Journal of the Nigerian Society of Physical Sciences <p>Journal of the Nigerian Society of Physical Sciences is a peer-reviewed journal published quarterly (February, May, August &amp; November) by the Nigerian Society of Physical Sciences. It offers an exciting publication outlet for Physical Science reports.</p> en-US (Babatunde James Falaye (Ph.D.)) (Graxynet) Fri, 31 Jul 2020 23:30:38 +0000 OJS 60 A Purusit Differential Game Problem on a Closed Convex Subset of a Hilbert Space <p>We study a pursuit differential game problem with finite number of pursuers and one evader on a nonempty closed convex subset of the Hilbert space <em>l<sub>2</sub></em>. Players move according to certain first order ordinary differential equations and control functions of the pursuers and evader are subject to integral constraints. Pursuers win the game if the geometric positions of a pursuer and the evader coincide. We formulated and prove theorems that are concern with conditions that ensure win for the pursuers. Consequently, wining strategies of the pursuers are constructed. Furthermore, illustrative example is given to demonstrate the result.</p> Abbas Ja'afaru Badakaya, Bilyaminu Muhammad Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 An Examination of a Second Order Numerical Method for Solving Initial Value Problems <p>This paper presents an examination of a Second Order Convergence Numerical Method (SOCNM) for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). The SOCNM has been derived via the interpolating function comprises of polynomial and exponential forms. The analysis and the properties of SOCNM were discussed. Three numerical examples have been solved successfully to examine the performance of SOCNM in terms of accuracy and stability. The comparative study of SOCNM, Improved Modified Euler Method (IMEM), Fadugba and Olaosebikan Scheme (FOS) and the Exact Solution (ES) is presented. By varying the step length, the absolute relative errors at the final nodal point of the associated integration interval are computed. Furthermore, the analysis of the properties of SOCNM shows that the method is consistent, stable, convergent and has second order accuracy. Moreover, the numerical results show that SOCNM is more accurate than IMEM and FOS and also compared favourably with the ES. By varying the step length, there are two-order decrease in the values of the final absolute relative errors generated via SOCNM. Hence, SOCNM is found to be accurate, stable and a good tool for the numerical solutions of IVPs of different characteristics in ODEs.</p> S. E. Fadugba, S. N. Ogunyebi, B. O. Falodun Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Dissolution of a Nigerian sourced Muscovite ore for use as an ingredient in paint production <p>Dissolution and characterization studies on the purification of muscovite ore in hydrochloric acid for use in paint production was investigated. Specific dissolution parameters including the effects of acid concentration as well as temperature on the dissolution of muscovite ore were studied. Important instrumentation techniques such as X-ray Fluorescence (XRF), X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) were employed for the better explanation of the dissolution process so as to fathom the availability of elements and compounds within the ore. The results revealed that the dissolution rates were considerably influenced as the acid concentration and temperature increased, while at optimal leaching conditions, about 85 % of the ore was found to have been reacted by 2.5 mol/L at 75<sup>o</sup>C temperature and at 120 minutes of leaching time. The reaction order for the dissolution can be deduced to be half order reaction as the value obtained was in the bracket of 0.50. The reaction kinetic data revealed the dissolution mechanism to involve diffusion and surface chemical mechanisms as the rate-controlling mechanisms while the different instrumentation techniques corroborated the dissolution as well as purification of the muscovite ore as an ingredient for possible use in paint production.</p> Daud Olaoluwa, Abdulhadi E. Abdulmalik, Taoreed A. Muraina, Sadisu Girigisu, Ayo F. Balogun Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations <p>Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned. However, there are numerous forms of them existing in lower and higher orders of the classical method. This work investigates the linear stabilities and abilities of some selected explicit members of these Runge-Kutta methods in integrating the singular Lane-Emden differential equations. The results obtained established the ability of the classical Runge-Kutta method and why is mostly used in computations.</p> M. O. Ogunniran, O. A. Tayo, Y. Haruna, A. F. Adebisi Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Perturbed Collocation Method For Solving Singular Multi-order Fractional Differential Equations of Lane-Emden Type <p>In this work, a general class of multi-order fractional differential equations of Lane-Emden type is considered. Here, an assumed approximate solution is substituted into a slightly perturbed form of the general class and the resulting equation is collocated at equally spaced interior points to give a system of linear algebraic equations which are then solved by suitable computer software; Maple 18.</p> O. A. Uwaheren, A. F. Adebisi, O. A. Taiwo Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Modelling and Forecasting Climate Time Series with State-Space Model <p>This study modelled and estimated climatic data using the state-space model. The study was specifically to identify the pattern of the trend movement i.e., increase or decrease in the occurrence of the climatic change; to use of Univariate Kalman Filter for the computation of the likelihood function for climatic projections; to modelling the climatic dataset using the state-space model and to assess the forecasting power of the state-space models. The data used for the work includes temperature and rainfall for periods January 1991 to December 2017. The data are tested for normality. Shapiro-Wilk, Anderson-Darling and Kolmogorov-Smirnov test of normality for the climatic data all showed that the variables are not normally distributed. The work spans the use of breaking trend regression model to fit climatic data to estimate the slopes which show much increase in climatic data has been recorded from the initial time data collection until the present. Investigations and diagnostic are carried out by checking for corrections in the residuals and also checking for periodicity in the residuals. The results of this investigation show significant autocorrelation in the residuals indicating the presence of underlying noise terms which is not accounted for. By treating the residual as an autoregressive moving average (ARMA) process whereby we can obtain its spectral density, the result from the parametric spectral estimate shows underlying periodic patterns for monthly data, thus, leads to a discussion on the need to treat climatic data as a structural time series model. We select appropriate models by considering the goodness of fit of the model by comparing the Akaike information criterion (AIC) values. Parameters are estimated and accomplished with some measures of precision.</p> A. F. Adedotun, T. Latunde, O. A. Odusanya Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 L-Stable Block Hybrid Numerical Algorithm for First-Order Ordinary Differential Equations <p>In this work, a one-step L-stable Block Hybrid Multistep Method (BHMM) of order five was developed. The method is constructed for solving first order Ordinary Differential Equations with given initial conditions. Interpolation and collocation techniques, with power series as a basis function, are employed for the derivation of the continuous form of the hybrid methods. The discrete scheme and its second derivative are derived by evaluating at the specific grid and off-grid points to form the main and additional methods respectively. Both hybrid methods generated are composed in matrix form and implemented as a block method. The stability and convergence properties of BHMM are discussed and presented. The numerical results of BHMM have proven its efficiency when compared to some existing methods.</p> B. I. Akinnukawe, K. O. Muka Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Measurement of the Excited Energies Identified in 42Ca using the ROSPHERE Gamma-ray Arrays <p>Excited energy states totalling 11 in number identified to be associated with the <sup>42</sup>Ca were detected via the ROSPHERE gamma-ray array detectors of IFIN-HH Bucharest from a <sup>28</sup>Si(<sup>18</sup>O, 2p2n), where a multi-particle of 2 protons and 2 neutrons were evaporated in a fusion reaction. The excited energies were identified using γ-ray coincidences. All detected gamma energies (γ) recorded were compared with various literatures from NNDC and this shows an excellent agreement with each and the results are presented together with their calculated relative intensities.</p> T. Daniel, A. A. McAsule Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 On the Investment Strategy, Effect of Inflation and Impact of Hedging on Pension Wealth during Accumulation and Distribution Phases <p>This paper studies the various results obtained in literature on the investment strategy, the effect of inflation and impact ofh edging on the Pension Wealth generation. The explicit solution of the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions are obtained, both in the accumulation and distribution phase, using Legendre transform, dual theory, and change of variable techniques. It is established herein that the elastic parameter ( B) is not equal to one (B = 1), based on the assumption of our model. Theorems are constructed and proved on the various wealth investment strategies.<br>Observations and significant results are made and obtained, respectively in the comparison of our various utility functions and some previous results in literature. Sensitivity analysis and Simulations on the various utility functions and optimal strategies during the accumulation and distribution phase are presented; when the existence of a elastic parameter that is not equal to one, when there is existence of modifying factors, when there is need for diversification of investment, when there is no significant effect of the choice of risk aversion strategy on investment returns during inflation period, when there is hedging ability of Inflation indexed Bond and Inflation-linked Stock and when there is insignificant effect of the orthogonal relationship between stock and time and nonpayment of pension benefits on the satisfaction of the investors.</p> Bright O. Osu, K. N. C. Njoku, B. I. Oruh Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 The Mass Resolution of Ca, K Isotopes and CO, N2 and C2H4 Isobars in Isotopes Separator On-Line trap Mass spectrometry <p>In Isotopes separator on-line trap, ions are trapped, cooled, accumulated, bunched and isotopes or isobars are separated, cyclotron frequencies are determined, which are followed by time of flight mass resolution. The mass resolution of isotopes in Penning trap mass spectrometry is achieved by the direct excitation of axial motion of ions, driven by RF field at the pure cyclotron frequencies of ions. The design and working of Isotopes separator on-line trap which is used for high-accuracy mass spectrometry in the mass resolution of calcium isotopes (<sup>40</sup>Ca<sup>+</sup>, <sup>42</sup>Ca<sup>+</sup>, <sup>44</sup>Ca<sup>+</sup>), potassium isotopes (<sup>39</sup>K<sup>+</sup>, <sup>41</sup>K<sup>+</sup>) and [<sup>28</sup>(CO)]<sup>+</sup>, [(<sup>28</sup>N<sub>2</sub>)]<sup>+</sup>, [<sup>28</sup>(C<sub>2</sub>H<sub>4</sub>)]<sup>+</sup> isobars found in mixtures is achieved from time of flight mass spectrometry are presented here.</p> Dyavappa B M Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Portfolio Strategy for an Investor with Logarithm Utility and Stochastic Interest Rate under Constant Elasticity of Variance Model <p>This paper is aim at maximizing the expected utility of an investor’s terminal wealth; to achieve this, we study the optimal portfolio strategy for an investor with logarithm utility function under constant elasticity of variance (CEV) model in the presence of stochastic interest rate. A portfolio comprising of one risk free asset and one risky asset is considered where the risk free interest rate follows the Cox- Ingersoll-Ross (CIR) model and the risky asset is modelled by CEV. Using power transformation, change of Variable and asymptotic expansion technique, an explicit solution of the optimal portfolio strategy and the Value function is obtained. Furthermore, numerical simulations are presented to study the effect of some parameters on the optimal portfolio strategy under stochastic interest rate.</p> Edikan E. Akpanibah, Udeme Ini Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000 Evaluation of Aquifer Protective Capacity and Groundwater Potential in Part of Iju, Akure-North, Ondo State, Nigeria <p>Groundwater potential and aquifer protective capacity of the overburden unit was evaluated in part of Iju, Akure North, Ondo State using integrated geophysical methods involving Very Low Frequency Electromagnetic (VLF-EM) profiling and Vertical Electrical Sounding (VES). Four major traverses were established of varying length extents. The VLF-EM measurements were taken along the four major profiles of 10 m station interval.<br>Forty two (42) Vertical Electrical Soundings were also conducted with half electrode spacing varying between 1 and 100 m and interpretation was done using the partial curve matching techniques and computer aided iteration. Five subsurface geological units were identified from geoelectric sections, consisting of the top soil, lateritic, weathered, partly weathered and fresh basement layers consecutively. For the first layer, resistivity<br>ranges between 23 and 323 Ωm with values of thickness ranging between 0.5 and 2.2 m. The resistivity and thickness of the second (lateritic) layer range from 132 to 430 Ωm and 1.6 to 4 m respectively. The resistivity of the weathered layer ranges from 4 to 94 Ωm and variable thickness between 10 and 24.4 m. The fourth layer has a resistivity value range of 65 to 120 Ωm and thicknesses between 20 and 30 m. The basement bedrock (fifth layer) has resistivity values between 770 and 820 Ωm. The depth to bedrock ranges from 1.8 to 31 m. The geophysical data and the basement aquifer delineated were then used to evaluate the hydrogeological setting and aquifer protective capacity of the study area. The observation from the results shows that close to 70 % of the study area falls within the zones of low groundwater potential, 25 % falls within medium potential zones while only 5 % make up the high potential zones. 75 % of the study area constituted the weak to poor protective capacity zones.</p> <p>&nbsp;</p> A. Olajide, S. Bayode, T. Fagbemigun, A. Oyebamiji, J. Amosun, A. Owasanoye Copyright (c) 2020 Journal of the Nigerian Society of Physical Sciences Sat, 01 Aug 2020 00:00:00 +0000