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1·The approach presents more freedom when choosing frame or orthogonal basis of one-way wave marching algorithm.

该方法在构造单程波的步进算法时，在选择标架或正交基等方面有更大的自由度。

2·The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied.

研究实对称矩阵、对角矩阵以及欧氏空间的规范正交基。

3·To simplify the calculation, a learning algorithm based on the expansion of the orthogonal basis functions is developed.

为简化模型的计算复杂度，开发了一种基于正交基函数展开的学习算法。

4·By introducing a group of function orthogonal basis into the input space, the input functions and the network weight functions are expressed in the expansion form.

在输入空间中引入一组函数正交基，将输入函数和网络权函数表示为该组正交基的展开形式，利用基函数的正交性简化过程神经元聚合运算。

5·Firstly, the image is projected on to the orthogonal basis of SVDQ, then the projection coefficient vector is used as algebraic feature of image and applied to recognition.

该方法将图像投影到SVDQ的各个正交基上，得到投影系数向量。将此向量作为图像的代数特征并用于彩色图像识别中。

6·The MSVD method constructs a self-contained orthogonal basis using the outer product of left and right eigenvector matrixes decomposed from 2D geochemical or geophysical maps.

该方法首先对地球物理和地球化学等网格数据进行二维矩阵的奇异值分解，之后用左特征向量矩阵与右特征向量矩阵的直积构造一个正交完备基。

7·By means of congruent transformation in matrix, the method of transforming real quadratic form into standard form and the method of normal orthogonal basis are given in this paper.

借助矩阵的合同变换法，给出了化实二次型为标准形的方法、求标准正交基的方法，并给出了正定二次型判定定理的新证明。

8·In consideration of the complexity of the aggregation operation of time in process neural networks, a new learning algorithm based on function orthogonal basis expansion is proposed.

该文在考虑过程神经网络对时间聚合运算的复杂性的基础上，提出了一种基于函数正交基展开的学习算法。

9·Then we introduce the basics of the theory of frames, which intuitively correspond to over complete, non-orthogonal systems of basis functions.

然后我们将完整的介绍架构理论的基础，亦即直观符合非正交系统的基本功能。

10·Using orthogonal testing on the basis of technology mechanism analysis, the parameters optimization and contrast test for five different technology processes have been carried out.

在工艺机理分析的基础上利用正交试验对五种不同工艺流程进行参数优化和对比研究。