多圆柱上Bloch型空间之间加权复合算子的本性范数

设φ(z)=(φ1(z),…,φ_n(z))是D~n到自身的一个全纯映射,ψ(z)是D~n上的全纯函数,其中D~n是C~n中的单位多圆柱.研究了单位多圆柱上Bloch型空阊之间的加权复合算子ψC_φ的本性范数,并给出了其上下界估计.     

Uncomplemented subspaces of Lorentz spaces

In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α) for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000.     

A note on solving Cauchy integral equations of the first kind by iterations

The successive approximation method was applied for the first time by N.I. Ioakimidis to solve practical cases of a Cauchy singular integral equation: the airfoil one. In this paper we study a more general case. We prove the convergence of the method in this general case. The proposed method has been tested for two kernels which are particularly important in practice. Finally, some numerical examples illustrate the accuracy of the method.     

Block-Projections Algorithms with Blocks Containing Mutually Orthogonal Rows and Columns

In this paper we present an algorithm which, for a given (sparse) matrix, constructs a partition of its set of row-indices, such that each subset of this partition (except the last one obtained) contains indices which correspond to mutually orthogonal rows. We then use such decompositions in some classes of block-projections methods, previously extended by the author to general inconsistent linear least-squares problems. Numerical experiments on an inconsistent and rank-deficient least-squares model problem are described in the last section of the paper.     

Block plan for a fractional 2 m factorial design derived from a 2 r factorial design

Summary For a given fractional 2 ^m factorial (2 ^m -FF) designT, the constitution of a block plan to divideT intok (2 ^r−1<k≦2 ^r ) blocks withr block factors each at two levels is proposed and investigated. The well-known three norms of the confounding matrix are used as measures for determining a “good” block plan. Some theorems concerning the constitution of a block plan are derived for a 2 ^m -FF design of odd or even resolution. Two norms which may be preferred over the other norm are slightly modified. For each value ofN assemblies with 11≦N≦26, optimum block plans fork=2 blocks with block sizes [N/2] andN−[N/2] minimizing the two norms are presented forA-optimal balanced 2⁴-FF designs of resolutionV given by Srivastava and Chopra (Technometrics,13, 257–269).     

Corrigendum to “On norms of composition operators acting on Bergman spaces” [J. Math. Anal. Appl. 291 (2004) 189-202]

A theorem and a corollary in the paper cited in the title were stated incorrectly, as was pointed out by Christopher Hammond. We now state correctly and prove both of them. These results still generalize and explain the geometric meaning of the Cowen-Hurst norm formula. We also include additional references and provide an example relevant for further study.     

Control of Stochastic Systems with Time-Varying Multiple Time Delays: LMI Approach

This paper deals with the class of continuous-time linear systems with Markovian jumps and multiple time delays. The systems that we are treating are assumed to have time-varying delays in their dynamics which can be different and also have uncertainties in the system parameters. The time-varying structure of the bounded uncertainties is considered. Delay-dependent conditions for stochastic stability and stochastic stabilizability and their robustness are considered. A design algorithm for a stabilizing memoryless controller is proposed. All the results are given in the LMI formalism.     

矩阵方程AXAT=C的对称斜反对称解

设A∈Rm×n,C∈Rm×m给定,利用矩阵的广义奇异值分解和对称斜反对称矩阵的性质,得到了矩阵方程(1)AXAT=C存在对称斜反对称解的充要条件和通解表达式;证明了若方程(1)有解,则一定存在唯一极小范数解,并给出了极小范数解的具体表达式和求解步骤.