The Roper-Suffridge extension operator and classes of biholomorphic mappings

In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs) and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

On the equivalence of a theorem of Kisynski and the Hille-Yosida generation theorem

We show that a theorem of Kisynski on the generation of Banach-algebra homomorphisms of certain convolution algebras is equivalent to the Hille-Yosida theorem on the generation of operator-valued one-parameter semigroups.

     

On the complexity of the approximate table representation of discrete analogs of functions of finite smoothness in the metric ofL P

For discrete analogs of classes of functions of finite smoothness, we study the quantity log Approx characterizing the minimal necessary length of tables that allow us to reconstruct functions from these classes with error not exceeding 1 in the metric of the spaceL ^p . Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 643–647, November, 1998. The author wishes to express his gratitude to his scientific adviser O. B. Lupanov for setting the problem and attention to the author's work. This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01068.     

关于G－分次环与G－集的Smash积的几个结果

设Ｇ为任意群，本文借助于环的矩阵表示给出了Ｇ－分次环与任意可迁Ｇ－集的Ｓｍａｓｈ积是素环或单环的刻画。     

因素空间理论与知识表示的数学框架（X）——基于因素空间的神经元模型

本文是文［１—９］的继续，该文及后续论文仍将系统地研究因素空间理论及其在知识表示中的应用。该文研究基于因素空间的神经元模型：首先讨论了因素空间的神经元机理，然后讨论了几种典型的神经元模型；特别提出了基于Ｗｅｂｅｒ—Ｆｅｃｈｎｅｒ法则的神经元模型以及基于变权的神经元模型。     

主轴内蕴法与高维张量方程AX—XA=C^＊

本文将主轴内蕴法推广到高维空间，并讨论了高维张量方程ＡＸ—ＸＡ＝Ｃ的解．     

Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models

We construct hierarchies of commutative Poisson subalgebras for Sklyanin brackets. Each of the subalgebras is generated by a complete set of integrals in involution. Some new integrable systems and schemes for separation of variables for them are elaborated using various well-known representations of the brackets. The constructed models include deformations for the Goryachev–Chaplygin top, the Toda chain, and the Heisenberg model.     

Simple Coherent State and New Form for Inhomogeneous Differential Realization of OSP(2,1) Superalgebra

The simple coherent state of the OSP(2,1) superalgebra is constructed and its properties are discussed in detail. The matrix elements of the OSP(2,1) generators in the coherent state space are calculated. The new form for inhomogeneous differential realization of the OSP(2,1) superalgebra is given.     

BAYESIAN ANALYSIS, LIKELIHOOD RATIO AND INFORMATION

ＢＡＹＥＳＩＡＮＡＮＡＬＹＳＩＳ，ＬＩＫＥＬＩＨＯＯＤＲＡＴＩＯＡＮＤＩＮＦＯＲＭＡＴＩＯＮ￥ＺＨＡＮＧＹＡＯＴＩＮＧＡＮＤＤＵＪＩＮＧＳＯＮＧＡｂｓｔｒａｃｔ：Ｗｅｐｒｅｓｅｎｔａｎｅｗｓｃｈｅｍｅｆｏｒｕｎｃｅｒｔａｉｎｒｅａｓｏｎｉｎｇｂａｓｅ...     

图形显示中的几何变换

本文主要获得了以下结果：（ｉ）透视仿射映射的矩阵表示；（２）透视仿射变换的矩阵表示；（３）一般仿射映射的几何中实现及矩阵表示；（４）一般仿射变换的几何实现及矩阵表示。