TOPICS & CONTRIBUTORS :
(please click on the hyperlinked title of each article to go
to the abstract)
Some Identities in Spinor Calculus
( page 1 – 8 of Vol 4 Namp Journals )
by Oluwole Odundun,
Department of Physics, Obafemi Awolowo University,
Ile-Ife, Nigeria.
Abstract
Using the methods of spinor calculus we prove two identities and point out that
a third identity can be similarly proved.
Frequency Dependence of electronic density of states in Super-conducting (…) Cum)On-x Systems
( page 9 – 16 of Vol 4 Namp Journals )
by G. C. Asomba,
Department of Physics and Astronomy,
University of Nigeria, Nsukka, Nigeria.
Abstract
We have calculated and exhibited the frequency dependence of the super-conducting
electronic density of states (dos), normalized to the undoped state, in (…)
Cum)On-x systems. This is achieved
using our recently introduced Bardeen-Cooper-Schrieffer (BCS) – like pairing
t-model (PtM [Physics C258, (1996) 30] and first principles derivations. Presently,
our calculations span negative and positive electronic energies (frequencies.)
The obtained results show dos irregularities. These are in sharp contrast with
the behaviour of dos in the BCS model of super-conductivity in Fermi liquid
systems (e.g., simple metals). Our results are, surprisingly, consistent with
experimental and band-structure determinations of the density of states in the
cuprate systems. These results are, delightfully, in good qualitative agreement
with the theoretical results by Charavarty et al. For YBaCu3O7-x
in the tunneling model by Anderson. We conclude that the PtM has successfully
reveled the irregularities in the dos of non-Fermi liquid (NFL) (…) Cum)On-x
systems: a feature widely experimentally established but only theoretically
indicated by the tunneling mode [Science 361 (1993) 337], to the best knowledge
of the present author. The present result goes further in establishing an NFL
phase in our pairing t-model as a generalized BCS model of electron pairing
and phase transitions.
Bardeen-Cooper-Schrieffer Model reveals possible non-Fermi Liquid Features
( page 17 – 30 of Vol 4 Namp Journals )
by G. C. Asomba,
Department of Physics and Astronomy,
University of Nigeria, Nsukka, Nigeria
Abstract
The Bardeen-Cooper-Schrieffer (BCS) singlet-pairing model, which newly incorporates
particle states non-orthogonality, has revealed fractional exclusion of some
electronic pair states. Fractional exclusion principle, as a generalization
of the Pauli exclusion principle, was recently discovered by Haldane in special
spin-
systems with extensive one-particle Hilbert space dimension. This principle
is freshly parameterized in our approximate mean-field BCS model and the latter
is analyzed via the matrix Green function instrument. The results show possible
non-equikinetic pair super-conductivity and magnetic non-Fermi liquid (NFL)
states, as recently observed in some correlated electron systems. Numerical
predictions of the NFL specific heat and variation of the magnetic exchange
with pair-kinetic-levels difference,
, qualitatively agree with recent experiments on Gd1-x
and
, which are well-known non-Fermi liquid systems.
Tight- Binding Potentials for Fcc Metals
( page 31 – 40 of Vol 4 Namp Journals )
by John O.A. Idiodi
Department of Physics, University of Benin, Benin City, Nigeria.
Abstract
A novel semi-empirical tight –binding potential to simulate properties
of fcc metals is proposed. The novelty lies in the fact that the attractive
part of the potential is of the form of an nth power dependence on the effective
coordination (or second moment of the local density of state) instead of the
usual fixed choice for n (½ or 2/3). The repulsive
part of the interaction potential is of course, the standard Born-Mayer type.
In order to use this potential for specific metallic solids, the model parameter
n and four other parameters are fitted on an equal footing to experimental data.
It turns out that the parameter n is not a constant for all metals. This work
furnishes an alternative prescription for determining tight–binding potentials.
WKBJ Approach to Quantum- Mechanical Tunneling Through a non-Rectangular Potential Barrier
( page 41 – 52 of Vol 4 Namp Journals )
by Kayode J. Oyewumi
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology, Ogbomosho, Oyo State, Nigeria
and
Ezekiel A. Bangudu
Department of Mathematics, University of Ilorin, Ilorin,Kwara State, Nigeria
Abstract
At classical turning points the validity of the WKBJ methods is no more guaranteed
and hence we implored the Kramers’ connection formulate that connects
asymptotic solutions in classically allowed and classically forbidden (inaccessible)
regions which are later applied to the transmission theory. The WKBJ method
is applied to the problem of quantum-mechanical tunneling through a non-rectangular
potential barrier (a special case of modified Pöschl-Teller potential barrier).
Due to inaccurate results of WKBJ near the top of the barrier, we used Kemble’s
method that accounts for a quadratic behavior for the potential near the top
of the barrier. In order to obtain the accuracy of the method we compare its
results with the exact and Kemble’s result for the potential. Although
WKBJ approximation is expected to give better results for a potential of large
amplitude.
Calculation of Phonon Dispersion curves and Density of States: Use of Simple Program with Personal Computers
( page 53 – 66 of Vol 4 Namp Journals )
by Salihu S. Duwa, Lawan S. Taura
Department of Physics, Bayero University, Kano, Nigeria.
and
N. Harhiaran
Department of Physics, Ahmadu Bello University, Zaria, Nigeria
Abstract
The phonon density of state and dispersion relation of one and two atoms crystal
structure has been evaluated for simple cubic and body centered lattices with
interatomic interactions up to and including second neighbours. The farce constants
in simple structures are determined by a optimization procedure using the dispersion
in the [100], [110] and [111] directions. The dispersion curves calculated with
a two neighbours, six parameters give a reasonable fit to the dispersion data
in the principal symmetry directions. The standard FORTRAN code available in
the literature has been substantially modified for adaptation for personal computer.
All the needed subroutines are suitably modified to create a versatile program
which can be used for any lattice phenomenon dispersion and density of states
calculations.
Lifetimes of Precipitating Ionospheric Electron Beams
( page 67 – 72of Vol 4 Namp Journals )
by B. Chike-Obi
Department of Physics, University of Ilorin, Illorin, Nigeria
S. Salihu Duwa
Department of Physics, Bayero University Kano, Nigeria
and
L. E. Akpabio
Department of Physics, Cross-River State University, Uyo, Nigeria.
Abstract
Using on the one hand, the binary collision approximation, we have calculated
the life times of ionospheric electron beams. On the other hand, treating space
plasma as a particle distribution with an enhanced high energy tail, in the
(Vlasov) kinetic equation, the growth times of the type of beam-plasma instability
excited by the incoming beams are calculated. We find that the value of growth
times, as indicators of the lifetimes of the electron beams are about 
the
characteristics lifetimes from the binary-collision approximation. This suggests,
as expected, that anomalous transport due to the instability is the dominant
process in the decay of the electron beams.
Generalized time Dependent Analytical Solution of Bloch Equations for Magnetic resonance Imaging with Time Varying rF B1(t) Magnetic Field
( page 73 – 86 of Vol 4 Namp Journals )
by O. B. Awojoyogbe
Department of Physics, Federal University of Technology Minna, Niger State,
Nigeria
Abstract
This study presents a generalized analytical solution of the Bloch equations,
which yield a time dependents signal that gives the fundamental relation of
MR imaging. The final result of Fourier transformation of the total MRI signal
is a set of images, each representing the spatial distribution of spins at a
simple velocity (distance/time). In this way, the analysis provides techniques
by which a magnetic resonance imaging sequence can be constructed so that the
signal induced by acceleration and higher order terms of motion (which is a
disturbing problem in the phase different method) can be eliminated or minimized.
Key words: bloch equations, magnetic resonance, pulse sequence
On the Relative Controllability of Perturbations of Nonlinear Functional Differential Systems with Distributed Delays in Control
( page 87 – 94 of Vol 4 Namp Journals )
by Iheagwam,V. Anyamele
Department of Mathematics and Computer Science
Federal University of Technology, Owerri, Nigeria.
Abstract
The purpose of this study is to examine conditions for the relative controllability
of perturbations of non-linear functional differential system with distributed
delays. Including system with implicit derivative in the perturbation function.
The method of solution involves the linearization of the non-linear base. With
enough smoothness conditions imposed on the perturbation function and an assumption
of the non-singularity of the controllability map, the question of the relative
controllability of the system under study, is settled in the affirmative using
Darbo’s fixed-point theorem. The result extends Chukwu’s efforts
[10,11] to systems with implicit derivative and carries over Balachandran’s
result in [6] to functional differential systems.
Stress Analysis for Aq Cracked Cylinder Under Longitudinal Shear Loading
( page 95 – 104 of Vol 4 Namp Journals )
by James N. Nnadi
Department of Mathematics, Abla State University,
Uturu, Abia State, Nigeria
Abstract
The problem-solved analytically concerns the stress distribution in an elastic
cylinder containing an edge crack and subjected to out–of plane shear.
Complete solution in a closed form is obtained for the displacement, which in
turn yields the expression for the stresses everywhere in the material. The
stress intensity factor and the energy release rate derived are proportional
to that of a cracked semi-infinite elastic material subjected to the same mode
loading
On the Superposition Theory of the Near Earth’s Surface Longitudinal and Transverse Elastic Waves.
( page 105 – 112 of Vol 4 Namp Journals )
by Vincent E. Asor
Subsurface Technology Services, Shell Petroleum, Warri
and
Ezekiel O. Okeke
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
The seismic events associated with the superposition of the longitudinal and
transverse waves propagating near the earth’s surface are presented. The
geophysical manifestations of these developments are usually in the form of
the Raleigh waves and kindred events. This study, consequently, is aimed at
analyzing some of the propagation characteristics of the Raleigh elastic surface
waves. In particular, the wave slowness for the elastic surface waves are analyzed,
thereby illustrating the geophysical role of the Raleigh surface wave slowness.
Further, the non-trivial dependence of the phase and group velocities maxima
of the surface waves on the material rigidity is shown to be of higher order
than those of the previous investigations (Bullen & Bolt, 1985).
Propagation of Error in Polynomial Evaluation
( page 113 – 122 of Vol 4 Namp Journals )
by P. B. Shola
Department of Mathematics,
University of Ilorin, Ilorin, Nigeria
Abstract
Polynomials especially those with coefficients of the same sign or strictly
of alternating signs are of great importance in the approximation of may mathematical
functions that occur in mathematical physics. Two standard algorithms namely
the Clenshaw, and Horner’s algorithms for evaluating polynomial are examined
with respect to the propagation of error. Using process graph, it is established
that the quantity 
controls
the upper bound in the relative error in the value of a polynomial at t.
Oscillatory and Asymptotic Properties of Odd Order Difference Equations
( page 123 – 136 of Vol 4 Namp Journals )
by O. K. Koriko
Department of Industrial Mathematics and Computer Science
Federal University of Technology, Akure, Nigeria.
Abstract
The oscillation criteria for certain odd order difference equations are established
indeed, we generalise the results of smith [4] on the oscillatory and asymptotic
behaviour for certain third order difference equations to a class of general
odd order difference equations.
Generating semi-Gaussian Two-Dimensional Quadrature Rules
( page 137 – 148 of Vol 4 Namp Journals )
by V. U. Aihie
Department of Mathematics,
University of Benin, Benin City, Nigeria
and
G. A. Evans
Department of Mathematics,
Loughborough University of Technology,
Loughborough, Leicestershire, LE 11 3TU.
Abstract
This paper generates semi-Gaussian two-dimensional quadrature rules. It is based
on monomial equations and experimentally executed. The rules generated were
tested and compared favourably with Gaussian product rules.
Parallel Iteration Methods for Linear System of Equations.
( page 149 – 174 of Vol 4 Namp Journals )
by M. N. O. Ikhile
Department of Mathematics, University of Benin, Benin city, Nigeria
Abstract
In [13] we considered some multipoint iteration method and their parallel cyclic
implementation for large spares linear system. Interestingly, parallel computing
methods offer a great promise of computing speed that can possibly be brought
to bear on the numerical solution of many important practical problems of interest.
In what follows we continue our investigations of these methods.
Toeplitz-Circulant Preconditioner for Solutions of Large Systems of Linear Equations
( page 175 – 182 of Vol 4 Namp Journals )
by Felix Okoro
Department of Computer Science and Statistics,
Ambrose Alli University, Ekpoma, Nigeria
Abstract
This paper considers the solution of discretized 3-dimensional Poisson equation
by constructing a circulant preconditoner. The method of solution of Toeplitz
matrices is applied with the Conjugate gradient method to obtain the solution.
By exploiting the Toeplitz structure of the discretized system, a fast convergence
method is attained.
On the Existence and Uniqueness of self Similar Diffusion Equations
( page 183 – 186 of Vol 4 Namp Journals )
by R. O.. Ayeni and F. B. Agusto
Department of Pure and Applied Mathematics,
Ladokek Akintola University of Technology
Ogbomoso, Nigeria
Abstract
We consider the diffusion equation 
.
We determine the criteria for self- similar solution of the form 
Numerical Solution of A Reacting Viscous Problem
( page 187 – 200 of Vol 4 Namp Journals )
by F. I. Alao
Department of Industrial Mathematics and Computer Science,
The Federal University of Technology, Akure, Ondo State, Nigeria
R. O. Ayeni
Department of Pure and Applied Mathematics,
Ladoke Akintola University of Technology,
Ogbomoso Oyo State, Nigeria
and
R. A. Ademiluyi
Department of Industrial Mathematics and Computer Science,
The Federal University of Technology, Akure, Ondo state, Nigeria
Abstract
A viscous fluid flowing through a cylinder is studied of particular interest,
a steady state of a reacting viscous fluid. The flow is reacting and heat is
generated through reaction and viscosity. To ensure that the problem represents
a physical problem, the numerical technique of solving the problem is discussed.
It is discovered that, the problem exists and the results show that the temperature
reacting system increases as viscosity and the heat release increase. The importance
of this research to our society is discussed.
Keywords: viscosity, temperature, density, pressure, diffusion coefficient, thermal conductivity and exponential factor.
Pulsating Flow in Viscoeloastic Tubes
( page 201 – 212 of Vol 4 Namp Journals )
by Emmanuel O. Oghre and Edward O. Ifidon
Department of Mathematics, University of Benin, Benin city, Nigeria
Abstract
The arteries and other blood vessels have been found to exhibit viscoelastic
behaviour when blood flows through them. In this consideration we found the
numerical solution of the velocity and pressure pulses in viscoelastic tubes.
Increase in frictional term in viscoelastic tubes showed a considerable change
in pressure and velocity pulses. The effects of tapering of the vessels were
also investigated.
Electric Nusselt Number in a Closed Cylindrical Container Filled With two immiscible fluids
( page 213 – 242 of Vol 4 Namp Journals )
by M. F. Hague, O. W. Olasoji and E. D. Mishelia
Department of Physics, Abubakar Tafawa Blewa University,
Bauchi, Nigeria.
Abstract
Electric Nusselt number (ENN) in a closed cylindrical container filled with
two immiscible fluids 
/water,
/ethyl
alcohol, /silicon
oil and
/kerosene (where stands
for air, 02, N2 and F12)
is measured under the influence of electric fields. The measurement is carried
out using a single platinum wire (diameter = 0.025 mm) mounted along the axis
of the cylindrical container, made of copper (diameter = 53.0mm). ENN is measured
with gas/liquid ratios of one-to-three, one-to-one and three-to-one respectively.
The ENN data have been correlated by dimensional analysis. The data have been
compared with the predicted relations and analytical expression and is well
correlated over the range of the Rayleigh number from 2.0 x10
to 4.0 x 10
.
An empirical correlation relationship is proposed to evaluate the efficiency
of convection and the results for gas/ liquid combinations in the combination
ratios one-to-three and three-to-one are presented.
Estimation of Formation Temperature from Borehole Measurements in Agbor Delta State, Nigeria
( page 243 – 256 of Vol 4 Namp Journals )
by J. C. Egbai
Ambrose All University, Ekpoma, Edo State, Nigeria
Abstract
Measurement of temperature in well holes has been the oldest logging technique.
A new numerical method that uses inverse methods for thermal stabilization of
a borehole after circulation of drilling mud has stopped was discussed. Five
geophysical parameter can be estimated for the method: (a) true formation temperature
(Tf); (b) mud temperature Tm; (c)
thermal inversion distance (V) into formation, (d) formation thermal conductivity
(K) perpendicular to the borehole and (e) efficiency factor (Z) for heating
the mud in the borehole after circulation of mud has stopped. The input data
measured include the mud temperature at the surface at the time circulation
stops, radius of the borehole, the densities and specific heats of the drilling
mud and the formation. The new inverse procedure shows that the true formation
temperature can be estimated from both synthetic data and field data. The mud
temperature can be estimated with fairly high degree of accuracy while thermal
inversion (V), thermal conductivity (K), and the efficiency factor (Z) can roughly
be estimated if high quality data are obtained. The formation temperature for
Agbor, delta state is within the range of 40. 49°C.
Effects of Horizontal oil Drainhole Length on Wellbore Pressure in Stratified Reservoirs
( page 257 – 268 of Vol 4 Namp Journals )
by E. S. Adewole, B. M. Rai and T. O. K. Audu
Faculty of Engineering, University of Benin, Benin Cit, Nigeria.
Abstract
Multilateral technology has proved to be highly efficient in the production
of stratified and layered reservoirs especially when the layers are not communicating
with one another. Although, when there is communication between layers the tight
layer is best produced by competing and producing the more permeable layer,
drilling a lateral pair helps in the economic enhanced recovery of one layer
if the other layer serves as a fluid injector. The length of drainhole is one
of the most important factors as it has for reaching operational technical and
economic consequences on the overall success. This then calls for the question:
how long should the drainhole be? This question is tackled by solving an appropriate
diffusivity equation relating reservoir pressure, rock and fluid properties
and reservoir geometry (dimensions) with time. The final result is obtained
by a numerical integration model using FORTRAN program at various well length
to study the changes in wellbore (flowing) pressures. It is discovered that
increasing the length of the drainhole does not lead to an increase in well
productivity as the wellbore flowing pressures are found to be decreasing. The
model enables the engineer to select an appropriated well length given reservoir
characteristics and fluid properties and, of course, be variables of operational
economics. It is further discovered that the model could be used to investigate
the role of length in a well pair that is intended to be used for enhanced oil
recovery programmes. This can be achieved by changing then mobility ratio, well
length, for given rock and fluid properties to observe the behaviour of the
wellbore pressure in each well.
A Simplified Computer Iteration Technique for the Interpretation of Vertical Electrical Sounding
( page 269 – 280 of Vol 4 Namp Journals )
by M. B. Asokhia, S. O. Azi, and O. Ujuanbi
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria.
Abstract
A major problem in resistively research work is interpretation of field curves.
This is due to the complexities of the earth structure as a result of which
it is extremely difficult to derive a suitable mathematical model that will
fit the earth model perfectly. As a result, the resistivity method has fallen
prey to a number of empirical procedures, which are purported to give quick
and simple solutions, but in the final analysis fail to achieve this end. This
paper proposes some acceptable assumptions to simplify the structure of the
earth in such a way as to facilitate the problem of deriving simple mathematical
models to fix the structure of the earth approximately. Such a technique was
used in interpreting vertical electrical sounding from Umuduruokoro, near Owerri,
Imo state. Within only about seven iterations a fit was found between field
curve and the theoretical curve with mean square error of less than two percent.
The driller’s log for the borehole drilled from this survey was in perfect
agreement with the result of this geophysical investigation.
Estimation of Magneto-Telluric noise by Method of Polarisation Analysis
( page 281 – 288 of Vol 4 Namp Journals )
by M. B. Asokhia
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria.
Abstract
Magneto-telluric (MT) survey is one of the latest methods of geophysical investigation.
The first paper on this method was published by Cagniard in 1953. The method
has the advantage of being able to probe up to 100km of the interior of the
earth. A major problem is interference of data by noise. Noise is a function
of coherence of signals. A common method of computing the noise present so far
is by method of normalized transformed functions of magnetic and telluric signals.
This work presents an alterative method of achieving the same purpose by method
of polarisation analysis of magnetic and telluric signal. The already existing
theories were used in interpreting the coherence of MT data from Sweden. The
coherence values of the same data were also computed by the method of the proposed
polarisation analysis. The results were so close that one could be substituted
for the other within limits of experimental error. It is suggested that more
research should be carried out to ascertain the better method of analyzing noise
in MT work.
Interpretation of Vertical electric Soundings at Afuze and Eme-Ora using Resistivity Transform Functions
( page 289 – 300 of Vol 4 Namp Journals )
by O. Ujuanbi and M. B. Asokhia
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria
Abstract
Geophysical survey work was recently carried out at Afuze, Owan East and Eme-ora
Owan West local government areas of Edo state using vertical electrical sounding
technique. It is usually difficult interpreting result in terms of lithological
variation with depth. One of the latest methods of interpretation is by matching
practical field curves with theoretically generated curves from resistivity
kernel functions. Researchers have formulated several kernel functions and research
work is still going on with the aim of identifying an optimum kernel function.
This work proposes resistivity transform function as an acceptable kernel function.
Detailed theory of the function is given and typical result using kernel function
for interpretation for the two towns are presented. Spontaneous potential loggings
were carried out in nearby boreholes in the two towns for correlation purposes.
The three sets of results - the available driller’s logs the geophysical
logs and the interpretation by method of kernel function all correlated very
well within limits of experimental errors.
Inventory Replenishment Policy when Demand is Quadratic: Direct and Inverse Methods
( page 301 – 308 of Vol 4 Namp Journals )
by F. E. U. Osagiede and S. E. Omosigho
Department of Mathematics, University of Benin, Benin City Nigeria
Abstract
We present two new methods for solving the inventory replenishment problem when
demand is given by 
over
a finite time horizon H. No shortage is allowed in the system. The replenishment
times 
where
are obtained and the order quantity at each replenishment time is derived. Examples
are given to illustrate these methods.
Keyword: inventory model, replenishment times, quadratic demand.
Failure-Time Model for a Component with Life Control Device
( page 309 – 316 of Vol 4 Namp Journals )
by Bashir M. Yakasal.
Department of Mathematical Sciences, Bayero University, Kano, Nigeria
Abstract
This paper we prose a failure-time model for component whose working-time length
can be exploited optimally, to a certain level by the use of life control device.
For realization of the problem we provide a prototype example, where we use
the data obtained from the experiment conducted on the life span of battery
sets installed in a particular brand of radio.
Keywords: failure- time rate; control level, Weibull; distribution
On Some Problems of the Variable end-Point Theorem
( page 317 – 326 of Vol 4 Namp Journals )
by Oghogho Omane Ikpoku and E. O. Okeke
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
In determining a minimizing arc in a class of admissible arcs joining an end
curve to a fixed point or an end curve to another en curve, the variable end-point
theory often proves to be a very efficient mathematical tool. This theorem is
utilized in this study to analyse the external curve joining.
(a) a hyperbolic end curve and a specified origin
(b) a hyperbolic end curse and a circular end curve
(a) was proposed by Glegg (1968), whilst (b) is the generalization. Further,
(b) usually involves a large number of unknowns. This study intends to suggest
an efficient analytical method of solution and also; in cases where the geometry
of the end curves may be more complex. The analysis is then applied to study
the mass transport across a model river flowing through a channel. Consequently,
in – section (2) and Figure 1, it is deduced that the mass flow velocity
of 11.2msec
is sufficient to move a considerable load of sedimental layers across the river.
In this calculation, only the length scales representing the width of the model
river and the focal distance of the bounding hyperbola from a specified origin
are involved. In Figure 2 of section (3), however, a more interesting analysis
arises as a result of the inclusion of the radius r of the other end bounding
circular curve.
Higher Order Forms for Optimal Widow Width in Multivariate Kernel Density Estimation
( page 327 – 334 of Vol 4 Namp Journals )
by S. M. Ogbonmwan and E. J. Osemwenhae
Department of Mathematics University of Benin, Benin city, Nigeria
Abstract
The univariate kernel density estimation (KDE) has received tremendous attention
in the literature. But this cannot be said of the multivariate kernel density
estimation (KDE), which has received very little attention so for. In this work,
a generalized higher order forms for the window width of the multivariate kernel
density estimation is considered. This extends the work of Ogbonmwan and Osenwenhae
(1998) the work provides ways by which the rates of convergence of the optimal
window width are increased leading to further reduction of the global error
- MISE
