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laguerre
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  拉盖尔
     The formula for X νν′ ,P νν′ in Morse potential is given using the orthogonality of associate Laguerre polynomial and the method of integration by parts.
     矩阵元Xνν′和Pνν′在有关量子力学问题中有相当重要的应用,本文利用广义拉盖尔多项式的正交性和分部积分的方法,推导Morse 势中 Xνν′、Pνν′的计算公式.
短句来源
     Modeling for Multi input Nonlinear System Based on Laguerre Neural Network
     基于拉盖尔神经网络的多输入非线性系统建模研究
短句来源
     This paper deals with the nonlinear eigenvalue problem over a finite interval a singular point at one end: where σ≥2, q (x, y, y′) is a read continuous function in (0, α)×R×R a laguerre function getted when q=0.
     本文研究在区间的一端有界另一端具有奇异性的非线性特征值问题: ■当σ≥2时,q(x,y,y')在(0,a)×R×R上连续,且当q(x,y,y')兰0时,得到拉盖尔函数。
短句来源
     According to the property of generalized Laguerre fu nction, the recursion relation of radial wave function about angular moment l -* is derived, so that the speed and accuracy of calculation are improved.
     利用广义拉盖尔函数的性质 ,导出了一个径向波函数关于角动量的递推关系 ,从而提高了计算的速度和精度 .
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     The focusing curves ( r z ), which higher order mode laser beams(i.e.: the mode TEM 11 、TEM 12 (or TEM 21 )、TEM 22 of Hermitian Gauss beams and the mode TEM 10 、TEM 11 of Laguerre Gauss beams) propagate through a focusing optical system (for example: a pair of lens focusing system), are obtainable on the basis of Huygens Fresnel principle and Sampling theory and by programming , calculating, and making use of Graftool.
     以惠更斯 -菲涅尔原理和取样理论为基础 ,利用计算机编程计算和绘图软件 Graftool得到高阶模激光束 (如厄米 -高斯光束 TEM1 1 、TEM1 2 (或 TEM2 1 )、TEM2 2 和拉盖尔 -高斯光束 TEM1 0 、TEM1 1 )经过会聚光学系统 (以双透镜聚焦系统为例 )传播后的聚焦曲线 (r- z)。
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  “laguerre”译为未确定词的双语例句
     Some Calculation Formulas for Laguerre Polynomials L_n~(α-n)(x) and Γ Function
     Laguerre多项式L_n~(α-n)(x)以及Γ函数的计算公式
短句来源
     Identification of Laguerre Model and Design Variable for Time-varying Systems(1)
     时变系统的Laguerre模型辨识及设计变量(1)
短句来源
     Identification of Laguerre Model and Design Variable for Time-varying Systems(2)--Kalman filter algorithms
     时变系统的Laguerre模型辨识及设计变量(2)——Kalman滤波法
短句来源
     The Adaptive Dynamic Matrix Control Based on Laguerre Series Models
     基于Laguerre级数模型的自适应动态矩阵控制
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     An Adaptive Predictive Control Algorithm Based on the Laguerre Function Approximate Model
     基于Laguerre函数模型的预测控制算法
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  相似匹配句对
     GENERALIZATION OF LAGUERRE' EQUATION
     连带拉盖尔方程的推广
短句来源
     AN APPLICATION OF LAGUERRE'S INEQUALITY
     Laguerre不等式的一个应用
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  laguerre
The scheme is supported by numerous examples concerning, in particular, the classical orthogonal expansions in Hermite, Laguerre, and Jacobi polynomials.
      
On the exact degree of approximation by Hermite-Fejér interpolation based on the laguerre abscissas
      
For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.
      
A new formula, defining Laguerre polynomials, is presented.
      
Completeness in analytic spaces of subsequences of Laguerre and Jacobi polynomials
      
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On the basis of the coincident relation between a radar signal and a radar ambiguity function, an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function. It is further pointed out that the condition is equivalent to the realizability condition given by Wilcox.When a desired function satisfies the sufficient condition (for example, the sloping Gaussian radar ambiguity function), then the synthesis of ambiguity functions...

On the basis of the coincident relation between a radar signal and a radar ambiguity function, an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function. It is further pointed out that the condition is equivalent to the realizability condition given by Wilcox.When a desired function satisfies the sufficient condition (for example, the sloping Gaussian radar ambiguity function), then the synthesis of ambiguity functions would reduce to the approximation of optimum radar signals. With proper choice of the ortho-normal bases, the problem of synthesizing an ideal radar ambiguity function can be completely solved. At the same time optimum radar signal generator and its corresponding matched filter can be constructed by a Laguerre network.

本文基于雷达信号和雷达模糊度函数间的一致关系,提出了任意平方可积的二维有界函数是雷达模糊度函数的充要条件,并且指出它包括了Wilcox提出的离散的可实现条件. 如果预给函数满足定理的充分条件时,模糊度函数的逼近就简化成相应的雷达信号的逼近了。如果适当地选择正交基,一种理想的雷达模糊度函数的综合是可以得到圆满的解决的。同时最佳雷达信号产生器和它的相应的匹配滤波器都能用Laguerre网络来构造。

This paper investigates a class of iterative processes that can be used to find the real zeros of entire functions, which by means of Landau's proof of Hadamard's theorem, has been proved to have the property of global convergence on real axis.The region where complex roots may exist is considered.A special case corresponding to an extended form of Laguerre's method is applied to Eiemann's function (?)(t), and a kind of necessary condition, capable of numerical evaluation for testing the validity of Riemann's...

This paper investigates a class of iterative processes that can be used to find the real zeros of entire functions, which by means of Landau's proof of Hadamard's theorem, has been proved to have the property of global convergence on real axis.The region where complex roots may exist is considered.A special case corresponding to an extended form of Laguerre's method is applied to Eiemann's function (?)(t), and a kind of necessary condition, capable of numerical evaluation for testing the validity of Riemann's hypothesis is obtained.In addition, the Algol 60 program of the iterative process is given.

本文由Hadamard因子分解定理出发,证明了推广的Laguerre迭代方法对求解一类超越方程具有大范围收敛性.对复根允许存在的区域作了讨论.得出了Riemann假定成立的一个必要条件.还给出了此迭代法的Algol 60程序.

In this paper, the field distributions of the linearly polarized modes EH1m and LPnm(n≥1) are discussed in the large radius hollow dielectric waveguides. The latter is certainly linear combinations of the degenerate waveguide modes. Then the coupling coefficients are between the free-space Gaussian-Laguerre modes and these linearly polarized waveguide modes. The results agree well with published experimental data. We also discussed the influences of input coupling hole with less diameter on output power...

In this paper, the field distributions of the linearly polarized modes EH1m and LPnm(n≥1) are discussed in the large radius hollow dielectric waveguides. The latter is certainly linear combinations of the degenerate waveguide modes. Then the coupling coefficients are between the free-space Gaussian-Laguerre modes and these linearly polarized waveguide modes. The results agree well with published experimental data. We also discussed the influences of input coupling hole with less diameter on output power of the optically pumped FIR laser.

本文讨论了大半径空芯圆柱形介质波导中存在的线偏振模EH_(1m)和LP_(nm)(n≥1)的场合分布,后者是一对简并模的线性组合.然后,我们计算了自由空间高斯-拉盖尔模TEM_(np)与这些线偏振模的耦合系数,得到的结果与已发表的实验资料符合得很好.我们还讨论了较小输入孔半径对光泵远红外激光器输出功率的影响.

 
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