二维各向同性谐振子的守恒张量及其应用

二维各向同性谐振子的第三守恒量是一张量.经研究得到了二维谐振子守恒张量的矩阵表示形式,并用守恒张量的各元素表示振子的运动方程及新坐标系下的轨道方程.     

SPECIAL ISSUE： DIALOGUE,INTERACTION AND NEW.DEVELOPMENTS IN PHILOSOPHY IN CONTEMPORARY CHINA - SPECIALIST FORUM ON CHINESE,WESTERN AND MARXIST PHILOSOPHIES：Contemporariness： a common field for dialogue between Chinese,Western and Marxist philosophies

如果说当代中国哲学的新开展意味着中国哲学的当代性展开,那么首要的问题就是理解何渭当代性。当代性不是一个历史学的概念,而是一个历史哲学的观念。当代性既不同于现代性,也不同于后现代性,而是在当下生活中的同时发生、同时在场。既然当代中国哲学是中国哲学的当代性展开,这就意味着当代中国哲学乃是在当下生活情境中发生、而且是与当代西方哲学和当代马克思主义哲学同时在场的。这就是三者之间的对话之所以可能的共同场域。     

用Laplace变换求Kratzer势径向波函数的二类递推关系

求解了Kratzer势的Schr(o)dinger方程,得到了归一化的波函数和能量方程.用Laplace变换使径向的二阶微分方程退化为一阶微分方程,直接积分后用级数展开,应用Laplace逆变换得出本征函数.另外,用Laplace变换方法给出了径向波函数关于量子数N和角量子数L的二类递推关系.     

多资产下组成比例交易费用的投资消费最优策略

交易费用的存在使用最优投资消费策略问题非常复杂。当存在交易费用的时候,持续对股票进行交易将会导致交易费用无限增加。因此不能频繁进行股票交易。对只考虑两种资产的情况已经有较多的研究,但是对于多种资产的情况却没有引起人们的重视。本文对HARA效用函数下,有限期间和无限期间具有成比例交易费用的最优投资消费策略的价值函数的解析解进行了研究。在多种风险资产可以用来进行交易的情况下,利用价值函数的凹性和近似性,通过变量代换的方式,将HJB方程从偏微分方程(PDE)转化常微分方程(ODE),对价值函数进行求解,给出交易区解析解的形式和非交易区要满足的HJB方程。      

A fixed-point method for the saddlepoint approximation quantile

A fixed-point method is proposed for calculating quantiles of the sample mean for a saddlepoint approximation. We show that this method has fast convergence rate and can be extended to more general statistics. Examples are given to show the accuracy of the approximation.     

Feature screening for case‐cohort studies with failure time outcome

Case‐cohort design has been demonstrated to be an economical and efficient approach in large cohort studies when the measurement of some covariates on all individuals is expensive. Various methods have been proposed for case‐cohort data when the dimension of covariates is smaller than sample size. However, limited work has been done for high‐dimensional case‐cohort data which are frequently collected in large epidemiological studies. In this paper, we propose a variable screening method for ultrahigh‐dimensional case‐cohort data under the framework of proportional model, which allows the covariate dimension increases with sample size at exponential rate. Our procedure enjoys the sure screening property and the ranking consistency under some mild regularity conditions. We further extend this method to an iterative version to handle the scenarios where some covariates are jointly important but are marginally unrelated or weakly correlated to the response. The finite sample performance of the proposed procedure is evaluated via both simulation studies and an application to a real data from the breast cancer study.     

On a Relation Between a Family of Distributions Attaining the Bhattacharyya Bound and That of Linear Combinations of the Distributions from an Exponential Family

Abstract

An unbiased estimation problem of a function g(θ) of a real parameter is considered. A relation between a family of distributions for which an unbiased estimator of a function g(θ) attains the general order Bhattacharyya lower bound and that of linear combinations of the distributions from an exponential family is discussed. An example on a family of distributions involving an exponential and a double exponential distributions with a scale parameter is given. An example on a normal distribution with a location parameter is also given.     

A spatial structural equation model for health outcomes

Population level risk factors in spatial epidemiology (e.g. socioeconomic deprivation) are often not directly available but indirectly measured through census or other sources. This paper considers multiple health outcomes (e.g. mortality, hospital admissions) in relation to unmeasured latent constructs of population morbidity, established as relevant to explaining spatial contrasts in such health outcomes. The constructs are derived using a factor analytic approach in which observed area social indicators are measures of a smaller set of latent constructs. The constructs are allowed to be spatially correlated as well as correlated with one another. The possibility of nonlinear construct effects is considered using a spline regression. A case study considers suicide mortality and self-harm contrasts in 32 London boroughs, in relation to two latent constructs: area deprivation and social fragmentation.     

Tables of percentage points of the k-variate normal distribution for large values of k

This paper gives tabulations of the upper α percentage points of the maximum absolute value of the k-variate normal distribution with common correlation ρ for values of k as high as 500. The tables are useful for performing multiple comparison procedures in experiments with large numbers of treatments.     

A Pairwise Likelihood Procedure for Analyzing Exchangeable Binary Data with Random Cluster Sizes

For the exchangeable binary data with random cluster sizes, we use a pairwise likelihood procedure to give a set of approximately optimal unbiased estimating equations for estimating the mean and variance parameters. Theoretical results are obtained establishing the large sample properties of the solutions to the estimating equations. An application to a developmental toxicity study is given. Simulation results show that the pairwise likelihood procedure is valid and performs better than the GEE procedure for the exchangeable binary data.