ABSTRACTS OF VOLUME 7:
Journal of the Nigerian Association of Mathematical Physics(2003)
ISBN: 1116-4336
-spaces
dinger
Equation in an infinite potential welldinger
Equation
Click here for Abstract
A Note on the Generalized Rotations of State Vectors in Complex Hilbert Spaces
( page 1 – 10 of Vol 7 Namp Journals )
by E. O Ifidon
Department Of Mathematics,
University of Benin
Abstract.
By considering the prolonged action of the group of symmetries G on the set
of states 
of
a quantum system, we obtain a generalized rotation of state vectors in complex
Hilbert spaces for which norms are preserved. New symmetries as well as new
representations are thus obtained, which for complex quantum systems aid in
the simplification of the system. The structure and properties of this new
algebra are extensible studied.
Conditional Expectations on Haagerup L-spaces
( page 11 – 18 of Vol 7 Namp Journals )
by A. A. Tijjani
Department of Mathematics
Ahmadu Bello University, Zaria, Nigeria.
Abstract
We consider the problem of extending conditional expectations to the Haagerup
L-space.
Conditional Expectations on Crossed Product of Von Neunmann Algebras
( page 19 – 22 of Vol 7 Namp Journals )
by A.A Tijjani
Department of Mathematics,
Ahmadu Bello University, Zaria,
Federal Republic of Nigeria
Abstract
Conditional expectations on crossed product of 
-finite
von Neumann algebras are studied by showing that the crossed product of expected
filtrations is expected.
On the Lie Algebra of an Algebraic Group
( page 23 – 26 of Vol 7 Namp Journals )
by Henry O. Omokaro
Department of Mathematics,
University of Benin, Benin City, Nigeria.
Abstract
Given an algebraic group G one can associate with it a Lie Algebra g. In this
paper we discuss how much the structure of g reflects the structure of G. Other
issues concerning g are also looked at.
A Generalisation of the RSA Congruence
( page 27 – 28 of Vol 7 Namp Journals )
by Henry O. Omokaro
Department of Mathematics,
University of Benin, Benin City.
Abstract
The RSA congruence [5] states that: If p, q are prime numbers and e, d positive
integers such that m < pq and ed 
1
mod (p-1)(q-1) then med 
m
mod pq. In this work the RSA congruence is extended to a wider class of integers.
It is proved to be true for a finite number of primes
instead of just two primes p and q.
A Cauchy Problem for a Quasi-Linear Hyperbolic First Order Partial Differential Equation
( page 29 – 32 of Vol 7 Namp Journals )
by Michael O.Egwurube
Department Of Mathematics and Computer Science
Federal University of Technology, Yola
and
Emmanuel J.D.Garba
Mathematical Sciences Programme
Abubakar Tafawa Balewa University, Bauchi
Abstract
A quasi-linear hyperbolic partial differential equation in a Banach space is
investigated using the technique of converting such problems to those that look
like the abstract Cauchy problem. It is then shown that this Cauchy problem
is m-accretive and thus admits solutions
A Method of Domain Decomposition for Solution of the Helmholtz Equation
( page 33 – 38 of Vol 7 Namp Journals )
by Felix Okoro*
Department of computer science,
Ambrose Alli University, Ekpoma, Nigeria.
and
Samuel Azi
Department of Physics
Ambrose Alli University, Ekpoma, Nigeria.
Abstract:
Domain decomposition methods for the solution of partial differential equations
are attractive on parallel computers. In this work, a discretization of the
Helmholtz equation is reduced to sub domains and separators sets [1]. A grid
point numbering makes the coefficient matrix take the block arrow head matrix
form. The Cholesky decomposition of the form L
A
L
is applied to the block matrices. A computational procedure using sequential
computer structure is applied to accelerate convergence. The diagonal block
system is solved via the Conjugate Gradient Method (CGM): A test problem comparing
the method with analytical solution is presented.
Keywords: Helmholtz equation, domain decomposition, conjugate gradient method, Cholesky decomposition.
Analysis of the nonlinear Schrodinger Equation in an infinite potential well
( page 39 – 46 of Vol 7 Namp Journals )
by A. N. Njah
Department of Physics, University of Agriculture, Abeokuta, Nigeria.
(e-mail: njahabdul@yahoo.com)
and
R. Akin-Ojo
Department of Physics, University of Ibadan, Ibadan, Nigeria.
Abstract
The Nonlinear Schrdinger
Equation (NLSE) in units of 
where 
are
real parameters, p is a positive integer and
is the eigenvalue (energy) is solved by numerical and perturbation methods in
an infinite potential well vis-a-vis the linear Schrdinger
(LSE). The eigenvalue
for the n
eigenvalue in the well is found for the cases p = 2[4] to be given by 
where
a = 2.46831[2.46773], b = -0.065982[-0.039568] and c = 1[1] using the numerical
method. Using the perturbation method leads to similar results. These results
are comparable with those of the LSE: 
,
where k = 2.5.
have the effect of increasing the values of the
Also as p increases for
the NLSE tends to
for the LSE. The analysis confirms that the NLSE describes small amplitude waves,
which are also self energizing.
Analysis of the nonlinear Diffusion Equation Associated with the Nonlinear Schrodinger Equation
( page 47 – 52 of Vol 7 Namp Journals )
by A. N. Njah
Department of Physics, University of Agriculture, Abeokuta, Nigeria.
(e-mail: njahabdul@yahoo.com)
and
R. Akin-Ojo
Department of Physics, University of Ibadan, Ibadan, Nigeria.
Abstract
We analyse numerically the Nonlinear Diffusion Equation (NLDE) 
obtained from the Nonlinear Schrdinger
Equation (NLSE). The diffusion process is found to be ballistic. This ballistic
bsehaviour increases with increase in both time
and the nonlinear parameter
, indicating that the NLDE describes a quantum diffusion process. The nonlinear
term is found to increase the rate of spreading or diffusion for 
.
The dependence of the variance of the distribution function 
on
and
p are determined.
A Mass-Dependent Effective Interaction for Shell-Model Calculations Derived for the fp Shell
( page 53 – 62 of Vol 7 Namp Journals )
by J.O. Fiase
Department of Physics, University of Botswana, P.B 0022, Gaborone, Botswana,
and
K. Ibikunle
Department of Physics, Ahmadu Bello University, Zaria, Nigeria
and
A. A. Akombor
Department of Physics, Benue State University
Makurdi, Nigeria
Abstract
An effective interaction suitable for shell-model calculations for the fp
shell is derived from the Reid soft-core potential folded with two-body correlation
functions. These correlations were designed to take into account the short-range
repulsion in the nucleon-nucleon force and also the large tensor component in
the Reid force. The interaction when compared with the experimentally fitted
data of Van Hees and Glaudemans in the fp - shell region of the nuclei show
reasonable agreement.
PACS number(s): 21.60.Cs.
A Class of (2m+1) Degree Polynomials Derived Via the Generalized Optimization of the Binding Energy per Nucleon, B
( page 63 – 70 of Vol 7 Namp Journals )
by P.O. Akusu
Nigerian Defence Academy
Department Of Physics,
Kaduna.
Abstract
A Hilbert spaces generalized functions, Xm,n(r), are identified for
the variational method determination of the binding energy per nucleon, B, for
all nuclei. In their application, the optimisation of B for all m,n=1,2,3…,
results in the emergence of a class of (2m+1) degree polynomials,
, which promise to have significant physical implication. These polynomials
were analysed with the use of the MATLAB.
On The Controllability of Perturbations of Non-Linear Delay Systems to Equilibrium State
( page 71 – 76 of Vol 7 Namp Journals )
by V.A. Iheagwam
Department of Mathematics and Computer Science
Federal University of Technology, Owerri
Abstract
The purpose of this research is to obtain a set of criteria for the controllability
of perturbations of non-linear functional differential systems to equilibrium
state. In this study, a relationship is established between the controllability
to the origin of the system under study and the location of the origin in the
interior of the domain of null controllability; to provide a necessary and sufficient
condition for the existence of equilibrium state for given non-linear dynamics.
Criteria for starlikeness in the unit disk
( page 77 – 82 of Vol 7 Namp Journals )
by A. T. Oladipo
Department of Pure and Applied Mathematics,
Ladoke Akintola University of Technology,
Ogbomoso, Oyo State, Nigeria
Abstract
Let 
be analytic in the unit disk U. By the method of differential subordination
for functions f(z) to be in the class S*[a, b] we give a subordination relation
for 
.
A simple algoraithm for the inventory problem with a linear incasing demand
( page 83 – 88 of Vol 7 Namp Journals )
by F. E. U. Osagiede and S. E. Omosigho
Department of Mathematics,
Univeristy of Benin, Benin City, Nigeria.
Abstract
We consider the inventory system where a product has linear increasing demand
over a finite horizon and no shortages are allowed. A new direct search method
is proposed. The search method is implemented by a compuer program written in
MATLAB and implemented on a PC. Numerous test problems taken from the literature
have baeen solved using the computer programme. The results are accurate and
the computer processing time for all the test problems was found to bse less
than one second. Unlike previous method, the proposed method is easy to implement.
Generalized efficiencies for higher order symmetric univariate kernels
( page 89 – 96 of Vol 7 Namp Journals )
by J. E. Osemwenkhaae and S. M. Ogbonmwan
Department of Mathematics,
Univeristy of Benin, Benin City, Nigeria.
Abstract
Much work has been done in kernel density estimation especially in obtaining
approximate/exact window widths, h. The Mean Integrataed Square Errors (MISE)
and the plotting and interpretation of contours in both univariate and multivariate
kernel density estimates are now realizable through the use of fast and cheap
computational devices. The problem of obtaining the efficiency of symmetric
kernels, especially for cases where the order of the smoothing parameter is
greater than two has not received much attention. In this work, we have provided
a formula for obtaining the generalized efficiency for any higher oder symmetric
kernel. We hope this will generate interests in researchers.
Empirical Bootstrap Likelihood for Contrasts of Parameters
( page 97 – 104 of Vol 7 Namp Journals )
by S. M. Ogbonmwan
Department of Mathematics
University of Benin, Benin City, Nigeria.
Abstract
The Bootstrap resampling technique is used to obtain simulated likelihoods for
contrasts
of parameters in this work. We obtained the exact bootstrap empirical likelihoods
and compared the results obtained with those of the bootstrap kernel density
estimates. The bootstrap likelihoods give the distribution functions for the
unknown contrasts of parameters. The comparisons show that good results can
be obtained from both the bootstrap exact empirical and the smoothed bootstrap
kernel likelihoods.
Key words: Bootstrap, Likelihoods, Contrasts, Kernel Density likelihood, exact empirical likelihood, confidence interval.
Effect Of Box-Cox Transformation Parameter On Forecast From ARIMA(p,1,0) models.
( page 105 – 110 of Vol 7 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 effect of applying a family of Box-Cox transformations
to time series data that exhibit stochastic upward linear trend which admits
differencing of order one. We examine the interaction between Box-Cox transformation
and forecasting from the ARIMA(p, 1, 0) model. We demonstrate the importance
of the Box-Cox transformation parameters =1,
=
0.5 and =
0.
Key words: Box-Cox transformations; Model fitting; Forecasting.
Minimal Repair and Replacement Policy Based On Salvage Value.
( page 111 – 114 of Vol 7 Namp Journals )
by Bashir M. Yakasai
Department of Mathematical Sciences, Bayero University Kano.
e-mail: bmyaksai@sci.buk.edu.nig
Abstract.
In most of the complex systems failures occur that when repaired the system
is returned to a condition similar to a working system of its kind and age.
Repair or replacement of a component from a system does not significantly affect
the condition of the whole system. In that case, conducting minimal repairs
will prolong life of the system. Therefore, in this paper we present a minimal
repair and replacement policy that is based on the salvage value of the system,
at its retirement age. Expressions for optimal replacement date, number of repairs
and average cost for the proposed policy are derived. Analytically, they do
not provide explicit expressions; however, numerical solutions are always possible.
Keywords: Minimal repair, replacement, salvage value, failure rate.
On the purely seasonal ARIMA Process
( page 115 – 126 of Vol 7 Namp Journals )
by Eleazar C. Nwogu
Department of Mathematical and Physical Sciences
Michael Okpara University of Agriculture
Umudike, Umuahia, Nigeria.
and
Iheanyi S. Iwueze
Department of Statistics
Abia State University,
Uturu, Nigeria.
Abstract
Because of their common occurrence in the analysis of seasonal time series,
this paper is devoted to the study of time series models whose non-zero autocorrelations
and partial autocorrelations are only at the multiples of the seasonal lag.
After the introduction of the concepts of stationarity, invertibility and moments,
we studied the autocorrelation function (acf) and partial autocorrelation function
(pacf) of the seasonal ARIMA (0,d,0) x (1,D,1)s time series model, where the
subindex s refers to the seasonal period. A numerical example is given to illustrate
the methods.
Key words: Sessional time series, stationarity, invertibility, moments, autocorrelation function, partial autocorrelation function.
Pressure Drop Profile of an inverted Five-Spot Oil Production Pattern with a Horizontal Well Water Injector
( page 127 – 134 of Vol 7 Namp Journals )
by E. S. Adewole and B. M. Rai
Department of Petroleum Engineering
University of Benin, Benin City, Nigeria.
Abstract
To a large extent the success of an inverted five-spot pattern with four vertical
oil producers and one water injector, depends on correct sizing of surface injection
facility and proper understanding of both reservoir and wellbore characteristics.
With vertical water injectors this pattern had been applied successfully in
the past. The advent of the nascent horizontal well technology therefore arouses
high curiosity about the applicability as fluid injector in such patterns. This
paper derives a sand face pressure drop distribution in an inverted 5-spot pattern
with a centrally located horizontal well injector. Source functions for a bounded
reservoir containing a centrally located horizontal well injector are utilized.
An analysis of the dimensionless pressure distributions shows that large patterns
will yield more clean oil production than small patterns. If the producers produce
oil at the same rate, a square pattern will yield equal volume of clean oil
for the same time while a rectangular pattern will produce early water in nearby
producers than the further ones.
Pressure Distribution in a Layered Reservoir with Lateral Wells
( page 135 – 146 of Vol 7 Namp Journals )
by E. S. Adewole, B. M. Rai and T. O. K. Audu
Department Of Petroleum Engineering
University of Benin, Benin City, Nigeria.
Abstract.
The production of oil and gas from a layered reservoir using lateral wells at
economic rates has been a major problem to both the reservoir and production
engineers. The problem manifests in such wells when they cannot deliver fluid
at the desired rates and volumes, good enough to justify the level of investment
(measured by discovery, drilling and completion efforts.) This is often traceable
to lack of good understanding of fluid dynamics in layered reservoirs when they
are drilled with lateral drainholes. In this paper, mathematical models are
constructed to study pressure distribution in a layered reservoir, with and
without crossflow, containing lateral wells. The pressure distributions are
utilized to investigate the wellbore, reservoir layers and layers fluid conditions
best suited for optimum oil recovery.
Migration Velocity Analysis by Fourier Transform in Seismic Data Processing
( page 147 – 154 of Vol 7 Namp Journals )
by J.C. Egbai and Arthur Ekpekpo
Department Of Physics,
Delta State University, Abraka, Nigeria.
Abstract
Migration is the transformation of apparent reflecting positions to true positions.
The information obtained from the field cannot be explained easily due to unwanted
signal. Velocity estimation, common-midpoint (CMP) stacking and migration generally
are considered independent processes. They all have a common theoretical base:
the scalar wave equation. This method operates in the Fourier transform domain
using the exact form of the double-square-root (DSR) operator. The theory of
migration velocity analysis based on wave field extrapolation was discussed.
A constant velocity of 3000m/s was used for extrapolation. In this work we apply
migration technique to provide an adequate approximation to the structure known
as resolved-time method. The technique of the migration could be extended to
prestack processes such as dip moveout (DMO), short-and receiver-gather downward
extrapolation and thus suggests a unified approach to processing data from irregular
surfaces. When the information from the field are fully processed, geological
interpretation could easily be facilitated. The various procedures and figures
are clearly shown. The velocity analysis described does not handle lateral variations
in velocity. It is based on a Fourier-transform domain formulation with only
vertically varying velocity used in extrapolation.
Resistivity Inversion – A Computer Iteration Technique for the Interpretation of Vertical Electrical Sounding
( page 155 – 168 of Vol 7 Namp Journals )
by J.C. Egbai and Arthur Ekpekpo
Department Of Physics, Delta State University,
Abraka, Nigeria.
Abstract
Resistivity inversion is a means of automatic interpretation of soundings in
terms of the resistivity distribution in the earth. There exists problem of
interpretation in geophysics of resistivity method which makes it difficult
due to the mathematical complexities implicit in the derivatives of suitable
theoretical models. The empirical procedures have not help matters in the test
of field data. As a result of these mathematical complexities, the resistivity
method has experienced some empirical procedures which have given rise to simple
and quick solutions. This work attempts to fix the structure of the earth approximately
with the simple mathematical model in the interpretation process. This procedure
was applied in the Vertical Electrical Sounding at Ogwashi-Uku, Delta State
using about seven iterations. The result shows that the iteration technique
is very economical in that it saves cost, energy and time with a very low root
mean percentage (RMS%) error between the theoretical and field curves. The high
accuracy of the iteration method could be seen from the Driller’s log
which confirms very perfect agreement with result of the geophysical survey.
Projectile Motion in a Resistant Medium under the Influence of an Electric Field
( page 169 – 172 of Vol 7 Namp Journals )
by R. O. Ayeni
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
e-mail:roayeni@essconskannet.com
and
O. O. Ayandokun
Oyo State College of Education, Oyo, Nigeria.
Abstract.
The motion of a particle which is projected into a resistant medium and subjected
to a uniform gravitational field and electric field is considered. The drag
force that acts upon the particle within the medium is proportional to the speed
raised to power n. The problem is formulated in terms of particle – speed
and local-path-angle variables, and the equations of motion that result into
non-linear and coupled. Of particular interest is the effect of the magnetic
field on the velocity.
Analytic curves for plume model of dispersion of air pollutants
( page 173 – 176 of Vol 7 Namp Journals )
by Awele Maduemezia, F.A.S.
P. O. Box 9598, University of Ibadan Post Office, Ibadan, Nigeria
Telephone: +234 - (0)803-301-8979
e-mail: awele@alum.mit.edu
Abstract
In this paper the results of a detailed curve-fitting computer code for the
determination of the Pasquill-Gifford parameters used for the specification
of air dispersion in the plume model, are presented. It is shown that the vertical
and horizontal variance parameters may both be written as 
(in metres)
where x is the distance from the source in kilometres, and the variance parameter,
is either y
(= sy) (horizontal) or z
(= sz) (vertical) and the curve-fitting coefficients a, and
Y are given once and for all in a Table.
Existence of Solution of a Time-Dependent Radial Porous Medium Combustion
( page 177 – 180 of Vol 7 Namp Journals )
by O. K. Koriko
Department of Industrial Mathematics and Computer Science,
Federal University of Technology,
Akure, Nigeria.
Abstract
A non-linear time-dependent partial differential equation describing combustion
in a radial porous medium is studied. Existence of a solution is established.
A liquid flow in an open container
( page 181 – 190 of Vol 7 Namp Journals )
by P.B. Shola
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Abstract
This article considers a two dimensional slow flow of a highly viscous liquid
in an open rectangular container, driven by the container’s base which
moves along its direction at a constant speed. Using perturbation technique,
the first deviation from the associated hydrostatic solution for a right angled
contact angle is obtained and presented.
Vibration under a moving load of a non-uniform Rayleigh beam on variable elastic foundation
( page 191 – 206 of Vol 7 Namp Journals )
by S. T. Oni and T. O. Awodola
Department of Industrial Mathematics and Computer Science
Federal University of Technology, Akure, Nigeria.
Abstract.
The problem of the vibrations under a concentrated moving mass of a non-uniform
Rayleigh beam resting on a variable elastic foundation is investigated. The
technique is based on the Generalized Galerking Method and Struble’s asymptotic
technique. Numerical results in plotted curves are presented. The results show
that the response amplitudes of the non-uniform Rayleigh beam decrease as the
rotatory inertia correction factor r
increases. Similarly, for fixed value of r,
the displacements of a non-uniform Rayleigh beam resting on a variable elastic
foundation decease as the foundation moduli F increases. Furthermore, the critical
speed for the moving mass problem is reached prior that of the moving force
problem for both illustrative
Asymptotic Analysis of imperfection sensitivity of the toroidal shell segment with random imperfection
( page 207 – 214 of Vol 7 Namp Journals )
by M. O. Oyesanya
Department of Mathematics
University of Nigeria, Nsukka, Nigeria.
Abstract.
The bifurcation of a toroidal shell segment with initial imperfection which
are subjected to lateral or hydrostatic pressure is studied under the assumption
that the initial imperfection are Gaussian random stress-free displacement whose
mean and autocorrelation function are given. We use perturbation scheme developed
by Amazigo [1]. A simple approximate asymptotic expression is obtained for the
bifurcation load for small magnitudes of the imperfection. The result is compared
with results obtained earlier under secondary bifurcation analysis for the imperfections
in the shape of the buckling mode.
Antiplane Shear Analysis for a Non-homogeneous Semi-infinite Layer
( page 215 – 224 of Vol 7 Namp Journals )
by James N. Nnadi
Department of Mathematics
Abia State University, Uturu, Nigeria.
Abstract.
Closed form stress field
,
near the free surface-interface junction of a nonhomogeneous layer of height,
h are obtained and shown to depend on material constants if loads are applied
on straight line segments of unequal lengths on the free surface. The special
case of self-equilibrating loads applied on segments of equal lengths lead to
independence of stresses on material constants. Stresses are not singular at
the junction. In a graph, we study the variation of
with 
as
the length,
, of loaded segment increases, when
is proportional to
.
Transverse Vibration of Euler-Bernoulli Beams on Elastic Foundation under Mobile Distributed Masses
( page 225 – 234 of Vol 7 Namp Journals )
by M. S. Dada
Department of Mathematics,
University of Ilorin, Ilorin, Kwara State. Nigeria.
Abstract
Uniform distributed moving masses vibration analysis is presented for Euler
Bernoulli beams on elastic foundation. The partial differential equation governing
the beam’s motion is reduced to ordinary differential equation and then
expressed as a system of linear equations by finite difference scheme. The analysis
is valid for Euler Bernoulli beams with various boundary conditions. However,
simply supported boundary conditions are used as an illustrated example. The
numerical results are presented in graphical forms and the limiting cases compared
well with known existing results. The numerical analysis shows that the foundation
stiffness and loads' distribution have significant effects on the dynamic deflection
of the beam.
Heat Transfer Modelling of Roofing Elements of Buildings in the Tropics
( page 235 – 244 of Vol 7 Namp Journals )
by E. E. Iheonu and A. P. Opoko
Nigerian Building and Road Research Institute
Building Research Department
Km 10 Ota-Idiroko Road,
Ota, Ogun State
Abstract
Mathematical models representing the behaviour of inside temperatures due to
the response of roofing element of a building structure to outside environment
variables have been developed for two tropical locations. Comparison between
the measured data and simulated results from the models showed that the variations
of the inner surface temperatures of the roofing element were very similar in
trend to the actual measured data but differed in magnitude significantly throughout
the period under study. Appropriate models have been recommended for the studied
locations. The application of the models may find relevance in other locations
that share similar climatic conditions with that of the studied locations in
the evaluation of the predictive ability of the models with regards to roofing
elements of building structures in the control of thermal fluxes within the
tropical environment.
Equatorial Ionospheric E-Region Critical Frequencies
( page 245 – 250 of Vol 7 Namp Journals )
by O.S. Oyekola
Department of Physics, University of Ibadan, Ibadan, Nigeria
Abstract
Studies of ionospheric E-region critical frequency indices have produced conflicting
results. We examine diurnal variation of the penetrating frequency at Ibadan,
Nigeria (geog. lat. 7.4°N) using the empirical law. Appreciable departure
was found when our data are compared with the experimentally observed hourly
mean and the median of critical frequencies for the same month. Diurnal variation
of E-layer critical frequency of the equilibrium curve for Chapman layer and
the plot obtained by empirical expression at Cambridge, England (geog. lat.
51° N), is given for comparison. These results can be explained by a rapid
recombination of electrons with positive ions
Einstein’s Gravitational Field Equations Exterior and Interior to an Oblate Spheroidal Body
( page 251 – 260 of Vol 7 Namp Journals )
by S. X. K. Howusu and P.C. Uduh
Department of Physics, University of Jos
PMB 2084, Jos, Plateau State,
Nigeria. email: howusus@yahoo.co.uk
Abstract
In this paper we derive the exact Einstein’s gravitational field equations
exterior and interior to a homogeneous oblate spheroidal massive body to open
the way for their solution and hence application to test particles in the universe.
Composite Targets and compositional inhomogeneities in sputter deposited thin films
( page 261 – 266 of Vol 7 Namp Journals )
by Usman M. Gana
Department of Physics
Bayero University, Kano, Nigeria.
Abstract
A numerical study of the compositional distribution of thin films from two components
targets has been carried out. The study, based on the string model, considered
both the composite nature of the targets and the deviation of the angular distribution
of some sputtered atoms from the normal co-sinusoidal distribution function.
Large improvements on the compositional homogeneity of the films could be obtained
by carefully selecting the number, area and placement of the chips (segregates)
on the host target surface
Electronic properties of Sodium clusters in spherical Jellium model
( page 267 – 274 of Vol 7 Namp Journals )
by C. A. Madu and B. N. Onwuagba
Department of Physics
Federal University of Technology, Owerri, Nigeria.
Abstract
We have investigated a wide range of electronic properties for Na clusters of
sizes between 2 and 36 with 
using
first-principles local spin density functional calculations. The Kohn-Sham single
particle equations were solved self-consistency on a one-dimensional mesh according
to Herman and Skilmann’s scheme. The Coulombic part of the energy is obtained
by solving Poisson equation while Gunnarsson and Lundqvist parameterization
technique was adopted in the calculation of the exchange-correlation energy
density and potential. The studies were carried out in the spherical Jellium
model approach. Peaks occurred at the magic numbers that correspond to the complete
filling of the shells which explain the prominent role played by the kinetic
energy of the Kohn-Sham independent electrons in the determination of the relatively
greater stability at the magic numbers. The results compared favourably with
previous experimental and theoretical values.
The two-electron Interaction in the ground state of the Hubbard-Hirsch Hamiltonian
( page 275 – 280 of Vol 7 Namp Journals )
by Edison A. Enaibe and John O. A. Idiodi
Department of Physics,
University of Benin, Benin City, Nigeria.
Abstract.
A single-band tight-binding model with on-site repulsion U and nearest-neighbour
exchange interaction J (the so called Hubbard-Hirsch Hamiltonian) is studied
with the help of a correlated variational approach. Two finite-sized lattices
with periodic boundary conditions are considered and the criteria for the occurrence
of a transition from an antiferromagnetic phase to a ferromagnetic phase are
discussed.
Auger Broadening Correction to the Low-energy tail of the Lithium X-ray K-emission spectrum
( page 281 – 284 of Vol 7 Namp Journals )
by U. S. Mbamara and E. N. Mgbenu
Department of Physics
Imo State University, Owerri, Nigeria.
Abstract
In this work the actual contribution of the Auger effect to the broadening of
the low-energy end of the K-emission spectrum of metallic lithium is investigated
and calculated. By applying the relevant selection rules and transition probability
for the Auger process to the Auger rate, an Auger width of 
is
obtained. When this result is incorporated into existing calculations for the
lithium spectrum, there is an appreciable elimination of the low-energy blur
existing between the final spectrum and the experimental spectrum of Tomboulian
and Bedo (1958)
Relative Deviation between a Uniformly Weighted Propagator and a Windowed Propagator of a Simple Harmonic Oscillator
( page 285 – 294 of Vol 7 Namp Journals )
by Eno Etim Ituen
Department Of Physics, University Of Uyo, Nigeria
Abstract
The paper elaborates more on the process of windowing in the computation of
the quantum propagator, ks, for a simple harmonic oscillator as a follow up
of Ituen 2002b. More window functions are analysed in this case, namely, random,
Wr, exponential, We, gaussian, Wg
and velocity, Wv window functions. The values of the propagator
as Kwr, Kwe, Kwg,
Kwv compares reasonably with Ks
and hence with the analytical result Kcl. The slight deviations
are measured as relative deviation ar, ae, ag, av
depending on the window functions, which gives a measure of their suitability.
Measurements were done with variations in time only; variations with space being
reserved as a further work.
Microseisms of 28-29 December 1998
( page 295 – 314 of Vol 7 Namp Journals )
by Jack Darbyshire
Centre for Applied Oceanography
Marine Science Laboratories, Menai Bridge
Anglesey, LL59 5EY, UK.
Abstract
Microseism records taken at Menai, Anglesey, showed a very narrow frequency
band centred on 0.125 Hz which appeared unchanged in frequency for over 24 hours.
It was not found possible to relate this to any sea wave activity off the coast
of the British Isles as this time. When, however, the North Atlantic Weather
Charts were referred to, there were two strong storms, one off Newfoundland
and one south of Iceland. The Newfoundland storm moved rapidly eastwards until
it arrived at a point where it could be intercepted by waves coming from the
Iceland storm which had been stationary. A wave prediction model was used to
estimate the three dimensional frequency-direction spectra over the relevant
areas. This showed that there was substantial interference caused by waves moving
in opposite directions over a considerable area, from 15°– 25°
longitude and 45°– 50° latitude. The wave interference effect
could be measured by taking the product of the spectral densities at each end
of all the azimuths involved. The results showed a strong correspondence with
the observed microseism frequency spectra, giving a similar narrow band of unchanging
frequency but with the double frequency being a little higher than the observed
value of 0.125 Hz.
