convergence on Density Function
密度函数上的几乎处处收敛(英文)
Strong law of large numbers for mixing random sequences
混合序列的完全收敛性和部分和的几乎处处收敛性
Monotone Convergence Theorems for the Integration of Function Sequence with Respect to Almost Everywhere Weak Convergence Probability Measure Sequence
函数序列关于几乎处处弱收敛概率测度序列积分的单调收敛定理
Statistical Convergence of the Random Variables and Using Statistical Convergence to Deal with Data;
随机变量的统计收敛性及统计收敛在数据处理方面的应用
Convergence and Convergence Rate of the Partial Sums of Wavelet Expansions at Lebesgue Point
小波级数的部分和在勒贝格点处的收敛性与收敛速度
On Superconvergence Properties and Postprocess of Finite Element Approximation of Non-smooth Solutions in One Dimensional;
一维非光滑解有限元逼近的超收敛性及后处理
A Convergence Theorem for the Gauss-Seidel Iterative Method with the Preconditioner (I+S′);
预处理子为(I+S′)的Gauss-Seidel迭代法的收敛定理
Convergence of a Batch Method for Gray Neural Network GNNM(1, 1)
灰色神经网络GNNM（1，1）批处理算法的收敛性
Convergence of Batch Gradient Descent Algorithm for High Order Double Parallel Neural Networks
高阶双并联神经网络批处理梯度算法收敛性
Super-convergence of Three-dimensional Finite Element in Function And Derivative Approximations on Lobatto Points and Gauss Points
Lobatto点和Gauss点处三维有限元函数和导数的超收敛
Convergence Characteristics of Preconditioned Euler Equations at Low Mach Numbers
低马赫数流动中的预处理Euler方程的收敛特性
Primary Study on Application of Digital Image Processing Technology on Convergent Measurement of Surrounding Rock of Tunnel;
数字图象处理技术在隧道围岩收敛量测中应用的初步研究
Some Ultra-convergent Derivative Recovery Schemes for Piecewise Linear Interpolation;
分片线性插值的几种强超收敛的导数后处理格式
The Postprocessing, Maximum Norm Estimates and Superconvergence for Finite Element Methods to Nonlinear Equations or Sobolev Type;
Sobolev型方程有限元方法的后处理最大模估计及超收敛性
Convergence Rate of Conditional Moments, Large Quantile Estimation and Almost Sure Central Limit Theorem on Maxima and Minima;
条件矩收敛速度，大分位数之区间估计及最大值与最小值的几乎处处中心极限定理
The main purpose is to introduce a newly published book the preprocessing and postprocessing for the finite element method was introduced, including superconvergence, preliminary treatment, expansion, correction, posterior estimate, selfadaptive processing and eigenvalue problem etc.
介绍了新出版的专著包括超收敛、代、推、正、验估计、适应处理和特征值等问题.
Here and there I saw several attractive young women but carefully avoided giving them more than a glance.
人群中随处可见几个年轻美貌的女子，我瞥了她们一眼便小心翼翼地收敛起目光。