平衡随机模型中方差分量的非负估计

众所周知, 对于平衡随机模型, 方差分量的方差分析估计为一致最小方差无偏估计. 本文基于方差分量的方差分析估计, 构造了一个二次不变估计类, 它包含了一些常用重要估计. 证明了该估计类在一定条件下在均方误差意义下一致优于方差分析估计, 并在此估计类基础上, 给出了方差分量的两种非负估计, 它们在均方误差意义下分别一致优于方差分析估计和限制极大似然估计, 且有显式解、容易计算.     

Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．     

关于无偏估计的若干问题

通过理论分析和实例讨论有关无偏估计的若干问题：无偏估计不一定存在；无偏估计一般不唯一；在均方误差意义下，无偏估计不一定优于有偏估计；均方误差最小的估计是最小方差无偏估计，但反之不然。     

Panel模型中常见估计的比较

本文研究了Panel模型中回归系数常见估计的比较问题,给出了在Pitman准则,协方差阵准则和广义均方误差准则下最小二乘估计,Within估计,Between估计及两步估计之间的优良性比较结果.特别地,本文证明了在Pitman准则下最小二乘估计一致地优于Between估计.     

线性混合效应模型中方差分量的估计

本文首先研究了含三个方差分量的线性混合随机效应模型改进的ANOVA估计, 此估计在均方损失下一致优于ANOVA估计. 由于这些方差估计取负值的概率大于零, 对得到的估计在某非负点采用截尾的方法得到非负估计是一种常用的方法. 对文章中提出的估计, 研究了此估计在某非负点截尾之后得到的估计在均方损失意义下优于截尾之前的估计的充分条件, 同时给出ANOVA估计在截尾之后优于它本身的充分条件, 而且将得到的结论推广到更一般的线性混合随机效应模型.     

状态概率的E-Bayes估计与多层Bayes估计

在文献[1]中提出了参数估计的一种方法--E-Bayes估计并给出了状态概率的E-Bayes估计的定义、E-Bayes估计公式、预测模型及其在证券投资中应用,本文在此基础上将给出状态概率的多层Bayes估计、状态概率的E-Bayes估计的性质--E-Bayes估计,多层Bayes估计的关系.最后,给出模拟算例.     

增加试验数据对岭估计的均方误差的影响

在线性模型中,对于回归系数的岭估计和广义岭估计,本文给出了选择岭参数的条件,在此条件下,岭估计和广义岭估计不仅能改善LS估计,而且增加试验数据时,它们的均方误差都会减少。同时,本文将增加试验数据换成增加附加信息,从而讨论了附加信息对混合岭估计和混合广义岭估计的影响问题。     

误差方差的非齐次估计的可容许的充要条件

研究误差方差的非齐次二次估计的可容许性．在平方损失下,给出了一个非齐次二次估计在非齐次二次估计类中是误差方差的容许估计的充要条件．     

混合系数线性模型的几乎无偏s-K估计

在连续测量数据情况下,给出了混合系数线性模型的几乎无偏s-K估计,讨论了该估计的相关性质,并在一定条件下证明了几乎无偏s-K估计优于s-K估计以及几乎无偏岭估计.     

指数分布串—并联混合系统产品的统计分析

给出单元寿命服从同一指数分布的串-并联混合系统产品参数的矩估计和极大似然估计,并通过大量Monte-Carlo模拟比较了估计的精度,得到在样本容量小于35时矩估计优于极大似然估计,而样本容量不小于35时极大似然估计优于矩估计.另外,还给出了参数的精确区间估计与近似区间估计,并通过大量Monte-Carlo模拟考察了区间估计的精度.     

Invariant sets and measures of nonexpansive group automorphisms

We write a formula for the LMO invariant of a rational homology sphere presented as a rational surgery on a link inS ³. Our main tool is a careful use of the Århus integral and the (now proven) “Wheels” and “Wheeling” conjectures of B-N, Garoufalidis, Rozansky and Thurston. As steps, side benefits and asides we give explicit formulas for the values of the Kontsevich integral on the Hopf link and on Hopf chains, and for the LMO invariant of lens spaces and Seifert fibered spaces. We find that the LMO invariant does not separate lens spaces, is far from separating general Seifert fibered spaces, but does separate Seifert fibered spaces which are integral homology spheres.     

Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators

The majority of first-order methods for large-scale convex–concave saddle point problems and variational inequalities with monotone operators are proximal algorithms. To make such an algorithm practical, the problem’s domain should be proximal-friendly—admit a strongly convex function with easy to minimize linear perturbations. As a by-product, this domain admits a computationally cheap linear minimization oracle (LMO) capable to minimize linear forms. There are, however, important situations where a cheap LMO indeed is available, but the problem domain is not proximal-friendly, which motivates search for algorithms based solely on LMO. For smooth convex minimization, there exists a classical algorithm using LMO—conditional gradient. In contrast, known to us similar techniques for other problems with convex structure (nonsmooth convex minimization, convex–concave saddle point problems, even as simple as bilinear ones, and variational inequalities with monotone operators, even as simple as affine) are quite recent and utilize common approach based on Fenchel-type representations of the associated objectives/vector fields. The goal of this paper was to develop alternative (and seemingly much simpler) decomposition techniques based on LMO for bilinear saddle point problems and for variational inequalities with affine monotone operators.     

An Endpoint Estimate for the Commutator of Singular Integrals

It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.     

Optimal Trajectories for Earth-to-Mars Flight

This paper deals with the optimal transfer of a spacecraft from a low Earth orbit (LEO) to a low Mars orbit (LMO). The transfer problem is formulated via a restricted four-body model in that the spacecraft is considered subject to the gravitational fields of Earth, Mars, and Sun along the entire trajectory. This is done to achieve increased accuracy with respect to the method of patched conics.The optimal transfer problem is solved via the sequential gradient-restoration algorithm employed in conjunction with a variable-stepsize integration technique to overcome numerical difficulties due to large changes in the gravitational field near Earth and near Mars. The optimization criterion is the total characteristic velocity, namely, the sum of the velocity impulses at LEO and LMO. The major parameters are four: velocity impulse at launch, spacecraft vs. Earth phase angle at launch, planetary Mars/Earth phase angle difference at launch, and transfer time. These parameters must be determined so that V is minimized subject to tangential departure from circular velocity at LEO and tangential arrival to circular velocity at LMO.For given LEO and LMO radii, a departure window can be generated by changing the planetary Mars/Earth phase angle difference at launch, hence changing the departure date, and then reoptimizing the transfer. This results in a one-parameter family of suboptimal transfers, characterized by large variations of the spacecraft vs. Earth phase angle at launch, but relatively small variations in transfer time and total characteristic velocity.For given LEO radius, an arrival window can be generated by changing the LMO radius and then recomputing the optimal transfer. This leads to a one-parameter family of optimal transfers, characterized by small variations of launch conditions, transfer time, and total characteristic velocity, a result which has important guidance implications. Among the members of the above one-parameter family, there is an optimum–optimorum trajectory with the smallest characteristic velocity. This occurs when the radius of the Mars orbit is such that the associated period is slightly less than one-half Mars day.     

Littlewood-Paley g-函数交换子的Hardy型估计

证明了当q>1时,Littlewood-Paley g-函数与LMO(BMO的一个子空间)函数的交换子g_(Ψ,b)是局部Hardy空间h~1(R~n)到空间h~1(R~n)+L~q(R~n)的一个连续映射.     

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

It is well known that the commutator Tb of the Calder′on-Zygmund singular integral operator is bounded on Lp(Rn) for 1 p +∞if and only if b∈BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσbe the operators that its symbol is S01,δwith 0≤δ 1, if b∈LMO∞, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L∞(Rn) into BMO(Rn); If [b, Tσ] is bounded from H1(Rn) into L1(Rn) or L∞(Rn) into BMO(Rn), then, b∈LMO_(loc).     

Simulation of Atomic Force Microscopy for investigating BaTiO3 and LiMn2O4 nanostructures based on Phase Field Approach

Atomic Force Microscopy (AFM) probes the surface features of specimens using an extremely sharp tip scanning the sample surface while the force is applied. AFM is also widely used for investigating the electrically non-conductive materials by applying an electric potential on the tip. Piezoresponse Force Microscopy (PFM) and Electrochemical Strain Microscopy (ESM) are variants of AFM for different materials. Both PFM and ESM signals are obtained by observing the displacement of the tip when applying electric fields during the scanning process. The PFM technique is based on converse piezoelectric effect of ferroelectrics and the ESM technique is based on electrochemical coupling in solid ionic conductors. In this work, two continuum-mechanical formulations for simulation of PFM and ESM are discussed. In the first model, for PFM simulation, a phase field approach based on the Allen-Cahn equation for non-conserved order parameters is employed for ferroelectrics. Here, the polarization vector is chosen as order parameter. Since ferroelectrics have highly anisotropic properties, this model accounts for transversely isotropic symmetry using an invariant formulation. The polarization switching behavior under the electric field will be discussed with some numerical examples. In the simulation of ESM, we employ a constitutive model based on the work of Bohn et al. [8] for the modeling of lithium manganese dioxide LiMn₂O₄ (LMO). It simulates the deformation of the LMO particle according to an applied voltage and the evolution of lithium concentration after removing a DC pulse. The modeling results are compared to experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Århus integral of rational homology 3-spheres III: Relation with the Le–Murakami–Ohtsuki invariant

Continuing the work started in [Å-I] and [Å-II], we prove the relationship between the Århus integral and the invariant (henceforth called LMO) defined by T.Q.T. Le, J. Murakami and T. Ohtsuki in [LMO]. The basic reason for the relationship is that both constructions afford an interpretation as integrated holonomies. In the case of the Århus integral, this interpretation was the basis for everything we did in [Å-I] and [Å-II]. The main tool we used was formal Gaussian integration. For the case of the LMO invariant, we develop an interpretation of a key ingredient, the map j_m, as formal negative dimensional integration. The relation between the two constructions is then an immediate corollary of the relationship between the two integration theories.     

Hardy型空间上的面积积分交换子

本文研究了面积积分交换子的端点估计.利用函数分解技术,证明了当q>1时,面积积分与LMO(R~n)(BMO(R~n)的一个子空间)函数的交换子是局部Hardy空间h1(R~n)到空间h1(R~n)+Lq(R~n)的一个连续映射,推广了Coifman,Rochberg和Weiss关于交换子的经典结果.     

Littlewood-Paley g_λ~*-函数交换子的Hardy型估计

研究了Littlewood-Paley g_λ~*-函数交换子的端点估计.利用函数分解技术,证明了当q1时g_λ~*-函数与LMO(R~n)(BMO(R~n)的一个子空间)函数生成的交换子[b,g_λ~*]是局部Hardy空间h1(R~n)到空间h~1(R~n)+L~q(R~n)的一个连续映射.推广了Coifman,Rochberg和Weiss关于交换子的经典结果.