查询词典 integral formula

The expression for radial wave function of a two dimensional harmonic oscillator is derived through an integral formula of general Lagurre function.

本文用广义Laguerre多项式的母函数表达式，证得文献〔1〕中，计算ρn次幂的类氢原子径向波函数Jd平均值的通式。

The transfer matrix and diffractive integral formula in frequency domain were acquired by rotating the input and output optical field π/2 in the phase space. Accordingly the fractional Fourier transforms of a first-order optical system in frequency domain were also obtained.

通过将输入输出光场在相空间中作π/2角旋转，得到了一阶光学系统在频域的传输矩阵和衍射积分公式，进而得到了一阶光学系统在频域的分数傅里叶表示。

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。

This is because Poisson integral formula can simplify the problems which have to be solved.

经典统计物理中能量均分原理的推导过程就是它的直接结果。

The results for hollow Gaussian beams propagating through a free space and a focusing lens system are derived in terms of Collins' integral formula.

第三章首次提出了空心光束的新的理论模型，并对该空心光束模型的传输特性和聚焦特性做了详细的理论分析。

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。

The author successfully applies the Gauss-type integral formula to the numerical solution to the constant differential equation and creates the Gauss-type implicit Runge-Kutta Method of which the accuracy of order 4 and degree 7 is already equivalent to that of the RK method with order 10 and degree 8 that is in common use.

成功地将高斯型求积公式用于常微分方程的数值解中，得到了高斯型隐式龙格库塔方法，4级7阶 GRK 法的精度已与目前较为常用的10级8阶 RK 法的精度相当。

During the simulation, surface current from primary electrode is computed. Taking rectangular triangle as the mesh unit, the integral formula of surface current can be simplified to a product of a difference expression and the surface area. So the computation complexity of FEM will be decreased and the time-cost will be cut down greatly.

在模拟过程中，需要计算主电极表面电流，通过选用直角三角形作为离散单元，将表面电流的二重积分表达式简化为一个差商表达式与主电极表面积的乘积，极大地降低了有限元分析的复杂度，减少了计算时间。

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。