算子函数

In chapter 1, firstly, by using classical analysis methods, such as the introduction of Bessel function and semigroup theory, we transform the pseudo-parabolic equation into an abstract operator equation and achieve the existence and uniqueness of the local solution.

在第一章中，利用经典的分析方法，引入Bessel势函数，将伪抛物型方程转化为抽象算子方程，首先，利用算子半群理论，论证了局部解的存在唯一性。

An sufficient and necessary condition on generalized Nevanlinna counting functions of the inducing maps is shown to characterize the collective compactness of composition operator sequence.

我们用诱导映射的Nevanlinna计数函数给出了Hardy空间与加权Bergman空间之间的复合算子序列为总体紧算子序列的一个充分必要条件。

On the basis of general Krawczyk-Hansen Operator, the interval iteration of the constrained functions are established; the interval extension of maximum entropy function is discussed; convergence is proved; region deletion rules are supplied and the algorithm of interval maximum entropy has been set up.

利用极大熵函数和罚函数将问题转化为无约束可微优化问题，借助广义Krawczyk-Hansen算子建立了约束函数的区间迭代；讨论了极大熵函数和罚函数的区间扩张，证明了收敛性等性质，给出了无解区域删除原则，建立了区间极大熵算法。

In the third chapter, we study the approximation and weighted approximation for a kind of generalized Baskakov operators of two-variable. Using different weight functions, we discuss the convergence on weighted space of polynomials and rate of convergence with Jacobi weight for this kind of two-dimensional product-type operators, which extends the results of one-dimensional operators.

第三章研究一类二元广义Baskakov算子的逼近及其加权逼近，主要针对于不同的权函数讨论了这类乘积型的二元算子及其导数在多项式权空间上的收敛性和加Jacobi权的收敛阶，把一元的结果推广到多元的情形。

In this paper, a mathematical description of mutation operator and a concept of mutation function for the study of evolutionary programming and evolution strategies are proposed, and several methods and examples of constructing mutation operator with uniformly distributed random variables are presented.

进化算法是研究全局优化算法中最重要的随机算法之一，本文给出了进化规划和进化策略的变异算子的数学描述，并提出变异函数的概念，在此基础上，给出了用均匀分布的随机数构造变异算子的几种方法和若干例子。

Moreover, we present a lattice path interpretation of the isobaric divided difference operators, and derive an expression for the flagged Schur function in terms of isobaric operators acting on a monomial.

并且，我们提供了齐次差分算子的一个格路径解释，从而证明了每一个带标志的Schur函数可以通过作用齐次算子序列在某个单项式上得到。

The paper proves that the search process of the non-crossover genetic algorithm is an ergodic homogeneous Markov Chain. The proof of global convergence of NCGA is presented is this paper. The upper bound of convergence speed of the NCGA is the same as the CGA. The possibly of retain the promising genes of NCGA is larger than CGA.

对于本人可以找到的32种典型的非线性优化测试函数，应用无交叉算子遗传算法，与基于经典遗传算法相比，在相同的进化代数的条件下，NCGA同样取得了略优的收敛速度，在相同CPU计算时间上NCGA也取得略优的结果； 3 提出了复合算子遗传算法。

For a normal operator, we express its numerical range interms of the function in its multiplication operator representation.

针对规范算子的部份，我们将数值域以乘积算子的表现函数来表示。

For a normal operator, we express its numerical range in terms of the function in its multiplication operator representation.

针对规范算子的部份，我们将数值域以乘积算子的表现函数来表示。

In the third part we investigate a kind of two-dimensional non-product-type operators on continuous function space and some important properties and a locally inverse theorem are obtained.

其中第三节在连续函数空间上研究这类非乘积型二元算子，讨论了该算子的一些重要性质，给出局部意义下的一个逆定理。

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。