HASHIN_FAILURE_CRITERIA_hard

使用Y矩阵来综合得到耦合矩阵M中各元素的matlab源代码(The Y matrix to obtain an integrated coupling matrix M of each element matlab source code)

crackprop_modeI_lefm_xfem_cpe4，ABAQUS基于线弹性断裂力学的扩展有限元法实例。(crackprop_modeI_lefm_xfem_cpe4 ABAQUS based on linear elastic fracture mechanics extended finite element method instance.)

一维波动方程TVD格式源程序，空间二阶精度，附带计算结果及说明(One-dimensional wave equation TVD scheme source, space second-order accuracy, with results and instructions)

己知一些离散的点，使用matlab利用最小二乘法拟合(Had a number of discrete points, with linear least squares fitting)

使用java语言调用cplex求解简单案例(use java language with cplex solver to solve some simple cases)

说明：  虽然现在网上的FFT程序很多，但是有的结果是错误的，比如说，经过一次正反变换后，不能得到原来的数列，所以，本人测试了多个程序，提供几个能用的，给大家，希望大家支持！ (Although many online FFT program, but some results are wrong, for example, through a positive and negative change, you can not get the original series, so I tested several programs to provide a few usable for everyone I hope we can support!)

平面波与涡旋光束干涉的干涉图样，可以用来制作全息图，从而产生涡旋光束(Interference pattern of plane wave and vortex beam interference, can be used to produce hologram, resulting in vortex beam)

说明：  通过matlab实现抽样检测功能，具体通过蒙特塔罗算法依照概率分布计算指定变量的分布规律，是初学者的好案例(The sampling detection function is realized by matlab, and the distribution rule of specified variables is calculated by Montreal algorithm according to probability distribution.)

适用于Engine计算的经典PISO算法(the classic PISO algorithm for the Engine calculation )

计算非线性系统的分叉图和李雅普诺夫指数，用于判断系统的混沌状态，独立的两个文件(a tool to calculate bifurcation and Lyapunov exponent)