应用函数

And it is proved to be more efficient than Newton method from the theorectical of view.

另一方面，将Newton-PCG算法应用于求解单和函数优化问题，利用单和函数优化问题的特殊性，进一步开发Newton-PCG技术建立了更有效的特殊算法。

And by applying the linear dispersion relation of wave, all the properties of wave refraction including wave rays, constant phase lines, phase function and crest lines etc., can be expressed in explicit functions. By introducing an orthogonal curvilinear coordinate along the wave ray and the constant phase line, and with an estimated scale factor, the refraction coefficients along any wave ray can then be determined. The present results are verified by ordinary wave ray theory and some previous numerical results.

就此特例情况在波浪的线性分散关係的应用下，前进波浪折射现象的整体特性，包括波向线、等位相线、位相函数与波峰线皆被导述出明確显然的函数表示；同时引入由沿著波向线与等位相线所构成的完全符合波浪折射几何通性的正交曲线座標，求出其尺度因子后，由能通量守衡原则定出沿著任一条波向线上的折射係数；並由之对往昔纯依两相邻的波向线间的几何类比所给定的折射係数给予导証之。

The distinguishing feature is a clear physical conception. HIFNC-Ⅱ is an orthonormal basis neural network model. The neurons' output nonlinear function in the hidden layer is an orthogonal system of polynomial, which optimizes the configuration of the neural network.

在智能控制理论方面，详细剖析了一种仿人智能控制器，证明了广义频率函数与非线性系统描述函数的关系，并将其应用于仿人智能控制器的稳定性分析，在理论上证明了HIC的鲁棒特性。

First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

First of all, the basis of the MRTD method is studied. In Chapter 2, waveletsanalysis and multiresolution analysis, the mathematical basis, are introduced, and thecharacteristics of the wavelets basis functions, including orthonormality, compactsupport, multiresolution and so on, are also introduced. The advantages of theapplications of these functions to the numerical electromagnetic calculations arediscussed. In Chapter 3, the algorithm basis of MRTD: the combination of the waveletsand the method of moments is studied. This Chapter shows that the MoM basedMRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

For first-order linear DPS with spatial-varying coefficient matrices a method is presented to approximate the system piecewisely by N partial differential equations with constant coefficient matrices.

它包括两大部分，一是关于分布参数系统的频率域数学描述即传递函数这一基本问题的应用研究，二是关于一类用多滞后型传递函数表示的分布系统的控制设计问题。

Then, with the assumption that the consumption of an investor is the continuous or piecewise continuous function of time, the corresponding optimal investment decision and the effective frontier are derived by using the stochastic linear-quadratic control.

假设投资者的消费是时间的连续函数或者分段连续函数，应用线性二次随机控制的方法得到了这两种情形下的最优投资决策和有效前沿。

For NC machining of plane section method, the machining path of tool cutting plane and implicit surface can be found, and the curve of the tool path is drawn by the positive-negative method.

把隐函数的优势应用到数控加工编程中，即对于截面法的数控加工，求出刀具切削平面与隐函数曲面的加工轨迹，再用正负法绘制刀具轨迹曲线。

A dollar to prove Taylor's formula and its application Various types of polynomial function is one of the most simple, using polynomial approximation function is similar to the calculation and theoretical analysis of an important element.

一元泰勒公式的证明及应用多项式是各类函数中最简单的一种，用多项式逼近函数是近似计算和理论分析的一个重要内容。

The model (1 - 1) researches the prey–preyer system with traditional II function:succeed in harvesting one( prey for food only having death rate), get the equilibrium of the system; To the equilibrium point, with the stability theories, analy the equilibrium stability; With keeping on the biggest development into target, get the biggest value of the target function.

模型(1 - 1)研究具有传统II类功能函数的Lotka -Volterra捕食-食饵系统：对捕食者进行单一捕获，得出非负平衡点；对平衡点，用稳定性理论，分析其局部稳定性；以最大可持续发展为目标，应用数分理论，得到目标函数的最大值。

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。