TOPICS & CONTRIBUTORS :
(please click on the hyperlinked title of each article to go
to the abstract)
NMR Measurements
Magnetic field
sub-configuration of 
ions in octahedral crystal field| 1) |
De-Sitter group approach to the Theory of Gravitation
( page 1 – 11 of Vol 3 Namp Journals )
by Awele Maduemezia
Department of Physics, University of Ibadan,
Ibadan, Nigeria
Abstract
By a suitable choice of metric, curved space-time is realized as a 4- dimensional
metric space of class 1, i. e., it is imbedded in (flat) (4+1) de-Sitter space.
By this stratagem an alternative derivation is achieved of one of the well-known
results of the theory of general relativity, namely the precession of the perihelia
of the planets Mercury, Venus, the Earth, and Icarus. The results are in good
agreement with experiment. The derivation leads to the emergence of a fundamental
unit of length, a = c
/
(8
G
)
= 0.481856 x 10
m, where
=10
Jm
is
a fundamental stress- energy surface density, and G is the Newtonian universal
gravitational constant.
| 2) |
Error Estimation in the Gauss and Newton-Cotes Quadrature Schemes for Weak Solutions of Quantum Stochastic Differential Equation
( page 12 – 35 of Vol 3 Namp Journals )
by E. O Ayoola
Department Of Mathematics, University Of Ibadan, Ibadan, Nigeria.
Abstract
Gauss and Newton-Cotes Quadrature Schemes For Computing Weak Solutions Of Lipschitzian
Quantum Stochastic Differential Equations (QSDE) driven by certain operator
valued stochastic processes associated with creation, annihilation and gauge
operators of quantum field theory in a local convex space are introduced and
their error estimates are studied. The work is accomplished within the frame
work of Hudson–Parthasarathy formulation of quantum stochastic calculus,
results concerning the consistency and convergence of the schemes in the topology
of the locally convex space are presented. This generalized analogous results
for classical initial value problem to he equivalent form of noncommutative
quantum stochastic differential equations involving unbounded linear operators
on a Hilbert space.
| 3) |
On Estimation of Entropy Value for an Organization
( page 36 – 42 of Vol 3 Namp Journals )
by S. E. Omosigho
Department of Mathematics, University of Benin, Benin City, Nigeria.
and
A. Q. Osagiede
Institute of Education, University of Benin, Benin City, Nigeria
Abstract
The paper considers the use of entropy to measure the stability of workforce
of an organization by making use of mainly wastage data of Edo State Teaching
Service to estimate the wastage probability of each length of service interval.
It is found necessary to study the degree of experience present in Edo State
Teaching Service due to the present economic situation and the state government
embargo on employment in recent years. The study also modifies the log-normal
model of Chu and Lin (1994) to calculate the wastage probabilities to tenure
classes. Entropy is also calculated based on this modified log -normal wastage
rates (probabilities) and a comparison is made between the two entropy values.
Bowey’s stability curves are drawn for the actual wastage proportions
(probabilities) of PPEB and the modified log-normal wastage proportions to authenticate
the entropy results.
| 4) |
Delay Differential Equations and Finite-Dimensional iterated Mapping
( page 43 – 47 of Vol 3 Namp Journals )
by Ibiyinka A. Fuwape
Department of Physic, Federal University of Technology,
Akure, Nigeria.
Abstract
Delay-differential Equation’s (DDE) are currently been used to model high
dimensional dynamical systems, which exhibit very complex hyper-chaotic behaviour.
An attempt has been made to replace the singularly perturbed differential-delay
equation, which is a continuous infinite dimensional dynamical systems with
finite dimensional iterated mappings
| 5) |
Synchronization of Chaotic Systems
( page 48 – 54 of Vol 3 Namp Journals )
by Ibiyinka A. Fuwape
Department of Physics, Federal University of Technology,
Akure, Nigeria
Abstract
A new approach for constructing chaotic synchronized systems by linking them
with common signals has been made. Attempts were made to synchronize the globally
coupled map (GCM), which is a model for non-linear spatially extended systems.
The transverse Iyapunov exponent was calculated numerically. A particular case
of N =3 has been investigated and some clustering have been observed for this
system
| 6) |
An Optimization Technique for the Retarded Differential Delay Equation
( page 55 – 74 of Vol 3 Namp Journals )
by F. M. Okoro
Department of Computeer Science and Statistics, Edo State University, Ekpoma,
Nigeria
and
M A. Ibiejugba
Department of Mathematics University of Ilorin, Ilorin Nigeria
Abstract
Models in natural settings sometime include the present and also the past states
of the system. This is natural in application in many branches of human endeavour.
In this work, the minimization of a quadratic cost functional subject to the
retarded differential delay equation is presented. The elegant algorithm of
the Extended Conjugate Gradient Method (ECGM) originated in [1].
| 7) |
An Extended Conjugate Gradient Algorithm For Discrete Optimal Control Problems.
( page 75 – 88 of Vol 3 Namp Journals )
by Francis O. Otunta
Department of Mathematics,
University of Benin, Benin City, Nigeria
Abstract
Discrete optimal control problem arise in many multistage and scheduling problems.
In principle also, continuous optimal control problems may be discretized appropriately
and subsequently be formulated as discrete optimal control problems. Herein,
we propose an algorithm, based on the conjugate gradient method for solving
discrete optimal control problems with constraints on the states and controls
for the dynamical system.
| 8) |
Mutipoint Iteration Methods For Sparse System of Linear Equations
( page 89 – 105 of Vol 3 Namp Journals )
by M.N.O Ikhile,
Department of Mathematics,
University of Benin, Benin City, Nigeria
Abstract
In this report we investigate the effects of incorporating past information
in the gauss-Jacobi iteration method for large sparse linear system of equations.
It is considered that under certain restrictions convergence is assured, by
the implementation requires extra-storage locations. This may not be a serious
handicap considering the enormous storage capacity of emerging parallel computers.
More consoling is the fact that the resultant algorithm possesses explicit potential
for parallelism, although the exploitation of these is not our purpose herein.
However, our finding raises the question as to whether there is any need pursuing
multipoint iteration methods for spares linear system of equations as a separate
method.
| 9) |
On Derivation of New Numerical Integrator for Solving Linear Stiff First Order Initial Value Problem with Constant Matrix of Order 2
( page 106 – 114 of Vol 3 Namp Journals )
by Julian Ibezimako Mbegbu
Department of Mathematics and Computer Science,
University of Benin, Benin City, Nigeria
Abstract
In the light of Fatunla [1], a new numerical integrator for solving stiff first
order initial value problem with constant matrix of order 2 was derived based
on the interpolating function 
where
A, B, C, are vectors with real entries and 
is
a complex eigen value with the
complex conjugate of 
Application
of this linear integrator to stiff first order initial value problem with constant
matrix of order 2 gives an encouraging approximation to the exact solution.
The integrator is exponentially fitted and L-stable.
| 10) |
Spin Density In Cu2O Plane of
YBa2Cu307
Probed by CuNMR Measurements
( page 115 – 120 of Vol 3 Namp Journals )
by E.O. Aiyohuyin
Department of Physics, University of Benin, Benin City, Nigeria
Abstract
The nuclear magnetic resonance (MMR) spin lattice relaxation time (T1
)
are calculated for 
Cu
sites in Yba2 Cu307.
The calculations are based on the phenomenology model of Millis et al (1990)
and the random phase approximation analysis of NMR by Bullet et. al (1990).
The results are compared with experiments. The antiferomagnetic length is estimated
to be 2.3 lattice constant at T= 100k and the total number of spins in the two
dimensional plane is found to be temperature dependent. The finding make excitions
mediated superconductivity conceivable [lsihara (1993)].
| 11) |
Unified Hamiltonian Model for Magnetism and Superconductivity in High-Tc Cuprate Systems
( page 121 – 135 of Vol 3 Namp Journals )
by G. C. Asomba
Department of Physics And Astronomy,
University of Nigeria of Nigeria, Nsukka, Nigeria
and
A. O. E Animalu
National Mathematical Center, Abuja, Nigeria
Abstract
A mean-field Hamiltonian model, applicable to the high-Tc cuprate oxide system,
is represented, under the name paring t-model (PtM), which unifies some known
Hamiltonian models for strong electron correlation (usually leading to magnetism)
and the popular Bardeen-Cooper-schrieffer (BCS) model for electron pairing (leading
to superconductivity). The PtM emphasizes electron kinetics as perhaps, the
most important operative factor in the high–Tc cuprates. The analysis
is based on a 4 x 4 matrix Green’s function method using the generalised
pseudospin matrices of the type: Ap
= 
p
(p,
= 0,1,2,3… where Ap
are dummies for the Pauli 
,
Dirac
Gell-mann 
matrices)
first introduced in the mapping of the novel pairing scheme in the multiple–band
cuprates, by one of us, and some of the 
components
recently used in the hadronic mechanics (Lie-isotopic) treatment of the Cooper
pair by one of us. Some of the new results obtained for the normal and superconducting
excitation energy, super-conducting energy gap, transition temperature and density
of states, for the cuprates, have similarities with the corresponding results
from experiment and the recent interlayer Josephson tunneling model by Anderson
but may have advantages over the latter.
| 12) |
Possible Electronic Energy Structure of High-Tc Cuprates
( page 136 – 150 of Vol 3 Namp Journals )
by G. C. Asomba
Department of Physics and Astronomy,
University 0f Nigeria, Nsukka, Nigeria
Abstract
Possible electronic energy structure of the high Tc cuprates is reported within
the framework of a simple algebraic Green’s function analysis. The starting
point is a two-band (d-p) restricted-hopping Hamiltonian in pseudospinor representation.
The analysis leads to antiferromagnetic (af) Mott-Hubbard or charge transfer
(ct) normal (undoped) state, depending on bandwidth
and levels separation (~U). In our so-called t-model pairing of electrons, doped
cuprates present as CT-assisted superconductors with AF exchange energetically
forbidden. Approximate numerical results from the analysis are consistent with
experiment and corresponding results form some other theories.
Keywords: two- band model, restricted hopping energy structure,
algebraic Greens function, electronic levels separation, antiferromagentic normal
state, CT-assisted superconductivity
| 13) |
Estimating the Stability of Some Alkalimetal Clusters Li, Li And Nana* using Local Spin Density Functional Formalism
( page 151 – 166 of Vol 3 Namp Journals )
by J. S. Ononiwu
Department of Physics,
Federal University of Technology, Owerrri, Imo State, Nigeria
Abstract
We present a self–consistent local spin density approximation (LSDA) used
in the density functional calculation of the stability of the alkali metal clusters
Li,Li*, Na, Na* in the framework of a jellium-like model. Here for the neutral
Li and Na clusters, the binding energy per atom obtained is about one fifth
of the dissociation energy. Also, the results for the ionization potentials
for and singly charged Li* and Na+ clusters enable us
to understand and account for the enhanced stability of these alkali metal clusters.
| 14) |
Implementation of Equivalent Crystal Theory within a generalized embedded-Atom Method
( page 167 – 178 of Vol 3 Namp Journals )
by J. O. A. Idiodi
Department of Physics,
University of Benin, Benin City, Nigeria
and
E. Aghemenloh,
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria
Abstract
This paper employs he concept of an equivalent crystal within a Generalized
Embedded-Atom Method to calculate the (III) surface energies of four fcc metals
– AL, Au, Pd and Pt. The results obtained for all four metals are found
to be comparable to fist principles calculations and experimental data.
| 15) |
Discrete Eigenvalues of a Modified Pöschl-Teller Potential Hole using Semi-Classical Approximation
( page 179 – 192 of Vol 3 Namp Journals )
by K. J. Oyewumi,
Department of Pure and Applied Mathematics,
Ladoke Akintoal Univeristy of Technology,
P. M. B. Ogbomoso, Oyo State, Nigeria.
and
E. A. Bangudu,
Department of Mathematics, University of Ilorin, P. M. B. 1515,
Ilorin, Kwara State, Nigeria.
Abstract
The use of a modified Pöschl-Teller potential hole is addressed using both
semi-classical path integral and exact methods. The exact results of eigenvalues
of a modified Pöschl-Teller hole is obtained on solving the one-dimentional
Schrödinger equation for this potential hole analytically, which shows
the accuracy of the semi-classical method. The approximate quantization rules
(the well known Bohr-Somerfeld quantization conditions) are derived from the
W.K.B.J formulae (solutions). The semi-classical method is then tested by the
quantization of the quantum mechanical systems of the modified Pöschl-Teller
potential hole, which practically gives the some results as using exact method.
| 16) |
Computation of the Kernel Function by inversion of resistivity field data from Schlumberger Configuration
( page 193 – 207 of Vol 3 Namp Journals )
by M. B. Asokhia, S.O. Azi, F. O. Onwuka and O. Ujuanbi,
Department of Physics, Edo State University, Ekpoma
Abstract
A major problem in geophysical investigations using electrical methods is the
interpretation of results in terms of lithological variation with depth. Interpretation
is commonly found by matching practical field curves with theoretically generated
curves from resistivity kernel function. The kernel function cannot be measured
in the field but has to be obtained from a transformation of measured apparent
resistivities. Several kernel functions have been identified. The need to formulate
an optimum kernel function leads to continued research on this subject. This
work reviews major previous kernel functions in literature with their peculiar
problems. Apparent resistivity value is then theoretically derived as an expression
involving an integral over the kernel function, which contains all needed information
about the present configuration of the earth. The integral equation is solved
to get the kernel function. Theoretical curves generated with the kernel function
were matched with practical curves from field data obtained in Owan West Local
Government Edo State, Nigeria. The interpretation based on this kernel function
agreed very satisfactorily with well logs in this area of Edo State.
| 17) |
Noise reduction and cancelling stationary sinusoidal noise in Seismic data acquisition in Atala prospect of River State
( page 208 – 221 of Vol 3 Namp Journals )
by J. C. Egbai,
Edo State University, Ekopma, Nigeria
Abstract
The process of noise reduction in seismic method of prospecting has brought
about improvement in data quality as well as operational efficiency. For his
research two primary approaches were used for reducing seismic noise to enhance
desired reflections. The first is based on recoding arrangement that will cancel
the unwanted signals before they are recorded in the field while the other is
to process the data after they are recorded by appropriate filtering. Noise
from the company’s (United Geophysical) plant was used to generate stationary
sinusoidal noise. The seismic monitor was highly contaminated with sinusoidal
noise. When this noise is large compared to seismic signals, it adversely affects
prestack seismic processing and subsequent interpretation. A digital least-square
filtering algorithm for cancelling stationary sinusoidal noise in the semi data
leaving the signal.
Generalized Solutions to nonlinear parabolic equations.
( page 222– 233 of Vol 3 Namp Journals )
by E. O. Ifidon and E. O. Oghre
Department of Mathematics, University of Benin,
Benin City, Nigeria.
Abstract
We consider the non-linear parabolic equation
where 
is
a distribution with compact support or more generally, a generalized function
associated with such a distribution. 
is
a bounded open set in
with smooth boundary 
and
,
is a positive integer. This equation arises often in chemical flow problems,
gas dynamics and other physical processes and is known to have no weak solution
in the classical distributional sense [1]. We show that the algebra of generalized
functions G(Q) [2] provides a suitable setting for the construction of solutions
to such a problem. We obtain existence, uniqueness as well as consistence results
for the solutions to the problem using non-classical methods which involves
the use of classical estimates and the induction hypothesis over the order of
he differential operators which defines the elements of G(Q).
On the numerical simulation to Blasius’ Equation for Dimensionless Shear Stress
( page 234 – 248 of Vol 3 Namp Journals )
by A. S. Adekola
Department of Physics, Federal University of Technology,
Akure, Ondo State, Nigeria.
Abstract
The fluid flow patterns were simulated numerically using fourth-order Runge
Kutta scheme attributed to Gill. The numerical simulation of Blasius’
equation is aimed at investigating the behaviour of fluid flow under steady
conditions and to estimate the dimensionless Shear Stress of flow. Carnaham
et al (1959), Ologunleko and Adekola (1998) used the forth-order algorithm attributed
to Kutta. Comparisons with their results showed that the procedure adopted by
Carnahan was approximate while that of Ologunleko and Adekola was exact but
the present numerical scheme has high level of convergence, which make it more
appropriate whenever Laminar-boundary layer of a fluid is to be studied.
The Dynamic Analysis of an Elastic plate with point-moving load
( page 249 – 257 of Vol 3 Namp Journals )
by Y. M. Aiyesimi
Department of Mathematics and Computer Science,
Federal University of Technology, Minna, Nigeria.
Abstract
This paper gives a mathematical analysis of the deflection profiles of an elastic
plate resting on an viscoelastic foundation subject to the effect of a point
load whose position at any time t is defined parametrically as 
where
R is the radius of the orbit and 
is
the circular frequency of the load (angular velocity). Since the plate itself
has a natural frequency and the moving load constitute an external vibration
as observed in the defining Equation 2.2 there arise the case of resonance.
In this paper therefore, the author determines mathematically the vibrating
conditions that give rise to the occurrence of his phenomena, which in actual
fact is a menace to structures for which the modelled plate represents.
Numerical solution for a non-Boussinesque radiative flow in the Annulus of concentric rotating spheres
( page 258 – 274 of Vol 3 Namp Journals )
by Y. M. Aiyesimi
Department of Mathematics and Computer Science,
Federal University of Technology, Minna, Nigeria.
Abstract
The thermal properties like the viscosity, conductivity and difussibility of
certain fluid have been shown by experiments to vary with its thermal state
like its temperature and pressure. For instance in Birds et al [1] the viscosity
of gasses at low density has been found to vary almost directly with the square
root of its absolute temperature whereas the viscosity of a pure liquid was
shown to decrease exponentially with its absolute temperature. In most of the
familiar researches carried out on fluid flow the analysis are based on the
invariance of this properties. The results obtained therefore from such analyses
re bound to be unreliable in view of the variance of the principles on which
such analyses re based with real fluid. This paper therefore carry out a numerical
investigation of the flow generated by a fluid whose viscosity, conductivity
and difussibility vary with its absolute temperature according to a model in
the annulus of rotating sphere. The results of this analysis is compared with
the results obtained from Newtonian analysis (constant properties.)
A steady flow of fluid in an open rectangular container
( page 275 – 285 of Vol 3 Namp Journals )
by P. B. Shola,
Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
Abstract
A steady slow flow of a viscous liquid in an open rectangular container is considered.
The flow is driven by the base of the container, which moves steadily along
is plane. The topside of the container is left open with the liquid in contact
with the air above it. Consequently, the upper boundary of the flow is a free
boundary and part of the unknown to be determined. Considering the inertial,
gravitational and surface tension forces a numerical procedure for obtaining
solutions for the cases when the capillary numbers are small is provided and
the curves of the free boundaries obtained here presented for some flow parameters.
Phase plane analysis of liquid front moving through a hot porous rock
( page 286 – 289 of Vol 3 Namp Journals )
by R. O. Ayeni,
Department of Pure and Applied Mathematics,
Ladoke Akintola Univeristy of Technology, Ogbomoso, Nigeria.
Abstract
It is known that not geothermal reservoirs may have temperatures as high as
200 to 300 °C and in such reservoirs the water vapour may have pressures
in the range of 1 – 30 atmospheres. In this work we show analytically
how pressure runaway occurs.
On the Evolutions of the Ocean wave generated low frequency Seismic noise
( page 290– 298 of Vol 3 Namp Journals )
by E. O. Okeke, C. Adejayan
Department of Mathematics, Univeristy of Benin,
Benin City, Nigeria
and
V. E. Asor,
The Shell Petrolleum Development Company of Nigeria Limited,
Warri
Abstract
The forward problem of ocean wave-seabed interaction in the shallow continental
shelf is investigated. Consequently, we have examined the multi-layer effects
of the transmission of acoustic wave through the layered medium. Thus, displacement
components of the medium associated with the seismic events in a homogeneous
elastic medium were compared with those oscillations in a multi-layered earth’s
structure. There from, it is deduced that each type of medium appears to support
acoustic waves trapped near the earth’s surface. However, in the multi-layered
case, the drop in the acoustic wave energy in downward direction is more apparent
and thus depict the effect of the wave refraction across the layers.
Criteria for unique solution of a radial porous medium combustion
( page 299 – 312 of Vol 3 Namp Journals )
by O.K. Koriko,
Department of Industrial Mathematics and Computer Science,
Federal University of Technology, Akure.
Abstract
The problem of finding conditions for a unique solution is considered. New criteria
for a unique and global existence are found. These are achieved through numerical
method.
On a family of methods for simultaneous inclusions of zeros of polynomial and analytic functions inside a simple smooth closed contour in the complex plane.
( page 313 – 322 of Vol 3 Namp Journals )
by S. E. Uwamusi
Department of Mathematics, Faculty of Science,
University of Benin, Benin City, Nigeria.
Abstract
A family of methods with k + 2 R-order which possesses high speed of convergence
for the simultaneous determination of zeros of polynomial and analytic functions
inside a simple smooth closed contour in the complex plane is considered. Neglecting
terms involving analytic function in our method leads to the well-known method
previously considered in [7]
The saturation of bean-excited ionospheric lower hybrid resonance through ion acceleration
( page 323 – 329 of Vol 3 Namp Journals )
by Salihu S. Duwa,
Department of Physics, Bayero University, Kano, Nigeria
and
B. Chike-Obi,
Department of Physics, University of Ilorin, Nigeria.
Abstract
Electron beams which precipitate into the aurora along the earth’s magnetic
field lines are responsible for the excitation of broadband electrostatic waves
at heights less than 1500km, with an intensity peak near the lower hybrid frequency.
It is argued that the lower hybrid wave become saturated by transferring energy
to ambient ions, to produce an ion conic, which is a distribution with the ions
concentrated on a cone in velocity space. The electron and ion populations are
modelled, at the outset, as displaced and ordinary Maxwellians, respectively.
The relaxation time of the electron beam and he rate of energy transfer from
it are estimated from the nonlinear diffusion coefficient in the limits 
where Vd and Ve
are the drift and the thermal speeds of the electrons.
Theoretical significance of field measurements of radioactive leaf and canopy temperatures
( page 330– 340 of Vol 3 Namp Journals )
by A. A. Olufayo
Department of Agricultural Engineering,
Federal University of Technology, Akure, Ondo State,
Abstract
The significance of the measurement of leaf and canopy temperatures was demonstrated
analytically from energy and radiative balance equations. Theoretical leaf and
canopy temperature was shown to be related to water status of the crop and the
difference between canopy and air temperatures was related to the vapour pressure
deficit of the air, the net radiation and the wind. Experimental work showed
that up to a difference of 50C was observed between well-watered and stressed
treatments, which confirmed the theoretical relationships.
Remotely sensed crop canopy temperature, ambient relative humidity and air Temperature: Theoretical Analysis and Experimental verification
( page341– 349 of Vol 3 Namp Journals )
by A. A. Olufayo
Department of Agricultlural Engineering,
Federal University of Technology, Akure, Ondo State.
Abstract
Recent advancement in infrared thermometry has permitted the measurement of
leaf or vegetation canopy temperature without contact. The aim of this paper
is to demonstrate from theoretical background the relationship between canopy
temperature, relative humidity and air temperature. Field experimental data
are presented to verify the theoretical relationships.
Sensitivity and error analysis of Blaney-Morin-Nigeria evapotranspiration model
( page 350 – 359 of Vol 3 Namp Journals )
by P. G. Oguntunde
Deparment of Agricultural Engineering,
Federal University of Technology, Akure, Nigeria.
F. I. Alao,
Department of Mathemtics and Compuer Science,
Federal University of Technology, Akure, Nigeria.
and
A. A. Olufayo,
Department of Agricultural Engineering,
Federal University of Technology, Akure, Nigeria.
Abstract
The response of Blaney-Morin-Nigeria model to errors in estimation of the input
parameters of temperature, relative humidity and radiation ratio is examined.
Direct response approach and application of partial derivatives method were
used for the purpose. The results showed that a±4°C change
in temperature caused about 10% change in evapotranspiration
. The response of the model to a±15% variation in Humidity was 28% and
a±15% change in radiation ratio alters by
15%. Based on the uncertainty of each measuring temperature, the overall performance
of BMN model was affected by 7.5% for temperature, 11.4% for relative humidity
and 7.5% radiation ratio. The implications of these results are discussed.
Analytical solutions of the Bloch equations for MRI
flow dependent magnetization and signals with spatially varying Magnetic
field
( page360 – 369 of Vol 3 Namp Journals )
by O. B. Awojoyogbe.
Department of Physics, Federal University of Technology
Minna, Niger State, Nigeria.
Abstract
Nuclear magnetic resonance (NMR) has been established as a powerful tool to
study the structure of complex molecules. Molecular motion, rate processes and
molecular interactions. Despite the tremendous theoretical and technical advanced
improvement of this new medical diagnostics in many research laboratories around
the world, there is a common belief however, that basic NMR properties of biological
materials are still far from being fully understood and a great deal of further
research is needed to clarify the quantitative and qualitative information in
various NMR studies. An ideal approach to extract this useful information would
be to find generalized solution in the Bloch equation, but this is obviously
a difficult task. In this study we present a generalized analytical solution
of the Bloch equation s for magnetic resonance imaging flow dependent magnetization
and signal with spatially varying
magnetic field.
An expression for Ez component of spatial non-uniform Electromagnetic source fields in low latitude.
( page 370 – 378 of Vol 3 Namp Journals )
by D. D. Abajingin and G. N. Obodi
Ondo State University, Ado Ekiti, Nigeria.
Abstract
In this presentation we obtained the expression for Ez
component of non- uniform source fields in low latitude. The plots obtained
both in space-frequency and space- time domains give a more accurate form than
our earlier expression. The non- homogenous differential equation was reduced
to Cauchy initial boundary values specified by functions defined as
and
. These functions are specified at plane t = 0
Potential distribution and focusing properties of an equidiameter co-axial cylindrical electrostatic lens
( page 379– 392 of Vol 3 Namp Journals )
by A. M. Awobode
Department of Physics, University of Ibadan, Nigeria
and
O. M. Oni
Departments of Pure and Applied Physics,
Ladoke Akintola University of Technology
P. M. B. 4000, Ogbomoso, Nigeria
Abstract
An alternative method of derivation of the results of Read et al (1970) is presented.
The values were obtained using a different parameterization of the potential
function, and using numerical approach. The results were used to plot the equipotential
lines, trace the electron ray path and determine the cardinal points of an equidiameter
co- axial cylindrical electrostatic lens over a range of voltage ratio and lens
separation. The cardinal points (f1 and f2)
thus measured from the electron ray path showed a close approximation to the
calculated value.
Electrostatic energy matrices for sub-configuration
of ions
in octahedral crystal field
( page 393 – 405 of Vol 3 Namp Journals )
by I. M. Mejeha
Department of Physics, Federal University of Technology,
Owerri, Imo State, Nigeria.
Abstract
In this paper, the problem of the interaction of the 
and
5d electrons of divalent samarium
ions in crystalline environment is discussed within the framework of the Yanase-Kasuya
coupling formalism and the Racah irreducible tensor operator techniques. Accordingly
the reduced matrix elements of the symmetric many-electron double tensor operators
of
rank (1, k), k = 1, 2, … 6, between SL-coupled wave functions of the 
sub-configuration
are calculated and presented. In additions the block coefficient on the electronic
wave functions of the sub-configuration
are also computed. With these the direct Coulomb and exchange matrices re computed
and their elements expressed in terms of Slater-Condon parameters 
