《高等应用数学》定积分的教学探索

数学教学改革多年都流于形式,传统性强,权威性高,是问题所在。本人将传统16课时定积分教学,打破传统模式,改造成6课时教学,收到了很好的效果,现在拿出来与读者共享。     

三主桁连续钢桁拱桥整体节点有限元分析

东平水道桥是武广高速铁路上一座四线铁路桁架拱桥,主跨结构为99m+242m+99m的三主桁连续钢桁拱,主桁采用整体节点形式,三主桁内力分析表明中桁处受力最大。节点板联结着主桁、腹杆、横梁、平联等各类杆件,结构及受力均较复杂,节点应力分布是设计中的关键问题之一。文章利用有限元程序对其特殊位置节点板进行应力分析,研究了其应力分布及传力特性,为设计提供依据和给同类桥梁提供参考。研究表明通过调整节点构造和板件刚度,节点具有足够的受力与传力功能。     

保险合同解释方法研究

保险合同是保险人致力于合同订立和履行上的一致性,为自己易于计算、节约成本而创造出来的格式化合同。该合同使得保险人对其所承担的风险、责任、险种等等一目了然,有其存在的必要性。但是,导致了当事人双方谈判地位不平等,个别交涉成本过高,契约正义被隐藏等问题。因此,司法裁判成为声张契约正义以及维护当事人合法权益的迂回模式之一。然而,在审理案件中,对合同的进一步阐释、对双方当事人真实意思表示的探求以及对合同争议焦点的解决,都起着至关重要的作用。这就涉及到如何适用多种解释方式对该合同进行解释。     

Moments of Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the moments and the descending factorial moments about a point n of mixed Poisson and compound mixed Poisson distributions, in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. As byproduct, we also obtain recursive formulae for the evaluation of the moments about the origin, central moments, descending and ascending factorial moments of these distributions. Examples are also presented for a number of mixing densities.     

阿贝尔（Abel）方程的一个特殊解法

给出奇异积分方程阿贝尔方程的一种技巧解法，作累次积分及变量替换推出此方程的解式，提出一个注记，拓展了求解积分方程的思路。变量替换、积分变换是求解微分方程和积分方程的一种重要方法。     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

积分第一中值定理的证明与推广

本文根据积分上限函数的性质利用微分中值定理证明了积分第一中值定理,用改进的介值定理证明了ξ∈(a,b),并推广了积分第一中值定理。     

Disciplinary sanctions in English Premiership Football: Is there a racial dimension?

This paper assesses the evidence for a racial difference in both the dispensation of formal disciplinary sanctions and in the number of fouls called by referees in professional football. The study uses a unique dataset comprising player match-level information drawn from five recent seasons of the English Premiership. These data were merged with data from other sources to identify, among other things, the racial affiliation of the player across four separate categories (viz., white, black, mixed race, and Asian). No systematic evidence of an unfair treatment of players from the non-white minority groups in respect of either the receipt of disciplinary cards or in the number of penalised fouls called by referees was detected.     

Analysis of Error with Malliavin Calculus: Application to Hedging

The aim of this paper is to compute the quadratic error of a discrete time-hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999) . More precisely, our basic assumption is that the asset prices satisfy the d -dimensional stochastic differential equation   dXⁱ_t = Xⁱ_t ( bⁱ ( X_t ) dt +σ _{i , j} ( X_t ) dW^j_t )  . We precisely describe the risk of this strategy with respect to n , the number of rebalancing times. The rates of convergence obtained are     for any options with Lipschitz payoff and  1/ n ^1/4  for options with irregular payoff.     

积分定义及对称性

本文给出了线、面、体积分定义的一般描述,并导出了利用对称性简化积分计算的定理。