No abstract

In this study we looked at the theorm Azela-Ascoli and its application to functional analysis, ordinary dierential equations and complex analysis. This theorem simplies the checking of compactness for subsets of spaces of continuous functions in much the same way the Heine-Borel theorem does for subsets of Rn

Aims/ Objectives: Multi-regime fundamental models use two or more equations to describe the association among the main maroscopic traffic variables encountered in traffic analysis. The paper investigates specific properties of some multi-phase speed-density equations.  Methodology: It first compares the characteristics of each of these equations by solving the nonlinear continuity traffic equation.  Results: It was observed that predicting vehicular trajectories with these model equations could lead to misinformation. The kinematic wave and stable shockwave properties of these models were also ascertained.  Conclusion: Based on the results, it was concluded that it would be more cumbersome to explain nonlinear traffic characteristics when these two and three regime models are adopted.

No abstract

Galois theory is about the connection between groups, fields and their extensions. It is the interplay between polynomials, fields, and groups. Galois field is about fields and their extensions. It has got many useful applications in computing and some other areas of abstract algebra and it has also been used to produce many useful theorems.