In this paper we carefully investigated some relationships between Birkhoff orthogonality duality map, and isosceles orthogonality, pythagorean orthogonality, and Roberts orthogonality, some characteristics of inner product spaces are also given.

The orthogonality in Banach spaces is portrayed by the first order extentive characteristic functions in Banach spaces,some results are given to Roberts orthogonality, isosceles orthogonality and Birkhoff orthogonality, etc.

In this paper, some results on point-wise difference between generalized orthogonalities in linear normed spaces are obtained; quantitative characterizatio- ns of the difference between Birkhoff orthogonality and isosceles orthogonality are presented.

The study shows that 2D-convolute integers can be obtained by ID-convolute integers through orthogonal combination.

This paper introduces some design patterns which according to release coupling,analyzes the characters of orthogonal component,and presents a design pattern which makes the orthogonal component into layer.

The article proves that linear \$a 11 x 1+…+a 1n x n,…,a k1 x 1+…+a kn x n\$ of \$k·n(1≤k≤n)\$ unknowns and integer coefficient is sufficient and necessary condition of orthogonal system of pattern \$m\$, and the greatest common factor of all the factors of \$k\$ level of integer matrix \$(a\-\{ij\})\-\{ k×n\}\$ and \$m\$ is one.