Department oF Mathematics and Statistics

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    Perturbed Galerkin Method for Solving Integro- Differential Equations
    (Hindawi, 0002-04-15) K. Issa; J.Biazar; T.O. Agboola; T. Aliu
    In this paper, perturbed Galerkin method is proposed to find numerical solution of an integro-differential equations using fourth kind shifted Chebyshev polynomials as ba- sis functions which transform the integro-differential equation into a system of linear equations. The system of linear equations are then solved to obtain the approximate solution. Examples to justify the effectiveness and accuracy of the method are pre- sented and their numerical results are compared with Galerkin’s method, Taylor’s series method and Tau’s method which provide validation for the proposed approach. The errors obtained justify the effectiveness and accuracy of the method.
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    Groups and Subgroups in Cryptography
    (University of Lagos, 2009) Adeshola, A.D.; T. Aliu
    This study looks into the Mathematical applications of groups and subgroups in cryptography through Eulier’s Phi Function and Lagrange’s theorem with some definitions, theorems, illustrations and examples.
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    Cryptography and Encryption
    (University of Lagos, 2010) Adeshola, A.D.; T. Aliu
    There is a strong need to devise new encryption mechanisms (algorithms) that offer enhanced security assurance, and guarantee the security of information transm itted over computer networks. This has generated a lot of interst, and has made cryptography an area of intrest in research all over the world today. In this study, we study Cryptography through the Euclid’GCD Algorithm Principle.
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    An analogue of the tau method for ordinary differential equation
    (2010) K. Issa; R. B. Adeniyi
    In this paper, we construct three orthogonal polynomials which are incorporated into the perturbation term of a numerical scheme analogue to the Ortiz recursive formulation of the Lanczos tau method. The method was implemented on some selected problems and the accuracy obtained justifies the desirability of the numerical scheme.
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    Application of linear programming problem on cost minimization on fish feeds
    (African Journal online, 2011) A.O. Adeoye; A.K. Dotia; M.O. Agboola; T.O. Aliu
    This research, application of linear programming problem on cost minimization on fish feeds was aimed to minimize the cost of production of fish feeds. The data used was collected using both primary and secondary data. Linear programming problem was used to analyzed the data and the optimum solution was obtained at 5th iterations with fingerlings feeds to be 8/9 of tons and growers feeds to be 10/9 tons and the minimum cost of producing the tones of fingerlings and growers is N498, 675.60. We then recommend that any fish farmer who really wants to embark on efficient and effective fish production should use linear programming problem to determine the minimums cost of production. In other to maximizes their profits
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    Syntax Recognition in Semi groups
    (University of Nairobi, 2011) Adeshola, A.D.; T. Aliu
    In this paper, we establish the fact that decimal integers are formed from the ten decimal or denary digits 0, …,9; English words are formed from the 26 letters of English alphabet (or 52 if we distinguish between lower and upper case); English sentences are formed from the finite, but large number of English words[2]. This prelimnary study has attempted a description of a core aspect of both Syntax and Semigroup. It endeavours to succintly explain what syntax entails and in chronological norder, a review of major thoughts on syntax evaluation is highlighted. As a way of finding possible areas of relationship in the curious presence of Syntax and Semigroup, section one explains the relationship through logarithm, setion two equally looks at the syntatic nature of prefix, suffix and subwords, and in section three, results are analyzed and finally, conclusion are discussed in section four.
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    Qualitative Study of Biological Pest Control System
    (Asian Journal of Mathematics and Statistics, 2012-11-23) Aderinto, Y. O.; Bamigbola, O.M.; Jimoh,F.M.; Ganiyu, M.A.; Aliu, T.
    Agricultural pests are the insects that feed on crops and damaged them. Most current agricultural pest control methods focused on chemical insecticides. Research works have shown that these chemicals have many disastrous consequences. However, effective control of these pests can be obtained through the use of living organisms to reduce the density of pest below economic damaging level and this is refers to as biological pest control. If a mathematical model for the biological system is provided, then the effects of such pests can be controlled by the methods of optimal control theory. In this study, the biological control of agricultural pest system via optimal control theory approach was qualitatively studied. In an attempt to minimize the pest population below injury level and stabilize the natural enemies’ population. The system was analysed, equilibrium point for the system was determined, stability and economic loss free equilibrium was equally established. Numerical values were employed to check for the validity of the method and the result was found to be effective.
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    Some Properties Of Symmetric Inverse Semigroup and Some Of it's Subsemigroup
    (Mathematical Association Of Nigeria(MAN), 2013) Ibrahim, G.R.; Bakare, G.N.
    In this paper, we studied the number of Nilpotent elements of order-preserving one-one partial transformation semigroup and number of Nilpotent elements of order decreasing +order preserving partial transformation semigroup . also, we showed that every idempotent of partial one-one transformation semigroup is contraction mapping.
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    Combinatorics Properties of Order-preserving Full Contraction Transformation Semigroup by Their Equivalence Classes
    (Department of Mathematics and Statistics, University of Victoria, Canada., 2013) Ibrahim, G. R; Makanjuola, S. O
    In this paper the cardinalities of equivalence classes of starred Green’s relations in order-preserving full contraction transformation semigroup of a finite set(OCT) and the elements in each equivalence classes were investigated. For each class tables were formed, elements were arrange based on their kernel and image sets, patterns of arrangement observed and formulae were deduced in each case through the combinatorial principles.
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    Economic Analysis and Modelling of Effects of NPK Fertilizer Levels on Yield of Yam
    (Journal of Mathematical Theory and Modeling, 2013) Olorede K. O.; Alabi M. A.
    This paper presents statistical analyses of effects and efficacies of NPK fertilizer levels on yield of four differentspecies of yam in three different locations of kwara state Nigeria. Four quantitative and equally spaced levels0kg/ha, 22.5kg/ha, 45kg/ha and 76kg/ha respectively, of the fertilizer type were considered in the experiment.Factorial design model was used in collecting data sets on yield variables of the plant, using fixed effects, in anexperiment conducted by the Kwara Agricultural Development Project (KWADP) Ilorin, in the year 2012. Thefour varieties of yam examined included white yam, water yam, aerial yam and bitter yam respectively.Observations were taken from Ekan-Meje, Omu-Aran and Omupo locations of the state on a number of responsevariables namely, number of yam plants, number of yam tubers and weight (kg) of yam tubers. Beforeconducting ANOVA, the data sets were inspected for homogeneity of error variances using Fligner-Killeen testin the R statistical package. The test revealed that homoscedasticity assumption was not violated and Shapiro-Wilk test of normality was further used to check normality of the residuals arising from the ANOVA model. Theresponse variables were modelled with orthogonal polynomials so as be able to predict response yield atintermediate factor levels. Fertilizer level of 22.5kg/ha was found to be the most effective and economical forgrowing yam with the corresponding optimum yield.
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    Statistical Analysis of Optimum Phosphorous Fertilizer Requirement for Improved Yield Performance of Cowpea in Nigeria
    (Journal of Biology, Agriculture and Healthcare, 2013) Olorede K. O.; Aiyelabegan A. B.
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    Economic Selection of Efficient Level of NPK 16:16:16 Fertilizer for Improved Yield Performance of a Maize Variety in the South Guinea Savannah Zone of Nigeria
    (Journal of Mathematical Theory and Modeling, 2013) Olorede K. O.; Mohammed I. W.; Adeleke B. L.
    This study investigates effects of different levels of NPK 16:16:16 fertilizer on yield and performance of maize. Data sets were obtained from a study conducted at the University of Ilorin Teaching and Research Farm, faculty of Agriculture, University of Ilorin during the 2010 cropping season. The study was conducted on a maize variety (Swan-1-SR-Y) sourced from Federal Ministry of Agriculture and Water Resources, Abuja, Nigeria using a completely Randomized Design (RCBD) replicated three times. Application of the fertilizer type was done at two equal splits of 2 weeks after planting and immediately after tasseling using ring method of application. The appropriate analysis of variance (ANOVA) model was used to collect observations at 2 weeks interval from week 5 to week 15 after planting on growth variables such as plant height (kg), leaf area (cm2), number of leaves, cob weight (kg) and grain weight (kg) respectively at equally spaced levels 0kg/ha, 30kg/ha, 60kg/ha, 90kg/ha and 120kg/ha of the fertilizer type. Before conducting ANOVA, the data sets were inspected for homogeneity of error variances using Fligner-Killeen test in the R statistical package. Shapiro-Wilk test of normality was used to check normality of the residuals. The normal probability plot showed no indication of outliers and the largest standardized residual was within . NPK 16:16:16 fertilizer level 60 Kg/ha was found to be the most efficient and economical for improving growth and yield performance of the maize variety in the ecological zone. The optimum yield of the maize variety due to application of the NPK 16:16:16 fertilizer levels is in the 13th week after planting.
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    A GENERALIZED SCHEME FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS BY THE RECURSIVE FORMULATION OF TAU METHOD
    (2013-05) K. Issa; R.B. Adeniyi
    The generalization of the recursive form of the tau method for both overdetermined and non-overdetermined ordinary differential equations of the initial value type is the main thrust of the work reported here. This will facilitate an automation of this variant of the method and consequently an efficient utilization of the technique. Results from the numerical experiment confirm the validity and effectiveness of the derived scheme.
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    CONSTRUCTION OF POLYNOMIAL BASIS AND ITS APPLICATION TO ORDINARY DIFFERENTIAL EQUATIONS
    (Mathematical Association of Nigeria, Kwara State, 2014) Aliu, T.; Bamigbola, O.M.
    The study identifies the versatility of basis functions in expansionary method by constructing basis functions of finite order, which satisfy some smoothness and differen- tiability conditions. Effort was intensified towards solv- ing empirical problems via the finite element method.
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    Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method
    (2014) W.A. Yahya; K. Issa; B.J. Falaye; K.J. Oyewumi
    We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.
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    On the number of Order-Preserving Alternating Semi group.
    (Nigeria Association Of Mathematical Physics, 2014) Bakare G.N.,; Ibrahim G.R.,; Makanjuola S.O.
    A semigroup is an algebraic structure consisting of non-empty set S together with an associative binary operation . A transformation X is a function from X to itself. A transformation is one of fundamental mathematical objects. They occur in theoretical computer science, where properties of language depend on algebraic properties of various semigroup.
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    Hydration Status in Nigeria: A Cross-Sectional Study
    (Pakistan Journal of Nutrition, 2014) Yunusa Olufadi; Alfred B. O. Soboyejo; Kabir Opeyemi Olorede; Kazeem Adesina Dauda
    Most literatures on daily water intake are focused on developed countries and to our knowledge; there is limited information on the hydration status of Nigerians. Our objective was to describe daily water intake (DWI) among Nigerian students, develop a model for the prediction of students’ DWI and examine the association between DWI and four predictor variables. Data on DWI for 150 students aged 18-26 years were collected through a survey conducted at Kwara State University in February, 2013 together with information on their age, weight, gender and awareness of dieticians’ recommendation. Our results indicates that students’ DWI varies by gender with male students drinking more than their female counterparts; although, the awareness rate is higher in females than males. We found that nearly half of participants (44%) drank less than 2.7 L of water/day, 25% between 2.7 and 3.7 L/day and 31% reported drinking more than 3.7 L of water/day. Results also revealed that students’ DWI decline with age but increases with weight and one-in-two of the students are unaware of the dangers of poor hydration. Arguably, this study is the first description of DWI among Nigerian students and fills the gap in the literature by developing two models for the prediction of students’ DWI. In light of the significance of the knowledge and awareness of Dieticians’ recommendation on DWI (as evidence in this study) and the low awareness rate existing among the students; nutrition and health promotion program on the benefits of adequate DWI by schools and health organizations is extremely important. This has the potential of improving the health of students.
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    An error estimation of a numerical scheme analogue to the tau method for initial value problems in ordinary differential equations
    (2014-03) K. ISSA; A. K. JIMOH
    In a recent paper, we constructed three classes of orthogonal polynomials for use in the perturbation term of a numerical integration scheme analogues to the tau method of Lanczos and Ortiz for ordinary differential equations. The resulting n-th degree approximant y_n(x) of the solution y(x) of the differential equation was accurate and hence justified the scheme. In this present paper, we report an error estimation of the method based on our earlier work. The estimate obtained is good as it correctly captured the order of the tau approximant.
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    FIXED POINT THEOREMS WITH APPLICATIONS TO n-TH ORDER ORDINARY DIFFERENTIAL EQUATIONS
    (Advances Inequalities & Applications, 2014-04-30) RAUF, K.; WAHAB, O. T.; OMOLEHIN, J. O.; ABDULLAHI, I.; SANUSI, O. A.
    In this article, we consider fixed point theorems with applications to n-th order differential equations. Some examples are also considered. Our results extend and generalize several existing results in the literature.
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    Comparison of some numerical methods for the solution of fourth order integro-differential equations
    (2014-11) A. K. Jimoh; K. Issa
    The numerical methods for solving fourth order integro-differential equations are presented. The methods are based on replacement of the unknown function by power series and Legendre polynomials of appropriate degree. The proposed methods convert the resulting equation by some examples considered show that the standard collocation method proved superior to the perturbed collocation method. Two examples are considered to illustrate the efficiency and accuracy of the methods.