查询词典 operator function

From our results, it can be known that the weakly asymptotic order of the information-based algorithm whose recover function is the classical Bernstein interpolation sequence is below that of the corresponding minimal information radius whose permissible information operator is function value.

通过我们的结果可以知道，以经典的Bernstein多项式算子列作为计算恢复函数的信息基算法，其在Wiener空间(或1-重积分Wiener空间)下的的平均误差的弱渐近阶均低于相应的以函数值计算为可允许信息算子的最小平均信息半径的弱渐近阶。

We utilize the intuitionistic fuzzy weighted arithmetric averaging operator to aggregate the intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one according to the score function and accuracy function.

然后对权重信息不完全的直觉模糊数的多属性决策方法进行了研究，基于正理想方案和算子，给出了一个具有最小偏差的目标规划模型，从而获得相应的属性权重，基于IFWAA算子对直觉模糊信息进行集结，进而根据得分函数和精确函数对方案进行排序。

We utilize the interval-valued intuitionistic fuzzy weighted arithmetic averaging operator to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one according to the score function and accuracy function.

然后对权重信息未知的区间直觉模糊数的多属性决策方法进行了研究，给出了一个基于最大偏差的目标规划模型，从而获得相应的属性权重，基于IIWAA算子对区间直觉模糊数信息进行集结，进而根据得分函数和精确函数对方案进行排序。

Firstly, we get the necessary and sufficient conditions for Toeplitz operators that commutes with another such operator whose symbol is a monomial, meanwhile, we completely characterize when the mellin transform of the bounded function on the interval 0,1 is a rational function.

首先得到了以有界函数为符号的Toeplitz算子和以单项式函数为符号的Toeplitz算子可交换的充要条件，同时给出了0，1区间上的有界函数的Mellin变换为有理函数的充要条件。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

Three methods for the computation of the isotropic tensor function,spectral decomposition method,eigenprojection operator method and representation theorem method,are compared.Different approaches to calculate the eigenvalues and their corresponding eigenvectors are also discussed.As an example,the exponent tensor function is calculated.

对计算各向同性对称张量函数的3种方法(谱分解法、特征投影算子法和表示定理法)进行了分析比较，同时也对如何计算特征根与特征向量的技巧进行了探讨，并利用3种方法对指数张量函数进行了实例计算。

In this paper we define distribution cosine functions covering the degenerate case. We also consider the degenerate distribution function generated by a multi valued operator A, its relation to the integrated cosine function and the wellposedness of the degenerate abstract Cauchy problem.

引 言分布半群的概念最早由 L ions在 6 0年代引入，近年来，其他类型的分布半群相继被定义和讨论[1— 4]，由于研究退化线性方程的需要，多值算子对应的 Cauchy问题也开始受到人们关注，在 [2 ，4]中有退化情形的分布半群的定义及研究。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

After a short-term load forecasting method based analogous and linear extrapolation is proposed, the load forecast and the priority of equipment action are led into static reactive power optimization. The aim function is constructed for the practical situation of power system. On the basis of traditional genetic algorithm the fitness function and the holding of population diversity are improved. The adjacent search operator is applied to improve ability of local search.

在提出基于相似日和线性外推的短期负荷预测新方法的基础上，将负荷预测和设备动作优先级引入静态无功优化中，并结合电网实际情况，构造了实用的目标函数，对遗传算法的适应度函数和群体多样性的保持进行了改进，采用邻域搜索算子增加遗传算法的局部寻优能力。

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。