关于常微分方程求解公式的注记

要对常微分方程中的一阶线性齐次方程以及一阶线性非齐次方程的求解公式进行一下更为明确的证明.     

一个含参数的拉普拉斯方程解对参数的依赖性

讨论了一个含参数的拉普拉斯方程解对参数的依赖性,得到了这个方程非负古典解的存在唯一性和不存在性。     

空气阻力与地球自转影响下自由落体的运动

讨论自由落体东偏时,同时考虑了空气阻力与地球自转的影响,并结合空气阻力模型建立了相应的落体运动微分方程。忽略二阶小量,依次得到落体的运动规律。最后利用Mathematica编程作出了落体的位移-时间图像,并与忽略阻力时的情形作了对比,定量地说明了在空气阻力与地球自转影响下与忽略空气阻力相比,自由落体的偏东量值变大,此外东偏量值还与质点所在处的纬度有关,纬度越小的地方东偏量值越大,在两极没有东偏量,在赤道处东偏最大。     

The impact of information sharing in supply chains on organisational performance: an empirical study

Information sharing has been cited as one of the major means to enhance supply chain performance. It allows companies to better coordinate their activities with their supply chain partners that lead to increased performance. This study conceptualises and assesses several factors that influence the degree of information sharing in supply chains, namely integrated information technologies, internal integration, information quality and costs–benefits sharing. The relationship between the degree of information sharing and organisational performance is then tested. Data from 150 manufacturing companies were collected and proposed relationships are examined using structural equation modelling. The results show that integrated information technologies and information quality have positive influence on the intensity of information sharing. However, internal integration and costs–benefits sharing do not relate to the intensity of information sharing. This study finds that information sharing does not directly relate to organisational performance. Its relationship is mediated by collaboration practices with supply chain partners. This suggests that information sharing is essential but insufficient by itself to bring significant performance improvements.     

Statistical inference for reciprocal gamma diffusion process

We consider the problem of parameter estimation for an ergodic diffusion with reciprocal gamma invariant distribution. Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite number of discrete eigenfunctions (Bessel polynomials) and eigenfunctions related to a continuous part of the spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered.     

The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes

Abstract.  The Pearson diffusions form a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein–Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. Explicit optimal martingale estimating functions are found. The discussion covers GMM, quasi-likelihood, non-linear weighted least squares estimation and likelihood inference too. The analytical tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions and Pearson stochastic volatility models. For the non-Markov models, explicit optimal prediction-based estimating functions are found. The estimators are shown to be consistent and asymptotically normal.     

运用信息技术构建研究性教学模式的教学方案——以常微分方程课程教学为例

运用信息技术构建研究性教学模式的教学方案是信息技术与课程教学改革相结合的一种较好的范例．以CAI技术和建构主义理论为依据，根据课程的教学目标和信息技术的特点，将现代信息技术与课程教学模式进行整合，创建新的课程教学模式，是信息时代对教师提出的重要研究课题．本文设计了常微分方程课程与信息技术整合的教学方案的总体目标和教学方案的具体实施，并从创设情境、探求新知、简单应用和小结与评价等四个方面设计了一个具体的教学方案．     

全要素生产率测算的半参数估计方法及其应用

构造了全要素生产率增长率测算的半参数增长速度方程，该方程具有以下性质：并不事先假定全要素生产率增长率与时间的表达式，通过估计获得这种结构关系；使用增长率相对指标，避免计量单位的影响。中国1979-2006年的实证结果表明：资本和劳动力的产出弹性分别为0.525和0.585，规模报酬递增；资本、劳动力和全要素生产率的平均贡献率分别为46％、12％和42％。     

Statistical methods to evaluate health effects associated with major sources of air pollution: a case-study of breathing patterns during exposure to concentrated Boston air particles

Summary.  We conduct a case-study evaluating the source-specific effects of particulate matter on respiratory function. Using a structural equation approach, we assess the effect of different receptor models on the estimated source-specific effects for univariate respiratory response. Furthermore, we extend the structural equation model by placing a factor analysis model on the response to represent the measured respiratory responses in terms of underlying respiratory patterns. We estimate the particulate matter source-specific effects on respiratory rate, accentuated normal breathing and airway irritation and find a strong increase in airway irritation that is associated with exposure to motor vehicle particulate matter.     

Confidence bands for the difference of two survival functions under the additive risk model

In many clinical studies, a commonly encountered problem is to compare the survival probabilities of two treatments for a given patient with a certain set of covariates, and there is often a need to make adjustments for other covariates that may affect outcomes. One approach is to plot the difference between the two subject-specific predicted survival estimates with a simultaneous confidence band. Such a band will provide useful information about when these two treatments differ and which treatment has a better survival probability. In this paper, we show how to construct such a band based on the additive risk model and we use the martingale central limit theorem to derive its asymptotic distribution. The proposed method is evaluated from a simulation study and is illustrated with two real examples.