##### Dynamic Model of a DC Motor-Gear-Alternator (MGA) System

W. C. Koech, S. Rotich, T. Rotich, F. Nyamwala

Asian Research Journal of Mathematics, Page 1-16
DOI: 10.9734/ARJOM/2016/28948

Mathematical models of control systems are mathematical expressions which describe the relationships among system inputs, outputs and other inner variables. Establishing the mathematical model describing the control system is the foundation for analysis and design of control systems. The present study designed a DC motor- gear-alternator (MGA) model where DC motor is the prime mover used to drive an alternator through specialized gears employed in between alternator and DC motor. The fundamental equations that describe the system were presented, and then developed transfer function and Simulink model for the system. The workability of the model is then tested using some numerical values. Results showed that the output voltage increases exponentially with time. Finally, the effect of each of the PID parameters on the closed-loop dynamics were discussed and demonstrated how to use a PID controller to improve the system performance.

Aims:

(i) To construct a mathematical model describing the dynamics of the MGA set coupled through a gear ratio.
(ii) To design transfer function, which is a compact description of the input/output relation for the model.
(iii) To construct a Simulink model of MGA System.
(iv) Test the model using numerical values (assumed data).

Place and Duration of Study: Moi University, Department of Mathematics and Physics, between May 2015 and July 2016.

##### On the Co-Common Neighborhood Domination Number

Ahmad N. Al-Kenani, Omar A. Al-Attas, Anwar Alwardi

Asian Research Journal of Mathematics, Page 1-11
DOI: 10.9734/ARJOM/2016/28756

In this paper, we introduce the concept of co-common neighborhood domination number (CCN-domination number) γccn(G) of a graph G and we study its relation with the standard domination number γ(G). We also define CCN-independence number βccn(G), total CCNdomination number γtccn (G), CCN-covering number αccn(G) and CCN-domatic number.

##### The New Iterative Method for Approximate Solutions of Time Fractional Kdv, K(2,2), Burgers, and Cubic Boussinesq Equations

Asian Research Journal of Mathematics, Page 1-10
DOI: 10.9734/ARJOM/2016/29279

In this paper, new iterative method is used to determine approximate solutions for the time fractional KdV, the K(2,2), the Burgers, and the cubic Boussinesq equations. The obtained approximate solutions are compared with the exact results. The study reveals that the present method is very effective, accurate and convenient.

##### Extensions of the Lusin's Theorem, the Severini-Egorov's Theorem and the Riesz Subsequence Theorems

Mangatiana A. Robdera

Asian Research Journal of Mathematics, Page 1-9
DOI: 10.9734/ARJOM/2016/29547

We give extensions of the Lusin's Theorem, the Severini-Egorov's Theorem, and the Riesz Subsequence Theorems to the setting of a non-additive vector valued set functions and sequences of functions taking values in general metric spaces.

##### An HIV/AIDS Model with Vertical Transmission, Treatment and Progression Rate

J. O. Akanni, F. O. Akinpelu

Asian Research Journal of Mathematics, Page 1-17
DOI: 10.9734/ARJOM/2016/28549

The Human Immunodeficiency Virus (HIV) infection which leads to Acquired Immunodeficiency Syndrome (AIDS) has become a deadly infectious disease in both developed and developing nations. It usually breaks down the body immune system, leaving the victim vulnerable to a lot of other diseases. Therefore, in this study a nonlinear mathematical model of HIV/AIDS with treatment, vertical transmission and progression rate were considered.

The basic reproduction number (R0) was evaluate by next generation matrix and the global stability was examine by the comparison approach. The disease – free and the endemic equilibrium of the model were determined by setting all compartments to be zero. The sensitivity analysis was carried out to determine the parameter that has high impact on the spread of the disease using partial derivatives and the Maple software 14 was used for numerical simulation of the model.

The disease free and endemic equilibrium were obtained and their stabilities studied. The model showed that the disease free equilibrium is locally asymptotically stable by using Routh-Hurwitz criteria and globally the disease free equilibrium is stable by comparism approach. The numerical simulation showed that by using treatment measures and controlling the rate of vertical transmission with time, the spread of the disease can be reduced significantly and by providing treatment at the pre-AIDs stage reduces the infection much faster than starting treatment after progression into AIDs.