A semigroup approach to the strong ergodic theorem of the multistate stable population process

In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications.     

半线性热方程解的爆破率

考虑半线性方程ｕｔ－△ｕ＝（１＋ｕ）ｌｎ２＋ｒ（１＋｜ｕ｜）的初边值问题，对解ｕ在爆破时刻Ｔ的爆破率进行估计．     

薄环形相对论电子注介质切伦可夫脉塞

轴向电子注通过介质慢波系统，当波的相速略低于电子注的速度时就可产生相干的切伦可夫辐射，这一现象是一切行波管的基础。本文利用线性理论，通过自洽求解粒子连续性方程和相对论运动方程与麦克斯韦方程组，分析了薄环形相对论电子注介质切伦可夫脉塞的注波互作用，得到了完全描述其薄环形电子注作用的跳变条件，导出了描述其不稳定性的色散方程和注波互作用的同步条件，并求得了波增长率。     

二阶非线性时滞微分方程解的渐近性

本文建立了二阶非线性时滞微分方程解的渐近性结果及全局吸引定理,改进和推广了二阶线性方程和一阶非线性方程的已知定理。     

新剑桥方程式的提出及其相关论证

文章从论述经济增长与货币供求关系入手,结合费雪方程式MV=PT和剑桥方程式Md=KPY,以及作者提出的通货关系式F=G/Q及Q/Qd=F/Fp,从而完整地提出分阶段的新剑桥方程式MV=G=FQ(比例关系),并确证货币供给、需求方程式MS+=FPQ=FQd=Md,其意义十分重大,使人们对于经济规律确定性的认识得到升华。通过实证形式,对庇古所提的"余额说",马歇尔、凯恩斯的"余额说"货币数量论式子进行了剖析,并"纠正"其谬误之处。指出哈罗德—多马模型的通货实质,也和弗里德曼所提的货币函数式子相通。这些关系式的提出及其形成的理论体系,可以为中国宏观调控和决策操作提供理论依据。     

Marginal Regression of Gaps Between Recurrent Events

Recurrent event data typically exhibit the phenomenon of intra-individual correlation, owing to not only observed covariates but also random effects. In many applications, the population may be reasonably postulated as a heterogeneous mixture of individual renewal processes, and the inference of interest is the effect of individual-level covariates. In this article, we suggest and investigate a marginal proportional hazards model for gaps between recurrent events. A connection is established between observed gap times and clustered survival data with informative cluster size. We subsequently construct a novel and general inference procedure for the latter, based on a functional formulation of standard Cox regression. Large-sample theory is established for the proposed estimators. Numerical studies demonstrate that the procedure performs well with practical sample sizes. Application to the well-known bladder tumor data is given as an illustration.     

An Empirical Test of Competing Theories of Hazard-Related Trust: The Case of GM Food

Few scholars doubt the importance of trust in explaining variation in public perception of technological risk. Relatively little, however, is known about the particular types of judgments that people use in granting or withholding trust. This article presents findings from an empirical study that explores several dimensions of trust relevant for citizens' judgments of scientists involved in the development of GM food. The relationship between particular dimensions of trust and perceptions of GM food risk is also explored, using structural equation modeling. Results suggest that trust judgments based on the perception of shared values are most important in relation to GM food risk, but that judgments about scientists' technical competence are also important.     

A unified approach to regression analysis under double-sampling designs

We propose a unified approach to the estimation of regression parameters under double-sampling designs, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available. We assume that the validation sample is a simple random subsample from the primary sample. Our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample. The resulting estimator is consistent even if such a model is misspecified, and it achieves higher asymptotic efficiency than the estimator based only on the validation data. Specific cases are discussed to illustrate the application of the estimator proposed.     

范德瓦尔斯方程的统计解释

本文用统计的方法导出范德瓦尔斯方程及修正值的具体表达式,并讨论修正量与状态量的关系,给出刚性球分子对气体体积、压强所造成的影响.     

非线性板方程组对称

本文中利用作者提出的计算微分方程对称的特征列集算法和编制的程序包，给出了（各向异性）非线性板方程组的全部古典对称