算子函数

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。

To overcome the local optimal problem existing in some maximum likelihood DOA estimation algorithms, improve the estimation accuracy, a global optimal solution of nonlinear maximum likelihood DOA estimation is obtained by real-valued genetic algorithm proposed in this paper.

所提出的实数遗传算法由含实数域结构和目标函数信息的实数交叉和变异算子构成，是较理想的获取非线性实变量函数全局最优解的方法。

Based on different linear operators, some of the properties and characteristics of p-valent analytic functions and meromorphic multivalent functions were investigated extensively in this paper.

近年来，基于不同的线性算子，某些p叶解析函数类或亚纯函数类的性质和特征被广泛地研究。

It realizes the global optimal computation via the local interacting agents with abilities of local perceptivity, competition and cooperation, self-learning etc. Then orthogonal design is introduced to generate an initial population of points that are scattered uniformly over the feasible solution space and to generate a crossover operator. As a result, the resulting algorithm is more robust and statistically sound. For high dimensional functions, a large memory is needed in generating an initial population with orthogonal design. To overcome this problem, a method called subspace partition is proposed, so that the memory is one tenth that of original one.

它以Multi-Agent系统为基础，通过Agent间的相互作用与每个Agent所具有的知识和自学习功能来提高算法的全局优化能力和收敛速度；同时利用正交试验设计方法产生较好的初始种群和设计正交交叉算子以获得更好的后代；针对正交试验设计产生初始化种群在函数维数很高时需很大存贮空间的缺点，提出了子空间分割法来产生所需的初始化种群，它只需要原来存贮空间的十分之一。

In the heredity community renewal process, the paper uses one kind of new crossover operator——Improvement Order Crossover, the better solution two difficult problems both has been able to maintain the fine characteristic of father generation, does not destroy the sub-way which produces already in the most superior routing, and can guarantee when participation in the crossover two individual body is same, causes the genetic algorithms not to be able precociously to restrain in the partial optimal solution.

在应用遗传算法求解时，提出采用惩罚策略处理目标函数中对车辆容量的限制和客户对不同时间窗的需求约束，从而使目标解所对应的染色体能够根据违反约束的程度，具有不同大小的适应度；在遗传群体更新过程中，本文采用一种新型的交叉算子——改进的顺序交叉，更好的解决了既不破坏父代染色体中已产生的最优子路径，还能保证当参与交叉的两个个体相同时，遗传算法不会早熟收敛于局部最优解的两个难题。

When processing the restrained conditions, we convert the restrained conditions into punish function and add it to fitness function which profits from the conventional method. We introduce the support vector machine to the selection operator, which increases the multiplicity of selection and increases the probability of the algorithm getting the overall optimal solution. Also, we use the adaptive probabilities of crossover and mutation in mixed GAs which enhances the efficiency of the algorithm. The result of tests about the system indicates that the improved genetic algorithm has more high convergence speed and better solution quality.

在生成初始种群时，不是简单的随机生成，而是用支持向量机对历史数据进行分类，用较优的一类历史数据作为初始种群；在约束条件的处理上，本文借鉴常规方法中的罚函数法，采用将约束条件作为罚函数包含到适应度评价中去的方法；在选择算子上，本文引入了支持向量机的方法，增加了选择的多样性，增加算法搜索到全局最优解的概率；同时针对交叉概率和变异概率在算法的前后期不同的情况，本文引入了Srinvivas等提出的动态自适应的方法，使得交叉概率和变异概率能够随着算法中个体的质量动态改变，提高算法的效率。

Based on the theory of nonequilibrium statistics and density operator equation, the generalized master characteristic function for the nonextensive reaction-diffusion systems affected by pressure is derived by equation satisfied by calculating the time variation of probability distribution function, where the pressure of the nonextensive systems is given in the framework of Tsallis statistics.

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出。与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性。

The commutators are generated by sublinear operator with rough kernels and BMOfunctions.

这些交换子是由BMO函数和具有粗糙核的次线性算子生成的。

The other problem in the dissertation reveals that the RBF centers and widths can be evoked by a cooperative-competitive genetic algorithm. Using the well-known credit apportionment problem and niching problem, the different fitness measures in the GA of RBF representation have been studied and the adaptive genetic operators have been given to trade off the problems because of the fitness measure problem.

另外，研究了一种基于全局搜索的遗传算法的带有不同尺度的RBF结构确定的方法，讨论了信度分配问题和小生境问题两个概念，并把两概念应用于基于GA的RBF表示的系统模型中，详细论述了在GA优化过程中，取不同评价函数测量形式，对搜索群体性能的影响，最后提出采用自适应的遗传操作算子来平衡由于评价函数所造成的抑制过度竞争出现早熟问题的方法。

This thesis is devoted to the study of 〓-type inequalities for martingales,such as the maximal inequalities,the inequalities for square functions,the inequali-ties for martingale transforms,the inequalities for singular integrals.

第三章证明了关于Hardy平均算子〓的双〓不等式、双〓凸引理，并通过考虑鞅的重排不等式，建立了鞅的双〓均方函数不等式、条件均方函数不等式，给出了这类不等式成立的一个充分必要条件。

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。