THE MULTI-PARAMETERS OVERRELAXATION METHOD

1.IntroductionRecently,manymathematicalliteratureshaveprovidedsomenewiterativemeth-odsforsolvingthelinearsystem.Kuang[2]presentedatwo-parameteriterativemethodcalledTORmethod,whichiseffectivetogivethenumericalsolutionofpartialdif-ferentialequations.Wang[,']extendedtheTORmethodtotheGTORmethedandimprovessomeresultsof[3,11,12].In[5],LialsodiscussedtheGTORmethod,andextendedthecorrespondingresultsof[10,11].Recently3SongandDai[9]presentedthemulti-parametersoverrelaxation(MPOR)method,whosespe…     

Théorèmes de Perron-Frobenius et Stein-Rosenberg booléens

The eigenelements of a Boolean matrix are defined. A “normal form” is given, which allows one to characterize those Boolean matrices the (Boolean) spectral radius of which is 0 or 1. Then the following results are proved: a Boolean Perron-Frobenius theorem, a “Truncated” Boolean Stein-Rosenberg theorem, and a Boolean Stein-Rosenberg theorem, which are the exact Boolean analoques of the usual corresponding theorems concerning real nonnegative matrices. Applications of these results are given elsewhere.     

Autour du théorème de Stein-Rosenberg

Summary The aim of this note is to present a synthesis of recent applications or extensions of the Stein-Rosenberg theorem on nonnegative matrices: convergence ofnon linear iterative process; truncated, or chaotic, or boolean Stein-Rosenberg theorems.The conclusion is the following: As it works through various mathematical contexts, the Stein-Rosenberg theorem expersses a rather deap idea of an essentially algorithmic nature.     

AOR迭代法的收敛性

1.引言 [1]定义了解线性方程组A_x=b的AOR迭代法,它以SOR迭代为特例,而且适当选取参数,有可能比SOR方法收敛快(见[2]).众所周知,使 AOR方法有意义的最基本条件是A的对角元素都不为零.然而,在实际计算中,有时需要求解的线性方程组其系数矩阵存在零对角元素.例如[3]中研究的线性方程组的系数矩阵具有如下形式:     

KKM property and fixed point theorems in metric spaces

In this paper, first part, we establish some fixed point theorems for a k-set contraction map on the nearly-subadmissible subsets of a complete metric space. The second part, we deduce a generalization of the approximate fixed point theorem for the lower semicontinuous mappings on a metric space.     

Systems of equilibrium problems with applications to new variants of Ekeland’s variational principle,fixed point theorems and parametric optimization problems

In this paper, we first establish some existence theorems of systems of generalized vector equilibrium problems. From these results, we obtain new variants of Ekeland’s variational principle in a Hausdorff t.v.s., a minimax theorem and minimization theorems. Some applications to the existence theorem of systems of semi-infinite problem, a variant of flower petal theorem and a generalization of Schauder’s fixed point theorem are also given.     

Separating sets with relative interior in Fréchet spaces

A separation theorem, valid in infinite dimensional spaces, and involving the relative interior of the sets to be separated, will be extended to Fréchet spaces. This theorem will be elucidated by means of a few examples. The second separation theorem is a generalization of an existing separation theorem, valid in Fréchet spaces. This paper consists of two parts: part I contains the first theorem, the second part contains the second generalization.     

SMOOTHING EFFECTS OF DISPERSIVE PSEUDODIFFERENTIAL EQUATIONS

ABSTRACT

We discuss smoothing effects of dispersive-type pseudodifferential equations whose principal part is not necessarily elliptic. For equations with constant coefficients, a restriction theorem and a smoothing estimate of the resolvent of the principal part obtain smoothing estimates of solutions in weighted Lebesgue spaces. Moreover, we discuss well-posedness of the initial value problem and an alternative approach to the smoothing effects of general dispersive equations with variable coefficients via pseudodifferential calculus. Our results are the natural generalization of smoothing effects of Schrödinger-type equations.     

A Generalization of a theorem of chang

Szigeti, Tuza and Révész have developed a method in [6] to obtain polynomial identities for the n×n matrix ring over a commutative ring starting from directed Eulerian graphs. These polynomials are called Euler-ian. In the first part of this paper we show some polynomials that are in the T-ideal generated by a certain set of Eulerian polynomials, hence we get some identities of the n×n matrices. This result is a generalization of a theorem of Chang [l]. After that, using this theorem, we show that any Eulerian identity arising from a graph which lias d-fold multiple edges follows from the standard identity of degree d     

Monge–Ampère measures on pluripolar sets

In this article we solve the complex Monge–Ampère problem for measures with large singular part. This result generalizes classical results by Demailly, Lelong and Lempert a.o., who considered singular parts carried on discrete sets. By using our result we obtain a generalization of Ko?odziej's subsolution theorem. More precisely, we prove that if a non-negative Borel measure is dominated by a complex Monge–Ampère measure, then it is a complex Monge–Ampère measure.     

A note on log etale Čech cohomolog

In this paper, we prove the comparison theorem between log etale cohomology and log etale Čech cohomology for certain log schemes, which is a generalization of a result of Artin on the comparison theorem between etale cohomology and etale Čech cohomology. It turns out that the naive generalization is not true, and we also give a counter-example for it. Received: 2 July 2000 / Revised version: 4 September 2000     

Cartan's conjecture with moving targets of same growth and effective Wirsing's theorem over function fields

We formulate a generalization of the Cartan's theorem and the Cartan's conjecture over function fields in the case where the coefficients of the linear forms can be nonconstant functions. This generalization is used to prove the Wirsing's theorem over function fields. Furthermore, the methods we use here provide effective results. Received September 4, 1998; in final form April 23, 1999 / Published online May 8, 2000     

On some riesz bases

In this paper we consider three problems concerning systems of vector exponentials. In the first part we prove a conjecture of V. Komornik raised in [14] on the independence of the movement of a rectangular membrane in different points. It was independently proved by M. Horváth [9] and S. A. Avdonin (personal communication). The analogous problem for the circular membrane was partly solved in [3] — the complete solution is given in [10]. In the second part we fill in a gap in the theory of Blaschke-Potapov products developed in the paper [19] of Potapov. Namely we prove that the Blaschke-Potapov product is determined by its kernel sets up to a multiplicative constant matrix. In the third part of the present paper we give a multidimensional generalization of the notion of sine type function developed by Levin [16], [17] and by our generalization we prove the multidimensional variant of the Levin-Golovin basis theorem [16], [6].     

On collinear Griffiths points

J. Tabov has proved [1] that four Griffiths points are collinear if the vertices of a given quadrangle are on a circle. In this article we prove some generalization of this result in a very simple geometrical way (based on Desargues theorem). Received 9 July 1999; revised 13 December 1999.     

A fractional version of the peano-sard theorem

Sard's classical generalization of the Peano kernel theorem provides an extremely useful method for expressing and calculating sharp bounds for approximation errors. The error is expressed in terms of a derivative of the underlying function. However, we can apply the theorem only if the approximation is exact on a certain set of polynomials.

In this paper, we extend the Peano-Sard theorem to the case that the approximation is exact for a class of generalized polynomials (with non-integer exponents). As a result, we obtain an expression for the remainder in terms of a fractional derivative of the function under consideration. This expression permits us to give sharp error bounds as in the classical situation. An application of our results to the classical functional (vanishing on polynomials) gives error bounds of a new type involving weighted Sobolev-type spaces. In this way, we may state estimates for functions with weaker smoothness properties than usual.

The standard version of the Peano-Sard theory is contained in our results as a special case.     

Viscosity approximation methods for resolvents of accretive operators in Banach spaces

In this paper, we first prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method, which is a generalization of the results of Reich [J. Math. Anal. Appl. 75 (1980), 287–292], and Takahashi and Ueda [J. Math. Anal. Appl. 104 (1984), 546–553]. Further using this result, we consider the proximal point algorithm in a Banach space by the viscosity approximation method, and obtain a strong convergence theorem which is a generalization of the result of Kamimura and Takahashi [Set-Valued Anal. 8 (2000), 361–374]. Dedicated to the memory of Jean Leray     

On the computation of inclusion regions for partitioned matrices

In this paper, we consider the problem of computing inclusion regions for the eigenvalues of a partitioned matrix. The algorithms derived are special cases of a generalization of a result of Feingold and Varga which, in turn, is a generalization to the partitioned case of the well-known Gerschgorin circle theorem.This research was sponsored in part by the National Research Council of Canada.     

Generalizations of a theorem of Rolewicz

The aim of this article is to give a unified treatment for the theorems of Rolewicz and Neerven type for uniform exponential stability of evolution families. We obtain necessary and sufficient conditions for uniform exponential stability of evolution families, generalizing a stability theorem due to Rolewicz and we present a new proof for the Rolewicz theorem, based on the theory of Banach function spaces. Finally, we apply our results and we deduce a generalization for a classical stability theorem due to Przyluski and Rolewicz.     

A Tree Version of Kőnig's Theorem

Kőnig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalization, in which the point in one fixed side of the graph of each edge is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell [2]. As an application we prove a special case (that of chordal graphs) of a conjecture of B. Reed. Received January 27, 2000/Revised November 2, 2000 RID=" " ID=" " The research of the first author was supported by grants from the Israel Science Foundation, the M. & M.L Bank Mathematics Research Fund and the fund for the promotion of research at the Technion.     

某些广义迭代法的Stein－Rosenberg型定理与比较定理

某些广义迭代法的Ｓｔｅｉｎ－Ｒｏｓｅｎｂｅｒｇ型定理与比较定理王新民（中国金融学院）ＳＴＥＩＷ－ＲＯＳＥＮＢＥＲＧＴＹＰＥＴＨＥＯＲＳＭＳＡＮＤＣＯＭＭＭＳＯＮＴＨＥＯＲＥＭＳＦＯＲＳＯＭＥＧＥＮＥＲＡＬＩＺＥＤＩＴＥＲＡＩＶＥＭＥＴＨＯＤＳ￥Ｗａｎ...