The diffusion layers in which branch numbers B equals n+1 are optimal, iff their corresponding matrices have no singular square submatrices.

Using the linear transform which has branch numbers as large as possible as the diffusion structure is a main method to devise block cipher.

Branch number is an important parameter in the linear and differential cryptanalysis on block ciphers, In the first chapter , we mainly discuss the branch number of Rijndael.

Fast calculation on branch coefficient in protection relay setting and coordination;

In this paper the function and structure of relay setting on-line coordination system are presented,in which accurate fault calculation model is adopted and branch coefficient is no more introduced,so the computation accuracy is improved.

Different elements influencing calculation of line branch coefficient and sideline current addition coefficient are fault points,fault types and operating modes.

Moreover, the analysis has indicated that the asymptotic heuristic branching factor is same as the brute-force branching factor.

The branching factor of a regular search tree has a decisive effect on the time complexity of a search algorithm.

The paper,using Bifurcation function,deals further more witi the wide application of L-S Method to local Bifurcation theory illustrated by several general examples.