Journal Articles

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Open Access
Ignition Time for a Porous Medium Model with Low Thermal Conductivity
(2003) Ajadi, Suraju Olusegun
The ignition time for a porous medium combustion arising from a porous medium combustion model is considered. The effect of the activation energy parameter as well as the parameter which measures the ratio of oxygen consumption to that of the solid(fuel), on the ignition time is presented.
Open Access
On Extended Type I Generalized Logistic Distribution
(2004) Olapade, A. K.
We consider a form of generalized logistic distribution which is called extended type I generalized logistic distribution. Some theorems that relate the distribution to some other statistical distributions are established. A possible application of one of the theorems is included.
Open Access
Thermal Instability in a Model Chain Branching - Chain Breaking Kinetics
(2005) Ajadi, S. O.
Thermal instabilities such as thermal explosion and thermal ignition are examined in a two-step reactions mechanism, comprising of a chain-branching and a chain-breaking step. The aim of this study is to examine the influence of the chain-breaking step on these instabilities and then compare our findings with the existing results for the one step model, which is mainly a branching step. The resulting mathematical equations were subjected to a variational method executed on the Mathematics package for the analysis of thermal explosion, while the thermal ignition is amenable to simple integration. These results show that the chain branching step leads to a complete departure from existing results for the one step model. It is established that the Frank-Kamenetskii parameter and the ignition time are monotonically decreasing functions of the heat parameters.
Open Access
Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space
(2005) Oyadare, 'Femi O.
This research work places a new and consistent inner product <.,.>p on a countable family of the real Lp function spaces, proves generalizations of some of the inequalities of the classical inner product for <.,.>p provides a construction of a species of Higher Orthogonal Polynomials in these inner-product-admissible function spaces, and ultimately brings us to a study of the Generalized Fourier Series Expansion in terms of these polynomials. First, the reputation of this new inner product is established by the proofs of various inequalities and identities, all of which are found to be generalizations of the classical inequalities of functional analysis. Thereafter two orthogonalities of <.,.>p which coincide at p = 2) are defined while the Gram-Schmidt orthonormalization procedure is considered and lifted to accommodate this product, out of which emerges a set of higher orthogonal polynomials in Lp{-1, 1} that reduce to the Legendre Polynomials at p = 2. We argue that this inner product provides a formidable tool for the investigation of Harmonic Analysis on the real Lp function spaces for p other than p = 2, and a revisit of the various fields where the theory of inner product spaces is indispensable is recommended for further studies.
Open Access
A Note on the Unsteady Flow of Dusty Viscous Fluid between Two Parallel Plates
(2005) Ajadi, Suraju Olusegun
We study the isothermal flow of a dusty viscous incompressible conducting fluid between two types of boundary motions- oscillatory and non-oscillatory, under the influence of gravitational force. Within the frame work of some physically realistic approximations and suitable boundary conditions, closed form solutions were obtained for the velocity profiles and the skin friction of the particulate flow. These results show that for a constant pressure gradient, only the velocity profile of the fluid and the skin friction are unaffected by gravity, while magnetic field is seen to affect both the fluid, particle velocities and the skin friction. Thus, our results are extension of previous results in literature, and graphical demonstration of some these solutions have been presented.
Open Access
On Negatively Skewed Extended Generalized Logistic Distribution
(2005) Olapade, A. K
In this paper, we considered a form of generalized logistic distribution which is call negatively skewed extended generalized logistic distribution or extended type I1 generalized logistic distribution. Some theorems that relate the distribution to some other statistical distributions are established. A possible application of one of the theorems is included.
Open Access
On Negatively Skewed Extended Generalized Logistic Distribution
(2005) Olapade, A. K.
In this paper, we considered a form of generalized logistic distribution which is call negatively skewed extended generalized logistic distribution or extended type I1 generalized logistic distribution. Some theorems that relate the distribution to some other statistical distributions are established. A possible application of one of the theorems is included.
Open Access
Incorporating Crown Dimensions into Stem Height and Basal Area Growth Models for African White Wood (Triplochiton scleroxylon)
(2006) Adesoye, P. O.; Ogunola, A. A.; Awotoye, O. O.; Ogunfidodo, A.
Four crown dimensions (crown diameter, crown projection area, crown length and crown ratio) were each, incorporated into nonlinear individual tree total height and basal area increment models for African white wood (Triplochiton scleroxylon K. Schum). The basic height/basal area growth model was formulated as a function of the tree size (i.e. total height or basal area), age and tree form (i.e. taper which is the ratio of diameter at breast height to total height). These increment models, with and without crown dimension were fitted to a modelling data set and the statistical significance of each of the crown dimensions was examined. All the models were then compared for predictive ability using an independent validation data set. The results obtained were similar for both the total height and basal area increment models. All the crown dimensions except crown projection area were found to be significant in the basic models (i.e. models without crown dimensions) in terms of model fit. However, for predictive ability, increment models (for both total height and basal area) with crown ratio term were found to have the smallest bias and the greatest prediction precision of all the models examined both with and without crown dimension. Therefore, for tree total height and basal area prediction of African white wood, models with added crown ratio term were found to be most appropriate.
Open Access
On Symmetric Extended Generalized Logistic Distribution
(2006) Olapade, Akintayo K.
In this paper, we consider a form of the generalized logistic distribution named symmetric extended generalized logistic distribution or extended type III generalized logistic distribution. The distribution is derived by compounding a two-parameter generalized Gumbel distribution with a two-parameter generalized gamma distribution. The cumulative distribution and some properties of this distribution like moments and related statistics are established. Some theorems that characterize the distribution are stated and proved. Estimation of the parameters and an application of the distribution are also presented.
Open Access
On the Boundedness and the Stability Results for the Solutions of Certain Third Order Non-Linear Differential Equations
(2006) Ogundare, B. S.
In this paper, we show the asymptotic stability of the trivial solution x = 0 for p = 0 and the boundedness as well as the ultimate boundedness result for p ≠ 0 with the use of a single complete Lyapunov function. The results obtained here improve on the results already obtained for this class of third order nonlinear differential equations.
Open Access
Convergence of Solutions of Certain Fourth-Order Nonlinear Differential Equations
(2007) Ogundare, B. S.; Okecha, G. E.
We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature.
Open Access
On the Boundedness and the Stability of Solution to Third Order Non-Linear Differential Equations
(2008) Ogundare, B. S.; Okecha, G. E.
In this paper we investigate the global asymptotic stability, boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation, using complete Lyapunov function.
Open Access
Thermal Instability in Reactive Viscous Plane Poiseuille/Couette Flows for Two Extreme Thermal Boundary Conditions
(2009) Ajadi, Suraju Olusegun
The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for critically using the variational method technique. The problem is characterized by two parameters: the Nusselt number (N) and the dynamic parameter. We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.
Open Access
On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations
(2009) Ogundare, B. S.
Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a numerical scheme referred to as the pseudo-pseudo-spectral method. Results: With the scheme developed, we were able to obtain approximate solution for certain linear differential equations. Conclusion: The numerical scheme developed in this study competes favorably with solutions obtained with standard and well known spectral methods. We presented numerical examples to validate our results and claim.
Open Access
Some Properties and Application of the Negatively Skewed Extended Generalized Logistic Distribution
(2009) Olapade, A. K.
In this paper, some results on properties of negatively skewed extended generalized logistic distribution of Olapade (2005) is presented. The survival and the hazard function, the mean, the median, the mode and the 100k-percentage point of the distribution are presented. The study of order statistics is also considered in addition to the estimation of the parameters of the distribution and an application of the distribution to model a chemical data.
Open Access
Some Properties and Application of the Extended Type I Generalized Logistic Distribution
(2009) Olapade, A. K.
In this paper, we present some results on properties of extended type I generalized logistic distribution of Olapade (2004). The mean, the median, the mode, the 100 k-percentage point of the distribution are presented. The study of order statistics is also considered in addition to the estimation of the parameters of the distribution and an application of the distribution to model a social data.
Open Access
Non-Isothermal Effect on the Motion of a Particulate Flow between Two Parallel Plates
(2009) Ajadi, S. O.; Odejide, S. A.; Fareo, A. G.
The non-isothermal flow of dusty, viscous, incompressible conducting fluid between two oscillatory parallel plates is studied. This flow is described by the continuity, momentum and the energy equation, which accounts for the heat and mass transfer. Closed-form solutions method initiated by the boundary conditions were obtained for zero and non-zero pressure gradient. These solutions show that the non-isothermal nature of the flow has led to a dramatic departure from the isothermal case. The solutions were further demonstrated graphically to elucidate the significance of parameters such as Prandtl number (Pr), the magnetic parameter (Bo) and the Grashoff number (Gr) on the velocity profiles.
Open Access
Nested Balanced Incomplete Block Designs of the Series I and II Type
(2009) Saka, A. J.; Adeleke, B. L.
Suppose there exists a Balanced Incomplete Block (BIB) design (v, b, r, k, ) for which an initial block solution could be obtained from t-initial blocks. Equally if it is possible to divide each initial block into m sub-blocks from the initial block for generating a BIB design with v treatments arranged into blocks of size k2. Then by systematic development of these initial blocks, we have NBIB designs for both the series II and I. Designs constructed in this paper, which are referred to as of series-I and series-II, are indeed of the Nested Balanced Incomplete Block Designs (NBIBD's) type and they do exist for some values of v. Meanwhile, NBIBD's for series-I exist for all odd values of v, while NBIBD's for series-II equally exist for all even values of v. Also if sequence of the treatment (v) for series-II is one fewer than series-I, both series-I and series-II give the same initial block and consequently the main block of size k1 for series-I is equal to k1 for series-II, and correspondingly the size of the sub-blocks, k2 for series-I is equal to k2 for series-II. Other design parameters exhibit similar interesting symmetry.
Open Access
On a Four-Parameter Type I1 Generalized Half Logistic Distribution
(2009) Olapade, A. K.
In this paper, we derived a four-parameter type II generalized half logistic distribution. The cumulative distribution function, the survival and hazard function, the moments, the median, the 100p-percentage point and the mode of the generalized distribution are established. Some theorems that characterized the probability distribution function are stated and proved.
Open Access
On Generalization of the Pareto Distribution
(2009) Olapade, A. K.
In this paper, we present a probability density function that generalizes the Pareto distribution. The cumulative distribution function and the moments of the generalized distribution are obtained while the distribution of some order statistics of the distribution are established. Included in this paper are the estimation of the parameters of the generalized Pareto distribution and some theorems that relate it to other statistical distributions are established.