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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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
Modelling Of Accident Data In Nigeria: Poisson And Poisson Gamma Regressio
(2015) Aderoju, S.A.; Jolayemi, E.T.
Poisson and Poisson-gamma (Negative Binomial) regression models belong to the group of generalized linear models that are suitable to model count data. While the two regression types often give similar results, there can be differences in the effects of the covariates they estimated depending on weather the data is equi-dispersed, over-dispersed or under-dispersed. This work therefore demonstrates the behaviours of Poisson and Poisson-gamma regression models when the data is overdispersed (variance greater than the mean). The two regression types were employed to model the number of people killed in road accidents as a function of the number of fatal, serious and minor accidents that occurred. Results from the two regression models indicated that number of people killed in road accidents is determined majorly by the number of fatal and serious cases of road accidents that occurred and not really by the number of minor accidents. The differences in the two regression models are described in the light of the over-dispersion in the data and the ability of the models to account for it. Road accident data of Kwara State, Nigeria for nine consecutive years from 2000 to 2008, primarily collected by the Nigeria Police Force (NPF), were employed in this study.
SOME RESULTS ON COMMON FIXED POINT FOR GENERALIZED f-CONTRACTION MAPPING
(Global Journal of Mathematics, 2015-03-20) Alata, S. M.; Rauf, K.; Wahab, O. T.
In this article, we prove some common fixed point theorems for the generalized f-contraction mapping in a complete cone metric space. Our results extend and generalized some recent results.
Computational error estimate for the power series solution of ODEs using zeros of Chebyshev polynomial
(Journal of Nigerian Association of Mathematical Physics, 2015-05) K. Issa; G. R. Ibrahim; G. N. Bakare
This paper compared the error estimation of power series solution with the recursive tau method for solving ordinary differential equations. From the computational viewpoint, the power series using zeros of Chebyshev polynomial is effective, accurate and easy to use.
Approximate Analytical Solutions of the Improved Tietz and Improved Rosen-Morse Potential Models
(2015-06) Yahya Wasiu Akanni; Issa Kazeem
In this article, the approximate analytical solutions of the improved Tietz and improved Rosen-Morse potential models are obtained using the parametric Nikiforov-Uvarov method. The energy eigenvalues and wave functions are obtained in the relativistic realm by solving the Klein-Gordon equation. Numerical results of the energy eigenvalues are obtained and studied.
Finite Element Methods on Derivative Least–Square and Semi-Standard Galerkin for Solving Boundary Value Problems
(The Pacific Journal of Science and Technology, Akamai University, 2015-11-15) Rauf, K.; Omolehin J. O.; Aniki, S. A.; Wahab, O. T.
In this paper, we derived a Derivative Least–Square Method (DLSM) and Semi-Standard Galerkin Method (SSGM) which are both Finite Element Methods (FEM) for Solving Boundary Value Problems. In the DLSM, the residue was differentiated into a new derivative of the residue R while in the SSGM, we took I, for which D is its basis function. The proposed methods were applied on several boundary value problems and the numerical results obtained are reliable and in good agreement with the exact solutions.
IMPROVED BAYESIAN FEATURE SELECTION AND CLASSIFICATION METHODS USING BOOTSTRAP PRIOR TECHNIQUES
(Faculty of Computer and Applied Computer Science, Tibiscus University of Timisoara, Romania, 2016) Oyebayo Ridwan Olaniran; Saidat Fehintola Olaniran; Yahya, Waheed Babatunde; Banjoko, Alabi; Garba, Mohammed Kabir; Amusa, Lateef; Gatta F.N
In this paper, the behavior of feature selection algorithms using the traditional t-test, Bayesian t-test using MCMC and Bayesian two sample test using proposed bootstrap prior technique were determined. In addition, we considered some frequentist classification methods like k- Nearest Neighbor (k-NN), Logistic Discriminant (LD), Linear discriminant analysis (LDA), Quadratic discriminant analysis (QDA) and Naïve Bayes when conditional independence assumption is violated. Two new Bayesian classifiers (B-LDA and B-QDA) were developed within the frame work of LDA and QDA using the bootstrap prior technique. The model parameters were estimated using Bayesian approach via the posterior distribution that involves normalizing the prior for the attributes and the likelihood from the sample in a Monte Carlo experiment. The bootstrap prior technique was incorporated into the Normal-Inverse-Wishart natural conjugate prior for the parameters of the multivariate normal distribution where the scale and location parameters were required. All the classifiers were implemented on the simulated data at 90:10 training-test data ratio. The efficiencies of these classifiers were assessed using the misclassification error rate, sensitivity, specificity, positive predictive value, negative predictive value and area under the ROC curve. Results from various analyses established the supremacy of the proposed Bayes classifiers (B-LDA and B-QDA) over the existing frequentists and Naïve Bayes classification methods considered. All these methods including the proposed one were implemented on a published binary response microarray data set to validate the results from the simulation study.
On The Air Traffic Flow Management Rerouting Problem (ATFMRP)
(University of Witwaterstrand, Johannesbourg, South Africa., 2016) Alochukwu, A.S; Mgudlwa, A.; Nanyanzi, A.; Aliu Tajudeen
Air Traffic Flow Management Problem(ATFM) is a set of strategic processes that reduce congestion problems and delays costs. 2 The fundamental challenge for ATFM arises when there is system disruption. 3 A major challenge encountered by air traffic managers is the problem of finding optimal scheduling strategies that mitigates congestion as well as minimizes delay costs when there is capacity reductions. 4 The problem of managing the air traffic so as to ensure safe and efficient flow of aircraft throughout the airspace is referred to as the Air Traffic Flow Management Problem (ATFMP)

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