应用函数

The multiresolution time-domain algorithm based on the scaling function of the Daubechies wavelet is introduced, and the perfectly matched layer absorbing boundary condition for the algorithm is deduced. In order to overcome the difficulties due to the nonlocalized property of the MRTD basis functions, the pure scattered-field formulation is adopted. The method presented is applied to the scattering analysis of multiple conducting objects, and the numerical results are compared with those by the traditional finite-difference time-domain method. It is shown that the computational resource is reduced drastically without sacrificing much accuracy.

对基于Daubechies小波尺度函数的时域多分辨分析算法进行了详细论述，推导了MRTD算法的完全匹配层吸收边界条件，为克服传统MRTD方法中基函数存在着非局部性的缺点，在源的加入上采用了纯散射场方法；并应用该算法对多目标的电磁散射特性进行了分析，数值结果表明，MRTD算法与传统的时域有限差分法结果相吻合，大大节约了计算资源。

The bending problem of simple-supported parallelogrammic plates on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by applying Green quasifunction method. The Green quasifunction is set up by using the fundamental solution of Poisson equation and the normalized boundary equation.

应用准格林函数方法，即利用方程的基本解和规范化的边界方程构造一个准格林函数，将Winkler地基上简支平行四边形薄板的弯曲问题化为两个耦合的第二类Fredholm积分方程，此积分方程的核表示式在区域的边界上具有奇异性。

In Chapter 2 the foundamental principle of GAs is introduced and the mathematic background of GAs is discussed. Then, a genetic algorithm based on non-Abel group theory and a parallel genetic algorithm based on supercube computer system are proposed.

遗传算法广泛地应用于函数优化和组合函数优化问题，然而如何改善其性能，提高收敛效率，仍然是当今遗传算法研究界的重要课题。

Among many methods to generate Walsh functions, Swick's copy theory is famous.

其中，Swick提出的复制方法应用最为广泛，该方法以Walsh函数的序码作为复制信息，可以复制出任意给定序数的Walsh函数。

By application of dissipative structure theory, the order degree entropy function of water resources system is established, and the rationality is testified. The water resources evolvement direction can be distinguished by finding out the change tread of order degree entropy. At the same time, the entropy change is also the basic criterion of weighing the validity of control.

7以耗散结构中的熵变理论为依据，建立了水资源系统的有序度熵函数，并证明了其合理性，应用该函数的变化趋势可以实现对水资源系统演化方向的判别，同时也成为衡量调控是否合理的基本标准。

Introducing satisfaction function instead of utility function, the authors obtain two -stage satisfaction programming arbitrating procedure.

在应用研究中，本文引入了满意函数以替代效用函数，以此得出了两阶段满意规划仲裁模型。

As their application, we obtain some indentities for the infinite products from the new expression in the special cases of these fuctions, and establish simultaneously a kind of inequalities with their convexities.

作为应用，在特殊情况下得出了这些广义函数的新的表达式，由此出发得到了一些关于自然数和合数的无穷乘积的恒等式，同时由广义函数各种凸性建立了若干解析不等式。

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。

Reconstructs the surface by one and two dimensional spline functions with 3D data obtained from laser scanning system.

针对获得的三维扫描数据，应用一元、二元的多种样条函数进行了三维表面信号的恢复和重建。文中研究了样条函数的构造和使用方法。

A new method for fast valving decision to maintain multi-machine power systems transient stability by feedforward neural network is proposed.

这种输入和输出的选取是通过详细的理论分析，使输入和输出间呈连续函数关系，再经对输入量进行简化而决定的，从而应用前向神经网络的函数逼近功能说明了所提神经网络结构的合理性。

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。