函数的积分

In chapter 4 by means of the decomposition technique of Bojanic and Cheng together with some analysis methods we study rates of convergence of sequence of integral Baskakov operators for a class absolutely continuous functions.

第四章主要讨论了积分型Baskakov算子对绝对连续函数的逼近阶估计。在这章中主要利用经典的Bojanic-Cheng分解方法，结合分析技术，讨论了积分型Baskakov算子对绝对连续函数的点态收敛阶。

The paper states the distinctions between Riemann integral and Lebesgue integral from the aspects of the definition of integral,the continuity of integrable function,the additivity of integral,integral limitation theorems and Newton-Leibnitz formula.

从积分的定义，可积函数的连续性，积分的可加性，积分极限定理，牛顿-莱布尼兹公式五个方面阐述了黎曼积分与勒贝格积分的区别。

And because of the limitations of Riemann Integration,it can only be used for continuous function.

而由于黎曼积分具有局限性，黎曼积分只能用于连续函数类的积分。

Area coordinates and general Duffycoordinates are employed to transform the singular integrals of the Time-Domain Electric Field Integral Equation into non-singular integrals, which can be accurately and efficiently evaluated by dividing the transformed domain of integration into sub-domains.

摘要该文首先利用参数坐标和广义Duffy坐标变换将时域电场积分方程的奇异性积分转换成非奇异性积分，然后根据时间基函数的特点将该积分转换成可以快速精确计算的分区域积分。

Chapter 4 The Computation of Complex Argument Fresnel Integral and Complex Ar gument Transition Function and Their Properties The computation of complex argument Fresnel integral and complex argument transition function is a difficult problem meeted in electromagnetic scattering of lossy dielectric wedges.

第四章 复宗量Fresnel积分和复宗量过渡函数的计算及其性质复宗量菲涅耳积分的计算和复宗量过渡函数的计算是有耗介质劈电磁散射中遇到的一个难题，目前无表可查，对其性质也知之不详。

Based on the quality of linear operation about indefinite integral, the article puts forward an indefinite integral principle of making linear combination and reducing power of integrand.

从不定积分的线性运算性质出发，给出了计算不定积分的被积函数线性组合化、降幂的积分原则，并结合实例分析了这一原则在不定积分计算中的指导作用

The indefinite integral formula of rational proper fraction function is worked out by utilizing the relation between derivation and indefinite integral, and indefinite integral is calculated by using derivative.

本文利用求导与不定积分的关系，得出了有理真分式函数不定积分公式，并利用导数计算其不定积分。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

In order to calculating the weak singular integral, the coordinate transform method is used.

为了获得被积函数的奇异积分高精度的解，采用坐标转化的方法，消除被积函数中的弱奇异积分。

The double integration can be simplified to standard Bessel integration through the relation of Bessel functions.

利用贝塞尔函数的性质可将该二重积分化为标准的贝塞尔积分，然后采用直接数值积分的方法计算该积分。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。