##### Determinants and Inverses of Symmetric Poeplitz and Qoeplitz Matrix#

Jinyu Chen

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/JAMCS/2017/36512

In this paper, we define symmetric Poeplitz and Qoeplitz matrices and give explicit formulae for the determinants and inverses of these matrices by constructing the transformation matrices.

##### SEIRS Model for Pediatrics with Lower Respiratory Tract Infection

O. Catherine Olayemi, O. Olasehinde Olayemi, Bukola Badeji-Ajisafe

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/JAMCS/2017/35296

The ability of the immune system to detect and eliminate most pathogens is essential for the survival of lower respiratory tract infection in 2016 by Olubadeji . Lower respiratory tract infection (LRTI) constituted the second leading cause of death in all age bracket in Nigeria, Loddenkemper  said that Chronic lower respiratory diseases rank as the third leading cause of death in the United States. Intense research has been on how to reduce the spread of infection, which involves the mathematical modelling of the spread of infection based on mathematical epidemiological approach, This is necessary because a threshold cannot be discerned from the data generated from the Hospitals, rather it requires a mathematical model to analyze and simulate the LRTI dynamics on the enviroment. It also enables the calculation of the basic reproductive number (R0) which is an important threshold for determining whether the environments are at risk or not.  In this paper, we adopt the susceptible- Exposed-infected-recovered-susceptible (SEIRS) model to depict the spread of infections in our environment. We qualitatively   analyze the model and establish that the virus-free state is locally asymptotically stable provided the basic reproduction number is less than unity. We solved the model numerically and simulate the solution for different scenarios on the network. The findings from our simulations are discussed.

##### Application of Quick Simplex Method on the Dual Simplex Method (A New Approach)

N. V. Vaidya

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/JAMCS/2017/36357

In this article, we suggest a new approach while solving Dual simplex method using Quick Simplex Method. Quick Simplex Method attempts to replace more than one basic variable simultaneously so it involves less iteration or at the most equal number than in the standard Dual Simplex Method.

This has been illustrated by giving the solution of solving Dual Simplex Method Problems.

It is also shown that either the iterations required are the same or less but iterations required are never more than those of the Dual Simplex Method.

##### Some Commutativity Theorems in Prime Rings with Involution and Derivations

Shakir Ali, Husain Alhazmi

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/JAMCS/2017/36717

Let R be a ring with involution ′∗′ . An additive map xx* of R into itself is called an involution if (i) (xy)*= yx and (ii) (x) = x holds for all x,y ∈ R. An additive mapping δ: R → R is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving derivations.

##### Analytical Modeling of the Thermoelectric Effect in Photovoltaic Cells: Combined Solar Photovoltaic and Thermoelectric Generator System (PV+TEG)

Géraud F. Hounkpatin, Macaire Agbomahéna, Basile B. Kounouhéwa, Vianou I. Madogni, Antoine Vianou, Cossi N. Awanou

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2017/32543

Aims: Analytical modeling of the combined systems photovoltaic-thermoelectric (PV + TEG). The advantage of these systems is double:

− On the one hand, they allow to cool the photovoltaic cells (PV), which avoids the loss of electrical efficiency observed in the devices,

− On the other hand, recover this lost energy in the form of heat, and transform it into electrical energy thanks to the thermoelectric modules operating in Seebeck mode.

Study Design: Laboratory of Radiation Physics LPR, FAST-UAC, 01 BP 526, Cotonou, Benin. Department of Physics (FAST) and Doctoral Formation Materials Science (FDSM), University of Abomey-Calavi, Benin.

Methodology: We considered the temperature distribution in the semiconductor plate of the Thermoelectric Generator System (TEG). We resolved the thermal conductivity equation described by: Where a2 is the thermal diffusivity, Q(x, y, z) is the heat flow going from the PV to the TEG module which is dissipated through the latter; using constants variation method. We assumed that the temperature along the y-axis is considered uniform.

Results: The results obtained show that, the temperature distribution in the form of a traveling wave is maintained by external heating. This depends on both the hot and cold side temperature and the temperature span.

Conclusion: The heat flux available at the hot side of the TEG is assumed to be what remains of the absorbed radiation of the PV power production.