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Volume 63, January – March, 2022 Issue

Journal of the Nigerian Association of Mathematical Physics Volume 63, (January – March, 2022 Issue),

22. Effects of MgO Nano Particles On Viscosity of Transesterified Rapeseed Oil

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by H. U. Jamo1, E. Tolufase2, F.U. Musa3, U. I. Ismail4, Aliyu S. A.5 and M.B. Abdullahi1
1Department of Physics, Kano University of Science and Technology, Wudil, P.M.B. 3244 Kano-Nigeria
2Department of Physics, Nigeria Police Academy Wudil, P.M.B. 3474, Kano-Nigeria
3Science and Technical Schools Board, Plot 546 Yan-Awaki Quarters Opp IBB Way Kano 4Department of Physics, Sule Lamido University, Kafin Hausa P.M.B. 048 Jigawa-Nigeria
5Department of Physical Sciences, Rabiu Musa Kwankwaso College of Advanced Studies, Tudun Wada, Kano

Abstract
Biodiesel is a renewable, biodegradable, environmentally benign, energy efficient, substitution fuel which can fulfill energy security needs without sacrificing engine’s operational performance. Thus it provides a feasible solution to the twin crises of fossil fuel depletion and environmental degradation. This research aimed at investigating the effects of MgO nanoparticles on viscosity of transesterified rapeseed oil. The crude rapeseed oil was purified, transesterified and nanoparticles were dispersed in the transesterified oil with concentration ranging from 0.2% to 1.0% in 0.2% interval. X-ray fluorescence (XRF), X-ray diffraction (XRD) and scanning electron microscopy (SEM) were used to observe the surface morphology and internal structure of the nanoparticles. Fourier Transform Infrared spectra (FTIR) were used to examine the structures of the samples. It was found out among other things that small amount of 0.6% of MgO nanoparticles in the oil could improve the viscosity of the fluid. It could be concluded that the optimum amount of MgO nanoparticles to be used for nanofliud is 0.6%. Hence, the transesterified rapeseed containing 0.6% of MgO nanoparticles has the potential to used as a biodiesel oil.

Keywords; MgO, Nano-fluid, Rapeseed oil, SEM, XRF, XRD

20. Consequential Dynamics of Violence: Mathematical Insights From Victims For Effective Control

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1Sarki D.S., 2Attang T.I., 3Yilleng MA., 4Iliya G., and 5Sarki B.D.
1,2,3,4Department of Mathematics, Federal College of Education Pankshin, Plateau State, Nigeria
5Department of Science and Technology, Faculty of Education, University of Jos, Plateau State, Nigeria

Abstract
We proposed, developed, and analysed a mathematical model of intergroup behavioural dynamics in a community that is divided between two distinguishable social groups. The model, built using a system of simple ordinary differential equations, is based on intuitively conceived assumptions on violence that are verifiable and conformable to findings in sociological studies. We obtained and performed sensitivity analyses on the basic threshold quantity to have a better understanding of the dynamics of violence in the society. We established correctional conditions that suggest rehabilitation possibilities and potentials.

Keywords: Terrorism, violence, victim, rehabilitation, mathematical model

19. Neural Network Modeling of Relative Humidity and Temperature Distribution Over Nigeria

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by 1Ibeh G. F, 2Ibeh L. M., 3Ogbonna R. C, 4Ofoma J. N and 5Akande S
1 Department of Physics with Electronics, Evangel University Akaeze Ebonyi State, Nigeria;
2 Department of Geography and Environmental Sciences, Ludwig-Maximilians, University of Munich, Germany
3,4 Department of Computer Science and Mathematics, Evangel University Akaeze, Ebonyi State, Nigeria;
5 Centre for Space Research and Application, Federal University of Technology Akure, Nigeria

Abstract
This paper used neural network model to study the distributions of relative humidity and temperature over Nigeria. The theoretical explorations of the relationship between the parameters were reviewed. This study was carried out on thirty-six point stations over Nigeria. Temporal variations of estimation and prediction of relative humidity and temperature were carried out in this study. The results revealed that temperature and relative humidity distributions over Nigeria are in variant. They were inversely proportional to each other as affirmed by other researched. Spatio-temporal variations revealed that relative humidity is higher in wet seasons compared to dry seasons in Nigeria. It is also higher within the Southern part of Nigeria as a result of coastal nature, moisture content in the atmosphere of the region and low temperature gradient. The influences of temperature on relative humidity were study. The results shows inversion with the rates of relative humidity and the rates of temperature both in wet and dry seasons, and within the Southern and Northern part of Nigeria. This could be because increase in temperature raises saturated vapour pressure, which leads to reduction in the relative humidity. The variation of temperature may be due to diabatic heating and adiabatic effects in the atmosphere. Based on the similar signatures of the estimated and observed temporal distributions of the parameters, forecast of two years ahead of the years of the study were successfully achieved. The result showed strong negative relationship between temperature and relative humidity. The correlation coefficient is calculated to be -0.94. This strong negative correlation signifies that as the temperature decreases, the relative humidity increase (and vice versa). The performance of neural network model in the distributions shows the ability of the model in studying atmospheric parameters as confirmed by other researchers.

Keywords: Relative Humidity, Temperature, Neural Network, Diabatic, Adiabatic and Nigeria

18. Feasibility Study of Using PV System As An Alternative Back-up Source Of Electric Power: A Case Study of Zion Hostel University of Jos

by 1N.E.J. Omaghali, 1E.B. Ani 1 , R.J. Pwajok and 2S.O. Anikoh,
1 Department of Physics, University of Jos, Nigeria.
2Federal Polytechnic Nasarawa, Nigeria.

Abstract
The geographical position of Nigeria gives it an advantage in terms of harnessing solar energy. Jos, a city which is located in Plateau State Nigeria, belongs to the north-central region and has latitudes and longitudes of 09°38’N and 08°57’E respectively and is about 1290 meters above sea level. Jos has an average annual temperature of around 27.43oC. In this research, we have used the solar installation as a prototype to design a solar backup system for the Zion Hostel, the University of Jos with the aim of a better, cleaner, cost-effective and more efficient alternative energy source.

Keywords: Solar PV Modules, Battery-Banks, Inverters, Panel Generating Factor, Solar Controllers.

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17. Seir Model With A Vaccination Parameter Using COVID-19 As A Case Study

by Edet Uduak Anietie1 and Etukudo Ini-Obong2.
1Department of Mathematics, University of Uyo, Uyo, Nigeria.
2Department of Economics, University of Uyo, Nigeria.

Abstract
The SEIR mathematical model with a vaccination parameter is formulated to study the spread of COVID-19. The equilibrium points of the system of differential equations are obtained. The local and global stabilities of the disease-free and endemic equilibria are presented. The basic reproduction number of the model is obtained. The parameters used in the model are estimated. The system of differential equations representing the model is solved numerically using the scilab software application. The result of the simulation shows that in the long term, the presence of a vaccination parameter causes the disease to converge to the disease-free equilibrium for any value of the basic reproduction number.

Keywords: Stability, SEIR Model, Vaccination parameter, COVID-19, Scilab

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16. A Discrete Time EOQ Model For Delayed Deteriorating Items With Shortages

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by 1Yakubu M.I. and 2Sani B.
Department of Mathematics, Ahmadu Bello University, Zaria-Nigeria

Abstract
In this work, a discrete time Economic Order Quantity (EOQ) inventory model was developed for delayed deterioration items with shortages. The model consist of three stages in its cycle. In the first stage, the inventory depletes to a certain level due to market demand only while the second stage depletion occurs due to combined effect of market demand and deterioration. In the final stage, shortage time is assumed by the stockist and are fully backlogged. In the first two stages, the demand rates are different but are all constants. The model is used to determine the optimal ordering quantity and replenishment cycle. Numerical example is given to illustrate the application of the model and sensitivity analysis carried out to see the effect of parameter changes.

Keywords: Stockist; Backlogged; Lost sale; Deterioration; Discrete

15. Three-Dimensional Stability Analysis of A Uniaxially Compressed Polynomially Thick Rectangular Plates Using Energy Method

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by Onyeka F C.1, 3, Nwa-David C D.2 and Okeke T E.3*
1 Department of Civil Engineering, Edo State University Uzairue, Edo State.
2Department of Civil Engineering, University of Nigeria, Nsukka.
3Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike.

Abstract
This study presents the three-dimensional (3-D) stability analysis of a uniaxially compressed thick rectangular isotropic plate that is clamped in one edge and the other three edges simply supported (CSSS). The energy method was applied in the coupling the three dimensional kinematics and constitutive relations to formulate the total potential energy equation. The formulated the total potential energy for the plate was transformed into equilibrium equation and used to obtain the shape function of the plate. The shape function derived was analysed through variational principle to get an exact polynomial displacement function which is a product of the coefficient of deflection and shape function of the plate. The expression for the critical buckling load and other formulae was obtained by the direct variation of the total potential energy equation to produce a reliable solution for stability analysis of any type of plate rectangular plate. The span to thickness ratio and aspect ratios were varied to ascertain the buckling behavior of different type of plate under uniformly distributed load. The outcome of the numerical analysis revealed that increase in the span- thickness ratio led to the increased value of the critical buckling load which implies that the plate structure is safe when the plate thickness is increased. The result showed that the critical buckling loads from the present study using the established 3-D model for both functions is satisfactory and were found to follow an identical pattern, but quite distinct in validation which shows the credibility of the derived relationships. The overall average percentage differences between the two functions recorded are 2.06%. This shows that at about 98% both approaches are the same and can be applied with confidence in the stability analysis of any type of plate with such boundary condition.

Keywords: CSSS rectangular plate, stability analysis 3-D plate, exact polynomial function, critical buckling load.

14. Solar Energy Driven-Photocatalysis: Kinetics and Sorption Studies of Cr(VI) Reduction in Paint Effluent

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by Osarumwense J. O and Chris-Abey O. F.
Department of Science Laboratory Technology, Faculty of Life Sciences,
University of Benin, Benin City.

Abstract
Solar energy driven-photocatalysis is a clean and relatively new technology adopted to assuage the environmental problems caused by industrial effluent discharge. Chromium is widely used for the production of pigments for the paint and textile industries. The hexavalent form of chromium, Cr(VI) is highly toxic to human if ingested, and it is capable of causing oxidative damages to the blood cells at low concentration which may lead to hemolysis. In this study, a mixture of titanium oxide (TiO2) and chromium contaminated effluent was irradiated under the sunlight for three hours in batch system. Some operational conditions such as catalyst dosage and exposure time were investigated during the photocatalytic process. Atomic absorption spectrophotometer (AAS) was used to determine the residual Cr(VI) ion in the mixture. The data obtained was subjected to a variety of kinetics models and adsorption equilibrium isotherms; the process was well modeled by pseudo-first kinetics order with a reaction rate constant of 0.0141 min-1.The intra-particle diffusivity model revealed that the uptake of Cr(VI) ion was more of the film diffusion than the intra-particle diffusion. The data obtained from adsorption fitted well into the Langmuir adsorption isotherm with coefficient of determination (R2) of 0.9387; while the Temkin isotherm indicates that the process was exothermic.

Keywords: Solar energy, Photocatalysis, Chromium (VI), Adsorption equilibrium, Intra-particle diffusion.

13. Investigating Trusted Routing Mechanism On A Full-Meshed Telecommunication Network Model

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by OSUOLALE A. TIAMIYU
Department of Telecommunication Science, University of Ilorin

Abstract
The article is on the study of the properties of the trusted routing mechanism via simulation experiments of a fully-meshed telecommunication network model. The description of the model, the experimental results and their interpretations are given.

Keywords: Trusted routing, routing mechanism, telecommunication network, node monitoring, trusted node,
network agent.

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