查询词典 Laguerre polynomial

We believethat the PH and generalized Laguerre function expansionmay be useful for systems with more electrons.

通过对计算结果，特别是激发态〓能量的分析，可以展望PHGL方法有应用于多电子原子体系的前景。

The order of Laguerre function affects seriously the variations of the carrier-envelope phase with the propagation distance increasing.

结果表明，拉盖尔函数的阶数对传输中超短脉冲拉盖尔-高斯光束的载波包络相位有很大的影响。

Using sensor output data as the compensator input, and the sensor input data as the compensator output, the compensator is designed based on the nonlinear dynamic Laguerre function.

用传感器的输出数据作为补偿器的输入，传感器的输入数据作为补偿器的输出，进行基于Laguerre函数的非线性动态补偿器的设计研究。

Heavy oil distillation column ; chaotic neural network ; Laguerre function ; predictive control ; adaptive control

重油分馏塔；混沌神经网络； Laguerre函数；预测控制；自适应控制

Volterra kernel functions were expanded on an orthogonal discrete Laguerre function set to produce a reduced system model with fewer parameters.

讨论了Volterra核的Laguerre展开法，通过将Volterra核函数在一个正交的Laguerre函数集上展开，得到一个简化的系统模型，使得待辨识的参数显著减少。

Generally,the eigenenergy converges as NGLF=7(NGLF is thenumber of gengralized Laguerre function).

NGLF=7（NGLF代表广义Laguerre函数的个数）时，本征能量在径向趋于收敛。

Using it and the Gauss- Laguerre correlation functions, we have estimated the size of photodetector aperture.

函数的卷积计算更加复杂和冗长，巍有的积分表中对于Gauss一Laguerre函数

It is very important for estimating the size of photodetector aperture to calculate the Gauss-Laguerre correlation functions.

我们应用Bartelt和Freude等人l'，【51提出的光纤中模式分析测量的新方法—用计算全息产生的光学匹配滤波器对光纤中的模式进行分析测量，需要知道Gauss一Laguerre函数的卷积表达式，以此来估算测量时所有光电检测管的孔径大小，估计测量结果的精度，减小测量误差。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。