Operators on the orthogonal complement of the Dirichlet space(Ⅱ)

In this paper we first prove that a dual Hankel operator R φ on the orthogonal complement of the Dirichlet space is compact for φ∈ W 1,∞(D),and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact.We also prove that a dual Hankel operator R φ with φ∈ W 1,∞(D) is of finite rank if and only if B φ is orthogonal to the Dirichlet space for some finite Blaschke product B,and give ...     

HANKEL OPERATORS ON HARDY SPACES AND SCHATTEN CLASSES

For a holomorphic function f on the unit ball B~N of C~N, it is proved that the reduced Hankel oporator R_f on Hardy space H~2(B~N) is of Schatten class S_p for p≥1 if and only if f is in a corresponding Sobolev space.     

Schatten p -class Toeplitz operators with unbounded symbols on pluriharmonic Bergman space

In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman space h2（Bn, dA） for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols.     

Dual Toeplitz operators on the sphere

Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in Cn . In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.     

Operators on Differential Form Spaces for Riemann Surfaces

In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator Cp is Predholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the Toeplitz operators on ∧1 2, a（M） for Riemann surface M are defined and some properties of these operators are discussed.     

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H²(D) and the Fock space g².The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.     

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H²(D) and the Fock space g².The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.     

Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.     

单位球加权Bergman空间上的Berezin变换与径向算子（英文）

In this paper, we analyze a class of bounded radial operators on the weighted Bergman space A2α(Bn, d Vα), we get that these kinds of operators are diagonal with respect to the standard orthonomal basis. We also investigate the connection between compactness of operators and the boundary behaviour of the corresponding Berezin transform. We further study a special class of radial operators, i.e., Toeplitz operators with a radial L1 symbol.     

Mean Oscillation and Hankel Operators on Fock-type Spaces

For 1 ≤ p ∞ we introduce a notion of “p-mean oscillation” on Cnin terms of the metric induced by reproducing kernel of F_Ψ~2. It is shown that the densely-defined Hankel operators ■ are simultaneously bounded if and only if f is of bounded “p-mean oscillation”.Furthermore, it is also shown that the densely-defined Hankel operators ■ are simultaneously compact if and only if f is of vanishing “p-mean oscillation”. Here the weight Ψ is a positive function of logarithmic growth satisfying certain suitable conditions.     

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.     

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 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 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.

     

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 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.     

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。     

一类树并的补图的色唯一性

彻底解决了一类不可约树并的补图是色唯一的 ,并得到了一些图的伴随多项式的最小根的重要规律 .