ABSTRACTS OF VOLUME 5:
Journal of the Nigerian Association of Mathematical Physics(2001)
ISBN: 1116-4336
using the WKBJ ApproximationComments on Superspace and Superfields
( page 1 – 4of Vol 5 Namp Journals )
by O. Adetunji Odundun
Department of Physics,
Obafemi Awolowo University,
Ile-Ife, Nigeria
Abstract
Two commutator relations useful in the discussion of superspace and superfileds
are proved.
Solution of Large Systems of Linear Equations using the Method of Alternating Direction Implicit (ADI) as Preconditioner
( page 5 – 16 of Vol 5 Namp Journals )
by Felix Okoro
Department of Computer Science, Ambrose Alli University, Ekpoma, Nigeria
Abstract
This paper solves the discretized 3-dimensional Poisson equation. The method
of Alternating Direction Implicit (ADI) is applied as a preconditioner with
the Conjugate Gradient Method (CGM). A fast convergence to the solution is attained.
An Iterative Method For Simultaneous Inclusion of Polynomial Zeros.
( page 17– 36 of Vol 5 Namp Journals )
by Monday Ndidi Oziegbe Ikhile
Department of Mathematics, University of Benin, Benin City, Nigeria
Abstract
Let 
be a polynomial of degree n. methods that not only enclose, but also isolate
the n zeros in a suitable interval have been proposed. See for examples, Petkovic
[7], Gargantini [1,2,3,], Gargantini and Henrici [4], Petkovic and Carstensen
[8], etc. These methods have the disadvantages of being complicated, but they
possess as one of their features the automatic determination of bounds for all
zeros. In this paper, we present an interval method and its analysis of the
order of convergence. However, the analysis is presented in circular interval
arithmetic introduced by Gargantini and Henrici [4,5]. We illustrate convergence
of the method by numerical examples. Extension of the approach to rectangular
arithmetic is analogous.
Convergent Embedded Explicit: Runge-Kutta (CEERK) Method of Order 4
( page 37 – 44 of Vol 5 Namp Journals )
by Julian Ibezimako Mbegbu
Department of Mathematics, University of Benin, Benin City. Nigeria
Abstract
Some mathematics modeling in the physical sciences have often led to system
of ordinary differential equation of the first order that is dependent on the
time variable t. Authors such as [1], [2], [4], [5] and [3] have contributed
greatly in the numerical solution of such a differential equation in this direction,
we shall propose a convergent embedded explicit Runge-Kutta (CEERK) method that
can cope with the differential equation. Numerical solution of the differential
equation obtained by the proposed CEERK method compares favorably with the classical
explicit Runge-Kutta method of order 4.
Keywords: Differential Equation Runge-Kutta, Embedded, time, stepsize .
Exact (permutation) Distribution for the WN Statistic
( page 45 – 62 of Vol 5 Namp Journals )
by S. M. Ogbonmwan and J. I.. Odiase
Department of Mathematics, University of Benin, Benin city, Nigeria
Abstract
A test statistic called the WN statistic as introduced
by Ogbonmwan (1983),. Which is based on functions of ranks, forms the basis
of this work. The test statistic involves a Multi-Sample Testing Procedure (M-STP)
that takes into consideration all the observations of the combined p
2 samples (treatments) in a one–way analysis of variance (ANOVA) problem.
The work here provides the exact (permutation) distribution for the WN
statistic.
Time Series Analysis of Malaria Data
( page 63 – 70 of Vol 5 Namp Journals )
by N. Ekhosuehi and S. E. Omosigho
Department of Mathematics, University of Benin, Benin City, Nigeria
Abstract
In this paper, we consider the time series data on reported cases of malaria
in a large hospital. The data is analysed and a time series model for the data
is proposed. The models provide a forecasting framework for planning purpose.
The proposed model is a variant of the Box-Jenkins (ARMA (p, q)) models. The
model identification is carried out using the correlogram and the partial correlogram
of the time series data.
Keywords: correlogram, partial correlogram, model identification
and diagnositc checking. Time series
Another Numerical Method for Linear Integral Equation
( page 71 – 78 of Vol 5 Namp Journals )
by V. U. Aihie
Department of Mathematics, University of Benin, Benin City Nigeria
Abstract
Another method for numerical solution of a linear integral equation when the
range of integration is finite is described. It consists essentially of using
Clanshaw-Curtis rule, which is predictable and saves a lot of time when the
need of increase in quadrature point arises. Its application is demonstrated.
The Vertical Electrical Sounding: A Viable tool for the investigation of Clay Deposits.
( page 79 – 88 of Vol 5 Namp Journals )
by O.Ujuanbi and M. B. Asokhia
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria
Abstract
The presence of clay deposits in Ozalla and Sabongida-ora both of Owan West
local government area of Edo State was investigated using the electrical resistivity
method. The Vertical Electrical Sounding (VES) was used for the investigation
using the Schlumberger electrode configuration. Interpretation of data was by
curve fitting in order to generate initial model for computer iterative technique.
Borehole data were also collected using spontaneous potential method as well
as driller’s log. The result shows that at Ozalla the overburden sand
is over 35m whereas the overburden sand is 3.8m at Sabongida-ora with a clay
thickness of over 50m. These results agreed very well with borehole records.
The use of the Gauss- Legendre Quadrature in Solving Flow Problems in Reservoirs Containing Horizontal Wells
( page 89 – 100 of Vol 5 Namp Journals )
by E. S. Adewole, B. M. Rai and T. O. K. Audu
Faculty of Engineering University of Benin, Benin-City, Nigeria
Abstract
In horizontal wells reservoir fluid flow is governed in behavior by well geometry
and reservoir properties in such a manner that none of the existing method can
be used alone to generate accurate pressure values for all the different flow
periods exhibited. Apart from the very early times, where the log approximation
could be used, this paper shows that accurate pressure distribution beyond the
early period can be computed using the gauss-Legendre quadrature. Results obtained
using this method support the expected physical behoviour of oil and gas reservoirs
and agree in principles with those published in literature.
Application of Equivalent Crystal Theory to BCC Metal Surfaces
( page 104 – 114 of Vol 5 Namp Journals )
by E. Aghemenloh
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria
and
J. O. A. Idiodi
Department of Physics, University of Benin, Benin city, Nigeria
Abstract
The equivalent crystal theory (ECT) method or Smith el al [Physics Rev. B44,
6444 (1991)] is employed here to calculate the surface energies of twelve bcc
metals. This is an extension of the work Smith et al which reported surface
energies for only two bcc metals and some fcc metals. It is also an extension
of a previous work of ours which dealt with only fcc metals..
Ionic and Electronic Properties of Sodium Clusters
( page 115 – 126 of Vol 5 Namp Journals )
by B. N. Onwuagba
Department of Physics, Federal University of Technology, Owerri, Nigeria
Abstract
The Cylindrically Averaged Pseudopotential scheme (CAPS) is used within the
local density approximation to study the ground-state ionic and electronic properties
of sodium clusters. In this approach calculations were carried out for the bond
length of dimer, the total energies, binding energies per atom, as well as volume
and surface energies of sodium cluster. The results obtained compare very well
with the ones obtained from quantum chemical methods, distance-dependent Huckel
type model and car Parrinello method who used full three dimensional approach
Linearized Comparative Analysis of Steel and Aluminum Solar Flat Plate Collector in Solid Absorption Refrigerator
( page 127 – 138 of Vol 5 Namp Journals )
by C. U. Okujagu, T. M. Abbey and J. K. Obianyi
Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria.
Abstract
An analysis of design parametric effect on a flat plate collector of a solar
refrigerator system shows that the emmissivity of the plate material gives the
most significant effect on the refrigerator performance. A linearization process
involving the least square method was used to determine the steady state transient
components of some useful parameters in the performance operation of the refrigerator
system for steel and aluminum plates and tubes. A comparative result obtained
form the analysis shows that the Coefficient Of Performance (COP), Condensate
(NH3) yield and Useful Cooling (UC) were much higher for
steel than aluminum plate and rubes due to the high thermal capacity and conductivity
of steel which results in low emmissivity and low radiative heat losses. This
implies that steel is a better material for the construction of flat plate collector
for a solar refrigerator system. It was also found that the cop, NH3
yield and useful cooling signals followed a diurnal cycle of absorption and
evaporation modes, which peaked at 12noon, with the best working period between
9am and 3pm (i.e 3 hours to 9 hours) after sunrise.
On the Attenuation of Solar Radiation by Absorbing Gases In The Atmosphere
( page 139 – 146 of Vol 5 Namp Journals )
by E. E. Iheonu
Nigeria Building and Road Research Institute, Building Research Department
Ota, Ogun State, Nigeria
Abstract
An expression for assessing the attenuation characteristics of the atmospheric
gases has been developed. The results from the application of the expression
in assessing the attenuation due to the influence of the uniformly mixed atmospheric
gases (O2, CO2, CH4,
N2O and CO) and water vapour are found, on the average,
to be in agreement with the findings of Bird and Hulstrom (1981, 1982).the proposed
expression may be relevant to solar radiation models at different strata in
the atmosphere for which the "reduced height" has appropriate value.
Phase Transition Globally Coupled Maps
( page 147 – 160 of Vol 5 Namp Journals )
by Ibiyinka A. Fuwape
Department of Physics, Federal University of Technology, Akure, Nigeria
and
Hilda A. Cerdeira
The Abdus Salam International Centre for Theoretical Physics, P. O. Box 586,
Trieste, Italy.
Abstract
Transition of intermittency is investigated in globally coupled maps. The distribution
of laminar phases for the various transition regions obeys - 3/2-power law decay.
The difference of the emerging two clusters at the various transition regions
show features of no- off intermittency. By applying noise of the system at the
transition regions, the small cluster attractor reduces to a large number of
clusters. The differences of the clusters also show features of no – off
intermittency.
On Some Observable wave forms on Ocean Beaches
( page 161 – 176 of Vol 5 Namp Journals )
by E. O. Okeke and V. E. Asor
Department of Mathematics, University of Benin, Benin City Nigeria
Abstract
This paper considers the theory of the observed shallow water waves. The interest
is essentially on the range of periods associated with beach long waves. This
range seems to be of environmental interest in the locality. This is so, considering
the proportion of ocean energy trapped with this range and often dissipated
along the shoreline. On the whole, the analysis re-enforces the concept of the
cnoidal and solitary oscillations as essential members of shallow water processes.
It is difficult to observe this considering the complicated wave patterns over
beaches. However, spectral decomposition of this pattern is quite revealing.
Existence and uniqueness for Self-similar Solutions for a viscous reacting flow
( page 177– 184 of Vol 5 Namp Journals )
by F. I. Alao
Department of Industrial Mathematics and Computer Science,
Federal University of Technology, Akure, Ondo State, Nigeria.
and
R. O. Ayeni,
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology, Ogbomoso, Oyo State Nigeria.
Abstract
In this paper, we examine a problem of the form;
and 
which
represents a viscous reacting flow problem. We provide an example and methods
of solving the problem. In particular, we re interested in a self-similar solution.
The conditions for the existence and uniqueness of self-similar solution are
investigated.
The Dynamic Response of Plates on Pasternak Foundation to Distributed Moving Load
( page 185 – 200 of Vol 5 Namp Journals )
by G. A. Gbadeyan and M. S. Dada
Department of Mathematics, University of IIorin, IIorin, Kwara State, Nigeria
Abstract
The dynamic analysis of the rectangular plate resting on a Pasternak foundation
and subjected to uniform partially distributed moving masses is carried out
. The effects of shear deformation and rotary inertia are neglected. The governing
partial differential equation is transformed into a set of coupled ordinary
differential equations that are eventually solved using finite difference technique.
It is found that an increase in the area of the distribution of the moving mass
causes reduction in the maximum dynamic deflection. Various values of the dynamic
deflection for various values of foundation moduli are obtained and presented
in tabular form. Moreover, the critical speeds of the moving masses and forces
were calculated. Finally, numerical examples are gives and the results compared
well with existing ones for the limiting cases in which the area of the load
distribution reduces to zero, and also the effect of inertia mass neglected.
Electronic Band Structure of Solid C60
( page 201 – 220 of Vol 5 Namp Journals )
by F. Mathew-Ojelabi
Department of Physics, University of Ado-Ekiti, Nigeria
and
J. O. A. Idiodi
Department of Physics, University of Benin. Benin City, Nigeria
Abstract
We present a group theoretical method for the construction of the molecular
orbitals of carbon 60 (C60) using 60 atomic orbitals (AO’s)
per C60 molecule. The geometry of the crystalline fcc
solid C60 and the hypothetical unidirectional structure
with space group
are adopted in our study. The goal is to provide all the relevant transformation
matrices that are required by group theory. These are then used to obtain analytical
expressions for the molecular orbitals (MO’s) in a form suitable for further
calculations. We limit our derivations to the lowest unoccupied molecular orbitals
(LUMO’s ) i.e the levels relevant to superconductivity in the doped compounds.
In a preliminary calculation, the MO’s are used to diagonalize a single
particle Hamiltonian in a band structure calculation.
Non-Local Theory of Superconducting Tc For Doped Fullerenes
( page 221 – 232 of Vol 5 Namp Journals )
by F. Matthew-Ojelabi
Department Physic, University of Ado Ekiti. Ado Ekiti, Nigeria
and
J. O. A. Idiodi;
Department of Physic, University of Benin, Benin city Nigeria.
Abstract
The electronic band structures of pure solid C60 (fullerene)
and the alkali metal doped solid C60 (the super- conducting
phase) have been calculated using a single-particle, tight- binding Hamiltonian.
An accurate and efficient non-local pseudo potential compatible with these bands
is employed for the description of the electron-phonon interaction in the McMillan
formula for the super-conducting transition temperature Tc.
Reasonably good agreement is obtained between our results for some super-conducting
parameters and the available experimental data.
Numerical Modeling of Dynamic Response of Water Absorption in Soaked Legume Grains.
( page 233 – 238 of Vol 5 Namp Journals )
by * A. S. Oyerinde,
Department of Agricultural Engineering, University of Uyo, Akwa-Ibom, Nigeria
A. S. Adekola.
Department of Physics, Federal University of Technology, Akure Ondo State, Nigeria
and
O. V. Ayodele.
Department of Forestry and Wood Technology, Federal University of Technology,
Akure, Nigeria
Abstract
Numerical models, which describe the dynamic response of water absorption in
soaked legume grains, are presented. Five legume grains were selected of the
study, white beans (Sokoto white); brown beans (Ife brown); soybeans (Glyxine
max); pigeon pea (Cajanus cajan) and Locust beans (parkia biglobossa.). The
numerical and experimental studies as presented in this work have been used
to formulate the model for each of the legume grains.
•*The model obtained which is a function of time is flexible and can be subjected to the desired time condition. This would facilitate and maximize the effective use of the legumes
Boded Elastic Cylindrical Solid Under anti- Plane Shear
( page 239 – 250 of Vol 5 Namp Journals )
by James N. Nnadi
Department of Mathematics, Abia State University, Uturu, Nigeria
Abstract
Longitudinal deformation fields within a long composite cylinder disturbed by
anti-plane shear are investigated. The cylinder is made up of two semi-circular
homogenous solids of different elastic moduli, perfectly bonded along their
interface. The general form of the displacement and the stress states along
the bond are deduced and depicted in graphical form.
Maximum Order Second Derivative Hybrid multi-step Methods for Integration of Initial value Problems in Ordinary Differential Equations
( page 251 – 262 of Vol 5 Namp Journals )
by R. A. Ademiluyi and S. J. Kayode
Department of Industrial Mathematics and Computer Science
The Federal University of Technology, Akure, Ondo State, Nigeria
Abstract
In this paper, we propose a k- step second derivative hybrid linear multi-step
formula of maxima order for solution of stiff and non-stiff initial; value problems
in ordinary differential equations. The method is motivated by second derivative
formulas:
,
in which the control parameter r is specified in advance and the step
size is h. We in our attempt, allowed this parameter r to
assume its exact value by solving the resulting non-linear equations of the
co-efficient. The resultant formulas are A- stable and of maxima order 2k+1
when k is even and 2k+2 when k is odd. The formulas are derived, analyzed and
implemented for k =`1 and k =2.the experimental results show a high degree of
accuracy.
Unsteady Backward power-Law flow Near a Moving Wall
( page 263 – 266 of Vol 5 Namp Journals )
by R. O. Ayeni and B. I. Olajuwon
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology. Ogbomoso, Nigeria
Abstract
In this paper we investigate the effect of a moving wall on the velocity field
of a power -law fluid. We show that when the fluid is dilatant (n > 1), momentum
penetration is finite.
Effect of Frank-Kamenetskii Parameter on Strong Detonations in a Converging Vessel
( page 267 – 272 of Vol 5 Namp Journals )
by P. O. Olanrewaju and R. O. Ayeni
Department of Pure and Applied Mathematics
Ladoke, Akintola University of Technology, Ogbomoso, Nigeria
Abstract
We examine strong detonations in a converging vessel. It is shown that when
Frank-Kamenetskii parameters differ even only by 1/30 there is an appreciable
difference in the temperature along the converging vessel.
On the Application of Lyapunov’s Theorem of Stability To the Convergence of the Reduced Gradient Method for Optimization Problems with Equality Constraints
( page 273– 278 of Vol 5 Namp Journals )
by I. N. Njoseh, P. N. Okonta and D. O. Ajayi.
Department of Mathematics, Faculty of Science, Delta State University, Abraka,
Nigeria
Abstract
In the paper, we shall look at the convergence result of the reduced gradient
method using the Cauchy problem for the system of ordinary differential equation.
Lyapunov’s theorem of stability will be applied to the convergence theorem
to show that any numerical method that solves the Cauchy problem can solve the
problem of the form 
where
f(x) is the objective function, G = {x
: h(x) = 0} and h(x) is the constraint function
Magnetisation of Some Ferrometals
( page 279 – 284 of Vol 5 Namp Journals )
by Ibiyinka .A. Fuwape
Department of Physics, Federal University of Technology, Akure, Nigeria
Abstract
The variation with temperature of the magnetization of Ni, Fe, C0,
Dy and Gd are studied. New data for C0, Dy and Gd is presented
along with previously reported measurement for Ni, Fe, and C0.
The coefficients of the T
term evaluated are compared with result form independent experiments
Determination of the Phase Shifts for the Scattering
Potential Arusing
the WKBJ Approximation
( page 285 – 294 of Vol 5 Namp Journals )
by K. J. Oyewumi
Department of Physics, University of Iiorin, Ilorin, Kwara State, Nigeria
and
E. A. Bangudu
Department of Mathematics, University of Iiorin, Ilorin, Kwara State, Nigeria
Abstract
In this paper phase shifts for the inverse quadratic potential are considered.
This scattering potential governs a large number of collision process involving
massive particles. The purpose of this work is to know how accurate .the approximation
method (the Langer’s modified WKBJ method) is, since the exact analytic
result of this scattering potential is known. In a further analysis, the partial
wave Born approximation method is also used.
On Optimal Design of a Low- Passage Active Filter Using Bessel Function Response
( page 295 – 308 of Vol 5 Namp Journals )
by T. A. Adewale
Department of Mathematics Sciences, Ondo State University, Akungba-Akoko, Nigeira
and
D. D. Abajingin
Department of Physics, Ondo State University, Akungba-Akoko, Nigeria
Abstract
At any level, decision–making is essentially a matter of choosing between
a number of alternatives. Such choices are totally subjective, being based on
our knowledge of the alternatives available and on the sum total of our personal
experience and culture. Choice suggests numerical weighting. Using numerical
values to quantify the preferred choice reduces intuitive decision making to
arithmetical calculation. In dealing essentially with circuit specification
in frequency domain, the design problem includes deciding the size order of
filter required and computing optimum value of the components. In this presentation,
Bessel function response is chosen to determine the filter order and a sum of
square objective function is formulated to determine optimum component by applying
a conjugate direction algorithm in minimizing the objective function. A measure
of the effect of variation in individual component value on circuit response
is computed as a measure of tolerance in terms of rejection rate and yield using
Gaussian distribution function. This is a didactic presentation of what we are
to do in the presence of this problem.
Keywords and phrases: template specification, Bessel response, conjugate direction algorithm, design objectives function, sensitivity to component variation Gaussian distribution, rejection rate percent, the yield or acceptance, tolerance analysis.
Erratum: Some Identities in Spinor Calculus (section
2)
( page 309 – 313 of Vol 5 Namp Journals )
( see section 1 , Namp Journals Vol. 4, 1, (2000), Page 1-8 )
by Oluwole Odundun
Department of Physics
Obafemi Awolowo University, Ile-Ife, Nigeria
Abstract
The Erratum concerns section two of the author’s work published in Namp
Journals Vol. 4, 1 (2000), Page 1-8.
