积分公式

At last, we deduce integral equation of control system with third nonlinear isolate vibration.

同时针对含有三次非线性隔振的控制系统，对其积分公式进行了推导。

In this paper,we mainly discuss the Poisson integral formula applied in the classical statistical physics.

而这又得益于泊松积分公式的特殊形式。

By using the analytical formula and diffraction integral formula,some numerical simulation comparisons are done,and it is shown that the results of the two methods are completely coincident.

数值计算显示，应用解析表达式所得的结果与应用衍射积分公式所得的结果完全一致。

Based on integral formula, discrete second electrical field is expressed as a sum of elementary contributions coming from charges accumulated on the surfaces of resistivity discontinuity.

基于地下电流场的积分公式，离散化的二次电流场被分解为电性不连续界面上的一系列点电荷电场的代数和。

In this paper, the propagation and focus properties for several modes describing hollow beam are analyzed, and the focus properties for hollow gaussian mode are particularly discussed. Furthermore, a new mode, high-order Bessel-Gauss mode, is put forward to describe hollow beams. The results for high order Bessel-Gauss beams propagating through lens focusing system and free space are derived by terms of Collins integral formula.

本文分析了几种描述空心光束数学模型的传输特性和聚焦特性，着重讨论了描述非中空光束的数学模型的聚焦特性；同时提出了一种描述完全中空的空心光束的新模型――高阶贝赛耳高斯模型，并且运用Collins积分公式，分析了这种新模型的空心光束的传输特性和聚焦特性。

Secondly, three kinds of mathematics model of optical vortex beams were introduced here. Then the propagation dynamics of optical vortex beams through the non-axis symmetry system is studied, this chapter includes the introduction of the symmetry vortex beam and the non- symmetry vortex beam, the deduction of the Collins diffract integral formula for the non-axis symmetry system, and the transformation of the vortex beam passing through the non-axis symmetry system has been described by using the numerical simulation. Then the general calculation for the orbit momentum of vortex beams, the matrix form for the orbit momentum of vortex beams, and the photon method to describe the orbit momentum of vortex beams are also introduced here. Finally, the interference about optical vortex beams was studied.

本文对涡旋光束进行了较为全面的介绍和研究，主要内容包括：（1）光学涡旋光束的基本理论，主要是介绍了单个光学涡旋光束在柱坐标中的一些表征，涡旋光束的奇异相位和光学涡旋的相位结构；（2）光学涡旋光束的三种数学模型；（3）光学涡旋光束在非轴对称光学系统中的传播动力学，其中介绍了对称涡旋光束与非对称涡旋光束，推导了非轴对称光学系统的 Collins 衍射积分公式，并利用计算机模拟图描述了对称涡旋光束经过非轴对称光学系统后涡旋形态的改变；（4）涡旋光束轨道角动量的一般计算，涡旋光束轨道角动量的矩阵形式，光子法描述涡旋的轨道角动量；（5）涡旋光束的干涉。

Using the Green function of an anisotropic medium in free space and Green identity, we derive the equation of electric field in an anisotropic medium for TM polarized wave.

本文由各向异性介质无界空间Green函数和Green恒等式出发，推导了TM波入射时各向异性介质中电场满足的方程，由此得出总电场的积分公式。

The analytical expression of a kind of integral including the product of the sums of two Bessel functions is given for the power calculation.

六、根据研究工作数值计算的需要，给出了一类包含有两个贝塞尔函数的和的积的积分公式。

Starting from the Huygens-Fresnel diffraction integral,the spectral shifts and spectral switches of femtosecond optical pulses in Young′s interference experiment are studied and analyzed numerically.

从惠更斯-菲涅耳衍射积分公式出发，对飞秒光脉冲在杨氏实验中的光谱移动和光谱开关做了研究和数值分析。

The Focusing property of flat-topped multi-Gaussian laser beam by lens with spherical aberration is discussed.

利用广义惠更斯-菲涅耳衍射积分公式，研究了平顶多高斯光束通过球差透镜的聚焦特性。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。