School of Physical Sciences (SPS)

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School of Physical Sciences (SPS)

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A Mathematical Model for Estimating the Weight of Human Beings Using Some Anthropometric Parameters (A Case Study of Taraba State of Nigeria’s Community)
(British Journal of Mathematics & Computer Science, 2015-03-27) Ogwumu, O. D.; Amoo, S. A.; Eguda, F. Y.; Adeyefa, E. O.; Abubakar, Samuel
The research is concerned with the development of a mathematical model for estimating the body weight of human beings in relation to some of their anthropometric parameters (height and waist sizes). The model was optimized to know whether it is possible for humans to have a maximum or minimum body weight. However, the optimization result showed that there is no specific body weight that could be called a maximum or minimum. Emphasis was laid mainly on a particular proportion of Nigerians from the north- west geopolitical zone (as a case study ) in order to be able to make generalizations about the entire country and beyond. Hence, the population sample for the research was the Taraba State of Nigeria’s Community. Moreover, several recommendations were made at the end of the model analysis which when adhered to, would bring about some medical breakthroughs to the entire human populace.
A Mathematical Model for Water Quality Assessment: Evidence-Based from Selected Boreholes in Federal University Dutse, Nigeria
(UMYU Scientifica, 2023-12-30) Eguda, F. Y.; Amoo, A. O.; Adamu, S. B.; Ogwumu, O. D.; Somma, Samuel Abu; Babura I. B.
The present study assessed the quality of water sampled from different boreholes on the campus of Federal University Dutse, Nigeria, using a mathematical modelling approach. A model for estimating water quality was developed based on physicochemical parameters such as pH, electrical conductivity, temperature, turbidity, and total hardness measured from each borehole. The correlation analysis of physicochemical data indicates a strong correlation of about 99% between the real-life data collected from six (6) different boreholes and the model’s predictions. From the results, the sensitivity analysis revealed that electrical conductivity plays the highest role in determining water quality, followed by total hardness, temperature has the third highest impact, followed by turbidity, the fourth, and pH has the least impact in determining water quality in the listed boreholes. Therefore, in any case of intervention, the water quality regulatory body should be sent regularly to the tertiary institutions in the state for routine check-ups.
A Mathematical Model of a Yellow Fever Dynamics with Vaccination
(Journal of the Nigerian Association of Mathematical Physics, 2015-11) Oguntolu, F. A.; Akinwande, N. I.; Somma, Samuel Abu; Eguda, F. Y.; Ashezua. T. T.
In this paper, a mathematical model describing the dynamics of yellow fever epidemics, which involves the interactions of two principal communities of Hosts (Humans) and vectors (mosquitoes) is considered .The existence and uniqueness of solutions of the model were examined by actual solution. We conduct local stability analysis for the model. The results show that it is stable under certain conditions. The system of equations describing the phenomenon was solved analytically using parameter-expanding method coupled with direct integration. The results are presented graphically and discussed. It is discovered that improvement in Vaccination strategies will eradicate the epidemics.
A MATHEMATICAL MODEL OF MEASLES DISEASE DYNAMICS
(Journal of Science, Technology, Mathematics and Education (JOSTMED), 2012-08-25) Abubakar, Samuel; Akinwande, N. I.; Abdulrahman, S.
In this paper a Mathematical model was proposed for measles disease dynamics. The model is a system of first order ordinary differential equations with three compartments: Susceptible S(t); Infected I(t) and Recovered R(t). The equilibrium state for both Disease Free and Endemic equilibrium are obtained. Conditions for stability of the Disease Free and Endemic equilibrium are obtained from characteristics equation and Bellman and Cooke theorem respectively. The hypothetical values were used to analyze the Endemic Equilibrium and the result was presented in tabular form. The results from the Disease Free and Endemic Equilibrium state showed that once the epidemic breaks out, the population cannot sustain it.
A MATHEMATICAL MODEL OF MONKEY POX VIRUS TRANSMISSION DYNAMICS
(Ife Journal of Science, 2019-06-10) Somma, Samuel Abu; Akinwande, N. I.; Chado, U. D.
In this paper a mathematical model of monkey pox virus transmission dynamics with two interacting host populations; humans and rodents is formulate. The quarantine class and public enlightenment campaign parameter are incorporated into human population as means of controlling the spread of the disease. The Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) are obtained. The basic reproduction number R 0 < h and R 0r 1 and R 1 < are computed and used for the analysis. The Disease Free Equilibrium (DFE) is analyzed for stability using Jacobian matrix techniques and Lyapunov function. Stability analysis shows that the DFE is stable if .
A Mathematical Study of Contaminant Transport with First-order Decay and Time-dependent Source Concentration in an Aquifer
(Universal Journal of Applied Mathematics, 2013-11-05) Olayiwola, R. O.; Jimoh, O. R.; Yusuf, A.; Abubakar, Samuel
A mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.
A Novel Seventh-Order Implicit Block Hybrid Nyström-Type Method for Second- Order Boundary Value Problems
(INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI), 2023-11-05) Joel Olusegun Ajinuhi; Umaru Mohammed; Abdullah Idris Enagi; JIMOH, OMANANYI RAZAQ
This paper introduces a novel approach for solving second-order nonlinear differential equations, with a primary focus on the Bratu problem, which holds significant importance in diverse scientific areas. Existing methods for solving this problem have limitations, prompting the development of the Block Hybrid Nystrom-Type Method (BHNTM). BHNTM utilizes the Bhaskara points derived, using the Bhaskara cosine approximation formula. The method seeks a numerical solution in the form of a power series polynomial, efficiently determining coefficients. The paper discusses BHNTM's convergence, zero stability, and consistency properties, substantiated through numerical experiments, highlighting its accuracy as a solver for Bratu-type equations. This research contributes to the field of numerical analysis by offering an alternative, effective approach to tackle complex second-order nonlinear differential equations, addressing critical challenges in various scientific domains.
AN ANALYSIS OF ALGEBRAIC PATTERN OF A FIRST ORDER AND AN EXTENDED SECOND ORDER RUNGE-KUTTA TYPE METHOD
(Faculty of Science, Kaduna State University, 2020) R. Muhammad,; Y. A. Yahaya; A.S. Abdulkareem
The algebraic pattern of a 6-Stage Block Hybrid Runge –Kutta Type Methods (BHRKTM) for the solution of Ordinary Differential Equations (ODEs) is carefully analyzed. The analysis of the methods expressed in the Butcher Tableau led to the evolvement of two equations that satisfy the Runge – Kutta consistency conditions. The reason behind the uniform order and error constant for the developed first order and extended second order methods is explained using the theory of linear transformation and monomorphism. The pattern was retained during the transformation.
An Assessment of Groundwater Quality in Tudun Fulani, Niger State, Nigeria
(Sule Lamido University Journal of Science and Technology (SLUJST), 2020-12) Bisiriyu, Muhammad Taoheed; Ganiyu, Mustapha Adekomi; Audu, Lawal Idris; Abdullahi, AbdulHakam Safiu; Animashaun, Iyanda Murtala
groundwater is the main source of drinking water in Tudun Fulani community in Bosso, Niger State, Nigeria. Objective: this study was conducted to assess the physicochemical and heavy metal characteristics of groundwater used for drinking and other domestic purposes in the area with a view to determining its suitability for these purposes. Method: twelve water samples comprising of seven hand-dug wells and five boreholes were collected from different locations in the area. Physicochemical parameters (pH, turbidity, electrical conductivity, total dissolved solids (TDS), total suspended solids (TSS), total solids (TS), alkalinity, total hardness, chloride) and heavy metals (lead, manganese, copper and iron) contents were determined using standard methods. Results: the results showed that the pH, electrical conductivity, TDS, TSS, TS turbidity, alkalinity, total hardness and chloride ranged between 5.72 – 7.32, 252.5 – 1098 μS/cm, 58 – 11.35 mg/L, 0.001 – 0.108 mg/L, 1.05 – 7.33 NTU, 10.60 - 104.20 mg/L, 26.6 – 170.2 mg/L, and 28.17 – 86.9 mg/L, respectively. The heavy metal analysis revealed lead, manganese, copper, and iron to range between 0.001-0.009 mg/L, 0.01-0.28 mg/L, 0.010 - 0.050 mg/L and 0.100 – 0.430 mg/L, while manganese and lead were not detected in one and six of the samples, respectively. Conclusion: the values of the parameters analysed in this study were below and within the permissible limits set by the World Health Organisation (WHO) for most of the water samples investigated; hence, the groundwater is suitable for drinking and for other life-supporting activities. However, only four samples (W1,W5 W6, and W7) were within the range of 100 - 300 mg/L set by WHO for total hardness. In addition, the pH values of water samples W4, W5, B4, and B5 were below the recommended standard, while the electrical conductivity of W5, turbidity of W3, W5 and iron contents of W2 and W7 were above the maximum limit set by WHO. Therefore, it is recommended that the indiscriminate discharge of wastes be checked in locations of W2 and W7 as high iron content in drinking water poses serious health risks to consumers.
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, 2023-10-12) Ajinuhi J.O.; Mohammed U.; Enagi A.I.; JIMOH, OMANANYI RAZAQ
In 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.
An Order (K+5) Block Hybrid Backward Differentiation Formula for Solution of Fourth Order Ordinary Differential Equations
(Çankaya University Journal of Science and Engineering, 2024) Raihanatu Muhammad; Hajara Hussaini; Abdulmalik Oyedeji
This paper covers the derivation and implementation of the 4-step linear Multistep method of Block Hybrid Backward Differentiation Formula (BHBDF) for solving fourth-order initial value problems in ordinary differential equations. In the derivation of the proposed numerical method, the utilization of collocation and interpolation points was adopted with Legendre polynomials serving as the fundamental basis function. The 4-step BHBDF developed to solve fourth-order IVPs has a higher order of accuracy (p=9). Furthermore, the proposed numerical block methods are employed directly to solve fourth-order ODEs. In comparison to some existing methods examined in the prior studies, the proposed method has a robust implementation strategy and demonstrate a higher level of accuracy.
Application of Adomian Decomposition Method (ADM) for Solving Mathematical Model of Measles
(National Mathematical Centre (NMC) Journal of Mathematical Sciences,, 2021-03-03) Somma, Samuel Abu; Ayegbusi, F. D.; Gana, P.; Adama, P. W.; Abdurrahman, N. O.; Eguda F. Y.
Adomian Decomposition Method (ADM) is a semi-analytical method that give the approximate solution of the linear and non-linear differential equations. In this paper the Adomian Decomposition Method (ADM) was used to solve the mathematical model of measles. The ADM solution was validated with Runge-Kutta built-in in Maple software. The graphical solutions show the decrease and increase in the classes with time. It was revealed from the graphical solution that the ADM is in agreement with Runge-Kutta. Keywords: Mathematical modeling, Adomian Decomposition Method, numerical solution
Application of Computerized Monte Carlo Simulation in Evaluating Definite Integrals and Testing of the Properties of Probability Density Functions
(International Journal of Modern Mathematical Sciences,, 2014-05) Ogwumu, David. O,; James, Friday. E; Abubakar, Samuel
This work explores a certain application of the Monte Carlo simulation technique in evaluating definite Integrals and x-rays the complexity of solving realistic models by mathematical methods to arrive at an analytic solution. The study has shown that certain complex problems that cannot be solved analytically could be subject to simulations to provide approximate solutions. The work equally studies numerous definite Integrals but provides a result for few through which it is possible to make a generalization in the end of the study. Five probability distributions were highlighted in this work (among others that were investigated) and their properties by Monte Carlo simulation using a PASCAL program where random numbers were generated after numerous trials. Some areas of applications of simulation and the probability distributions studied have been discussed in this study alike.
APPROXIMATE SOLUTIONS FOR MATHEMATICAL MODELLING OF MONKEY POX VIRUS INCORPORATING QUARANTINE CLASS
(Transactions of the Nigerian Association of Mathematical Physics, 2021-03-30) Somma, Samuel Abu; Akinwande, N. I.,; Ashezua, T. T.; Nyor, N.; Jimoh, O. R.; Zhiri, A. B.
In this paper we used Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) to solve the mathematical modeling of Monkeypox virus. The solutions of HPM and (ADM) obtained were validated numerically with the Runge-Kutta-Fehlberg 4-5th order built-in in Maple software. The solutions were also presented graphically to give more insight into the dynamics of the monkeypox virus. It was observed that the two solutions were in agreement with each other and also with Runge-Kutta.
Arsenic level determination in selected well water from Sokoto state, Nigeria
(Elixir International Journal, 2014-10-23) Galadima, A; Bisiriyu, M.T
Twenty samples of domestic water sourced from different underground wells in the Gidan Dare and Gidan Igwai areas of Sokoto were collected and analyzed in the laboratory. The pH and the electrical conductivity (EC) of the water samples were also determined. The mean results obtained from the analyses were pH (7.68, 6.72) and electrical conductivities (1061µs/cm, 1057µs/cm) for Gidan Dare and Gidan Igwai, respectively. The results also showed mean arsenic concentrations of 0.110mg/L and 0.217mg/L for Gidan Dare and Gidan Igwai water samples, respectively, which are above the World Health Organization (WHO) drinking water guidelines. Wells in Gidan Dare and Gidan Igwai were found to be contaminated with an abnormal concentration of arsenic, high enough to cause serious adverse health effects to its consumers. The high arsenic concentrations could be attributed to both natural and anthropogenic activities such as erosion, underground weathering, toxic chemicals, improper waste and sewage disposal waste from industries, agricultural activities and vehicular emissions.
Bifurcation Analysis on the Mathematical Model of Measles Disease Dynamics
(Universal Journal of Applied Mathematics, 2013-12-12) Abubakar, Samuel; Akinwande, N. I.; Abdulrahman, S.; Oguntolu, F. A.
In this paper we proposed a Mathematical model of Measles disease dynamics. The Disease Free Equilibrium (DFE) state, Endemic Equilibrium (EE) states and the characteristic equation of the model were obtained. The condition for the stability of the Disease Free equilibrium state was obtained. We analyze the bifurcation of the Disease Free Equilibrium (DFE) and the result of the analysis was presented in a tabular form.
Biomass Valorisation: A Sustainable Approach Towards Carbon Neutrality and Circular Economy
(Springer Nature Singapore, 2024) Elijah Yanda Shaba; Mary Jumai Jiya; Alheri Andrew; Adamu Makanta Salihu; Emmanuel Mamma; Samuel Kelechi Anyanwu; John Tsado Mathew; Abel Inobeme; Benjamin Nma Yisa; Jonathan Jiya Saba
Biostratigraphy and Depositional Environments of Wells BB-3, D-01 and BL-1X Deep Offshore, Niger Delta Basin, Nigeria: Insights from Palynological Studies
(Journal of Natural and Applied Sciences, 2022-06) Usman, H.O.; Unuevho, C. I.; Chukwuma-Orji, J. N.; Alkali, Y. B.
Biostratigraphic studies was carried out on BB-33, D-01 and BL-1X wells deep offshore Niger Delta Basin Nigeria. Palynological analysis was carried out on 295 ditch cuttings samples (BB-3 =82, D-01 =109, and BL-1X = 104). Open hole geophysical log data was also provided for the studied intervals 10700-15600 ft, 8060-16800 ft and 7900-13000 ft in BB-3, D-01 and BL-1X wells respectively belonging to the Agbada Formation. Lithologically, the section varies from alternation of sand and shale units with carbonaceous debris, mica flakes, ferruginised materials and glauconites at some intervals as accessory minerals. Palynomorphs recovered from the analyzed intervals were mainly Zonocotites ramonae, Monoporites annulatus, fungal spores/hypae, species of Sapotaceoidaepollenites and Laevigatosporites and were found to dominate the microfloral assemblage of the analyzed intervals. Sphaeromorph, acritarch, species of Leoisphaeridia coupled with Pediastrium, Botryococuss, Operculodinium centrocarpum, Lingulodinium machaerophorum, Achomosphaera ramulifera, Spiniferites ramosus and indeterminate dinoflagellate cysts were the marine indicators present. Samples from the section are dated early Miocene to early Pliocene age based on the independent paleontological evidences. The deduced depositional environments of the strata penetrated by the wells range from outer neritic through bathyal to deep marine.
COA-SOWUNMI'S LEMMA AND ITS APPLICATION TO THE STABILITY ANALYSIS OF EQUILIBRIUM STATES OF THE NON-LINEAR AGE-STRUCTURED POPULATION MODEL
(International Journal of Mathematics and Physical Sciences Research, 0205-04-10) Akinwande, N. I.; Somma, Samuel Abu
Abstract: In this work, we present a result in the form of a lemma which we name COA-Sowunmi’s Lemma, its proof and application to the stability analysis of the transcendental characteristics equation arising from the perturbation of the steady state of the non-linear age-structured population model of Gurtin and MacCamy [11]. Necessary condition for the asymptotic stability of the equilibrium state of the model is obtained in the form of constrained inequality on the vital parameters of the model. The result obtained is then compared with that of an earlier work by the [4].
COMPARATIVE STUDY OF BIOETHANOL PRODUCTION FROM IRISH AND SWEET POTATO PEELS BY HYDROLYSIS AND FERMENTATION PROCESSES USING Saccharomyces cerevisiae
(FUW Trends in Science & Technology Journal, www.ftstjournal.com, 2021-10-12) Bisiriyu, Muhammad Taoheed; Habu, Christopher; Amos, Pigweh Isa; Amunike, Perpetual Chiamaka; Isah, Abdulrahman Adamu
The quest for green and sustainable sources of energy has led to various studies on the production of biofuels such as bioethanol from different agricultural materials. This study presents a comparative analysis of bioethanol produced from Sweet and Iris potato using simultaneous saccharification and fermentation (SSF). 5.00, 10.00, and 15.00 g each of the Sweet and Irish potato peels were hydrolyzed using dilute acid (5% H2SO4). A dried baker’s yeast strain (Saccharomyces cerevisiae) was subsequently introduced to ferment the substrates for 7 days. The bioethanol yield, average bioethanol yield, density, and proximate composition of the substrates were determined. The yield of bioethanol for Sweet potato peels at 5.00, 10.00, and 15.00 g were 43.50, 64.50 and 82.00 cm3 while for Irish potato peel at 5.00, 10.00 and 15.00 g were 22.00, 41.50, and 59.00 cm3, respectively. The average bioethanol yield for Sweet potato and Irish potato peels were 63.33 and 40.83%, while the density for Sweet and Irish potato peels were 0.853 and 0.891 g/cm3, respectively. The proximate composition for Sweet potato peel was 5.10±0.01% moisture, 4.00±0.023% ash, 2.99 ± 0.044% lipid, 3.50±0.03% fiber, 7.00±0.05% protein, and 77.41±0.01% carbohydrate while for Irish potato peel were 8.75± 0.63% moisture, 3.55± 0.05% ash, 4.48± 0.03 lipid, 4.50± 0.55% fiber, 4.38± 0.67% protein and 74.34±0.15% carbohydrate. Therefore potato peels can be harness as a potential feedstock for bioethanol production with Sweet potato peel having a higher yield of bioethanol compared to Irish potato due to higher carbohydrate content.