“一个看似简单的问题”不简单——对《趣味物理学》中一个问题的分析

笔者执教高中的时候,正在研究一个有关液体压强的问题.忽然,来一位学生把别莱利曼的《趣味物理学(续编)》递给我,让我看文中第6.8节"一个看似简单的问题".该学生怀疑它的正确性.追忆往事,撰成此文.1问题的提出文献[1]中原题:您的面前是盛满30杯水的茶     

浅谈狭义相对论的三个效应

狭义相对论中由"光速不变"而产生了三个常见的相对论效应:时间膨胀、长度收缩和同时的相对性.实际上,光速不变原理所导致的效应不止这些,下面就介绍三个很有意思的相对论效应:前灯效应(headlight effect)、光行差效应(aberration effect)和角压缩效应(angular compresson effect).     

激光脉冲参数对冲击点火的影响

针对激光脉冲参数对冲击点火的影响进行理论分析和数值模拟.首先从冲击波的产生和碰撞过程出发,理论分析冲击脉冲峰值功率、脉宽和上升沿时间对点火的影响;然后通过数值模拟,以点火时间窗口作为评价标准,验证理论分析结果.研究表明:冲击脉冲峰值功率是点火成败的关键因素之一,脉冲宽度则需达到百皮秒以提供足够的点火能量,上升沿时间在小于600 ps的情况下不会对点火造成明显影响. 关键词： 冲击点火 激光冲击脉冲 点火时间窗口     

Risk models for the Prize Collecting Steiner Tree problems with interval data

Given a connected graph G=(V,E)with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree(PCST)problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c+e]while taking risk(c+e xe)/(c+e c e)of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p+v]for its inclusion in T while taking risk(yv p v)/(p+v p v)of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.     

A class of weighted estimators for additive hazards model in case-cohort studies

Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose＇a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.     

On the Well-Posedness of Determination of Two Coefficients in a Fractional Integrodifferential Equation

The authors study an inverse problem for a fractional integrodifferential equation, which aims to determine simultaneously two time varying coefficients, a kernel function and a source function, from the additional integral overdetermination condition. By using the fixed point theorem in suitable Sobolev space, the global existence and uniqueness results of this inverse problem are obtained.     

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

数学奥林匹克等级教练员培训班

为了帮助广大中学数学奥林匹克教练员拓宽知识面,提升教学研究能力和竞赛培训水平,今年我们继续举办数学奥林匹克等级教练员培训班,有关事宜通知如下。一、培训对象：中学数学教师。二、培训时间：2014年7月6日报到,7月7日至7月13日培训。三、培训地点：湖北省武汉市华中师范大学（武昌珞喻路152号）。四、证书发放：学习结束,经考核合格将颁发“中国数学奥林匹克二级教练员证书”。     

基于逆模糊数的模糊时间序列预测的新方法北大核心

Song和Chisson于1993年提出模糊时间序列预测理论．虽然至今已经提出许多模糊时间序列预测模型,但是迄今为止尚未给出预测未知年数据的模糊时间序列预测模型．提出基于逆模糊数的模糊时间序列预测的新方法该模型对广西大学已知的2001-2012年的注册数进行预测分析,平均预报误差率比相关文献的方法有所改善．还对广西大学未知的2013年和2014年注册数进行预测研究．方法是短期预测的一种模糊时间序列预测方法．