| 1. | Construction and classification of a set of complete orthogonal basis functions in the arbitrary triangular domain
任意三角形区域中一组完备正交基的构造与分类 |
| 2. | In this paper , we ' ll give another simple method to seek normal orthogonal basis by using the properties of positive definite matrix
摘要利用正定矩阵的性质，得到标准正交基的另一种较简单的求法。 |
| 3. | According to the principle of discontinuous finite - element method and selection of orthogonal basis shape functions , the computational scheme is developed for the shallow water equations
摘要根据间断有限元法的基本原理，选用正交化基函数，构造求解一维浅水方程的计算格式。 |
| 4. | By introducing a set of appropriate orthogonal basis functions into the input space , the input functions and the weight functions are expanded under the orthogonal basis functions , and the time aggregation operation of the process neurons is simplified by using the orthogonality of the basis functions
在输入空间中引入一组合适的函数正交基，将输入函数和网络权函数表示为该组正交基的展开形式，并利用基函数的正交性简化网络聚合运算过程。 |
| 5. | One is the non - orthogonal gabor - daubechies frame , or g - d frame , a complete set of discrete window fourier functions which are constructed by space - shifting and harmonically modulating a gaussian window . although a g - d frame is not an orthogonal basis , it bears considerable advantages for the study of physical problems , especially those related to the wave field extrapolation , due to the optimal localization properties of the gaussian window function under the heisenberg uncertainty principle
其一为将高斯窗函数经平移和调制而构成的一组窗口富里叶框架( gabor - daubechies框架，或g - d框架)基本函数，另一种为在富里叶分析和小波包理论基础上发展起来的局部余弦基函数。 |
| 6. | Expanding the system ' s hamiltonian to a real symmetric matrix in an appropriate orthogonal basis vector and then diagonalizing it , we get the energy spectrum of the system and calculate the energy level spacing distribution function and the spectral rigidity . then we study the statistical character of the energy spectrum under the changing of magnetic field intension and find that the system ' s motion transfers from regular to chaos gradually
将系统的哈密顿量在一个适当的正交基矢下展开并对角化，得到系统的能谱，分别计算系统能谱的能级间距分布函数和谱刚度，研究了该系统量子能谱的统计特征随磁感应强度大小的改变而表现出的系统运动由规则到混沌的渐进变化。 |
| 7. | The other is the local cosine bases developed as a kind of orthogonal basis based on the fourier analysis and wavelet - packet theory . in this thesis , theoretical analysis and numerical applications are mainly focused on the beamlet - domain wave field extrapolation using g - d frame propagators . the whole thesis consists of six chapters
通过对具体信号的分析，对不同变换方法的信号表示效率进行了对比，并总结了g - d框架及对其进行尺度扩展组成的gabor函数族在应用于波场相关的研究中时，优于其它正交分解方法的特性。 |
