条件概率中的“条件”与事件发生的“条件”的关系剖析

在解答条件概率问题的过程中,厘清条件概率中的“条件”与事件发生的“条件”是关键一环,解题者往往对条件概率中的“条件”与事件发生的“条件”之间的关系分析不到位,认识不明晰,导致问题的关系不清,解答产生意想不到的错误．下文对条件概率中的“条件”与事件发生的“条件”的常见关系举例剖析,供读者参考．     

隐含条件:审题教学的一项重要任务

数学问题的条件,一般有显性条件和隐含条件之分.所谓显性条件,就是文本或图形直接给予的条件,这类条件一读就能发现;而隐含条件则隐藏于题目的文本与图形之中,需要对题中的已知条件进行深度解读、开发,才能发现.直观、明显是显性条件的特点,所以对这类条件的教学往往是教师审题教学的主要内容.而隐含条件的内隐性往往使其在审题教学中被边缘化,成为陪衬,这样的审题教学生态显然是失衡的.笔者认为,审题教学不仅要重视显性条件分析,还应关注隐含条件的剖析,要将其放在培养和发展学生审题能力的高度上加以     

有限Boole语义中公式的条件随机真度

基于条件概率的思想,利用赋值集的随机化方法,在有限Boole语义中引入公式的条件随机真度,证明了条件随机真度的MP规则和HS规则。引入公式间的条件相似度和条件伪距离,建立了条件随机逻辑度量空间,证明了条件随机逻辑度量空间中逻辑运算的连续性,并初步研究了给定条件下的近似推理理论。     

n值G?del命题逻辑系统中公式的条件随机真度

基于条件概率的思想,利用赋值集的随机化方法,在n值命题G(o|¨)del逻辑系统中引入公式的条件随机真度,证明了条件随机真度的MP规则和HS规则.引入公式间的条件随机相似度和条件伪距离,建立了条件随机逻辑度量空间,证明了条件随机逻辑度量空间中二元运算的连续性.     

已有降维方法的推广

SAVE,PHD和SIRⅡ已被证明是有效的降维方法,这些方法基于下面的两个假设1线性条件和常数方差条件.但是,常数方差条件非常强.当常数方差不成立时,即使线性条件成立,SAVE,PHD和SIRⅡ经常会找到中心空间之外的方向.通过去掉了常数方差条件,在较弱条件下推广了SAVE,PHD和SIRⅡ从而使得在较弱的条件下,能得到中心空间的正确估计.     

条件独立性与条件回归独立性

引入随机变量条件独立、强条件回归独立、逐对条件回归独立、连续条件回归独立、邻对条件回归独立、累积条件回归独立诸定义,证明它们之间的等价关系.     

全概率公式的推广

首先给出了普通事件在普通条件和Fuzzy条件下的Fuzzy条件概率及Fuzzy事件在普通条件和Fuzzy条件下的Fuzzy条件概率公式,并通过对普通事件的全概率公式进行推广,得到普通事件和Fuzzy事件分别在普通划分和Fuzzy划分下的全概率公式     

非全局Lipschitz条件下随机延迟微分方程Euler方法的收敛性

大多数随机延迟微分方程数值解的结果是在全局Lipschitz条件下获得的.许多延迟方程不满足全局Lipschitz条件,研究非全局Lipschitz条件下的数值解的性质,具有重要的意义.本文证明了漂移系数满足单边Lipschitz条件和多项式增长条件,扩散系数满足全局Lipschitz条件的一类随机延迟微分方程的Eul...     

注意挖掘隐含条件

有些数学题目中,常有一些条件隐含在题意中没有明确给出,这些条件就是所谓的隐含条件,而利用好这些隐含条件,可以简捷地解题,下面通过几个例子加以说明.     

关于一类二层规划问题的一阶最优性条件研究

本文针对一类具有特定结构的二层规划问题, 将下层问题用其KKT条件代替, 把二层规划问题转化成带有互补约束的单层优化问题.然后利用Fritz-John条件,在适当的条件下,得到了二层优化问题的一阶最优性条件.本文所给条件简单、容易验证,并且不同于[1]的条件.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.