paper2

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

采用5点3次平滑算法和SG平滑算法对曲线进行平滑处理，结果良好(The curve is smoothed by 5-point 3-order smoothing algorithm and SG smoothing algorithm, and the result is good.)

说明：  用MATLAB编写的18个智能优化算法的测试函数程序(Prepared using MATLAB Intelligent Optimization Algorithm 18 function testing procedures)

国外的一个惯性导航系统仿真工具箱，自己点滴注释过，能进行导航解算，组合导航。(An inertial navigation system simulation toolbox。 own drip comment,can solve navigate and integrated navigation.)

matlab中很好的位置式PID控制算法(good position in the matlab PID control algorithm)

here the all program which have mimo ofdm system materials.

Region Growing (2D3D grayscale)

matlab 程序 进行优化分析 使用的方法是惩罚函数法进行优化。(it is called penlty methods，it can optimize the function ,obtaining the minium value)

Taflove书的2维时域有限差分完美边界的程序！欢迎下载！(Taflove book two-dimensional finite-difference time-domain boundary perfect program! Welcome to download!)

研究阵列信号的算法，Esprit算法的仿真程序，已经测试过了，不错(Algorithm of array signals, Esprit algorithm simulation program, has been tested, and good)