多元盘Bergman空间上可逆的Toeplitz算子乘积

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

强乘积图的最小强半径（英文）

A strong product graph is denoted by G₁?G₂,where G₁ and G₂ are called its factor graphs.This paper gives the range of the minimum strong radius of the strong product graph.And using the relationship between the cartesian product graph G₁ ×G₂ and the strong product graph G₁?G₂,another different upper bound of the minimum strong radius of the strong product graph is given.     

SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cⁿ with some restricted conditions.We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of Cⁿ with an arbitrary norm and the unit polydisk in Cⁿ under certain restricted assumptions.Finally we ...     

Toeplitz Products on Bergman–Sobolev Spaces over the Unit Polydisk

In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman–Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.     

The Martingale Hardy Type Inequalities for Dyadic Derivative and Integral

Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.     

Sharp Distortion Theorems for a Subclass of Biholomorphic Mappings Which Have a Parametric Representation in Several Complex Variables

In this paper, the sharp distortion theorems of the Fr′echet-derivative type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball of complex Banach spaces are established, and the corresponding results of the above generalized mappings on the unit polydisk in C~n are also given. Meanwhile, the sharp distortion theorems of the Jacobi determinant type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball with an arbitrary norm in C~n are obtained, and the corresponding results of the above generalized mappings on the unit polydisk in C~n are got as well. Thus, some known results in prior literatures are generalized.     

Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.     

Classification of Hardy Submodules and Characteristic Space Theory（A Brief and Selective Survey）

This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules.     

Fekete and Szeg problem in one and higher dimensions

In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C~n.     

Commuting of Toeplitz Operators in Several Complex Variables

1 IntroductionLet be the unit ball Bn or the polydisk Dn in Cn, and dA denote the Lebesgue measure on , normalized so that the measure of equals 1. L2/a() is The Bergman space. For z, the Bergman reproducing kernel is a function Kz L2/a). The normalized Bergman reproducing kernel k is the function Kz Kz2. Here, as elsewhere in this paper, the norm 2 and the inner product are taken in the space L2(,dA).Let P denote the orthogonal projection of L2(, dA) onto L2/a(). For a function f L …     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the dependence of the growth rate on the length of the defining relator

Let { } be a sequence of finitely presented groups with generating setA={a1, …, am}, and letRk be the symmetrized set of words over the alphabetA∪A−1 obtained from the defining words and their inverses by all cyclic shifts. We shall assume that the words inRk are cyclically irreducible, and their lengths tend to ∞ ask increases. In the paper, it is proved that ifRk satisfies the small cancellation conditionC'(1/6) and the number of relators increases not very rapidly with increasingk, then the growth rate ψ(Gk) tends to 2m−1 ask→∞. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 611–617, April, 1999.     

On the stability of the solution of the thermistor problem

The stability of the stationary solution of the thermistor problem 1s proved using a Liapunov functional for a class of physically relevant electrical conductivity.     

On the Decomposition of the Riesz Operator and the Expansion of the Riesz Semigroup

For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues denote by E(λ_i; T) the eigen-projection corresponding to an eigenvalue λ_i. In this paper we will show that if the operator sequence is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T_p and T_r: T = T_p + T_r, where T_p is the weak limit of T_n and T_r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body.     

一般正则泛函的W-极小的正则性

本文讨论了一般的正则泛函：Ｆ（ｕ；Ω）＝∫_{Ωｆ（ｘ，ｕ，Ｄｕ）ｄｘ的局部Ｗ－极小的Ｃ^１，α正则性．获得了处理Ｗ－极小ｕ的Ｈ?ｌｄｅｒ连续的指数估计．}     

On the relation between the A-polynomial and the Jones polynomial

This paper shows that the noncommutative generalization of the A-polynomial of a knot, defined using Kauffman bracket skein modules, together with finitely many colored Jones polynomials, determines the remaining colored Jones polynomials of the knot. It also shows that under certain conditions, satisfied for example by the unknot and the trefoil knot, the noncommutative generalization of the A-polynomial determines all colored Jones polynomials of the knot.

     

On the approximation of positive operators and the behaviour of the spectra of the approximants

LetT be a positive linear operator on the Banach latticeE and let (S _n ) be a sequence of bounded linear operators onE which converge strongly toT. Our main results are concerned with the question under which additional assumptions onS _n andT the peripheral spectra (S _n ) ofS _n converge to the peripheral spectrum (T) ofT. We are able to treat even the more general case of discretely convergent sequences of operators.     

宏观因素影响下的系统中元件重要性研究

为研究复杂系统在工作环境中其组成元件对系统安全运行的重要性,将汪培庄先生的因素空间理论与笔者提出的空间事故树理论相结合,构造了一套元件重要性研究方法.构建系统T={U,C,D},将元件作为研究对象集合U,系统工作的宏观环境作为因素集C,元件重要性排序集作为D.对宏观环境中的工作时间a1和温度a_2进行划分形成不同的状态区域S_q,计算在S_q中元件xj的失效权重γ(AS_q(x_j))和在S_q中系统T的失效权重δ(AS_q(T))),从而得到x_j在S状态下的等效失效权重Z(AS_q(x_j)),研究状态S_q下的原件重要性排序D_η,及元件x_j失效性对a_1及a_2的敏感性.使用一个实际的电气系统维修情况统计资料,使用上述方法进行了研究,结果表明:不同工作环境下元件对系统的重要程度是不同的.元件对温度和使用时间是敏感的,并得到了在10³0°且5030°且50⁷5d环境下工作系统可靠性是最高的结论.在给定工作环境下,重要性大的元件多储备,重要性小的元件少储备,以满足系统维修需要,并指导实际工程.     

关于循环子半群的结构与数量问题及拟环的特征与结构

彻底解决了所有循环半群及其子群的结构和数量问题,并讨论了拟群分解问题,同时,对群论基本定理作了部分推广,并给出了定理的另一部分不可推广的反例,最后,建立了一类特殊环－拟环。