This paper analyses the note on computation of quadrilateral with sides different from each other in the book 《Yang Hui Suan Fa(杨辉算法)》 from the <Collections of works about science and technology in the ancient China>,and reaches a conclusion that this note was written in the time when the book <Yang Hui Suan Fa> was published in Ming Dynasty.

There are plenty of errors in Shi Yan Zhai s MS of Yang Hui s Xiang Jie Jiu Zhang Suan Fa (Detailed Analysis of the Mathematical Rules in the Nine Chapters; only half of thee book remains).

Numerical simulation of 1 dimension based on the Yang Gu algorithm shows that the combination efficiency is greater than 98.

Using Y-G algorism, substituting the descrete components such as gratings, and lenses by two binary phase-only elements H1 and H2, the new type phase-only wavelength division multiplexer (WDM) is designed.

Some Varieties of "Yanghui triangle";

Recurrence formulas of transformation between Chebyshev polynomial and generic polynomial are abtained, and calculation method of Chebyshev polynomial coefficient analogy Yanghui triangle and transformation method between chebyshev polynomial and generic polynomial are also obtained.

Taking advantage of the combination of the numbers and their shapes,this article introduces the relationship of some special arrays with the pyramid numbers and the Yanghui Triangle.