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- ItemOpen AccessA Comparative Study of the Means of Multivariate Normal Distributions(Obafemi Awolowo University, 1985) Gordor, Benony Kwaku; Chattopadhyay, A. K.This work is a comparative study of the means of two multivariate normal distributions. Since this distribution is analogous to the univariate distribution, this latter distribution has been included in the real work. The method considered is that of testing of hypothesis concerning the population means and finding confidence intervals for these parameters on the basis of two independent samples from two populations with these distributions. The univariate normal distribution is specified by two parameters - the mean, x and the variance a2. Likewise its multivariate analogues specified by two vector-valued parameters - the mean and the variance-covariance matrix E. Hence the problem of comparing the means of two (multivariate or univariate) normal distributions has been discussed under different conditions of the variance-covariance matrices (and variances in the case of univariate) of the two distributions. As an example, an analysis o+ some data which were collected on students from a secondary school has been given.
- ItemOpen AccessA Survey of the Structure Theory of Annihilator Complemented Algebras.(Obafemi Awolowo University, 1985) Benyah, Francis; Oshobi, E. O.In this Thesis we study the structure theory of some algebra, namely, Annihilator Algebras, Modular Annihilator Algebras, and Complemented Algebras. Of particular interest are the works of F. F. Bonsall, A.W. Goldie, Bruce Barnes and Freda Alexander. We also investigate the relationship between these algebras, as well as give simple examples to illustrate their structures.
- ItemOpen AccessA Thermal Explosion Theory for Parallel Reactions.(Obafemi Awolowo University, 1986) Okoya, Samuel Segun; Ayeniss, R. O.The equations for reacting fluids were considered with particular interest on the effect of pre-exponential factor. We assumed constant and variable pre-exponential factors and considered parallel reactions. Essentially our notion of blow up implies non-existence and so we consider in general uniqueness and existence of the resulting equations. We also examined the conditions for thermal explosion. We show that even where there is reactant consumption; there exist one, two or more solutions of the problem depending on the activation energy of the system when the vessel is spherical. Analytical solutions were obtained for the system and bounds on solutions were provided in cases of interest. We discussed the effects of Frank-Kamenetskii parameter, the so called parameter from the introduction of effective activation energy and the initial temperature. Important theorems were stated and proved with respect to these parameters. To emphasize these theorems we illustrated the conclusions graphically. We established that for finite activation energy in unsteady case there is no thermal explosion whether there is diffusion or otherwise. In the limit of large activation energy we compared the explosion time for two step reactions with that obtained when effective activation energy is employed. We discuss in details the conditions for the occurrence of steady solutions.
- ItemOpen AccessCharacterization of Bol Loops of Small Orders.(Obafemi Awolowo University, 1986) Solarin, A. R. T.; Sharma, B. L.Finite Bol loops of small orders are characterised in this study. There exist up to isomorphism 6 non-associative Bol loops of order 8, 2 non-associative Bol loops of order 4p and every Bol loop of order 2p or p2 is a group (where p is an odd prime). Some properties of loops satisfying identities of Bol-Moufang type are discussed. The common properties between these loops and loops satisfying Bol identity are investigated. A general construction Theorem which yields Bol loops of order 2p2 is given. It is also proved that there exist only two non-isomorphic Bol loops of order 2p2. This settles some of the open problems stated by Niederreiter, H. and Robinson, K.H. concerning existence of Bol loops of orders 18, 50 and 98. It is also proved that there are 6(p + 7) and -(p + 5), non-isomorphic Bol loops of order 3p, when 31p-1 and 31p-1 respectively and that Bol loops of order 3p are isomorphic to their loop isotopes. These results are at variance with the claims of Niederreiter, H. and Robinson, K.H. Finally, it is proved that there exist a total of 472 non-isomorphic Bol loops of order 16. This result has been verified on the computer and the relevant programmes are listed in the Appendices.
- ItemOpen AccessIgnition Time for a Porous Medium Model with Low Thermal Conductivity(2003) Ajadi, Suraju OlusegunThe 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.
- ItemOpen AccessOn 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.
- ItemOpen AccessThermal 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.
- ItemOpen AccessConstruction 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.
- ItemOpen AccessA Note on the Unsteady Flow of Dusty Viscous Fluid between Two Parallel Plates(2005) Ajadi, Suraju OlusegunWe 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.
- ItemOpen AccessOn Negatively Skewed Extended Generalized Logistic Distribution(2005) Olapade, A. KIn 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.
- ItemOpen AccessOn 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.
- ItemOpen AccessIncorporating 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.
- ItemOpen AccessOn 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.
- ItemOpen AccessOn 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.
- ItemOpen AccessConvergence 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.
- ItemOpen AccessOn 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.
- ItemOpen AccessThermal Instability in Reactive Viscous Plane Poiseuille/Couette Flows for Two Extreme Thermal Boundary Conditions(2009) Ajadi, Suraju OlusegunThe 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.
- ItemOpen AccessOn 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.
- ItemOpen AccessSome 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.
- ItemOpen AccessSome 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.
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