On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

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.     

群作用的几乎周期性与等度连续性

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.     

Fuzzy HX环的推广

为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性：同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。     

OnQ-order andR-order of convergence

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.     

非参数回归函数之改良基于分割的估计的强相合性（英）

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．     

Error Estimates for Multilevel Approximation Using Polyharmonic Splines

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.     

On the covariance of the level sizes in random recursive trees

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     

Iterative solutions for low lying excited states of a class of SchrSdinger equation

The convergent iterative procedure for solving the groundstate Schr?dinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.     

（0,1;0）-INTERPOLATION ON INFINITE INTERVAL （-∞, ＋∞）

In this paper, we study the explicit representation and convergence of （0, 1;0）-interpolation on infisite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values areprescribed at two set of points namely the zeros of Hn（x） and H′n （x） and the first derivatives at the zerosof H′n（x）.     

求幂级数收敛半径的方法

指出了文 [1 ]中一个考研题的错误解法 ,并给出求幂级数收敛半径的几种方法