The Application of Group Theory in Communication Operation Pipeline System

Abstract

To resolve the “pipeline” crisis for telecom operators, this study pioneers the application of Group theory in communication operation pipeline system. The pipeline entity group model was built for information transmission in the pipeline system to analyze operation of pipeline entities. The equations of pipeline system network traffic were established according to the flux conservation principle and matrix of pipeline network. Based on pipeline entity group model, dimensionality of the matrix was reduced. The solution scheme of the flow state transition relationship of the pipeline system is obtained, which will be very useful for the telecom operators to construct high-level mobile e-commerce application model and architecture.

Subgroup Graphs of Finite Groups

“…According to [1], the rebirth of the axiomatic method and the view of mathematics as a human activity in the nineteenth century forms the major development that change the bearing on the evolution of group theory as a mathematical concept. [1], further noted that the evolution had caused the previous classical algebra polynomial equations Meanwhile, this concept has been applied in the field of physics, chemistry and biology, (see [2], [3], [4], [5]) for details.…”

Representations of Generalized Self-Shrunken Sequences

“…The basic structure of groups can be found in many mathematical phenomena such as symmetry and certain types of transformations. Group theory has applications in robotics, computer vision/graphics and medical image analysis, physics, chemistry, computer science, and even puzzles like Rubik's cube can be represented using group theory [33][34][35][36][37]. As we show in this paper, group theory also has applications in cryptography, since the set of output sequences of the generalized self-shrinking generator has the structure of an additive group and some of the properties of this family of sequences can be deduced as a consequence of this fact.…”