矩形公式

The postbuckling behavior of a long rectangular plate with initial deflection under uniaxial compression is discussed based on the large deflection theory of thin plates.

本文应用薄板大挠度理论，对有初挠度的长矩形板在纵向压力作用下的屈曲后行为进行近似分析，推导出计算板的极限强度和有效宽度的理论公式。

Based on the method that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, the propagation characteristics of a Gaussian beam passing through apertured spatial filter systems are analysed and the corresponding analytical formulae are obtained respectively.

根据矩形函数可以展开为有限复高斯函数之和的方法，从柯林斯衍射积分公式出发，对高斯光束通过受限空间滤波器传输特性进行分析，得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟，得出一组直观的结果。

In this paper ,the precise-ly formula of magnetic induction of t he coil of rectangular carrying current by an point in space is obtained,and analyze the distributive properties by magnet field of the rectangle and the square.

本文精确导出了矩形载流线圈在空间任一点的磁感强度公式，并对长方形、正方形磁场分布的特点进行了一些分析。

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。

The calculation model was constructed by equating CWG with rectangular waveguide. The scattering formula was deduced by Integral Equation Method, which was validated by Finite Element Method.

通过将同轴波导等效为窄边是磁壁的矩形波导，建立了金属支撑杆的散射场计算模型，用积分方程法得到了散射场的计算公式，其计算结果与有限元方法仿真结果吻合良好。

According to two hypotheses: one for the relation between the dynamic complex stiffness and the material dynamic characteristics, another for the relation between the static displacement and the force acting on the element, the predicting formula for rectangular cross section are obtained respectively using the static stiffness formulation from the beam——column theory and the G〓bel method.

利用粘弹性材料的标准导数和分数导数模型的本构关系，建立了动态储能和损耗模量函数的关系式，由材料特性实验确定其中的参数，按元件的动态复刚度和材料动态特性之间与元件静态位移与作用力之间的关系假定，依柱梁理论或G〓bel的方法建立的静刚度表达式，建立了矩形截面环元件的刚度和阻尼的预测公式。

First, we deduce theoretical formulae of calculating equivalent dielectric constant and resonance frequency of rectangular microstrip antennas with air gaps from electromagnetic field theory based on the modified theory of cavity model. Then, we discusses the radiant principle of microstrip antennas on the base of transmission line theory and analyzes the problem of air gaps how to influence pattern and other idiocratic parameters of a microstrip antenna in detail.

本论文的主要工作是根据修改的微带天线的腔模理论，利用电磁场理论推导了具有空气隙的矩形微带天线的等效介电常数和谐振频率的理论计算公式，同时以传输线理论为基础，论述了微带天线的辐射原理。

With the assumption that reinforced concrete was perfectly rigid-plastic,a kinematically admissible failure mechanism suitable for the shear failure of rectangular beams was presented and based on which theoretical calculation formulas were derived.

视钢筋混凝土梁为理想刚塑性体，提出了矩形截面梁剪切破坏时的破坏机构，以该机构为基础，推导得出了理论计算公式。

Practical microstrip antenna problems, such as the effect of superstrate on input impedance and radiation pattern are studied.

根据所得的新公式建立了多层介质覆盖矩形贴片微带天线的积分方程，并利用有效的数值技术求解出上述方程，得到了贴片上的电流分布，进而求出天线输入阻抗和辐射方向图。

This article comminutes the symbols of the formula and records their position by the outline rectangles of symbols, and then normalized these symbol. Then designed Artificial Neural Network that recognizes these symbol.

本文通过计算公式中字符的最小外接矩形，将字符依次分割开并记录其位置信息，然后进行归一化处理，利用本文设计的适合本文中字符识别的识别模块，即二层感知器神经网络识别模块，将归一化后的字符识别出来。

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。