约束最小二乘估计的优良性

对于线性模型y=Xθ ε,ε服从椭球等高单峰分布,未知参数θ满足不等式约束a′θ≥0,证明了在参数估计优良性的集中概率准则下,θ的约束最小二乘估计θ~*优于最小二乘估计θ.     

Theory of optimal consumption and portfolio selection under a Capital-at-Risk (CaR) and a Value-at-Risk (VaR) constraint

The solution to the optimal portfolio selection and consumptionrule subject to Capital-at-Risk and Value-at-Risk constraintsis derived via the use of stochastic dynamic programming.     

基于Bayes方法的诊断模型分析

文中证明了在Bayes框架下,当漂移参数7服从有信息先验时,在相当广泛的统计模型中,数据删除模型(CDM)和均值漂移模型(MSOM)的参数估计不相等,几个数值例子验证了相应的结论.     

Analogue of Aharonov-Bohm effect in spin gauge theory

We predict the possibility of observing analogue of the Aharonov-Bohm effect due to long range interaction between spins originating in the framework of spin gauge theory developed earlier. The effect is predicted for both electrons (fermions) and photons. Appropriate experimental set-ups are suggested.     

一种新的两道工序柔性流水车间排序问题

本文针对F_2(p),h11.1|m_1=1,m_2=μ≥2|C_(max)这一问题给出了几种近似算法,并对每种近似算法进行了最坏情形分析,给出了最坏情形界.     

Multivariate approximation in the worst case setting over reproducing kernel Hilbert spaces

We study the worst case setting for approximation of d variate functions from a general reproducing kernel Hilbert space with the error measured in the L_∞ norm. We mainly consider algorithms that use n arbitrary continuous linear functionals. We look for algorithms with the minimal worst case errors and for their rates of convergence as n goes to infinity. Algorithms using n function values will be analyzed in a forthcoming paper.We show that the L_∞ approximation problem in the worst case setting is related to the weighted L₂ approximation problem in the average case setting with respect to a zero-mean Gaussian stochastic process whose covariance function is the same as the reproducing kernel of the Hilbert space. This relation enables us to find optimal algorithms and their rates of convergence for the weighted Korobov space with an arbitrary smoothness parameter α>1, and for the weighted Sobolev space whose reproducing kernel corresponds to the Wiener sheet measure. The optimal convergence rates are n^-(α-1)/2 and n^-1/2, respectively.We also study tractability of L_∞ approximation for the absolute and normalized error criteria, i.e., how the minimal worst case errors depend on the number of variables, d, especially when d is arbitrarily large. We provide necessary and sufficient conditions on tractability of L_∞ approximation in terms of tractability conditions of the weighted L₂ approximation in the average case setting. In particular, tractability holds in weighted Korobov and Sobolev spaces only for weights tending sufficiently fast to zero and does not hold for the classical unweighted spaces.     

信息化课堂教学设计--以“刚体定轴转动的角动量及角动量守恒定律”为例

遵循“学生主体、教师主导”的教育教学理念,借助信息化教学工具,合理有效地设计好每一个教学环节.采用演示、体验、探究、问题导向和分组讨论等教学手段和方法,让学生在课堂中自主发现问题、分析问题并解决问题,实现“学生做中学、教师做中教”,大大提升教学效果.     

STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM

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Apollonius coordinates,theN-body problem,and continuation of periodic solutions

This paper treats theN-body problem and its relation to various restricted problems. For each solution of the Kepler problem a generalization of the pulsating coordinates used to express the Hamiltonian of the elliptic restricted three-body problem is given. These coordinates are called Apollonius coordinates. The method of symplectic scaling is used to give a precise derivation of the elliptic restricted problem showing the precise asymptotic relationship between the restricted problem and the full three-body problem. This derivation obviates the proof of the fact that a nondegenerate periodic solution of the elliptic restricted three-body problem can be continued into the full three-body problem under mild nonresonance assumptions. Also, the method of symplectic scaling is used to give a precise derivation of the elliptic Hill lunar equation showing the precise relationship between the elliptic Hill lunar equation and the full three-body problem. A similar continuation theorem is established.     

Dual-parameter elastic-plastic fracture criterion of metals and alloys in the plane strain case

In recent years, some investigators discussed the applicability of the HRR theory for engineering materials based on the results of numerical analyses and experimental studies. In the present paper, the finite element method is employed to analyze the crack tip fields of the engineering elastic-plastic material with a variety of geometry configurations of cracked specimens from elastic state to intensely general yielded state in the plane strain case. The results indicate that the HRR theory loses its validity of application for engineering elastic-plastic materials in the plane strain case. The reasons for this are analyzed. A dual-parameter fracture criterion is suggested for this case.