几何概型中的交汇问题

几何概型是高中数学的新增内容,是新课程高考的一大亮点和热点,是对古典概率的进一步发展,是等可能事件的概念从有限向无限的延伸,是中学数学知识的一个重要交汇点,已成为联系多项内容的媒介.本文展示几何概型与集合、函数、方程、三角形、解析几何的交汇与整合问题. 一、几何概型与集合的交汇     

区分易混概念是学好概率的关键

一、"非等可能"与"等可能"混同例1掷两枚骰子,求所得的点数之和为6的概率.错解:掷两枚骰子出现的点数之和不同情况为{2,3,4,…,12},故共有11种基本事件,所以概率为P=1/11.     

第四届全国环境力学研讨会简介

由于社会与经济可持续发展的重要需求,近年来环境力学研究得到迅速发展,成为力学学科一个新的重要生长点.     

Integrating Factors and Conservation Laws of Generalized Birkhoff System Dynamics in Event Space

In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.     

Radiation energy flux of Dirac field of static spherically symmetric black holes

By the statistical entropy of the Dirac field of the static spherically symmetric black hole, the result is obtained that the radiation energy flux of the black hole is proportional to the quartic of the temperature of its event horizon. That is, the thermal radiation of the black hole always satisfies the generalised Stenfan--Boltzmann law. The derived generalised Stenfan--Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space--time metric near the event horizon and the average radial effusion velocity of the radiation particles from the thin film. Finally, the radiation energy fluxes and the radiation powers of the Schwarzschild black hole and the Reissner--Nordstrõm black hole are derived, separately.     

图论在离散事件动态系统中的应用

运用图论方法和极大代数方法,研究了非强连通图中的强连通分支的最大圈长平均值与该图的赋权邻接矩阵的特征值之间的关系,并进一步证明了其等价性.     

绿色化学理念及其在新教材中的体现

中国加入WTO后,面临着前所未有的发展机遇与挑战。频频被媒体披露的众多排污企业污染反弹事件、农副产品或食品因某些物质超标而遭遇的出口受限事件等,说明了当前不少公民“绿色化学”意识的淡薄。因此,提高整个中华民族的科学文化素养(包括绿色化素养)是广大教育工作者义不容辞的责任。令人欣慰的是,随着“绿色化学”概念的凸现,新的统编高中化学教材多处渗透了体现人文情怀的绿色化学理念,为深入开展绿色化教育创造了有利条件。     

长期事件研究方法论——一个综述

本文对国外长期事件研究方法论文献进行了全面的梳理,并着重介绍和分析了期望收益模型(或收益基准)选择、异常收益度量,以及检验统计量的设定与检验力等。研究发现,在各期望收益模型、两种度量异常收益方法—AAR(或CAR)与BHAR的选择,以及各检验统计量是否存在错误设定等问题上,国外学界并未达成共识,争论仍在继续。     

概率论中一些易混淆的概念的教学探讨

从理论和实践相结合上对《概率论》课程中的一些概念教学进行了探究.