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- ItemOpen AccessA Characterization of Analyticity Using Cauchy Integral Formula(2010) Makinde, D. O.In this paper, we obtain a general characterization of analyticity of function of a complex variable using Cauchy integral formula.
- 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 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 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 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 AccessDisappearance of Criticality and Ignition Times of an Exothermic Chemical Reaction in a Reactor(2015-08-21) Adeleye, Olabode EmmanuelThis study determined the criticality, disappearance of criticality and ignition times in some limiting cases for an unsteady state energy balance equation. It also obtained the critical and transitional values of modified Semenov's number Ф, reduced temperature excess and activation energy parameter for three cases: (I) convective only, (II) radiative only and (III) both convective and radiative heat losses considering Arrhenius, bi-molecular and sensitized kinetics cases. This was with view of incorporating both convective and radiative heat losses in an exothermic chemical reaction with pre-exponential factor. The transient variation of temperature equation was solved under physically reasonable assumptions, employing; Semenov's sufficient and necessary conditions for thermal explosion for case I and the modified El-Sayed definitions were used for cases II and III. Moreover, a parameter a being the ratio of the convective heat transfer coefficient (I), to the radiative hear transfer coefficient Ф2, was Introduced into case III to allow for extension of the study to accommodate both convective and radiative heat losses. Subsequently, the ignition times were obtained using a three-term regular perturbation, standard techniques and a numerical procedure. The critical and transitional values of the parameters θ, β and Ф for Arrhenius, bimolecular and sensitized kinetics in case I were investigated. The results showed that in the special case II, the modified Semenov's number at critical point was obtained, while the dimensionless critical temperature obtained was a polynomial of degree 5. Moreover, a transcendental equation involving; the transitional values of θ, β and the reaction order n, was obtained in the form of a polynomial of degree 4. In the event of case III, the modified Semenov's number at critical point was obtained in terms of the other parameters, while the dimensionless critical temperature was obtained as a transcendental equation relating α, βc and n in a polynomial of degree 5. A transcendental equation incorporating; a, θtr, βtr and n in a polynomial of degree 4 was obtained as the point at which transition takes place. In addition, the ignition time obtained numerically for n = 0, β = 0.012, Ф1 =55 and Ф2= 70, was 1.35 X 10-13 seconds. This showed that the reaction was very fast. For the first case, (a) Фtr decreased steadily as n increased provided n ≤ 1, (b) θtr decreased as n increased if n ≤ 0 and increased sharply for 0
- ItemOpen AccessFostering the Practice and Teaching of Statistical Consulting among Young Statisticians in Africa(2011) Awe, Olushina OlawaleStatistical Consulting is unarguably one of the most challenging and rewarding aspects of statistics. It is both an art and a science because it involves both statistical and non-statistical skills. This article considers the usefulness of statistics, importance of statistical consulting and stresses the need to improve the practice of statistical consulting among young statisticians in Africa by including it in the curriculum of statistics programs in all African Universities and institutions of higher learning. The need to establish a statistical consulting unit in all the universities in Africa, whose activities will include providing advice for researchers on a full range of topics including statistical procedures for experiments, statistical and bio-mathematical modeling, statistical computing, and interpretation of results, is also proposed.
- ItemOpen AccessGlobally Stable Periodic Solution of Certain Fourth Order Non-Linear Differential Equations(2010) Ogundare, B. S.In this paper, we give criteria for the existence of a unique solution to a certain fourth order nonlinear differential equations which is bounded together with its derivatives on the real line, globally stable and periodic by the use of a complete Lyapunov function.
- 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 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 AccessModeling Socioeconomic Factors Affecting Age at Marriage among females in Kogi State, Nigeria(2012) Adarabioyo, M. I.; Awe, O. O.; Lawal, F. K.This paper is aimed at determining the effect of socioeconomic factors such as cultural background, level of education and religion in relation to age at marriage among women in Kogi State Nigeria. The survey area is made up of diverse ethnic groups with three major languages. The stud) reveals that education is an important factor which increases the age at marriage in the State. The study equally proved that religion and cultural background does not affect age at marriage among women in Kogi State, Nigeria. A Saturated one-way and two-way model was fitted to reveal the behavioral pattern of the distribution.
- ItemOpen AccessMultivariate Regression Techniques for Analyzing Auto-Crash Variables in Nigeria(2011) Awe, Olushina Olawale; Adarabioyo, MuminiIt is unequivocally indisputable that motor vehicle accidents have increasingly become a major cause of concern for highway safety engineers and transportation agencies in Nigeria over the last few decades. This great concern has led to so many research activities, in which multivariate statistical analysis is inevitable. In this paper, we explore some regression models to capture the interconnectedness among accident related variables in Nigeria. We find that all the five variables considered are highly interrelated over the past decade, resulting in a high risk of mortality due to auto-crash rate. The result of our analysis, using an appropriate statistical software, also reveals that the simple regression models capture the relationships among the variables more than the multiple regression model considered.
- ItemOpen AccessNested Balanced Incomplete Block Designs of the Double Cyclic Type(2010) Saka, A. J.; Adeleke, B. I.A Nested Balanced Incomplete Block Design (NBIBD) is a design with two systems of blocks, each block from the first system containing m-blocks from the second. Consequently, by ignoring either system of blocks leaves a Balanced Incomplete Block Design (BIBD) whose blocks are those of the other system. Designs k = s2, where s is a prime or prime power. Otherwise the imposed relationship between the parameters of the designs would not be satisfied. In particular, double cyclic design for v = 7 and two distinct double cyclic designs for v = 13 were constructed and presented in Table 1.
- ItemOpen AccessNested 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.
- ItemOpen AccessNon-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.
- 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 a Certain Integral Univalent Operator(2011) Makinde, D. O.In this paper, author proves some properties of a certain integral operator.
- ItemOpen AccessOn a Four-Parameter Type I Generalized Half Logistic Distribution(2011) Olapade, A. K.In this paper, we derived a four-parameter type I generalized half logistic distribution. The cumulative distribution function, the survival and hazard function, the moments, the 100p-percentage, point and the mode of the generalized distribution are established. Two theorems that characterized the probability distribution function are stated and proved.
- ItemOpen AccessOn 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.
- ItemOpen AccessOn a Six-Parameter Generalized Burr XII Distribution(2010) Olapade, A. K.In this paper, we derive a probability density function that generalizes the Burr XII distribution. The cumulative distribution function and the n-th moment of the generalized distribution are obtained while the distribution of some order statistics of the distribution is established. A theorem that relates the new distribution to another statistical distribution is established.
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