NONNESTED MULTILEVEL PRECONDITIONING METHODS WITH SIMPLE AND IDENTICAL COARSE MESH CORRECTION SPACES

1　ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｌｔｉｌｅｖｅｌｍｅｔｈｏｄｓｈａｖｅｂｅｃｏｍｅｓｏｍｅｏｆｔｈｅｍｏｓｔｐｏｐｕｌａｒｍｅｔｈｏｄｓｆｏｒｓｏｌｖｉｎｇｌａｒｇｅｓｙｓｔｅｍｏｆｌｉｎｅａｒｅｑｕａｔｉｏｎｓｒｅｓｕｌｔｉｎｇｆｒｏｍｔｈｅｆｉｎｉｔｅｅｌｅｍｅｎｔｄｉｓｃｒｅｔｉｚａｔｉｏｎｏｆｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.ＴｈｅｐｉｏｎｅｅｒｗｏｒｋｏｆｍｕｌｔｉｌｅｖｅｌｍｅｔｈｏｄｓｉｓｔｈｅＹｓｅｒｅｎｔａｎｔ’ｓＨｉｅｒａｒｃｈｉｃａｌｂａｓｉｓｍｅｔｈ…     

ADirect Method for the Problem of the Solid Cylinder in Elasticity

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＳａｉｎｔＶｅｎａｎｔｐｒｏｐｏｓｅｄｔｈｅｆａｍｏｕｓｓｅｍｉ－ｉｎｖｅｒｓｅｓｏｌｕｔｉｏｎｍｅｔｈｏｄ［１］，ｔｈａｔｓｏｍｅａｐｐｒｏ－ｐｒｉａｔｅａｓｓｕｍｐｔｉｏｎｓｔｏｔｈｅｄｅｆｏｒｍａｔｉｏｎｓｈｏｕｌｄｂｅｍａｄｅｂｅｆｏｒｅｈａｎｄｔｏｆｉｎｄｔｈｅｓｏｌｕｔｉｏｎ，ａｆｔｅｒ－ｗａｒｄｓｃｈｅｃｋｉｎｇｔｈｅａｓｓｕｍｐｔｉｏｎｓｂｅｉｎｇｖａｌｉｄ．Ｔｈｅｒｅａｆｔｅｒ，ｔｈｅｓｅｍｉ－ｉｎｖｅｒｓｅｓｏｌｕｔｉｏｎｂｅｃｏｍｅｓｔ…     

Analysis and Forecast on the Car Market of Our Country

§１．　ＦｏｒｅｃａｓｔａｂｏｕｔｔｈｅＣａｒＭａｒｋｅｔＤｅｍａｎｄａｎｄｔｈｅＱｕａｎｔｉｔｙｏｆＣａｒＰｏｓｓｅｓｓｉｏｎｉｎＯｕｒＣｏｕｎｔｒｙｉｎ２０００Ｉｎｔｈｉｓｓｅｃｔｉｏｎ,ｗｅｓｈａｌｌｆｏｒｅｃａｓｔｔｈｅｃａｒｍａｒｋｅｔｄｅｍａｎｄａｎｄｔｈｅｑｕａｎｔｉｔｙｏｆｃａｒｐｏｓｓｅｓｓｉｏｎｉｎｏｕｒｃｏｕｎｔｒｙｉｎ２０００ｂｙｍｅａｎｓｏｆｔｗｏｓｔａｔｉｓｔｉｃｓｍｅｔｈｏｄｓ,ｉ．ｅ．ｔｅｎｄｅｎｃｙｉｎｆｅｒｅｎｃｅａｎｄｒｅｇｒｅｓ－ｓｉｏｎａｎａｌｙｓｉｓ．…     

Probabilistic Norm of Operators and Continuity of Bounded Operators

Ｔｈｅｅｑｕｉｖａｌｅｎｃｅｂｅｔｗｅｅｎｃｏｎｔｉｎｕｉｔｙａｎｄｂｏｕｎｄｅｄｎｅｓｓｏｆｔｈｅｌｉｎｅａｒｏｐｅｒａｔｏｒｓｏｎａｇｅｎｅｒａｌｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅ（ｂｒｉｅｆｌｙ,ＰＮｓｐａｃｅ）ｗａｓｄｉｓｃｕｓｓｅｄｕｎｄｅｒｓｏｍｅｈｙｐｏｔｈｅｓｅｓ（［１］,Ｔｈｅｏｒｅｍ２．４）．Ｔｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｄｉｓｃｕｓｓｔｈｅｅｑｕｉｖａｌｅｎｃｅｉｎｔｈｅｍｕｃｈｍｏｒｅｇｅｎｅｒａｌｓｅｔｔｉｎｇｂｙｍｅａｎｓ…     

A Mathod to Solve Systems of Fuzzy Linear Equations

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｗｉｌｌｃｏｎｃｅｒｎｗｉｔｈｓｏｌｖｉｎｇｔｈｅｓｙｓｔｅｍｓｏｆｆｕｚｚｙｌｉｎｅａｒｅｑｕａｔｉｏｎｓＡｘ＝ｂｆｏｒｘ，ｗｈｅｒｅＡｉｓａｍａｔｒｉｘｏｆｆｕｚｚｙｎｕｍｂｅｒｓ；ｘａｎｄｂａｒｅｖｅｃｔｏｒｓｏｆｆｕｚｚｙｎｕｍｂｅｒｓ．Ｉｎ［２］，ｕｓｉｎｇｔｈｅｎｅｗｓｏｌｕｔｉｏｎｃｏｎｃｅｐｔ，ｓｉｘｎｅｗｓｏｌｕｔｉｏｎｓａｒｅｄｅｆｉｎｅｄ．Ｔｈｉｓｄｉｓｃｕｓｓｉｏｎｗａｓｒｅｓｔｒｉｃｔｅｄｔｏｓｑ…     

基于BP网络和RBF网络的模糊系统建模

Ｗｈｅｎａｐｐｌｙｉｎｇａｆｕｚｚｙｃｏｎｔｒｏｌｍｅｔｈｏｄｏｒａｎｉｎｔｅｌｌｉｇｅｎｃｅｃｏｎｔｒｏｌｍｅｔｈｏｄｔｏａｎｅｆｆｅｃｔｉｖｅｃｏｎｔｒｏｌｏｖｅｒａｃｏｍｐｌｅｘｓｙｓｔｅｍ,ｉｔｉｓｓｏｍｅｔｉｍｅｓｎｅｃｅｓｓａｒｙｔｏｉｄｅｎｔｉｆｙｓｙｓｔｅｍａｔｉｃｓｔｒｕｃｔｕｒｅａｎｄｐａｒａｍｅｔｅｒｓ．Ｍａｔｈｅｍａｔｉｃａｌｌｙ,ｉｔｉｓｊｕｓｔｔｈｅｐｒｏｂｌｅｍｓｏｆｕｎｉｖｅｒｓａｌｆｕｎｃｔｉｏｎａｌａｐｐｒｏｘｉｍａｔｉｏｎａｎｄｆｕｎｃｔｉｏｎａｐｐｒｏｘｉ…     

Two Dimensional Submanifolds in Four Manifolds with Boundary

§０．　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒａｃｌｏｓｅｄ４－ｍａｎｉｆｏｌｄ,ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔａｎｙｔｗｏｄｉｍｅｎｓｉｏｎａｌｈｏｍｏｌｏｇｙｃｌａｓｓｃａｎｂｅｒｅｐｒｅｓｅｎｔｅｄｂｙａｎｅｍｂｅｄｄｅｄｓｕｒｆａｃｅ．Ａｆｕｎｄａｍｅｎｔａｌｐｒｏｂｌｅｍｉｎ４－ｄｉｍｅｎｓｉｏｎａｌｔｏｐｏｌｏｇｙｉｓｔｏｆｉｎｄａｓｕｒｆａｃｅｗｉｔｈｍｉｎｉｍａｌｇｅｎｕｓｗｈｉｃｈｒｅｐｒｅｓｅｎｔｓｔｈｅｇｉｖｅｎｈｏｍｏｌｏｇｙｃｌａｓｓ．Ａｓｐｅｃｉａｌｃａｓｅｏｆｔｈｉｓｑ…     

THE TRACE INDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS （III）

§1.ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｈｅｏｒｙｏｆｉｎｔｅｇｒａｂｌｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｏｆｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎｓｈａｓｕｎｄｅｒｇｏｎｅａｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｓｉｎｃｅｔｈｅｌａｔｅ1960’ｓ(ｓｅｅａｓｈｏｒｔｓｕｒｖｅｙｉｎ[1]ａｎｄｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ).ＢｏｔｈｔｈｅｆｉｎｉｔｅａｎｄｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｉｎｔｅｇｒａｂｌｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｈａｖｅｂｒｏａｄａｐｐｌｉｃａｔｉｏｎｓｉｎｖａｒｉｏｕ…     

ON INTERACTION OF SHOCK AND SOUND WAVE （II）

Ｉｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｔｉｎｕｅｏｕｒｄｉｓｃｕｓｓｉｏｎｉｎ[5].Ｍａｉｎｌｙｗｅｗｉｌｌｅｓｔａｂｌｉｓｈａｐｒｉｏｒｉｅｓｔｉｍａｔｅｓｆｏｒｔｈｅｌｉｎｅａｒｉｚｅｄｐｒｏｂｌｅｍ(Ｇ),ａｎｄｔｈｅｎｐｒｏｖｅｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｓｏｌｕｔｉｏｎｔｏｎｏｎｌｉｎｅａｒｐｒｏｂｌｅｍ.Ｉｎ§5ｗｅｇｉｖｅｓｏｍｅｔｅｃｈｎｉｃａｌｐｒｅｐａｒａｔｉｏｎｓ.Ｔｈｅｎｔｈｅｗｈｏｌｅ§6ｉｓｄｅｖｏｔｅｄｔｏｔｈｅｅｓｔａｂｌｉｓｈｍｅｎｔｏｆｅｎｅｒｇｙｅｓｔｉｍａｔｅｓ.Ｉ…     

Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎ [1 ] ,ｔｗｏｏｐｅｒａｔｏｒｃｌａｓｓｅｓｏｆＤ ｎｅａｒｓｕｂｎｏｒｍａｌｏｐｅｒａｔｏｒｓａｎｄｎｅａｒｓｕｂｎｏｒｍａｌｏｐｅｒａｔｏｒｓｗｅｒｅｉｎｔｒｏｄｕｃｅｄ .ＴｈｅｅｌｅｍｅｎｔａｒｙｐｒｏｐｅｒｔｉｅｓｏｆｓｕｃｈｏｐｅｒａｔｏｒｓｗｅｒｅｏｂｔａｉｎｅｄｂｙｕｓｅｏｆｔｈｅＭ Ｐｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅ.Ｍｏｒｅｏｖｅｒ,ａｎｅｗｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｆｏｒａｎｏｐｅｒａｔｏｒｔｏｂｅｓｕｂｎ…     

Forecasting the partisan composition of the house as a function of seniority

This note examines the influence of seniority of the partisan composition of the House of Representatives. A model is developed to compute the re-election probabilities as a function of the levels of seniority. These estimates, together with the composition of the immediately preceding congress, are then used to estimate the composition of any congress and the results compared to the actual electoral outcomes. The end result is a partisan composition or the House independent of the short-term fluctuations created by issues relevant to the individual elections. In addition, measures of accuracy of the estimates are computed in order to assertain how much of the variation in the data is left to be explained by issue-oriented factors.     

Robustness of the controllability for the heat equation under the influence of multiple impulses and delays

For many control systems in real life, impulses and delays are intrinsic properties that do not modify their behavior. Thus, we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system, that could model a real situation, do not modify properties such as controllability. In this regard, we prove the approximate controllability of the semilinear heat equation under the influence of multiple impulses and delays, this is done by using new techniques, avoiding fixed point theorems, employed by A.E. Bashirov et al.     

Field theory for the function field of the quintic fermat curve

We study the structure of the function field K of the quintic Fermat curve F(5) in the following way: Let K m be a g-maximal rational subfield of K. Then the field extension K/K _m is obtained by the projection from F(5) to a line with a center p, ∈ F(5). By using this fact, we consider the field extension K/K m from several point of view.     

On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation

Summary Brakhage and Werner, Leis and Panich suggested to reduce the exterior Dirichlet boundary value problem for the Helmholtz equation to an integral equation of the second kind which is uniquely solvable for all frequencies by seeking the solution in the form of a combined double- and single-layer potential. We present an analysis of the appropriate choice of the parameter coupling the double- and single-layer potential in order to minimize the condition number of the integral operator.This research was carried out while the second author was visiting the University of Göttingen on a DAAD-stipendium     

On the Davis-Kahan-Weinberger solution of the norm-preserving dilation problem

Summary This recently published solution of a problem which has found application in several different areas represents a major contribution to the dilation theory of contractions in Hilbert, spaces. For finite-dimensional dilations, which is the case in typical applications to numerical analysis, the general solution can be reduced to pure matrix results. Our main purpose here is to present a simplified approach to this particularly significant case, by relying on some basic tools of matrix theory.Presented at the International Conference on Numerical Analysis, on the Occasion of the 25th Anniversary of the founding of Numerische Mathematik, March 19–21, 1984, at the Technische Universität Munich     

Holder Zygmund Space Techniques to the Navier-Stokes Equations in the Whole Spaces

With the use of Hölder Zygmund space techniques, local regular solutions to the Navier-Stokes equations in R^n are shown to exist when the initial data are in the space {a|(-Δ)^{-β/2}a ∈ C^0(R^n)^n}\quad(0 < β < 1)     

Spectral approximation of the periodic-nonperiodic Navier-Stokes equations

Summary In order to approximate the Navier-Stokes equations with periodic boundary conditions in two directions and a no-slip boundary condition in the third direction by spectral methods, we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure. The compatibility between these two spaces is checked via an infsup condition. We analyze a spectral and a collocation pseudo-spectral method for the Stokes problem and a collocation pseudo-spectral method for the Navier-Stokes equations. We derive error bounds of spectral type, i.e. which behave likeM ^– whereM depends on the number of degrees of freedom of the method and represents the regularity of the data.     

On the congruence modularity conjecture

A new condition of compatibility with projections, applicable to some Maltsev filters, is defined and shown to hold, among others, for the filter of congruence-modular varieties. As a consequence, it is shown that there exist no simple counterexamples (in a specified sense) to the modularity conjecture. This paper is dedicated to Walter Taylor. Received November 5, 2005; accepted in final form April 3, 2006.     

Computing the CS and the generalized singular value decompositions

Summary If the columns of a matrix are orthonormal and it is partitioned into a 2-by-1 block matrix, then the singular value decompositions of the blocks are related. This is the essence of the CS decomposition. The computation of these related SVD's requires some care. Stewart has given an algorithm that uses the LINPACK SVD algorithm together with a Jacobitype clean-up operation on a cross-product matrix. Our technique is equally stable and fast but avoids the cross product matrix. The simplicity of our technique makes it more amenable to parallel computation on systolic-type computer architectures. These developments are of interest because a good way to compute the generalized singular value decomposition of a matrix pair (A, B) is to compute the CS decomposition of a certain orthogonal column matrix related toA andB.The research associated with this paper was partially supported by the Office of Naval Research contract N00014-83-K-0640, USA     

On the solution a of second order singularly-perturbed boundary value problem by the Sinc-Galerkin method

Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the Sinc-Galerkin method for solving second order singularly perturbed boundary value problems. The method is then tested on linear and nonlinear examples and a comparison with spline method and finite element scheme is made. It is shown that the Sinc-Galerkin method yields better results.Received: January 3, 2003; revised: July 14, 2003