布朗运动在薛定谔方程中的应用

借助[Duke Math.J.,1998,91(2):393-408]中的方法,利用布朗运动证明了一类二维薛定谔型方程的端点Strichartz估计不成立,并且证明了二维薛定谔方程的极大函数估计不成立.     

系统辨识中LS估计的渐近正态性的注记

文献[1]中,我们用有关鞅的中心极限定理,证明了系统辨识中LS估计的渐近正态性。然而[1]中的条件是苛刻的。本文利用Mcleish的相依变量的中心极限定理改进了[1]的结果。     

一个二相Stefan—Signorini问题古典解的存在性

本文通过利用参考文献[1]中的结果以及参考文献[2]中关于二相Stefan问题的估计思想,证明了一个在初始时刻仅出现一相的一维二相Stefan-Signorini问题古典解的存在性.     

半导体理论中一类抛物—椭圆耦合方程组混合初边值问题解的存在唯一性

本文讨论了在磁场影响下半导体器件中载流子运动的数学模型,这是一个抛物—椭圆耦合组的混合初边值问题。我们证明了该问题解的存在唯一性,而且给出了解的L~∞估计,从而推广了[5]、[6]、[7]中的一些结果。     

回归函数最近邻估计的重对数律

本文回答了孙东初在[7]中提出的问题,证明了回归函数最近邻估计m_n(x)的重对数律.     

关于半离散Galerkin近似解的L_∞估计的一个注记

在《计算数学》和《高等学校计算数学学报》上最近发表的文章[1]和[2]中,分别讨论了抛物和二阶双曲方程半离散Galerkin近似解(分片线性函数情形)的L_∞估计。文章作者采用正则Green函数方法证明了阶为h~2ln(1/h)的误差估计式。值得指出,[1]和[2]中所给出的估计式的一个不足之处就是它们所需要的精确解的正则性过于强。在这个注记里,我们将说明如下事实,利用熟知的半离散Galerkin近似解的超收敛估计和有限元函数空间的一个弱嵌入性质,可以证明得到阶也是h~2ln(1/h)的误差估计式,然而对解的正则性的要求则较[1]和[2]中估计式所需要的弱得多。 先讨论抛物问题,文[1]讨论的是热传导问题     

两个大气动力学模式整体强解的存在唯一性

文中用能量估计的方法,证明了大气动力学中的基本模式——正压无辐散模式与斜压准地转-准无辐散模式整体强解的存在唯一性,从而推广了作者在文[3]～[5]中所得到的结果并证实了曾庆存在[1]中的一个猜测.     

岭型主成分估计的最优性

本文研究岭型主成分估计的回归最优性,证明了岭型降维估计类中。岭型主成分估计具有Φ-最小、E-最小和 D-最小性,且协方差阵的正交不变范数最小。推广了[2]中某些结果.     

众数的核估计问题

设 X_1,…X_n,为 iid 样本,其总体的分布函数、密度函数、众数分别记为 F(x)、f(x)、θ,即有 f(θ)=supf(x)。我们来考虑θ的估计问题。Parzen[1]在研究密度 f 的核估计问题时首先提出了 θ 的核估计方法,并在一定假设条件下证明了这种估计具有弱相合性。陈桂景在[7]中进一步证明了众数 θ 的核估计还具有强相合性,而且当 f 的二阶导函数连续有界时,这种估计的强收敛速度可达到 O((1nn/n)~(2/7))。那么,一个自然的问题是,     

光滑度量测度空间上的加权扩散方程的梯度估计

本文主要考虑了一类加权非线性扩散方程正解的梯度估计.在m-维Bakry-(E)mery Ricci曲率下有界的假设下,得到加权多孔介质方程(γ＞1)正解的Li-Yau型梯度估计,此外对于加权快速扩散方程(0＜γ＜1),证明了Hamilton型椭圆梯度估计,结论分别推广了Lu,Ni,Vázquez and Villani在文[1]和Zhu在文[2]中的结果.     

An estimate of the attraction domain with a specified exponential stability index in a wheeled robot control problem

The problem of synthesizing a law for the control of the plane motion of a wheeled robot is investigated. The rear wheels are the drive wheels and the front wheels are responsible for the turning of the platform. The aim of the control is to steer a target point to a specified trajectory and to stabilize the motion along it. The trajectory is assumed to be specified by a smooth curve. The actual curvature of the trajectory of the target point, which is related to the angle of rotation of the front wheels by a simple algebraic relation, is considered as the control. The control is subjected to bilateral constraints by virtue of the fact that the angle of rotation of the front wheels is limited. The attraction domain in the distance to trajectory - orientation space, is investigated for the proposed control law. Arrival at a trajectory with a specified exponential stability index is guaranteed in the case of initial conditions belonging to the given domain. An estimate of the attraction domain in the form of an ellipse is given.     

AR（p）模型中的缺失数据估计

运用EM算法,对含有缺失数据的AR（p）模型进行参数估计,通过最大似然准则就非左端缺失的情况进行插补.最后,用蒙特卡洛方法给出实验分析,表明如下结果：（i）误差与AR模型的阶数正相关,与缺失比例正相关;（ii）当AR模型的特征根模长相对较小时,误差与数据长度负相关,且误差被控制在了标准差的30％以内;（iii）当模长中等时,误差基本控制在1个标准差左右;（iv）当模长较大时,误差与数据长度正相关,而且误差也相对较大.     

Discrete dynamic programming with outcomes in random variable structures

Multiobjective approach is the common way of generalization single-criterion dynamic programming models. Another way is to consider partially ordered criteria structures. That approach is rather rare. The aim of the paper is to present such a model. Generalization of Bellman’s principle of optimality is employed to create a forward procedure to find the set of all maximal elements. As this set is usual large, the second problem under consideration is to find its subsets. To reduce the number of solutions presented to decision maker we propose to apply a family of narrowing relations. That approach is similar to scalarization in multiobjective programming. Ordered structures of random variables based on mean–variance, stochastic dominance and inverse stochastic dominance are considered. Numerical illustration is given at the end of the paper.     

Self-triggered filter design for a class of nonlinear stochastic systems with Markovian jumping parameters

This paper is concerned with the self-triggered filtering problem for a class of Markovian jumping nonlinear stochastic systems. The event-triggered mechanism (ETM) is employed between the sensor and the filter to reduce unnecessary measurement transmission. Governed by the ETM, the measurement is transmitted to the filter as long as a predefined condition is satisfied. The purpose of the addressed problem is to synthesize a filter such that the dynamics of the filtering error is bounded in probability (BIP). A sufficient condition is first given to ensure the boundedness in probability of the filtering error dynamics, and the characterization of the desired filter gains is then realized by means of the feasibility of certain matrix inequalities. Furthermore, a self-triggered mechanism is designed to guarantee the filtering error dynamics to be BSP with excluded Zeno phenomenon. In the end, numerical simulation is carried out to illustrate the usefulness of the proposed self-triggered filtering algorithm.     

Torsional oscillations in symmetrical structures

A two-time perturbation technique is used to study the lateral and torsional motions of a nonlinear symmetrical structure subject to a lateral sinusoidal ground motion. It is shown that when the ground acceleration frequency is about one-third of or three times the natural frequency of the lateral motion, the symmetrical structure is particularly susceptible to torsional oscillations even when the natural frequency of torsion is not close to the natural frequency of the lateral motion. The implication of this type of nonlinear coupling between the lateral and torsional motions in real structures subject to earthquakes is also discussed.     

Computational error analysis of periodic solutions for singular semilinear parabolic problems

By using the monotone method, a theoretical and computational method is given to find, to the degree of accuracy desired, approximate solutions of a class of singular semilinear parabolic problems. So that the error between the actual solution and its approximation is within a given error tolerance, the number of iterations is determined. Since each iterate is in terms of an infinite series, the number of terms to be retained in each iterate is determined so that its error from the exact iterate is within a given error tolerance. An improved rate of convergence is then given to show that it is possible to reduce the number of terms retained in each iterate. An algorithm is also described to obtain numerical solutions. For illustration of the computational methods developed, a numerical example is given.     

(<Emphasis Type="Italic">T</Emphasis>, <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>) Policy Inventory Model for Deteriorating Items with Time Proportional Demand

An EOQ model is reconsidered here in which the demand rate is changing linearly with time and the deterioration is assumed to be a constant fraction of the onhand inventory. The planning horizon is finite and known and the replenishment periods are assumed to be constant. The problem is to find the optimal number of replenishments, which are instantaneous. When there is no deterioration, the model developed is related to the corresponding model for nondeteriorating items. An example followed by sensitivity analysis is given to illustrate the derived results.     

Non-Convex Strong Duality Via Subdifferential

In this article, the strong duality is treated. It is shown that the strong duality is equivalent to the non-emptiness of the subdifferential of a sort map involving the constraint functions. It is also noted that this technique is useful to verify the Assumption S. Indeed, the linearity of a constraint function h is not required as usually seen in the literature. Moreover, it is shown that this condition is easer to verify in the applications. We apply this new principle to the bi-obstacle problem, to the elastic-plastic torsion problem and to the continuum model of transportation.     

连续区间数的中位算子及其灵敏度分析

研究决策信息以区间数形式给出的方案决策问题。考虑到区间数非均匀分布的特点,为避免区间极端值在区间数确定中产生较大误差,本文将中位数概念运用到区间数的确定上,提出OIP(Ordered Interval Point)有序中位算子。取单位区间单调函数(BUM函数)为二分之一所表示的值为权重,将区间数确定为一个实数,并研究算子单调性和有界性的初等运算性质。通过比较OIP算子与COWA算子对态度参数和区间长度的反应灵敏度,获得了在一定条件下OIP算子对态度参数反应更稳健,对区间长度反应更灵敏的结论。最后用算例证明该算子的可行性和有效性。     

基于熵的群决策专家选择研究

群决策是研究多人如何做出统一的有效抉择.在群决策中专家决策水平直接反应到决策结论上,是影响事业的成败关键,因此专家的选择对于群决策而言是至关重要的.建立了评价群决策专家的指标集,从专家选择角度定义了理想专家,给出了专家选择的熵模型,并通过一个例子说明该模型的有效性.