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81.
We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)  相似文献   
82.
求解最小Steiner树的蚁群优化算法及其收敛性   总被引:11,自引:0,他引:11  
最小Steiner树问题是NP难问题,它在通信网络等许多实际问题中有着广泛的应用.蚁群优化算法是最近提出的求解复杂组合优化问题的启发式算法.本文以无线传感器网络中的核心问题之一,路由问题为例,给出了求解最小Steiner树的蚁群优化算法的框架.把算法的迭代过程看作是离散时间的马尔科夫过程,证明了在一定的条件下,该算法所产生的解能以任意接近于1的概率收敛到路由问题的最优解.  相似文献   
83.
??In this paper, by applying the moment inequality for asymptotically almost negatively associated (AANA, in short) random sequence and truncated method, the equivalent conditions of complete moment convergence of the maximum partial for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of{15},{16} and {17}, respectively.  相似文献   
84.
In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation.  相似文献   
85.
The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 103. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ~ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ~ 5 × 103.  相似文献   
86.
We give sufficient conditions for a sequence to have theQ-order and/or theR-order of convergence greater than one. If an additional condition is satisfied, then the sequence has an exactQ-order of convergence. We show that our results are sharp and we compare them with older results.This work was supported in part by the National Science Foundation under Grant No. DMS-85-03365. The author wishes to thank J. E. Dennis and R. A. Tapia for helpful comments, and the referee for pointing out a number of typographical and mathematical errors in the original version of this paper.  相似文献   
87.
设(X,Y),(X1,Y1),…,(XnYn)为取值于 Rd× R的 i.i.d.随机变量,E(|Y|) <∞.设mn(x)为回归函数m(x)=E(|Y|X=x)基于分割的估计,本文在对mn(x)进行改良的条件下得到改良的基于分割的强相合估计.  相似文献   
88.
Polyharmonic splines are used to interpolate data in a stationary multilevel iterative refinement scheme. By using such functions the necessary tools are provided to obtain simple pointwise error bounds on the approximation. Linear convergence between levels is shown for regular data on a scaled multiinteger grid, and a multilevel domain decomposition method.  相似文献   
89.
林木仁 《数学研究》2002,35(4):421-428
得到εdx/dt=A(t)x的扰动系统具有指数型二分性一个充分条件,作为应用得到其扰动系统概周期解及有界解的存在性,推广了[1,2,3]的结果。  相似文献   
90.
In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002  相似文献   
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