算出

We discussthe propertiesofthe adjoint operator of unilateral weightedshift,prove that is astrongly irreducible Cowen- Douglas operator, and compute the 0 group of the commutant algebra of .

计算了代数я={f：f在开圆D盘上解析，在■上连续}的K_0群，讨论了内射单边加权移位算子的伴随算子的性质，证明了是强不可约的Cowen-Douglas算子，然后计算出的换位代数的K_0群

Different from the scattering theory used in the derivation of conventional generalized screen propagator, in this paper, a high order formula of generalized screen propagator for oneway wave equation is proposed by using the asymptotic expansion of singlesquareroot operator.

不同于常规广义屏传播算子的推导中使用散射理论，本文利用单平方根算子的渐近展开，推导出了单程波方程广义屏传播算子的高阶表达式。

In the third chapter, we obtain the average errors(asymptotic order or weakly asymptotic order) of the Lagrange interpolation sequence, the Hermite-Fejer interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes on the 1-fold integrated Wiener space.

第三章分别给出了基于第一类Chebyshev多项式零点的Lagrange插值算子列、Hermite-Fejer插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差的值。

Firstly, a new two-tuples hybrid weighted averaging operator based on uncertain information processing is proposed. Properties of the operator are also analyzed. A method for group decision making with linguistic information based on T-HWA operator is presented.

首先提出了一种基于不确定信息处理的二元语义混合加权平均算子，并对该算子的性质进行了分析，然后给出了一种基于T-HWA算子的语言群决策方法。

In the bounded linear operator approximation theory of Hilbert Space,the isolate point of operator essential spectrum is always a problem. In this paper,a general method to treat this problem is given.

孙辉在Hilbert空间线性算子逼近论中，算子本质谱的孤立点通常是处理一些问题的主要障碍之一，本文给出处理算子本质谱的孤立点的一般方法。

We will prove that the only compact dual Toeplitz operator is the zero operator, and that a densely defined dual Toeplitz operator with square integrable symbol is bounded if and only if its symbol is essentially bounded.

首先，我们证明了只有零算子是紧的对偶Toeplitz算子，同时给出了以平方可积函数为符号稠定义的对偶Toeplitz算子有界当且仅当它的符号函数是本性有界的。

In the section, the definitions and main properties of the operator have been discussed systematically, the operational rules of one dimensional PGOPO have been strictly established based on the theory of convergence in the mean square, error and convergence analysis of approximation by PGOPO has been discussed.

系统地论述了分段广义正交多项式算子的定义、性质，并为一维PGOPO算子严格地建立一套在均方收敛意义下的代数运算规则，给出了分段广义正交多项式算子作用下的误差及收敛性分析结果。

Chapter 4 presents detailed analysis of Whitney-type hexahedron and prism using differential form.

第2章介绍微分形式中几个常用典型算子的性质，包括微分算子、外积和Hodge星算子；给出了微分形式对电磁学物理量的分类及Maxwell方程的微分形式。

It is proved that if the optimal solution tree has an inter-node, the necessary and sufficient condition that tree structure GAs are solution foundable is that the initial population contains an inter-node; the upper limit of solution foundable probability is also calculated and the population size is proved to increase at most in a polynomial of increasing problem complexity and the probability upper limit.

本文接着给出了当初始群体随机产生，只有杂交算符作用或只有复制与杂交算符作用的遗传算法有解的充要条件，并加以证明；而且求出了这时有解的概率上限，并证明群体大小的增加不超过问题复杂性和有解概率上限的某个多项式。

Supposing that one thousand Families in this City, would be constant Customers for Infants Flesh, besides others who might have it at Merry-meetings, particularly at Weddings and Christenings, I compute that Dublin would take off Annually about twenty thousand Carcasses, and the rest of the Kingdom (where probably they will be Sold somewhat Cheaper) the remaining eighty thousand.

假如我们城市的那一千个家庭都成为幼儿肉的长期消费者，不算那些在欢庆会——尤其是在婚宴和洗礼会上的，我算得都柏林每年将卖出两千具童尸，王国的其他地方(那些地方也许会卖得便宜一点)可以卖出余下的八千。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。