Application of Group Theory in Analyzing Operation Pipeline Systems

Abstract

Considering the barrier to effective communication, and in order to enhance network operations, this research work presents an algebraic approach, taking into account the obstacle to efficient communication computation. This research effort, which is diverse in content but consistent with results from previous works in this area of study, applies group theory to address the pipeline dilemma facing telecommunications businesses. The purpose of the pipeline entity group is to analyze the operation of pipeline entities and to transmit information within the pipeline system. By the application of group theory, the result is justifiable for the symmetric and translation operations pipeline entity described to be a member of the group elements of the order 12 pipeline entity group. The transformation is classified into six (6) dimensional types and is defined as a characteristics transformation matrix that satisfies the property of group associativity, closure, also the associative, distributive, and inverse transformation properties of group based on the expression of the pipeline entity group model, two-dimensional natures, symmetry principal, 3 Ordered model symmetry transformation procedure components of the data framework. The flux conservation principle and pipeline network measurements are taken into consideration when establishing the equation for pipeline system network traffic. For the purpose of developing a sophisticated multi- and mobile e-commerce application model and building it for telecom businesses and operators, the relationship governing the transition of flow states within the pipeline system's solution framework is determined.