MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONL INEARINTEGRO-DIFFERENTIAL EQUATIONS

1. IntroductionWe consider a Volterra integro-differential equationwith initial condition u(0) = not where f, P, k are continuous on their respective domainsJ, JxR and axs (n:~ {(t,s): 05s5t5T}) such that (1.l) possesses a unique solutionu E C'(J).It has been shown in [1] that the collocation approximation for (1.1) by discolltinuous piece--wise polynomial spline collocation at the Gauss points restore optimal local superconvergenceat the knots but does not yield global superconvergence on…     

Reconstruction of sampling in shift-invariant space using generalized inverse

A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples.The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model,then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimalnorm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.     

On Minimum Norm Control for an Elastic Robot System

In this paper, we discuss a robot system formulated as a vibrating elastic system. By regarding the damping coefficient of structure as the control variable and adjudging its optimality by norm minimum, we have proved the existence, the uniqueness and the approximation of the optimal control element by utilizing space L2(0,L) 's the reflexivity, the smoothness and the strict convexity.     

ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY

1. IntroductionLet D be an unbounded open set in R"(n 2 2) with finite Lebesgue measure. We considerthe following eigenvalue problem on a.where A = Z:=, 6 denotes the Laplacian on a and r ~ oa, the boundary of g. In thispaper we have a special interest in r which is considerably irregular like a fractal.Let N(A) denote the eigenvalue counting function of (P): the number of eigenvalues notexceeding A. When n is a bounded open set, it is well known that Weyl's classical asymptoticformulae f…     

CORRECTION NYSTROM SOLUTIONS OF NON-SMOOTH FREDHOLM EQUATIONS

1.IntroductionTherearemanynumericalresultsaboutthenon-smoothintegralequationswherek(s,t)=k.(t)~k(s/t)/tandf(s)aregiven,uistheunknownsolution(e.g.[1-6]).Buttherearefewresultsaboutthehighorderandadaptivemethodscorrespondingly.Becauseoftheefficiencyinsolving…     

粗糙近似算子的拓扑性质

通过闭包与内部算子研究模糊粗糙集的拓扑结构,证明了自反、传递关系下的近似空间中模糊集的上、下近似算子分别为一个模糊拓扑的闭包、内部算子,且相应的模糊拓扑满足(TC)条件;反之,满足(TC)条件的模糊拓扑的闭包与内部算子也恰为一自反、传递关系下的近似空间中的上、下近似算子.     

基于切比雪夫逼近的图像背景构建

提出一种基于像素邻域的切比雪夫逼近构造背景的方法,通过构造视频图像序列在Banach空间的线性包,该线性包与图像序列中任何一幅图片构成不相容线性方程组,通过切比雪夫逼近,求出最佳逼近系数。通过对所得系数设定阈值,提取出背景。实验表明,在采用固定摄像机方案下的视频监视系统,在无需大量的图片下也能提取背景,也具有较好的抑制噪声效果。     

AN EXTRAPOLATION METHODFOR FINITE ELEMENT APPROXIMATION OF INTEGRODIFFERENTIAL EQUATIONS WITH PARAMETERS

In this paper,we discuss the accelerating convergence method for finite elementapproximation of integro-differential equations with parameters.As applications,we give theerror estimates of finite element for the first kind of Fredholm integral equation,particularlyfor the Volterra integral equation with kernel condition k(x,x)=0.     

CORRECTION NYSTROM SOLUTIONS OF BIE IN POLYGONAL DOMAIN ON THE PLANE

ＣＯＲＲＥＣＴＩＯＮＮＹＳＴＲＯＭＳＯＬＵＴＩＯＮＳＯＦＢＩＥＩＮＰＯＬＹＧＯＮＡＬＤＯＭＡＩＮＯＮＴＨＥＰＬＡＮＥ￥ＳＨＩＪｕｎ（ＭａｔｈｅｍａｔｉｃｓＤｅｐａｒｔｍｅｎｔ，ＧｒａｄｕａｔｅＳｃｈｏｏｌ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ...     

神经元网络在股价预测中的应用

利用时延神经元网络模型（ＴｉｍｅＤｅｌａｙＮｅｕｒａｌＮｅｔｗｏｒｋ）对四川长虹的股价作了预测。股价的涨跌预报可视作高维空间的非线性分类问题,本文使用增益可调的反向传播算法,对其走势作了预报。借助前馈神经网络对非线性函数的逼近能力,本文对四川长虹股价这个时间序列作了连续若干天的一步预测。最后,我们采用不同形式的误差函数对预测结果作了比较。     

ERROR ESTIMATION OF THE APPROXIMATION ALGORITHM FOR THE WINDY POSTMAN PROBLEM

If we restrict the postman to traversing each edge at most twice in the windypostman problem (WPP), we will get a new problem: 2WPP. An approximation algorithmhas been posed by M. Guan for the WPP. In the present paper, we improve the estimatederror given by M. Guan and show that we can estimate the error for the 2WPP by findinga minimum cost circulation. We also pose a new sufficient condition for the equivalencebetween WPP and 2WPP, which can be checked in polynomial time steps.     

SOME DISCUSSION ON THE CONDITIONS OF COMPLETE CONVERGENCE FOR SUMS OF B-VALUED RANDOM ELEMENTS

1. Introduction and Main ResultsSince the definition on complete convergence of real random variables was introduced by Hsuand Robbins[1], there have been extensive literature on the complete convergence of i.i.d. realvalued random variables, see Baum and Katz ([2]), Bat and Su ([3]). In 1989, Yul4] extendedsome results in Bat and Su ([3]) to real valued independent but not necessarily identicallydistributed case. The main purpose of this paper is to extend the results of Yu[4] to B-value…     

A METHOD TO APPROXIMATE DISTRIBUTIONSOF RELATED STATISTICS

1.IntroductionandResultSupposethereisand--dimensional(d21)randomsampleXi,fromsomeprobabilityspace(fi,I,P)to(R',B,),Xi4Fi,Fibeingunknown,15i5n,n21.Whatconcernsusisthedistributionalpropertyofsomep-dimensional(p21)statisticTi~Ti(XIt''IX.;FI1'',Fi)whichisus…     

Pawlak粗糙集的公理系统

粗糙集合理论是一种新的有效处理不精确、不确定、含糊信息的理论,粗集公理系统研究是粗集理论及应用研究的基础。利用模糊关系及其运算的矩阵表示,建立Pawlak粗近似空间的公理体系,该公理系统由三条相互独立的非常简洁的表达式构成。获得的结果深刻地揭示了经典等价关系与模糊等价关系的本质区别,进一步深化了Pawlak粗集理论。     

DOMAIN DECOMPOSITION WITH NON-MATCHING GRIDS FOR COUPLING OF FEM AND NATURAL BEM

In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.     

ON APPROXIMATION OF MAX n／2-UNCUT PROBLEM

Using outward rotations, we obtain an approximation algorithm for MAX n/2-UNCUT problem, i.e., partitioning the vertices of a weighted graph into two blocks of equal cardinality such that the total weight of edges that do not cross the cut is maximized. In many interesting causes, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.     

成败型产品环境因子的经典近似限

利用Poisson近似和正态近似,本文导出了二项分布,负二项分布以及二项～负二项分布环境因子的经典近似限。     

变精度上近似算子与程度下近似算子的逻辑或运算模型

本文主要探索精度与程度结合的粗糙集扩张模型, 提出了变精度上近似算子与程度下近似算子的逻辑或运算模型. 研究了该新模型的精确描述与基本性质, 提出了模型的常规算法与结构算法, 进行了算法分析与算法比较, 得到了结论: 常规算法与结构算法具有相同的时间复杂性但结构算法具有更优的空间复杂性, 并用一个医疗实例对模型与算法进行了说明. 该模型具有精度与程度复合描述的具体含义, 部分扩张了变精度粗糙集模型、程度粗糙集模型和经典粗糙集模型, 进而得到了已有近似算子的相应性质.     

基于样条逼近的评价方法研究

样条逼近是从结构（空间或时间）性数据集合中提取特征的有效方法，本文提出基于样条逼近的评价方法，并进行评价方法应用研究，首先给出可变结点的样条逼近中数据集合点结点位置的选取准则，是使逼近的误差最小；给出数据集合点位置的选取方法及算法。对于上述分划的子区间，使用主成分分析方法对每个子区间进行评价，得到相应子区间的评价值，由于每个子区间的指标数不同，对子区间的评价值进行修正以体现这种差别；之后利用上述修正的子区间的评价值计算综合评价值。最后给出了应用结果。     

The Equivalent Representation of the Breadth-One D-Invariant Polynomial Subspace and Its Discretization

This paper demonstrates the equivalence of two classes of D-invariant polynomial subspaces, i.e., these two classes of subspaces are different representations of the breadth-one D-invariant subspace. Moreover, the authors solve the discrete approximation problem in ideal interpolation for the breadth-one D-invariant subspace. Namely, the authors find the points, such that the limiting space of the evaluation functionals at these points is the functional space induced by the given D-invariant subspace, as the evaluation points all coalesce at one point.