In order to weld more solder point and obtain laser welding with high efficiency in laser spot welding based on dual galvanometer scanning during the equal time,the scanning path is represented as cycle-matrix of distance,and a genetic algorithm was applied to the path optimization.

Study on the improved topological index of distance matrix and its application;

The element of matrix in the distance matrix S*_~ij is defined and the topological index W* based on the distance matrix is defined as well.

According to the adjacency matrix and distance matrix of the two units, the sequential formulas to calculate Wiener topological indices or molecular topological indices have been given.

Based on the minimum matrix distance criterion, the method equals to aggregating individual pairwise judgment matrices to find a matrix, the sum of whose distances to the individual matrices is minimized, and then the latter reduces to a goal programming model.

Eigenvalues of a kind of circulant matrices and its application on subdivision;

VLSI decoding design of low-density parity-check codes based on circulant matrices

Making use of some relations between discrete Fourier transformation and convolution, I give a sufficiency and necessary condition which estimates that a matrix is a circulant matrix, and give concretely an accounting formula of m-orders circulant matrices.

An algorithm for computing the inverse of two kind circulant matrix;

On the properties and generalized inverse of (-1)-circulant matrix

Based on the special charicteristics of circulant matrix, a new formula of inversion for a type of specific matrix is proved in this paper.

Four theorems are presented and proved for eigenvalues and eigenvectors of circular matrix including symmetrical circular matrix, which forms the uniform mathematical principle of phase-sequence transformation for 3-phase and high phase order AC power networks.

Circular matrix may be diagonalized while diagonalized matrix is equal to similar circular matrix.

The generalization of a theorem for circular matrix is given by using generalized Vandermonde matrix,and several properties of generalized circular matrix are obtained.