Moderate and Small Deviations for the Ranges of One-Dimensional Random Walks

We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm. We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm.     

条件泛函及其导数非参数估计的强一致收敛速度

研究了条件泛函及其导数的非参数估计,对随机与固定设计的条件泛函,分别利用核估计和非参数加权估计,在核函数及权函数满足一定条件下,证明了估计一致强收敛于待估函数的速度可达到最优。从而进一步推广和发展了Hrdle,etal.(1988)、Severini,etal.(1992)的许多结果。     

最小树的一般算法

本文根据设计并行算法的基本原则,给出了最小树的两个对偶定理.在此基础上,建立了两种对偶的同步并行算法的雏型.这两种算法恰恰在对偶的意义下,概括了以往的最小树算法.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

一类周期种群系统的适定性及最优控制

本文研究了一类非线性周期种群系统的适定性及最优控制问题 .利用压缩不动点原理讨论了该种群系统的周期解的存在唯一性 .并用变分法给出了最优控制所满足的必要条件 .     

线性加指数效用函数的组合投资研究

应用无差异曲线法较好地解决了在投资决策分析中具有特殊重要地位的线性加指数效用函数的最优组合投资比例的求解问题,并给出实例予以说明.     

The Möbius distribution on the disc

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.