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Eigenfunctions of integrable planar billiards are studied — in particular,
the number of nodal domains, ν of the eigenfunctions
with Dirichlet boundary conditions are considered. The billiards
for which the time-independent Schrö dinger equation (Helmholtz
equation) is separable admit trivial expressions for the number
of domains. Here, we discover that for all separable and nonseparable
integrable billiards, ν satisfies certain difference equations.
This has been possible because the eigenfunctions can be
classified in families labelled by the same value ofm mod kn, given
a particular k, for a set of quantum numbers, m, n. Further, we observe
that the patterns in a family are similar and the algebraic representation
of the geometrical nodal patterns is found. Instances of
this representation are explained in detail to understand the beauty
of the patterns. This paper therefore presents a mathematical connection
- 2014-10-06 20:57:54下载
- 积分:1
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Odefun5
间歇反应釜的matlab建模,M文件,c可自由改变(Modeling of batch reactor)
- 2013-12-16 20:15:44下载
- 积分:1
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Rain_dataset
Dataset mikky glass for matlab
- 2015-03-12 20:12:50下载
- 积分:1
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VI-Math
XXY 平台移動計算,利用三點位置算出中心進行偏移動作(XXY mobile computing platform using three shift operation center position calculating)
- 2013-12-24 08:38:07下载
- 积分:1
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Pseudo-random_97-iter
伪随机采样,97小波迭代收缩压缩传感,效果不错,方法简单(Pseudo-random sampling, iterative shrinkage of wavelet compression sensor 97, the effect is good, simple)
- 2011-04-29 14:38:09下载
- 积分:1
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backstepping-control
设计了柔性机器人的反演控制,并进行仿真分析。柔性机械臂的动力学方程具有高度非线性、强耦合以及时变等特点。(nversion control of flexible robot design and simulation analysis. Dynamic equations of flexible manipulator is highly nonlinear, strong coupling and time-varying characteristics.)
- 2014-12-04 09:38:28下载
- 积分:1
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dianjifanzhen
这是一个用来控制电机正反转的matlab程序。(This is a matlab program used to control the motor reversing.)
- 2012-10-27 10:53:09下载
- 积分:1
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Open-pit-mine-arrangement
露天矿生产的车辆安排 数学建模 matlab 程序(Open-pit mine production vehicles arrangement Mathematical modeling matlab code
)
- 2011-12-31 09:53:29下载
- 积分:1
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GK_3_simulation_phase_shift
基于三次谐波注入的级联H桥多电平逆变器的Matlab仿真(Research and Simulation Study on PWM Modulation Strategy Based on Third Harmonic Injection)
- 2014-03-08 22:41:13下载
- 积分:1
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goldPpowell
matlab编写的黄金分割法求极值,C语言写鲍威尔修正算法,对n阶n次函数都实用,详细说明。(Matlab written in golden section method extremum, written in C language Powell correction algorithm, function of order n n practical details.)
- 2012-07-01 13:39:31下载
- 积分:1