School of Physical Sciences (SPS)
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Item 2-DIMENTIONAL MODELS OF THE STRUCTURAL FEATURES WITHIN THE LOWER BENUE AND UPPER ANAMBRA BASINS NIGERIA, USING (2009) AEROMAGNETIC DATA(Journal of Science, Technology, Mathematics and Education (JOSTMED),, 2015-08) ADETONA, Adebayo Abbass, ABU MallamAnalysis base on the CET shows that the basement rocks to the North and Southern edge of the study area intrude into the sedimentary formation. At the lower (middle-portion) of the study area (within Angba and Otukpo sheets) are structures that are Basaltic rocks that intrude into the basement. It is believed that these structures must have predated the depositional period of the sedimentary formation. Several fracture and fault lines are detected on the CET map, most prominent among is that which start from the Eastern end (latitude 7.450 and longitude 8.300 ) and ends at the Southern end (Latitude 7.000 longitude 7.450 ).cutting the South Western corner of the study area diagonally. Secondly is that which runs vertically and is parallel to the course of River Niger within this area, supporting the assertion that the River Niger is structurally controlled. The 2-dimentional models of the six profiles revealed sedimentary formations whose susceptibility values are zero (0). Maximum depth of about ten (10) kilometers was obtained within the Southern end of the study area, but a maximum thickness of sedimentation of about four (4) kilometers was observed on profile six within Nkporo formation. The basement susceptibility varies from 0.002 to 0.004 but in some places it is as high as 0.007. Structural, 2-dimensional, Exploration Targeting, Total Magnetic IntensityItem A 4-Step Order (K + 1) Block Hybrid Backward Differentiation Formulae (BHBDF) for the Solution of General Second Order Ordinary Differential Equations(2023-12) Muhammad R; Hussaini AIn this paper, the block hybrid backward differentiation formulae (BHBDF) for the step number 𝑘 = 4 was developed using power series as basis function for the solution of general second order ordinary differential equation. The idea of interpolation and collocation of the power series at some selected grid and off- grid points gave rise to continuous schemes which were further evaluated at those points to produce discrete schemes combined together to form block methods. Numerical problems were solved with the proposed methods and were found to perform effectively.Item A Comparative Study Of Two Iterative Techniques For Systems Of Linear Algebraic Equations(Academic Staff Union of Universities, Nigeria, 2021-12-20) Khadeejah James AuduThis study compares numerically two iterative methods for solving systems of linear algebraic equations: the Symmetric Accelerated Overrelaxation technique and the Symmetric Successive Overrelaxation method. Four numerical problems are applied to analyze and compare the convergence speeds of the two approaches. On the basis of performance metrics including spectral radius, convergence time, accuracy, and number of iterations required to converge, the numerical results demonstrate that the Symmetric Accelerated Overrelaxation approach needed less computing time, a smaller spectral radius, and fewer iterations than the Symmetric Successive Overrelaxation approach. This demonstrates that the Symmetric Accelerated Overrelaxation is superior to the Symmetric Successive Overrelaxation. Researchers and numerical analysts can benefit from the findings of this study; it will help them comprehend iteration techniques and adopt an appropriate or more efficient iterative strategy for solving systems of linear algebraic equations.Item A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics(Elsevier BV, 2023-12) Adesoye Idowu Abioye; Olumuyiwa James Peter; Hammed Abiodun Ogunseye; Festus Abiodun Oguntolu; Tawakalt Abosede Ayoola; Asimiyu Olalekan OladapoThis study proposes a fractional-order mathematical model for malaria and COVID-19 co-infection using the Atangana–Baleanu Derivative. We explain the various stages of the diseases together in humans and mosquitoes, and we also establish the existence and uniqueness of the fractional order co-infection model solution using the fixed point theorem. We conduct the qualitative analysis along with an epidemic indicator, the basic reproduction number R0 of this model. We investigate the global stability at the disease and endemic free equilibrium of the malaria-only, COVID-19-only, and co-infection models. We run different simulations of the fractional-order co-infection model using a two-step Lagrange interpolation polynomial approximate method with the aid of the Maple software package. The results reveal that reducing the risk of malaria and COVID-19 by taking preventive measures will reduce the risk factor for getting COVID-19 after contracting malaria and will also reduce the risk factor for getting malaria after contracting COVID-19 even to the point of extinction.Item A MATHEMATICAL MODEL OF SCABBY MOUTH DISEASE INCORPORATING THE QUARANTINE CLASS.(39th Annual Conference of the Nigerian Mathematical Society, (NMS), 2021-04-23) Abdurrahman, Nurat Olamide; Somma S. A.; Aboyeji Folawe Ibironke; Akinwande Ninuola IfeoluwaWe propose a mathematical model to study the transmission and control of scabby mouth disease in sheep, incorporating the vaccinated and quarantine classes. The Disease-free equilibrium was obtained, and the reproduction number was also computed. The local stability of DFE was analyzed for stability. Sensitivity analysis of the basic reproduction number with respect to some parameters of the model was carried out, and the sensitive parameters withR_0 are presented graphically. The local stability of DFE is stable if R_0<1. The sensitivity analysis shows that the contact rateα is the most sensitive parameter to increase the spread of the disease, and vaccination rate ω is the highest sensitive parameter to control the transmission of scabby.Item A MATHEMATICAL MODEL OF YELLOW FEVER DISEASE DYNAMICS INCORPORATING SPECIAL SATURATION INTERACTIONS FUNCTIONS(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Akinwande, N. I.; Abdulrahman, S.; Ashezua, T. T.; Somma, Samuel AbuWe proposed an Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Process functions, obtained the equilibrium states of the model equations and analyzed same for stability. Conditions for the elimination of the disease in the population are obtained as constraint inequalities on the parameters using the basic reproduction number 0 R demographic and epidemiological data. . Graphical simulations are presented using someItem A Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Interactions Functions(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Akinwande, N. I.; Abdulrahman, S.; Ashezua, T. T.; Somma, Samuel AbuWe proposed an Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Process functions, obtained the equilibrium states of the model equations and analyzed same for stability. Conditions for the elimination of the disease in the population are obtained as constraint inequalities on the parameters using the basic reproduction number 0R . Graphical simulations are presented using some demographic and epidemiological data.Item A MULTIGRID METHOD FOR NUMERICAL SOLUTION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS(IJSAR Journal of Mathematics and Applied Statistics (IJSAR-JMAS), 2022-12) I. O. Isah; A. Ndanusa; R. Muhammad; K. A. Al-MustaphaTechniques and analyses of multigrid method for solving elliptic partial differential equations (PDEs) in two dimensions are presented. The focal point of this paper is the applicability of the parametric reaccelerated overrelaxation (PROR) iterative method as a smoother in multigrid solution of elliptic PDEs. The two-dimensional Poisson equation on a unit square domain with Dirichlet boundary conditions is adopted as the model PDE. We present some practical formulae and techniques for building the various multigrid components using Kronecker tensor product of matrices. In addition, we carryout smoothing analysis of the PROR method using Local Fourier Analysis (LFA) and show how optimal relaxation parameters and smoothing factors can be obtained from analytic formulae derived to ensure better convergence. This analysis combines full standard coarsening strategy (doubling) and second order finite difference scheme. The result of PROR smoothing factors in comparison with those of other widely used smoothers is also presented. Results obtained from numerical experiment are displayed and compared with theoretical results.Item A non-linear differential equation model of COVID-19 and seasonal influenza co-infection dynamics under vaccination strategy and immunity waning(Elsevier BV, 2023-12) Rabiu Musa; Olumuyiwa James Peter; Festus Abiodun OguntoluThis study presents a mathematical model of the transmission dynamics of COVID-19 and influenza co-infection. The potential impacts of the influenza vaccine only on the co-infection dynamics and the potential impacts of both vaccines on the co-infection dynamics are thoroughly studied. The basic reproduction number for the two diseases using the next-generation matrix approach and the stability of the sub-model is examined. The model assessed the scenario whereby both diseases’ waning immunity occurs concurrently to check the epidemic peaks. The numerical simulation results show that the diseases would continue to be endemic in the population if the immunity waning rates increase. The epidemic peak can be reduced by increasing vaccination and vaccine efficacy rates. The results show that the COVID-19 contact rate significantly increases the epidemic level more than the co-infection contact rate. A similar result was obtained when it was observed that the COVID-19 post-recovery waning rate has more significant effects on the epidemic peak than the co-infection post-recovery waning rate. A possible reason for this counter-intuitive occurrence is that two infections cannot have the same viral load nor the same within-host competitiveness. This means an infectious co-infected person will transmit the infection with the highest within-host competitiveness. Here, it is suspected that COVID-19 has a within-host competitive advantage over influenza in the co-dynamics.Item A NOTE ON COMBUSTIBLE FOREST MATERIAL (CFM) OF WILDLAND FIRE SPREAD(Proceedings of 3rd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2021-10-28) Zhiri, A. B.; Olayiwola, R. O.; Somma Samuel Abufire is presented. The equations describing the fractional components of forest fire were carefully studied. The reaction before a forest can burn or before fire can spread must involves fuel, heat and oxygen. The coupled dimensionless equations describing the phenomenon have been decoupled using perturbation method and solved analytically using eigen function expansion technique. The results obtained were graphically discussed and analysed. The study revealed that varying Radiation number and Peclet energy number enhances volume fractions of dry organic substance and moisture while they reduced volume fraction of coke.Item A Note on Combustible Forest Material (CFM) of Wildland Fire Spread(Proceedings of 3rd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2021-10-28) Zhiri, A. B.; Olayiwola, R. O.; Somma, Samuel AabuIn this paper, a mathematical model for combustible forest material of a wildland fire is presented. The equations describing the fractional components of forest fire were carefully studied. The reaction before a forest can burn or before fire can spread must involves fuel, heat and oxygen. The coupled dimensionless equations describing the phenomenon have been decoupled using perturbation method and solved analytically using eigen function expansion technique. The results obtained were graphically discussed and analysed. The study revealed that varying Radiation number and Peclet energy number enhances volume fractions of dry organic substance and moisture while they reduced volume fraction of coke.Item A STUDY OF CHEMICALLY DEPOSITED OXIDE- BASED TERNARY THIN FILM OF ZINC TITANATE (ZnTiO3) DOPED WITH NATURAL DYES AND THEIR POTENTIAL PHOTOVOLTAIC APPLICATIONS.(journal of nano and material science research, 2025) Eze, C. N.The ternary metal oxide thin film of ZnTiO3 doped with three different natural dyes were synthesized on glass substrate via solution growth (SG) at room temperature. Chemical baths were used which contained Zinc Sulphate (ZnSO4.7H2O), Sodium Hydroxide (NaOH), Titanium Chloride (TiCl3), distilled water and calibrated drops per bath of organic dyes: Lawsonia inermis, Beta vulgaries and Jatropha curcas respectively. Each deposit which was set at a temperature of 80 0C lasted for 1 h and each deposit was annealed at 400 0C for 1 h. These deposited nano thin films were characterized for their structural, morphological, optical properties, elemental composition and electronic (chemical) structure and presence of functional groups by means of X-ray diffraction (XRD), Scanning Electron Microscope (SEM), UV-VIS spectrophotometer, Energy Dispersive X-ray Fluoroscopy (EDXRF) and photoluminescence Fourier Transform Infrared Radiation Spectroscopy (FTIR). Polycrystalline thin films were evidenced which marked porosity offered them maximum surface area for dye loading which is critical for photosensitization in dye sensitized solar cells (DSSCs). Such doping presented band gaps of doped ZnTiO3 from 1.84 eV to 3.45 eV depending on dopants applied as against undoped film band gap that was 3.55 eV. The FTIR results showed good photophysical, carboxylate and modification properties of the dyes which helps in sunlight harvesting, anchoring and surface structure modification of the films. The dye influenced the optical properties of the samples and in particular, the reduction of the energy band gap, Eg from an increase in absorption coefficient α, giving high absorbance A, low extinction coefficient k, low reflectance R, which inferred its potential applications in solar energy devices when used in construction, poultry houses, solar cells and DSSCs.Item A TWO POINT BLOCK HYBRID METHOD FOR SOLVING STIFF INITIAL VALUE PROBLEMS(JOURNAL OF MATHEMATICAL SCIENCES, 2011) Muhammad RIn this paper, a self starting hybrid method of order (3, 3,3) is proposed for the solution of stiff initial value problem of the form y' = f(x.y). The continous formation of the integrator enables us to differentiate and evaluate at grid and off grid points. The schemes compared favourably with exact results and results from Okunuga (2008)Item Agreement between the Homotopy Perturbation Method and Variation Iterational Method on the Analysis of One-Dimensional Flow Incorporating First Order Decay(SCHOOL OF PHYSICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA, 2019-06-28) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.In this paper, a comparative study of reactive contaminant flow for constant initial concentration in one dimension is presented. The adsorption term is modeled by Freudlich Isotherm. An approximation of the one-dimensional contaminant flow model was obtained using homotopy-perturbation transformation and the resulting linear equations were solved semi-analytically by homotopyperturbation method (HPM) and Variational Iteration Method (VIM). Graphs were plotted using the solution obtained from the methods and the results presented and discussed. The analysis of the results obtained show that the concentration of the contaminant decreases with time and distance as it moves away from the origin.Item An Accelerated Iterative Technique: Third Refinement of Gauss-Seidel Algorithm for Linear Systems(MDPI, 2023-05-01)This study presents a novel accelerated iterative method referred to as the Third Refinement of the Gauss-Seidel Algorithm (TRGS) for solving large-scale linear systems of equations. By integrating a three-level refinement strategy into the classical Gauss-Seidel method, the proposed technique significantly improves the convergence rate and computational efficiency. The method is rigorously analyzed for consistency, stability, and convergence, and is evaluated through numerical experiments on various benchmark problems. Results demonstrate that the TRGS algorithm outperforms both the traditional Gauss-Seidel and other refinement-based methods in terms of iteration count and solution accuracy. This advancement offers a valuable contribution to numerical linear algebra, particularly in scientific computing where fast and accurate solutions to linear systems are critical.Item An Appraisal on the Application of Reproduction Number for the Stability Analysis of Disease - Free Equilibrium State for S-I-R Type Models(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD) 2024, 2024-02-28) Abdurrahman, Nurat Olamide; Somma S. A.; Akinwande, N. I.; Ashezua, T. T.; Gweryina, R.One of the key ideas in mathematical biology is the basic reproduction number, which can be utilized to comprehend how a disease epidemic profile might evolve in the future. The basic reproduction number, represented by R0 , is the anticipated number of secondary cases that a typical infectious individual would cause in a population that is fully susceptible. This threshold parameter is highly valuable in characterizing mathematical problems related to infectious diseases. If R0 < 1, this suggests that, on average, during the infectious period, an infected individual produces less than one new infected individual, suggesting that the infection may eventually be eradicated from the population. On the other hand, if R0 < 1, every infected person develops an average of multiple new infections, it suggests that the disease may continue to spread throughout the population. We discuss the Reproduction number in this work and provide some examples, both for straightforward and complicated situations.Item An Implicit Runge-Kutta Type Method for the Solution of Initial Value Problems(KASU JOURNAL OF MATHEMATICAL SCIENCES, 2020-06) R. Muhammad; Y. A. Yahaya; A. S. AbdulkareemIn this research paper, an implicit block hybrid Backward Differentiation Formula (BDF) for 𝑘=2 is reformulated into a Runge-Kutta Type Method (RKTM) of the same step number. The method can be used to solve both first and second order (special or general form) initial value problem in Ordinary Differential Equation (ODE). This method differs from conventional BDF as derivation is done only once. It can also be extended to solve higher order ODE.Item An insight into advanced glass systems for radiation shielding applications: A review on different modifiers and heavy metal oxides-based glasses.(CELL PRESS, 2024) Al-Buriahi, M. S., Kurtulus, R., Eke, C., Alomairy, S.; OLARINOYE, OYELEKEIonizing radiation from natural and many synthetic sources is a remarkable tool in many scientific, production, quality control, food preservation, medical, security, and other technological processes. The need to protect humans (public and personnel), gadgets, the environment, and animals from the harmful effects of radiation, while maintaining and expanding the scope of application has made radiation protection an important topic to discuss. Among the methods and materials available for radiation control, shielding and the use of glass shields are the most effective and attractive methods and materials, respectively. In this report, the basic parameters for measuring shielding competences, basic shielding materials and their shortcomings, and glass shields are discussed. Five categories of glasses, namely, borate, germanate, silicate, phosphate, and tellurites, with important shielding attributes, are reviewed. The role of chemical composition, density, and mean atomic number as gamma shielding delineating factors was emphasized. The weaknesses and comparable advantages of each glass system were presented as well. The review concludes by looking at the trend and future of glass shields and research in radiation technology. The data and analysis presented in this review provides scientists and radiation protection technologist on the impact of certain chemical oxides on shielding efficacies of different glass systems.Item AN OPTIMIZED SINGLE-STEP BLOCK HYBRID NYSTRÖM-TYPE METHOD FOR SOLVING SECOND ORDER INITIAL VALUE PROBLEMS OF BRATU-TYPE(African Journal of Mathematics and Statistics Studies, 2023-12-12) Joel Olusegun Ajinuhi; Umaru Mohammed; Abdullahi Idris Enagi; Onanmayi Razaq JimohIn this paper, a global single-step implicit block hybrid Nyström-type method (BHNTM) for solving nonlinear second-order initial-boundary value problems of Bratu-type is developed. The mathematical derivation of the proposed BHNTM is based on the interpolation and multistep collocation techniques with power series polynomials as the trial function. Unlike previous approaches, BHNTM is applied without linearization or restrictive assumptions. The basic properties of the proposed method, such as zero stability, consistency and convergence are analysed. The numerical results from three test problems demonstrate its superiority over existing methods which emphasize the effectiveness and reliability in numerical simulations. Furthermore, as the step size decreases as seen in the test problems, the error drastically reduces, indicating BHNTM's precision. These findings underscore BHNTM's significance in numerical methods for solving differential equations, offering a more precise and dependable approach for addressing complex problems.Item Analysis of Electrical Resistivity Survey Data for Aquifer Potential and Protective Capacity at Mararaba Dan-Daudu Minna, North Central Nigeria(Published by Science Publishing Group online, 2023) ADETONA, Adebayo AbbassAbstract: It is a fact that basement complex regions lacks sufficient overburden that can host sustainable water table, water bearing fractured/weathered rocks referred to as aquifers are usually identified via suitable geophysical methods to proffer solution to water challenges within these regions. This current study targets the exploration of groundwater potential within the Mararaba Dan-daudu community, a suburb of Minna metropolis. Electrical resistivity method was employed to delineate aquifer prospects and their protective capacity within the area of study. The data from thirty-six Vertical Electrical Sounding (VES) survey points were acquired and analysed. Survey points were aligned along six profiles (A – F) with six VES points per profile. Interpretation of VES points along profiles was helpful in determining the number of layers and thickness. The analysis revealed mainly three layers comprising of sand and fresh laterite at the first layer, fractured/weathered basement at the second layer and fresh basement at the third layer. Iso-resistivity mapping was also done at various depths (surface, 5 m, 10 m, 15 m, 20 m, 30 m and 40 m) respectively to investigate the lateral variations of resistivity over a horizontal plane. These showcased the electrical conductance sliced at the depths of interest. Thirteen VES points (A1, A5, A6, B1, B3, B6, C6, D6, E6, F1, F2, F4 and F5) were mapped as having good prospective aquifer properties. Longitudinal conductance was computed for the outlined VES points to determine their Aquifer Protective Capacity (APC). The result of (APC) rating for the 13 VES revealed the frequency and percentage of APC ranged as: 2 VES locations (15.4%) have good APC, 8 VES locations (61.5%) have moderate APC and 3 VES location (23.1%) have weak APC. with only 3 VES locations out of 13 VES locations in the study area revealed weak APC, the results proved that the groundwater potential of the study area has moderately good APC