非完整相对运动动力学系统的非等时变分方程和积分不变量

首先给出非完整相对运动动力学系统的非等时变分方程,然后研究它们的解,并证明在一定条件下可利用第一积分来得到非等时变分方程的特解.最后利用正则方程和变分方程证明,可由第一积分直接构造系统的积分不变量.     

Nonparametric testing for simple regression under progressive censoring with stagering entry and random withdrawal

In the context of (multi-center) clinical trials and life testins problems, a general model incorporating both the staggering entry and random withdrawal and pertaining to a simple regression problem (including the two-sample location problem as a special case) is conceived, and, within this framework, a scheme allowing progressive censoring (continuous monitoring of experimentation from the beginning) is developed along with the proposal for and study of some nonparametric testing procedures, The proposed tests rest on the construction of certain two-dimensional time-parameter stochastic processes from a triangular array of progressively censored linear rank statistics and their weak convergence to appropriate Gaussian functions. Asymptotic properties of these procedures are studied. A computer program pertaining to the numerical computations and practical administrations of these testing procedures is also provided at the end.     

先秦从“数词+动词”结构到“动词+数词”结构的演变

先秦动量范畴的表达式“数词＋动词”具有表达功能上的歧义：可表动量，亦可作为一种从陈述到指称转换的功能结构式。这种蕴涵两种功能的单一结构式在表达上违背了话语交际中的“足量原则”，因此“数＋动”结构要么单袁动量，要么只是作为一种从陈述到指称转换的功能结构式。在历史演变过程中，“数＋动”结构选择了转变语序——“动＋数”结构表动量，在词汇层面，“数＋动”结构保持了其造词功能（陈述性〉指称性）。但是由于“数＋动”结构在文言中表动量的优势语序不可能完全退出表动量功能的语序集合，在动量范畴演变过程中“数＋动”依然存在，在句法层面单表动量范畴的语例增多，在动量词范畴成熟后，“数＋动”结构的数词与动量词结合成为普遍用法。     

布朗运动的实验设计

以布朗运动理论为指导,设计了一个新的布朗运动实验,并对微粒所做的布朗运动进行了定量的描述、测量和实验结果的分析.     

A Semiparametric Binary Regression Model Involving Monotonicity Constraints

Abstract.  We study a binary regression model using the complementary log–log link, where the response variable Δ is the indicator of an event of interest (for example, the incidence of cancer, or the detection of a tumour) and the set of covariates can be partitioned as ( X ,  Z ) where Z (real valued) is the primary covariate and X (vector valued) denotes a set of control variables. The conditional probability of the event of interest is assumed to be monotonic in Z , for every fixed X . A finite-dimensional (regression) parameter β describes the effect of X . We show that the baseline conditional probability function (corresponding to X  =  0 ) can be estimated by isotonic regression procedures and develop an asymptotically pivotal likelihood-ratio-based method for constructing (asymptotic) confidence sets for the regression function. We also show how likelihood-ratio-based confidence intervals for the regression parameter can be constructed using the chi-square distribution. An interesting connection to the Cox proportional hazards model under current status censoring emerges. We present simulation results to illustrate the theory and apply our results to a data set involving lung tumour incidence in mice.     

用极化理论分析锥体的后向散射场

在一致性几何绕射理论基础上，采用等效电流的方法给出了有限锥体在完全极化平面波照射下后向散射场的散射极化矩阵表示式。通过能量散射矩阵［Ｇ］得出最佳散射的极化条件。由米勒矩阵［Ｍ］分析了相差的密度函数，并得出各自相应的数值结果。     

Models for residual time to AIDS

The distributions of the time from Human Immunodeficiency Virus (HIV) infection to the onset of Acquired Immune Deficiency Syndrome (AIDS) and of the residual time to AIDS diagnosis are important for modeling the growth of the AIDS epidemic and for predicting onset of the disease in an individual. Markers such as CD4 counts carry valuable information about disease progression and therefore about the two survival distributions. Building on the framework set out by Jewell and Kalbfleisch (1992), we study these two survival distributions based on stochastic models for the marker process (X(t)) and a marker-dependent hazard (h()). We examine various plausible CD4 marker processes and marker-dependent hazard functions for AIDS proposed in recent literature. For a random effects plus Brownian motion marker process X(t)=(a+bt+BM(t))⁴, where a has a normal distribution, b<0 is an unknown parameter and BM(t) is Brownian motion, and marker-dependent hazard h(X(t)), we prove that, given CD4 cell count X(t), the residual time to AIDS distribution does not depend on the time since infection t. Using simulation and numerical integration, we find the marginal incubation period distribution, the marginal hazard and the residual time distribution for several combinations of marker processes and marker-dependent hazards. An example using data from the Multicenter AIDS Cohort Study is given. A simple regression model relating the cube root of residual time to AIDS to CD4 count is suggested.     

随机跳跃幅度的最优消费与证券选择策略问题

在最优消费与证券选择问题中,假定投资市场有两种资产可供选择:一种为无风险资产(银行债券),另一种为风险资产(股票).由于受重大信息的影响,风险资产的价格往往会产生跳跃.文章研究了这种带跳跃的投资问题,用泊松过程与布朗运动模拟了投资者的财富过程.为使投资者在整个生命周期的消费效用期望值最大,在跳跃幅度为一随机变量的条件下,利用贝尔曼动态规划原理,导出了最优消费及投资策略所满足的方程组,并且在跳跃幅度的概率分布已知的情况下,针对具体的参数值,给出了最优初始策略的数值解与最大消费效用期望值.     

均匀磁场中粒子的运动方程

本文证明了亥姆霍兹线圈在其中心附近产生均匀磁场；推出了运动电荷受磁场力作用时的运动方程。     

右Brown运动的若干性质

给出了右Ｂｒｏｗｎ 运动的首中点及首中时的分布，并证明了右Ｂｒｏｗｎ 运动是暂留的