2. New One-Boson-Exchange Potential functions
6. The F-Region Equatorial Ionospheric Electrodynamics Drifts
8. First order normalization in the perturbed restricted three–body problem with variable mass
Remarks on thermal explosions in the early evolution of the earth.
An investigation of groundwater condition in Agbede by Geelectrical resistivity method.
Variable order one-step methods for initial value problems I
An application of the maximal independent set algorithm to course allocation
The turning points in the solution of n-queens problem using backtracking method
Software package for analysis of completely randomized block design
Active control versus recursive backstepping control of a chaotic system
Synchronization of Forced damped Pendulum via Active Control
23.
Some thermodynamic non-Fermi liquid properties of correlated electron
systems.
24. Plasma heating by non-linear wave-Plasma interaction
26.Some remarks on certain Bazilevic functions
On the successive coefficients of certain Univalent functions
On a differential subordination of some certain subclass of Univalent function
31. Dynamic analysis of a Bernoulli-Euler beam via the Laplace transformation technique
The period of relaxation oscillations of a nonlinear system using singular perturbation methods
On the steady state temperature profiles of biological tissues during microwave heating.
36. Vorticity determination in a hydraulic jump by application of method of characteristics
38.Existence of a secondary flow for a temperature dependent viscous couette flow.
40. Fairing NURBS curve by dual parameter optimization
Viscous dissipation effects on the flow of a radiating gas between concentric elliptic cylinders
Radiation effect of magnetohydrodynamic flow of gas between concentric spheres
45. On the dynamic buckling of lightly damped cylindrical shells modulated by a periodic load
One Leg hybrid P-stable substitution LMM for oscilatory IVPs in ODEs.
Hessian Spectrum to perturbation factor for gradient method algorithm
Jacobian approach to optimal determination of perturbation parameter for gradient method
50.A family of block methods for special second order initial value problems [I.V.Ps].
51.Numerical integrators for Stiff and Stiff oscillatory First Order initial value problems
57. A software for the RSA Encription
60.Effect of queue discipline on the performance of a queueing system
62. Mathematical model for bird flu disease transmission
63. The effect of stochastic migration on an HIV/AIDS transmission model.
64.Qualitative study of Kermack and Mckendrick’s epidemic model
66. Thermal neutron counts and derivated charts
67. On the fluctuating filtrate
On the possibility of multiplicity of temperature fields in a microwave heating cancer therapy
Relative null controllability of linear systems with multiple delays in state and control
Relative controllability of nonlinear systems with multiple delays in state and control
77. Stability of discrete control systems
79. Euclidean null controllability of linear systems with delays in state and control
80. Relative controllability of nonlinear neutral systems with multiple delays in state and control
82. On compactoid and limited sets in non-Archimedean locally convex spaces
84.A study of the Hubbard-Hirsch model within the Hartree-Fock Approximation (HFA)
88. Excitation of low-frequency electrostatic instability on the auroral field lines due to precipitation electron beam
89. On iterative solution of non-linear equation
Neutrino mass
by
Amagh Nduka
Departments of Physics and Mathematics,
Federal University of Technology, Owerri, Nigeria.
Abstract
The place of the neutrino in atomic theory and the mass of this particle are two problems that have received considerable attention for many decades. In spite of the heavy investment recourses, human material, theses problems have remained intractable. It turns out that geometrization of matter is a necessary prerequisite for the resolution of many problems of considerable current interest. In this paper we discuss the geometrization of matter, and deduce therefore the mass of the neutrino.
Pg 1 – 4
New One-Boson-Exchange Potential functions
by
J. O. Fiase, F. Gbaorun and +L. K. Sharma+
Department of Physics, Benue State University, Makurdi, Nigeria.
+ Department of Physics, University of Botswana, Gaborone, Botswana.
Abstract
A new one-boson-exchange potential (OBEP) is derived by fitting the oscillator matrix elements of the sum of the OBEP functions to those of the matrix elements derived by the lowest order constrained variational (LOCV) technique. The results give a reasonable fit to the OBEP model.
pg, 5 – 10
Contribution of oblateness of the sun to radar sounding according to Newtonian mechanics
by
Y. Y. Jabil and S. X. K. Howusu
Department of Physics, University of Jos, Nigeria.
Abstract
The Newtonian theory of radar sounding in the gravitational field of a spherical sun is well known [1]. It is now well established that most of the astronomical bodies including the sun are spheroidal (proplate or oblate) in shape [5,11,12]. The Newtonian mechanics has been used to resolve satisfactorily the radar sounding phenomenon to the order of c-5 within the gravitational field established by the homogenous spherical massive sun. In this paper the Newtonian mechanics shall be used to resolve satisfactorily the radar sounding phenomenon within the gravitational field established by the homogenous spheroidal oblate massive sun.
Pg 11 - -14
Theoretical model analysis of molecular orientations in liquid protein dielectrics
by
A. A. Laogun and N. O Ajayi
Department of Physics, University of Benin, Benin City, Nigeria.
Abstract
In this study, some theoretical model functions have been used to explain the molecular behaviour of four different types of proteins; human haemoglobin, Insulin, egg-white lysozyme and b - globulin molecules in solution. The results of the computational fitting procedures showed that the dielectric dispersion of the protein molecules generally followed the Debye and Cole-Cole functions. The dielectric parameters obtained from the dispersions, relating to the structural and electrical properties of the molecules were tabulated. The relationships between the dispersion amplitude D and the molecular dipole moment m of the proteins and also between the relaxation time t and the energy of activation DH of the molecules have been highlighted. The molecular interpretation of the polarization effects responsible for the dielectric dispersions have been discussed.
Pg 15 - -20
Optmizied random phase approximation for the phase diagram of C60 material
by
F. Matthew-Ojelabi and K. A. Aduloju
Department of Physics, University of Ado-Ekiti, Ado-Ekiti. Nigeria.
Abstract
This paper determines the phase diagram of C60 fluid by an efficient and robust optimized random phase approximation (ORPA) method of Pastore et. al (1995), imposes physical requirements as in the original ORPA scheme with a view to achieving consistency within the liquid structure factor. Our perturbation/variational approach for the Helmholtz free energy of the C60 molecules is based on the Lennard-Jones intermolecular interaction. We observe that higher accuracy is obtainable by treating all the grid points within the exclusion hole of the pair distribution function as independent variables. Our numerical results show appreciable improvement in both the thermodynamic functions and the structure factor.
Pg 21 -26
The F-Region Equatorial Ionospheric Electrodynamics Drifts
by
Oyedemi S. Oyekola1 and Emeagi E. Iheonu2
1Department of Physics, University of Ibadan, Ibadan, Nigeria (osoyekola@yahoo.com)
2Building Research Department, Building Physics Unit, NBRRI, Km 10, Ota-Idiroko Road, Ota, Ogun State, Nigeria (e-mail: eeiheonu@yahoo.com)
Abstract
The ionospheric plasma drift is one of the most essential parameters for understanding the dynamics of ionospheric F-region. F-region electromagnetic drifts are calculated for three seasonal conditions from ionosonde observations acquired during quiet period of a typical year of high and low solar activity at Ibadan (7.4oN, 3.9oE, dip 6oS), Nigeria. The vertical plasma drifts derived from h’ (f) ionosonde data are compared with vertical drifts obtained by incoherent scatter radar and AE-E satellite measurements during nighttime periods under similar solar and geomagnetic conditions. We find comparable variability among the ionosonde drifts at Ibadan, Jicamarca VHF radar drifts, and AE-E satellite drifts during high solar flux and geomagnetic quiet conditions at equinox and solstices periods. The equinoctial average evening upward drifts enhancements by the three methods are roughly similar and occur at the same local time (19 LT) for all the seasons. Additionally, the evening reversal time from upward daytime to downward nighttime does not vary much except during the winter months; and occurs earliest in summer and equinox, but least during winter period. Also the data indicate asymmetry of evening reversal times about the dip-equator between the Peruvian, Indian, and the African equatorial regions. Our observations are in conformity with some results obtained at other equatorial ionospheric stations
Pg 27 – 34
On temperature control of buildings by adobe wall design: Duffin and Knowles’ exponential transmission line model revisited
by
E. E. Iheonu
Building Physics Unit
Nigerian Building and Road Research Institute Ota, Ogun State, Nigeria.
Abstract
Duffin and Knowles (Solar Energy, Vol. 27(3), 1981) developed an equation for attenuation factor of an Adobe wall modelled as 4-terminal electrical transmission line network. The modelled electrical system and the derived formula for the real attenuation factor of the wall have been critically examined and then modified by taking into cognisance the true conceptualisation of a physical filter network as analogue of the thermal wall. By comparing results from the two versions of the exponential transmission line network models, it is shown that the effect of the correction on the attenuation factor is significant.
Pg 35 – 40
First order normalization in the perturbed restricted three–body problem with variable mass
by
Jagadish Singh
Department of Mathematics, Faculty of Science,
Ahmadu Bello University, Zaria, Nigeria
e-mail jgds2004@yahoo.com
Abstract
This paper performs the first order normalization that will be employed in the study of the nonlinear stability of triangular points of the perturbed restricted three – body problem with variable mass. The problem is perturbed in the sense that small perturbations are given in the coriolis and centrifugal forces. It is with variable mass as the mass of the third body varies with time. It is found that these perturbations and varying mass are capable to bring a change in the Lagrangian function, and consequently in the basic frequencies. They become successful in affecting the angle coordinates but remain unsuccessful in changing the action momenta coordinates. The transformation utilized for reduction of the second order part of the Hamiltonian to the normal form is also dependent on the perturbed basic frequencies.
Keywords: Normalization, Perturbed, RTBP with variable mass,
Pg 41 – 46
A 2-dimensional finite element simulation of cooling in castings
by
John A. Akpobi and Imafidon A. Lawani.
Abstract
In this work we present a 2 dimensional finite element simulation of the cooling process in castings. A one way coupling +technique was used to predict the behavior of thermal strains and stresses from the temperature history of casting. The temperature distribution across the casting at different times, the cooling pattern of the casting in different cooling media, the cooling times and the build up of thermal strains and stresses were simulated in this work. The model was validated with experimental cooling times in the scenarios considered.
Keywords: Casting, one way coupling, thermal history, thermal strains and stresses
Pg 47 – 58
Analysis of Stokes waves theory as a diffusion problem
by
E. O. Okeke1 and B. S. Oyetunde2
1Department of Mathematics, University of Benin, Benin-City
2Department of General Studies, Mathematics and Computer Science Unit,
Petroleum Training Institute, Effurun, Warri.
Abstract
This mathematical model concerns the theory of Stokes waves. These wave types belong to the class of ocean surface waves found in deep and intermediate waters. In this consideration, the fifth order expansion was obtained using Korteweg de Vries equation with diffusion term. This study suggests that the phase velocity grows with increase in wave steepness whilst the group velocity shows the opposite tendency .The effect of diffusion introduced through depth distribution is obvious as the solutions apparently depend strongly on the water depth in inverse form. Interestingly, this analysis strongly suggests that the peak for potential energy lies between second and third order solutions while that of kinetic energy attains the peak at second and then becomes fairly stable. High seismic response associated with sea-bed motion corresponding to second order solution strongly support the result. However, the effect of additional terms on the wave profile appears somewhat insignificant. The wave profile of first order to fifth order in this consideration remains unchanged as expected.
Pg 59 – 68
Remarks on thermal explosions in the early evolution of the earth.
By
R. O. Ayeni, A. O. Popoola and O. J. Fenuga
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
1.0 Introduction
Earth’s origin and the formation of its shells are fundamental problems of natural sciences. Owing to the joint efforts of space physicists and space chemists, planetologists and geophysicists the main physicochemical processes have been studied, computer models of planet formation from smaller bodies of asteroid dimensions have been developed and the times of planet formation supported by isotope data have been calculated. It is evident that during the formation of the main structural units of the Earth – its core and mantle – there was a considerable energy generation due to gravitational differentiation (equivalent heat by 2500 0C) [3].
The presence of fluid core of an electrically conducting fluid permits the interaction of the fluid flow and the magnetic lines of force to produce an electromotive force (e.m.f) which helps the magnetic field to regenerate itself. The subject of the study of the processes of regeneration of a magnetic field is known as the dynamo theory [2].
During the gravitational differentiation (GD) in the large material volume in the Earth’s gravitational field the generated potential energy becomes heat due to viscous dissipation [3].
In this paper we study the time evolution of the Earth. Of course, the planetary scales and characteristic geologic times of the thermal processes in the interior differ from the corresponding characteristics of the classical thermal explosion, but, and in essence and form, they are analogous to the thermally activated processes [3].
Pg 69 – 70
An investigation of groundwater condition in Agbede by Geelectrical resistivity method.
by
Otobo Egwebe1, C. O. Aigbogun2, and S. O. Ifedili.1
1 Department of Physics, University of Benin City.
2 Department of Physics, Igbinedion University, Okada, Edo State.
Abstract
Vertical soundings (VES) for the purpose of drilling groundwater boreholes for the inhabitants were conducted in Agbede to determine: the depth to the aquifer (Ajali Formation which consists of porous and permeable coarse sandstones); the thickness of overlying aquiclude (Imo Shale which consists of non porous/ permeable thick clays) and to locate where the small lenticular sands within the Imo Shale called perched aquifer exists. Perched aquifers are hydraulically separated, are relatively small, and they occur above the water table when there is an impermeable layer of rock (aquiclude) above the main aquifer. The VES curves of the area were qualitatively interpreted and the result showed an ascent at the first decade (dry top soil), a decent at the second decade (Imo Shale) and with the right most segment ascending int6o the third decade which is an indication of the presence of the Ajali Formation below the Imo Shale. The geoelectric section from the from the VES revealed that the Ajali Formation could not be encountered even at a depth of 494.03m, indicating that the clay is as thick as 500m. Also perched aquifer could be encountered between the depths of 52.76-55.43m with thicknesses 9.89-10.86m but not in all locations.
Pg 71 – 76
The application of geophysics in environmental impact assessment: A case study in Jeddo, Delta State, Nigeria
by
Otobo Egwebe
Department of Physics, University of Benin, Benin City.
Abstract
Geophysical study using the Schlumberger vertical electrical sounding (VES) was conducted with half current electrode spacing ranging from 1-215m. Also five boreholes were drilled to the depths, 15.2-30m close to five of the VES locations for the purpose of comparing the derived geoelectric sections from VES curves with the geologic sections from the boreholes. The results from VES curves showed the presence of clay of thicknesses, 15.2-26.4m at depths 0-4.4m in two VES locations, while sands of thicknesses,12.2-116.1m were exposed in seven VES locations. Also the logs derived from soil samples collected from the boreholes showed clay presence of thicknesses, 15.2-23.9m at depths 0-3m in the two boreholes close to the VES locations where thick clay presence was detected, while three boreholes showed exposed sands of thicknesses, 12.2-30m. The application of geophysics for the purpose of subsurface study in environmental impact assessment has been discussed.
Pg 77 - 82
Characterization of formations and groundwater potential of Amai and Obiaruku in Delta State using resistivity and seismic refraction measurements
by
1E. C Okolie, 2F. C Ugbe, 3J. E. A, Osemeikhian
1Department of Physics, Delta state University Abraka, Nigeria.
2Department of Geology, Delta state University Abraka, Nigeria.
3Department of Physics, Ambrose Alli University Ekpoma, Nigeria.
Abstract
Obiaruku and Amai are two communities with remarkable high population due to their nearness to flowing waters which is one of the bases of early settlements. Although, the two towns are only 3 kilometres apart their geological and geophysical presentations vary remarkably. While Obiaruku is flanked by the early stage of the fast flowing North - South fresh-water river Ethiope, Amai has slow flowing filthy stream which spreads out and sometimes over flows its bank. Moreover, while Amai has numerous hand dug wells which are filled up to 2.5 metres or less depending on the season under investigation, Obiaruku has no evidence of hand dug well all the year round. The disparities in presentations are of interest. It becomes necessary to carryout a geophysical investigation of the formation strata and groundwater potential for the ever growing population of these communities. Hence a characterization of the formations and groundwater distributions were carried out using Schlumberger array of electrical resisitivity and up-hole shooting of seismic refraction surveys. Twelve Vertical Electrical Sounding (VES) stations were sounded using Self Averaging System SAS ABEM 300C tarrameter and eight refraction sounding sites were shot using Seismograph OYO MESEIS 160mx. The study shows that while Obiaruku has QA and HA curve types, which have basically four or more distinct resistive layers, Amai consists of A-type curve which has mainly three or four distinct resistive layers. The soil formation in Amai is highly conducting clay while that of Obiaruku is mainly laterite. Moreover, while Groundwater is at 45 – 50 m depth in a region of unconfined aquifer at Obiaruku, it is as low as 20 m in a zone of confined aquifer at Amai.
Pg 83 -90
Variable order one-step methods for initial value problems I
by
G. C. Nwachukwu and F. O. Otunta
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
A class of variable order one-step integrators is proposed for Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). It is based on a rational interpolant.
Pg 91 -96
An application of the maximal independent set algorithm to course allocation
by
*V. V. N. Akwukwuma and K. C. Ukaoha,
Department of Computer Science, University of Benin, Benin City.
*e-mail: vakwukwuma@yahoo.com
Abstract
In this paper, we demonstrated one of the many applications of the Maximal Independent Set Algorithm in the area of course allocation. A program was developed in Pascal and used in implementing a modified version of the algorithm to assign teaching courses to available lecturers in any academic environment and it proved to be very effective.
Keywords: maximal independent sets, graphs, course allocation, bipartite graphs.
Pg 97 -106
The turning points in the solution of n-queens problem using backtracking method
by
1S. C. Chiemeke and 2E. O. Osaghae
1Department of Computer Science, University of Benin, Benin City, Nigeria.
e-mail: schiemeke@yahoo.com
2Department of Computer Science, Delta State Polytechnic, P.M.B 03,
Otefe-Oghara, Delta State, Nigeria.
Abstract
Conventional backtracking method has been the generally accepted method for solving n-queens problem. However, this method may prolong execution time for fairly large n-queens (example, n = 30) and most cases, failed to find solution to large n queens problem. In this paper, we asserted that, even/odd numbered values of n-queens problem can affect the corresponding solutions of the standard backtracking. We also observed that, using a set of even and odd numbers, the odd number experience a turning point before the even numbers. The algorithm of the standard backtracking method was implemented in C programming language and, we used Microsoft Notepad as our output file to display the arrangement of the queens.
Pg 107 -114
Software package for analysis of completely randomized block design
by
*Onyinye Ifeyinwa Ojukwu and Julian Ibezimako Mbegbu
Department of Mathematics, University of Benin, Benin City, Nigeria
Abstract
This study is to design and develop statistical software (package), OYSP1.0 which conveniently accommodates and analyzes large mass of data emanating from experimental designs, in particular, completely Randomized Block design. Visual Basic programming is used in the design. The statistical package OYSP 1.0 when implemented on a micro computer gives an encouraging result
Pg 115 -120
Three algorithms for Egyptian fractions
by
Orobosa Izevbizua and Joseph Osemwenkhae
Department of Mathematics, University of Benin, Benin City
Abstract
The ancient Egyptians used a number
system based on unit fractions, i.e. fractions with one in the numerator. This
idea let them represent any fraction
as
the sum of unit fractions e.g 
Further,
the same fraction could not be used twice (so
is
not allowed). In this work we examine a number of algorithms for generating
Egyptian fractions in more detail, implement them and analyze their performance.
Keywords: Unit fractions, Splitting Algorithms, Paring Algorithm, Distinct divisors, Length of Egyptian fraction, Lexicographic
Pg 121 -126
Measure synchronization in a coupled Hamiltonian associated with the motion of particles in a periodic potential
by
†U. E. Vincent, *A. N. Njah, *A. O. Obawole and *M. T. Azeez
†Department of Physics, Bisi Onabanjo University, Ago-Iwoye, Nigeria.
*Department of Physics, University of Agriculture, Abeokuta, Nigeria
Abstract
We report here, the existence of measure synchronization (MS) in a coupled Hamiltonian system associated with the motion of particles in a periodic potential of the pendulum type. We show that the oscillators can assume chaotic MS stares vis quasiperiodic measure desynchrononized state. In the chaotic MS state, the phase difference of the tow oscillators performs a stick-slip and random-walk-like motion analogous to the phenonomention of intermittency already established in the classical chaotic pendulum.
PACS: 05.45.Pq; 05.45. Xt; 05.45.Ac
Keywords: Measure synchronization; Hamiltonian systems; Chaos
Pg 127 - 136
Active control versus recursive backstepping control of a chaotic system
by
A. N. Njah
Department of Physics, University of Agriculture Abeokuta, Nigeria.
e-mail: njahabdul@yahoo.com
Abstract
In this paper active controllers and recursive backstepping controllers are designed for a third order chaotic system. The performances of these controllers in the control of the dynamics of the chaotic system are investigated numerically and are found to be effective. Comparison of their transient performances show that the rate of convergence of error is faster for the active controllers than for the recursive backstepping controllers. However, the flexibility in the choice of the control laws for recursive backstepping design gives room for further improvement in its performance and enables it to achieve the goals of stabilization and tracking.
PACS: 05.45.-a, 05.45.Pq, 05.45.Ac
Keywords: Active Control; Recursive Backstepping control chaotic system
Pg 137-142
Synchronization of Forced damped Pendulum via Active Control
by
A. N. Njah
Department of Physics, University of Agriculture, Abeokuta, Nigeria
e-mail: njahabdul@yahoo.com
Abstract
In this paper active controllers are designed to synchronize two identical forced damped pendula. The performance of the controllers in the synchronization of the chaotic dynamics of the two pendula, resulting from different initial conditions, is investigated numerically and found to be effective. Transition from nonsynchronous state via both temporary phase lock (TPL) and intermittent synchronous states to complete synchronous state was observed.
PACS: 05.45.-a, 05.45.Pq, 05.45.Ac
Keywords: Active Control; synchronization; chaotic pendulum
Pg 143 - 148
Some
thermodynamic non-Fermi liquid properties of correlated electron systems.
by
G. C. Asomba and D. U. Ugwoke
Department of Physics and Astronomy,
University of Nigeria, Nsukka, Nigeria.
Abstract
A mean-field
Hamiltonian model has been used to investigate some thermodynamic properties of
the normal states of non-Fermi liquid (NFL) systems,
.
This Hamiltonian is like that of the Bardeen-Cooper-Schrieffer model [Phys. Rev.
108 (1957) 1175] but differs from the latter in (i) being multiband, (ii) the
gap in energy being a function of the hopping integral and (iii) band energies
of electrons being dependent upon spin orientation. The Hamiltonian is,
therefore, similar to the Paring t-model [Physica
258
(9166) 30] but differs from it in not incorporating hybridization term and
hybrid pair superconductivity. The analysis of the model yields magnetic energy
spectrum for 
bands`
and non-magnetic energy spectrum for the O (2p) bands. Inverse temperature
dependences of electronic specific heat
,
entropy function 
and
pair susceptibility 
are
computed and exhibited. The specific heat dependence upon inverse temperature
shows a linear form at very high temperature. It displays inverse-square-law
temperature dependence, approximately, for lower temperatures. In the very low
temperature range, the actual curve of the theoretical specific heat with
temperature is rather like that of the
versus
curve
obtained for 
and
down
to millikelvin temperature. This is in contradistinction to the linear
temperature dependence 
of
Fermi liquid systems. The specific entropy dependence on temperature shows
correct physical response of systems to order (disorder) with varying
temperatures. The pair susceptibility is linear at very high temperature and
constant 
at
moderate/low temperatures. The latter is as in Fermi liquid systems, but the
former is an NFL manifestation.
Keywords: Mean-field model, Green’s function, thermodynamic functions, inverse temperature.
Pg 149 – 156
Plasma heating by non-linear wave-Plasma interaction
by
I. M. Echi and A. Ojo
Department of Physics, University of Ibadan, Ibadan, Nigeria
Abstract
We simulate
the non-linear interaction of waves with magnetized tritium plasma with the aim
of determining the parameter values that characterize the response of the
plasma. The wave-plasma interaction has a non-conservative Hamiltonian
description. The resulting system of Hamilton’s equations is integrated
numerically using fourth order Runge-Kutta scheme. It is found that for wave
amplitude a as
low as 0.01Bo the response of the plasma is remarkably different from
the prediction of linear response theory. The response cannot be explained in
terms of whether or not the wave frequency
w is a harmonic of
the ion cyclotron frequency W.
The scaled drift velocity of the ions
and
the scaled phase velocity of the waves
were
found to be more relevant in explaining the response characteristics. For
>>,
the plasma response is found to be chaotic while for
<<,
the response is either periodic or quasi-periodic. For
» the
waves do not interact with the plasma. The energy deposition (heating) by the
waves in the plasma is found to be enhanced when the interaction occurs in the
chaotic mode. In this mode, plasma diffusion is negligible suggesting that
chaotic interaction of waves with plasma may enhance containment of the plasma.
Keywords: Wave-plasma-interaction, Phase-space, Poincare sections, Chaotic-response, Quasi-periodicity.
Pg 157 – 166
On finitely many fixed points
by
J. O. Olaleru
Department of Mathematics, University of Lagos, Lagos, Nigeria.
email Address: olaleru1@yahoo.co.uk
Abstract
Let C be the
finite union of closed convex sets in a complete metrisable locally convex
space. If f: C → C with 
compact,
then f can be approximated by a map g: C → C which has only a finite number of
fixed points. This result, which is a generalization of the result of Baillon
and Rallis, is proved in this paper.
Keywords: fixed point, locally convex space, homotopy, 2000 AMS Mathematics Classification: 47H10, 46A03
Pg 167 – 170
Some remarks on certain Bazilevic functions
by
K. O. Babalola
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
e-mail: abuqudduus@yahoo.com
Abstract
In this note we give some sufficient conditions for an analytic function f(z) normalized by f¢ (0) = 1 to belong to certain subfamilies of the class of Bazilevic functions. In earlier works, the closure property of many classes of functions under the Bernardi integral have been considered. The converse of this problem is also considered here.
Keywords: Bazilevic functions, analytic and univalent functions
Pg 171 – 176
On the successive coefficients of certain Univalent functions
by
K. O. Babalola
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
e-mail: abuqudduus@yahoo.com
Abstract
The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. The result obtained is sharp, and is used to provide a new, short proof of the well-known conjecture of Robertson on the coefficient of close-to-convex functions.
Keywords: Successive coefficients, starlike, convex, close-to-convex, univalent functions
Pg 177 – 180
On a differential subordination of some certain subclass of Univalent function
by
Y. O. Aderinto
Department of Mathematics,University of Ilorin, Ilorin, Nigeria
Abstract
We generate some results for some particular subclasses of starlike and close-to-convex functions using Briot-Bouquet differential subordination method.
Pg 181 – 184
On the dynamic Stability of a quadratic-cubic elastic model structure pressurized by a slowly varying load
by
A. M. Ette
Department of Mathematics and Computer Science, Federal University of Technology
Owerri, Nigeria.
e-mail:tonimonsette@yahoo.com
Abstract
The main substance of this investigation is the determination of the dynamic buckling load of an imperfect quadratic-cubic elastic model structure , which ,in itself, is a Mathematical generalization of some of the many physical structures normally encountered in engineering practice and allied fields. The load function in which the time variable is explicitly expressed, varies very slowly over a natural period of oscillation of the structure. The nonlinearity is quadratic-cubic in nature and multiple-scaling two-timing regular perturbation technique is utilized. The result shows that the dynamic buckling load depends on the first derivative of the load function evaluated at the initial time .Besides , it is established that it is possible to relate the dynamic buckling load to its static equivalent and this by-passes the labour of repeating the entire arduous process for different imperfection parameters .
Pg 185 – 196
Asymptotic solution on the dynamic buckling of a column stressed by a dynamically slowly varying load
by
A. M. Ette
Department of Mathematics and Computer Science, Federal University of Technology
Owerri, Nigeria.
e-mail:tonimonsette@yahoo.com
Abstract
This paper analysis the dynamic stability of a dynamically oscillatory system with slowly varying time dependent parameters. It utilizes the concept of multiple times scaling in an asymptotic evaluation of the dynamic buckling load of the imperfect elastic structure under investigation. Unlike most similar investigations to date , the time dependence is explicit in the formulation and this creates a situation of non-autonomous differential equation that accurately models the dynamic stability of the structure .The dynamic buckling load is obtained nontrivially and the results are found to generalize earlier results obtained for step loading situation. It is established that the results depend strongly on the first derivative of the load function evaluated at the initial time.
Pg 197 – 202
Dynamic analysis of a Bernoulli-Euler beam via the Laplace transformation technique
by
M. Jiya, Y. M. Aiyesimi, and A. A. Mohammed
Department of Mathematics and Computer Science, Federal University of Technology,
Minna, Nigeria.
e-mail: jiyason@yahoo.com
Abstract
In
this paper the dynamic analysis of a simply supported Bernoulli-Euler beam
subjected to a distributed load was investigated. The simplified form of the
mathematical expression defining the dynamic displacement of the beam was
formulated using the variational Indicator of the Hamiltonian principle. The
method of Integral Transformation was used to obtain the series solution for the
governing equation. The effect of the various beam parameters on dynamic
deflection profile of the beam was simulated, it was observed that the
contribution is mainly done by the first mode and higher modes of vibration can
be neglected.
Pg 203 -210
The period of relaxation oscillations of a nonlinear system using singular perturbation methods
by
E. E. Joshua
Department of Mathematics, Statistics and Computer Science
University of Uyo, Uyo, Nigeria.
e-mail: joshie_en@yahoo.com
Abstract
We determine the period of relaxation oscillations of a physical system governed by the nonlinear Liénard equation ε x² + (ax2 - b) x¢ + x +cx3 = 0 where a, b, c > 0, 0 < ε << 1, using singular perturbation methods. These methods which involve considering matched asymptotic expressions of different layers yield a uniformly valid expansion for the above equation and hence the relaxation oscillations. The van der Pol equation is a special case of the above equation.
Pg 211-222
On the steady state temperature profiles of biological tissues during microwave heating.
by
*F. A. Adebile and B. N. Akintewe
Department of Mathematical Sciences, Federal University of Technology
Akure. Nigeria.
*e-mail: eaadebiletri@yahoo,com
Abstract
The Maxwell equations are solved together with the Pennes Bio-heat equation analytically. The procedure of solution is provoked by the solution to the Maxwell equation. The result revealed the effect of the model parameters such as: the thermal conductivity, blood perfusion coefficient, and the thickness of the tissues and the location of the effect of the electric field. Our result agrees with the results obtained by El-dabe et al (2003) the results are significant to medical experts and engineers.
Key words: Maxwell equation microwave heating, Pennes Bio-heat Biological tissue equation steady state. Author to which correspondence should be addressed
Pg 223 – 228
Self-similar solution for coupled thermal electromagnetic model during microwave heating of biological tissues.
by
*E. A. Adebile, B. N. Akintewe, O. K. Olaleye,. and V. Idoko
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
*e-mail: eaadebiletri@yahoo.com.
Abstract
An investigation into the existence and uniqueness solution of self-similar solution for the coupled Maxwell and Pennes Bio-heat equations have been done. Criteria for existence and uniqueness of self-similar solution are revealed in the consequent theorems
Keywords: Self-similar variable, Maxwell equation, Pennes Bio-heat equation, Microwave heating, biological tissues.
Pg 229 – 234
Impact of electric and magnetic fields in a resistant medium on the velocity of a particle subject to varying path angles
by
1O. J. Fenuga and 2R. O. Ayeni
1Department of Mathematical Sciences, Olabisi Onabanjo University, Ago-Iwoye, Nigeria.
e-mail: fenuga_oj@yahoo.Co.UK
and
2Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
e-mail: ayeni_ro@yahoo.Com
Abstract
In this paper, we compare the impact of electric and magnetic fields in a resistant medium on the velocity of a particle subject to varying path angles by using numerical integration of finite difference method. The results show that the magnetic field has much impact on the velocity than the electric field.
Pg 235 – 238
Vorticity determination in a hydraulic jump by application of method of characteristics
by
A. E. Eyo
University of Uyo, Uyo, Nigeria
Abstract
The method of characteristics for solving systems of partial differential equations coupled with jump conditions is used in analysing flow downstream of a hydraulic jump instead of the normal analytical approach adopted in Hornung [1]. It is shown that the method of characteristics together with the jump conditions can correctly be used as an alternative method to determine the mean vorticity downstream of the hydraulic jump as a function of the Froude number and height ratio. The mean vorticity does not increase from zero as a function of Froude number minus one but, however, it approaches a constant value at large Froude number. The present work extends the model of Hornung [1] to include non linear velocity profile used in calculating the torque with a view to determining the mean vorticity. The result obtained by this method generalizes that of [1].
Pg 239 – 248
Hydrodynamic dispersion of a reactive solute in Electro-Osmotic flow using quadratic polynomials
By
O. T. Gideon
Department of Mathematics Statistics and Computer Science,
Kaduna Polytechnics, Kaduna, Nigeria.
and
Y. M. Aiyesimi
Department of Mathematics and Computer Science, Federal University of Technology, Minna
Abstract
The objective of this paper is to study the effect of the dispersion coefficients and the reaction parameter on the hydrodynamic dispersion of a reactive solute in electro-osmotic flow through the method of finite elements using quadratic Lagrange polynomials.
Pg 249 -256
Existence of a secondary flow for a temperature dependent viscous couette flow.
by
Olabisi Onabanjo University, Ago Iwoye, Nigeria.
e-mail: adesanyaolumide@yahoo.com
Lagos State University, Ojo, Nigeria.
Ladoke Akintola University of Technology, Ogbomosho, Nigeria.
Abstract
We model a viscous fluid flowing between parallel plates. The viscosity depends on temperature. We investigate the properties of the velocity and we show that the temperature and velocity fields have two solutions. The existence of two velocity solutions is new. This means that there exist secondary flows
Pg 257 – 260
A Continuous formulation of some classical initial value volvers by non-Perturbed multistep collocation approach using Chebyshev polynomials as basis functions
by
Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
Abstract
This paper is concerned with the construction of some classes of multistep methods for the numerical integration of initial value problems in ordinary differential equations. For this purpose we employ the Chebyshev polynomials as basis function in a non-perturbed collocation approach. The continuous schemes thus obtained yield four classes of initial value solvers namely the Optimal order methods, the Adams-Bashforth methods, the Adams-Moulton methods and the Backward differentiation formulae at appropriate grid points. A theorem in support of the accuracy of the continuous schemes is also established.
Pg 261 – 274
by
John A. Akpobi and Ufuoma D. Egbedi
Department of Production Engineering, University of Benin, Benin City, Nigeria.
Abstract
The curve fairing problem has seen many innovations especially in Computer-Aided Design (CAD) applications where product design depend largely on aesthetic, producibility and functional requirements. A major factor for evaluating these requirements is the geometric fairness of the product being modelled. This paper addresses the geometric fairing problem in which we model the shape of the product using Non Uniform Rational B-Splines (NURBS). The concept of curvature plot is used to interrogate the curve for defects and the corresponding knot and weight (at the defective regions) are sequentially modified in a sense that a fair curve ultimately results. Finally, results of our implementation are presented to show the validity of the proposed scheme.
Keywords: NURBS, virtual array, convexity, knot vector, homogeneous coordinate vector, inflection point, curvature discontinuity, curve fairing.
Pg 275 – 292
Perturbed segmented domain collocation Tau-method for the numerical solution of Second Order Boundary Value problems
by
*e-mail: oataiwo2002@yahoo.com and allforgod2004@yahoo.com
Department of Mathematics, Faculty of Science, University of Ilorin, Ilorin, Nigeria.
.
Abstract
This paper concerns the numerical solution of second order boundary value problems using a Perturbed segmented domain collocation-Tau method. The entire interval for which the problem is defined is partitioned into two segments and the solution technique is demonstrated on each of the segments. The Chebyshev polynomials shifted as the case may be, into a given interval are used as a basis for a collocation solution via the perturbed collocation method for each segment. For a given problem two different solutions are obtained, which are valid for different intervals within the domain. Numerical examples are given to illustrate the efficiency, accuracy and computational cost of the method.
Keywords: Collocation, Segmented domain, Auxiliary equation, Partitioning, Residual equations
Pg 293 – 298
Viscous dissipation effects on the flow of a radiating gas between concentric elliptic cylinders
by
R. O. Oladele, J. A. Gbadeyan and O. A.Taiwo*
Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
.
Abstract
The solution of a boundary layer flow problem often neglects the effects of viscous dissipation. However, the present treatment incorporates these effects with a view to assessing their global contributions to velocity and temperature distributions in the flow field. Hence, fluid motion induced between two differentially heated concentric elliptic cylinders is investigated under transient condition and significant viscous dissipation. When the temperatures of the cylinder are large enough for radiative heat transfer to be significant. The solution approach is via an explicit finite difference algorithm on a PC 1512 micro-computer. The numerical results obtained for the two cases show that the velocity and the temperature of the fluid are increased as a result of increase in thermal internal energy of the fluid caused by viscous dissipation.
Pg 299 - 304
Radiation effect of magnetohydrodynamic flow of gas between concentric spheres
By
J. A Gbadeyan and A. S. Idowu*
Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
*e-mail: idowu_ms@yahoo.com
Abstract
Time independent flow of fluid between two concentric rotating spheres permeated by magnetic filed is studied. Prevailing mode of heat transfer is radiation while optically thin limit case is considered. The mathematical model of the problem with the induced magnetic field is developed and the resulting differential equations were solved using perturbed numerical technique. It is found that the magnetic field has no effect on the temperature distribution. However, when the magnetic field is introduced a decrease in velocity is obtained with an increase in either radiation parameter or Reynolds number.
Pg 305 -314
Perturbation analysis on the dynamic buckling of a lightly damped spherical cap modulated by a slowly varying sinusoidal load (1)
by
A. M. Ette
Department of Mathematics and Computer Science
Federal University of Technology, Owerri, Nigeria
e-mail: tonimonsette@ yahoo.com
Abstract
This investigation makes a conscious effort at analytical determination of the dynamic buckling load of an imperfect lightly damped spherical cap modulated by a sinusoidally slowly varying dynamic load. Essentially, the formulation is that of an elastic nonlinear oscillatory system, with small perturbations and with coefficients that are harmonically and dynamically slowly varying. The imperfection is discretized into an axisymmetric and a non-axisymmetric mode which are also the shapes of the equally discretized buckling modes. The dynamic buckling load is obtained and is related to the static buckling load. This by-passes the labour of repeating the entire process for different imperfection parameters.
Pg 315 – 326
On the dynamic buckling of lightly damped cylindrical shells modulated by a periodic load
by
A. M. Ette
Department of Mathematics and Computer Science
Federal University of Technology, Owerri, Nigeria
e-mail: tonimonsette@ yahoo.com
Abstract
The dynamic buckling load of finite imperfect, lightly but viscously damped cylindrical shells subjected to a periodic load, is determined using the technique of multiple scaling (two-timing) regular perturbation analysis. The geometric imperfection, assumed deterministic, are also assumed small and are expanded in a double Fourier series. The dynamic buckling load is obtained asymptotically and the result is found to be implicit in the load parameter.
Pg 327 – 344
One Leg hybrid P-stable substitution LMM for oscilatory IVPs in ODEs.
by
M. N. O. Ikhile and M. V. Ayo
Department of Mathematics, University of Benin,, Benin City, Nigeria.
email: mnoikhilo@yahoo.com and vimayo10@yahoo.co.uk
Abstract
This presents P-stable successive substitution one-leg hybrid LMM for the numerical solution of oscillatory second order IVPs in ODEs without explicitly defined first order derivative. These problems occurs amongst others, in orbital mechanics where the methods to be presented finds ready applications and need not any a priori knowledge of the period of the solution of the defining ODE.
Pg 345 -354
Hessian Spectrum to perturbation factor for gradient method algorithm
by
J. O. Omolehin
Department of Mathematics, University of Ilorin, Ilorin, Nigeria
e-mail:emolehin-joseph@yahoo.com
Abstract
In this paper, the eigen values of the associated Hessian
matrix of our control problem are considered for optimal selection of the
perturbation factor 
or
perturbation parameter for gradient method. The perturbation factor is
calculated as an n-dimensional vector as against real number. The numerical
results generated compare favorably with the existing works.
Keywords: Hessian; Matrix; Gradient; Spectrum; Minimize C.R. Categories: G.1.7
Pgs 355 -362
Jacobian approach to optimal determination of perturbation parameter for gradient method
by
J. O. Omolehin*, K. Rauf*, B. Opawoye*, and W. B. Yahya†
•Mathematics Department, University of Ilorin, Ilorin, Nigeria
†Statistics Department University of Ilorin, Ilorin, Nigeria
Abstract
In this work,
the optimal determination of the perturbation factor
or
perturbation parameter for gradient method is considered. The spectrum analysis
of the associated Jacobian of the associated matrix has laid the basis for the
judicious selection of the perturbation factor. Numerical work is carried out to
prove our hypothesis.
Keywords: Hessian; Matrix; Gradient; Spectrum; Minimize C.R. Categories: G.1.7
Pg 363 – 370
Control approach to Queue Theory
by
J. O. Omolehin
Department of Mathematics,, University of Ilorin, Ilorin, Nigeria
Abstract
The rigid condition for simple queue problem is minimized by considering multiple channels through control approach. The result control problem is solved using Conventional Conjugate Gradient Method and the optimal system performance is obtained
Keywords: Queue; Gradient; Parameter; Minimize; Functional C.R. Categories G.1.7
Pg 371 – 378
A family of block methods for special second order initial value problems [I.V.Ps].
By
V. A. Aladeselu,
Department Of Computer Science, University Of Benin, Benin City, Nigeria.
Abstract
In this paper, efforts are directed towards generating a 2-block 2-point numerical method for solving the special second order initial value problems of the form Y// = F(X, Y), Y(0) = YO, Y/(0) = YOO .. The scheme so developed, is in the same line of thought as Shampine and Watts (1969, 1972) [9]; Chu and Hamltion (1987) [2]; Fatunla (1991)[3]. The scheme is of orders 5/6, zero-stable and convergent. It is thus possible, with this scheme, to assign computational tasks at 2 points within the block to two different processors working simultaneously.
Pg 379 – 384
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Numerical integrators for Stiff and Stiff oscillatory First Order initial value problems
by
V. A. Aladeselu,
Department of Computer Science, University of Benin, Benin City, Nigeria.
Abstract
In this paper, efforts are geared towards the numerical solution of the first order initial value problem (I.V.P) of the form Y/ = F(X,Y), XÎ[ a, b] , Y(a) = Y0, where Y/ is the total derivative of Y with respect to X.. The scheme so developed for the stated equation is in the same line of thought as Fatunla (1980). It is of order 6, L-stable and exponentially fitted.
Pg 385 – 390
Periodic solutions of periodic differential equations
by
F. A. J. Bello
Department of Mathematics and Statistics, Kwara State Polytechnic, Ilorin
Abstract
In this paper we extend the work of Bello [4] where he
considered the periodic solutions of certain dynamical systems inside a
cylindrical phase space with differential equations of the form
(+)
with the property that there is a
and
a natural number K such that
(**)
with necessary and sufficient condition that the
fundamental matrix 
of
the characteristic equation 
(***)
of (*) have negative real parts (See [1], [7]),
is
stable asymptotically. The extension considered the periodic solutions of
the differential equations of the type
(****)
with the property (**). The periodic solutions and the asymptotic behaviour of the solutions were investigated and analysed. Some theorems were proved and examples given to illustrate certain properties of the solutions.
Pg 391 - 398
A generalised interpolating post–processing method for integral equation
By
V. U. Aihie
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
Interpolating post-processing method for integral equation
has been demonstrated to be superior to the iteration method by Qun Lin, Shechua
Zhang and Ningning Yan. They demonstrated that it is of order
.
This paper describes the generalization in the choice of h, the mesh size
which leads to a higher order of (where
)
and hence an improved accuracy of the method.
Keywords: Integral equation, interpolation post-processing, super convergence.
Pg 399 - 402
On the existence and uniqueness result for a two-step reactive-diffusive equation with variable pre-exponential factor
by
**P. O. Olanrewaju, **R. O. Ayeni,**A. O. Ajala,**O. Adebimpe, and *A. O. Ajayi
**Department of Pure and Applied Mathematics , Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
e-mail: Oladapo_anu@yahoo.ie
*Department of Computer Science and Engineering, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
Abstract
We examine
the existence and uniqueness result of the steady-state solutions for the
exothermic chemical reactions taking the diffusion of the reactants in a slab
into account and assuming Arrhenius dependence with variable pre-exponential
factor. We establish the criteria’s and conditions for existence
and uniqueness of solution for the newly formulated problem. It is shown that if
and
where
positive
constants are then the newly formulated model will have only one solution. We
further discovered that there are certain values for n, m, r and
b that the problem
can accommodate for solution to be stable. Similarly, Frank-Kamenetskii
parameters d1,
d2
must not exceed some values for the solution to exist and at the same time
stable. Finally, the Frank-Kamenetskii parameter must not exceed the critical
value for the solution to have physical implication or application and r must
not be large for convergence of the solution (i.e r < 1).
Keywords: Exothermic chemical reaction, variable pre-exponential factor, two-step Arrhenius reactions
Pg 403 - 408
On a Subclass of analytic functions
by
Abiodun Tinuoye Oladipo
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
e-mail: atlab_3@yahoo.com
Abstract
Abstract. In this work we establish some conditions for univalence and our results include starlikeness, convexity and close-to-convexity
Keywords: Analytic, Univalent, Starlikeness, Convexity, Close-to-convexity Salagean derivative.
Pg 409 – 412
Heuristic framework for parallel sorting computations
by
E. D. Nwanze and E. E. Obasohan
Department of Computer Science, University of Benin, Benin City
Abstract
Parallel sorting techniques have become of practical interest
with the advent of new multiprocessor architectures. The decreasing cost of
these processors will probably in the future, make the solutions that are
derived thereof to be more appealing. Efficient algorithms for sorting scheme
that are encountered in a number of operations are considered for multi-user
machines. A heuristic framework for exploiting parallelism inherent in some of
these schemes are worthy of investigation and valid suggestions are given for
adequate implementation by associating processors in a multiprocessor platform.
This exercise involves a closer investigation of the associated savings in
employing simultaneous sorting techniques for, say
processors.
A deterministic 
time
algorithm using 
processors
will substantially reduce the run time for a sorting scheme and is considered to
be asymptotically optimal.
Pg 413 – 422
by
E. E. Obasohan
Department of Computer Science, University of Benin, Benin City
and
H. O. Omokaro,
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
In Omokaro 2003[12], we extended the RSA Congruence to a finite number of primes. The extended RSA Cryptosystem was later obtained in Omokaro 2004[13] as an analogue of the RSA Cryptosystem to obtain the extended RSA Cryptosystem. In this work we provide a software for the enciphering of data in RSA cryptosystem
Pg 423 - 432
Quantum computer gate simulations
by
Adetunmise C. Dada
Department of Physics, Obafemi Awolowo University,
Ile-Ife, Nigeria
email: techada@yahoo.com
Abstract
A new interactive simulator for Quantum Computation has been developed for simulation of the universal set of quantum gates and for construction of new gates of up to 3 qubits. The simulator also automatically generates an equivalent quantum circuit for any arbitrary unitary transformation on a qubit. Available quantum computer simulators attempt to emulate the various physical realisations of quantum computation, simulate existing quantum algorithms or are aimed at facilitating the development of new algorithms. However, because of the level of advancement and complexity of quantum computation algorithms, these simulators tend to be quite complex, at least from a novice’s point of view. As a result of this, beginners are often at a loss when trying to interact with them. The simulator here proposed therefore is aimed at bridging the gap somewhat, making quantum computer simulation more accessible to novices in the field.
Pg 433 - 446
Effective utilization of weighting adjustment for the estimates of means in survey non-response
by
*O. R. Oniyide and D. A. Agunbiade
Department of Mathematical Sciences
Olabisi Onabanjo University, Ago-Iwoye, Nigeria.
Abstract
This paper provides a useful application for comparison on the use of Adjusted Estimates (Weighting Adjustment) as against Unadjusted Estimates for estimate of Mean in survey Non-response .The use of response propensity and the predicted mean of the outcome variable for cell creation are stressed .The results from our empirical study emphasize the efficacy of Weighting Adjustment over the Unadjusted estimates .We adopt the following criteria: Variance, Bias and Mean Square Error in reaching our conclusion.
Keywords: Weighting adjustment, potential stratifiers, adjustment cells, non-Response.
Pg 447 - 452
Effect of queue discipline on the performance of a queueing system
by
1S. A. Ojobor and 2S. E. Omosigho
1Department of Mathematics and Computer Science, Delta State University, Abraka, Nigeria.
e-mail: ojoborsun@yahoo.com
2Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
The effect of three queue discipline namely first in, first out (FIFO), last in first out (LIFO) and service in random order (SIRO) on some measures of performance of a single sever queue are examined. The measures of performance are average waiting time and queuing time. The comparison of the systems were carried out by writing an appropriate program in BASIC to simulate the queue discipline. This is due to the versatile nature of simulation and the fact that it is extremely difficult to obtain numerical results mathematically for the single server queue when the queue discipline is not FIFO and the arrival process is non-stationary. The approach adopted is to generate arrival time and service times for n customers through a single sever queuing system under each queue discipline. The measures of performance were calculated for each system using appropriate expressions. The result show that the average queuing time and average waiting time are higher when the queue discipline is LIFO, whereas the total idle time for all the systems were found to be same in most cases.
Keywords: Queues, waiting time, Queuing time & Service time.
Pg 453 - 456
A mathematical model for Lassa fever
by
1Daniel Okuonghae and Robert Okuonghae
Department of Mathematics, University of Benin, Benin City, Nigeria
Abstract
A mathematical model for the dynamics of Lassa fever is presented. Contributions from regular contact with the species of rats that carry the virus that cause Lassa fever and infectious contact with those suffering from the disease is seen as significant in the spread of the disease. Steady states of the model are examined for epidemic and endemic situations. A second model that incorporates the effect of vaccination on a subset of the target population is proposed, although at the moment there is no vaccine against the disease. However our model shows that in the interim, control of the rodents carrying the virus and some isolation policy for infected individuals are the best strategies against the spread of the disease.
Keywords: Mathematical model, steady state, Lassa fever, epidemic, endemic
Pgs 457 – 464
by
1T. T. Yusuf and 2K. O. Okosun
Department of Mathematical Sciences, Federal University of Technology, Akure.
e-mail: ttyusuf@yahoo.com1, e-mail: kazeem_oare@yahoo.com2
Abstract
Bird flu (Avian influenza) is a contagious disease of animals caused by viruses that normally infect only birds and, less commonly, pigs. These viruses are highly species-specific, but have, on rare occasions, crossed the species barrier to infect humans. The world at large never considered it a serious threat to mankind until the outbreak in Asia, Europe, USA and now in Africa. The aim of this paper is to use mathematical modelling to examine the population dynamics with respect to the disease and its transmission. The model population comprises birds and humans. The appropriate systems of ordinary differential equations formulated were solved numerically and the results were analysed. The result shows that the spread of the virus will continue as long as we have infected birds and there is tendency of human infection sooner or later.
Pg 465 – 470
by
Department of Mathematics and Computer Science,
Federal University of Technology, Owerri, Nigeria
Abstract
In [3] we developed a mathematical
model of the transmission dynamics of HIV/AIDS in Nigeria. In this paper, we
consider the effect of stochastic migrating into the susceptible class. A system
of stochastic ordinary differential equations (SODEs) was then formulated. This
was analyzed. Also the Fokker-Planck equation
is
used to transform the system into a system of deterministic partial differential
equation. This latter equation was analyzed and it was shown that the stochastic
migration has no significant effect on the model.
Pg 471 -476
Qualitative study of Kermack and Mckendrick’s epidemic model
by
Department of Mathematics and Computer Science,
Federal University of Technology, Owerri
Abstract
In this paper, we carry out a qualitative study of Kermack and Mckendrick’s epidemic model. We derive a special case of this model for recurrent diseases (relapse – recovery model). Using the new model, we investigate the severity of the epidemic and then test the stability of the original model. It is then shown that the number of invectives after a very long time from the inception of the epidemic is a constant. It is also shown that the steady state is unstable. Trajectories that help to know the extent of the severity are also presented. Through these trajectories it is shown that the severity of this epidemic can be estimated when the rate of infectiousness (r) and the removal rate (d.) are estimated.
Keywords: Qualitative study, Kermack and Mckendrick’s epidemic model recurrent diseases, relapse – recovery model. Severity.
Pg 477 – 480
Mathematical models to simulate the East African trypanosomiasis population dynamics.
by
Daniel Okuonghae and 1Joseph Osemwenkhae
e-mail josemwenkhae@yahoo.com
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
This paper presents mathematical models for the East African trypanosomiasis or sleeping sickness. It is aimed at modelling the population dynamics for the human and domestic animal victims as well as the dynamics of the tsetse fly population that acts as the vector that spreads the parasite causing this disease. Since sleeping sickness is caused by two protozoan parasites that are morphologically similar but cause dramatically different diseases in humans and domestic animals, this paper examines the East African sleeping sickness only. An extended model is provided to show the significance of infectious contacts between the tsetse flies and animals that serve as the reservoir for the parasite that causes this disease. Steady states for the models are also presented and analysed.
Keywords: Mathematical model, steady state, trypanosomiasis.
by
+Olusogo O. Odusote and Ayomide O. Balogun
Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria.
Abstract
The neutron diffusion equation was
solved under a “single cylinder one group (thermal neutrons)” approximation. The
resulting equation was applied with a mixing index,
,
for various formation matrices and porosities. The ratio of counts from two
different detectors was plotted as a function of porosity for these formations.
These plots are useful for wireline log interpretations.
Pg 489 - 492
by
*Olusogo O. Odusote,
Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria.
e-mail: sog_odusote@yahoo.com
and
Olamide O. Odusote,
Department of Chemical Engineering, Ladoke Akintola University of Technology,
Ogbomosho, Nigeria.
Abstract
We show by the application of the ‘stick-slip’ phenomenon, that, the filtrate through a porous medium could be oscillatory under low-intensity driving forces. The frequency of the oscillation is dependent on the nature of the porous medium and the external driving forces. It is, therefore, possible to characterize the medium by the use of low amplitude external driving forces.
Pg 493 - 496
A new poof of multiple solutions of combustions problems
by
1R. O. Ayeni, 1A. M. Okedoye, 2F. O. Balogun, and 3F. I. Alao
1Department of Pure and Applied Mathematics Ladoke Akintola University of Technology, Ogbomoso, Nigeria
2Department of Mathematics, Adeyemi college of Education, Ondo, Nigeria
3Department of Industrial Mathematics, Federal University of Technology, Akure, Nigeria.
Abstract
We revisit
the combustion problem
,
for the plane (n = 1), cylinder (n = 2) and sphere (n = 3)
vessels. Using polynomial approximations. We show that the problem has two (2)
solutions.
Pg 497 - 498
On the possibility of multiplicity of temperature fields in a microwave heating cancer therapy
by
R. O. Ayeni, A. M. Okedoye
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomso, Nigeria
and
E. A. Adebile
Department of Industrial mathematics, Federal University of Technology, Akure, Nigeria
Abstract
We investigate a steady temperature dependent perfusion during a cancer therapy. We show how the choice of perfusion could lead to more than one temperature fields which could lead to an undesired result.
Pg 499 - 502
Unsteady Magneto-Hydrodynamic (MHD) flow of a uniformly stretched vertical permeable surface I in the presence of heat generation/absorption and a first order chemical reaction.
by
*A. M. Okedoye, T. Adeniran, S. O. Adewale and R. O. Ayeni
Department of Pure and Applied Mathematics Ladoke Akintola University of Technology Ogbomoso, Nigeria.
*e-mail: micindex@justice.com
Abstract
Numerical results are presented for the transient and steady state Velocity, Temperature and Concentration fields. These results are obtained by solving the partial differential equations describing the conservation, momentum energy and species concentration by an explicit finite – difference method in time – dependent form. It was discovered that a maximum exist which confirm that maximum velocity and temperature occur in the body of the fluid and not in the surface as previously reported. A parametric study was conducted and the results were presented and discussed.
Pg 503 - 510
Biomechanics of the brain; some remarks on Biot’s equations of consolidation theory with deformation-dependent permeability
by
R. O. Ayeni, A. W. Ogunsola and A. O. Popoola
Department of Pure and Applied Mathematics Ladoke Akintola University of Technology, Ogbomoso, Nigeria
and
O. O. Eweoya
Department of Anatomy, College of Health Sciences
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
Abstract
We revisit models of hydrocephalus in the literature. In particular, we examine the class of models based on Biot’s theory of consolidation with fixed boundary forcing. Instead of fixed boundaries we take free boundaries. We prove existence and uniqueness of solutions. As in the fixed boundary forcing, we show that in a free boundary, the pressure is higher when the permeability depends on deformation. On the other hand, the total filtration is lower. Unlike the fixed forcing, the effect of the deformation on permeability reduces over time:
Keywords: Consolidation theory, variable permeability, free boundary, upper and lower solutions.
Pg 511 – 516
Relative null controllability of linear systems with multiple delays in state and control
by
R. A. Umana
Department of Mathematics and Computer Science
Federal University of Technology, Owerri, Nigeria
Abstract
Sufficient conditions for the relative null controllability of linear systems with time–varying multiple delays in state and control are developed. If the uncontrolled system is uniformly asymptotically stable, and if the linear system is controllable, then the linear system is null controllable.
Key words: Null controllability, multiple delays, time-varying.
Pg 517 - 522
Relative controllability of nonlinear systems with multiple delays in state and control
by
R. A. Umana
Department of Mathematics and Computer Science
Federal University of Technology, Owerri, Nigeria
Abstract
Sufficient conditions are developed for the relative controllability of nonlinear systems with time-varying multiple delays in the state and control. The results are obtained by defining an appropriate control and its corresponding solution by an integral equation. This equation is then solved using the Schauder’s fixed point theorem.
Pg 523 - 528
Criteria for exponential asymptotic stability in the large of perturbations of linear systems with unbounded delays.
by
Vincent A. Iheagwam
Department of Mathematics and Computer Science, Federal University of Technology, Owerri, Nigeria
e-mail: vinanyameleiheagwam@yahoo.com
Abstract
The purpose of this study is to provide necessary and sufficient conditions for exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear systems with unbounded delays. A strong relationship is established between the two types of asymptotic stability. It is found that if the exponential estimate of the solution of a system tends to zero as t �¥ the system is said to be uniformly asymptotically stable. But if the solution of a system approaches the origin faster than any exponential function, then the system is said to be exponentially asymptotically stable. Utilizing the exponential estimate of the solution, stability criteria for the linear part of our system of interest is derived. With enough smoothness conditions on the perturbation function, and appeal made to Lyapunov’s stability results and some Gronwall-type inequalities the required stability results are established for the linear perturbation.
Pg 529 - 536
On the convergence profile of a discretized scheme for a two-dimensional constrained optimal control problem
By
**O. Olotu and *S. A. Olorunsola
**Department of Mathematical Sciences,. The Federal University of Technology, Akure, Nigeria.
*e-mail: segolotu@yahoo.ca
*S. A. Olorunsola
Department of Mathematical Sciences, University of Ado Ekiti, Nigeria.
Abstract
The convergence profile of a discretized schame for an optimal control problem constrained by ordinary differential equation with matrix coefficients is examined. Various penalty parameters are considered for the penalty function method. It is observed that convergence is exhibited for these penalty parameters after certain number of iterations with a predetermined interval of convergence.
Pg 537 - 542
Relative controllability of nonlinear neutral Volterra Integrodiferential systems with delays in control
by
P. C. Jackreece
Department of Mathematics and Computer Science, Niger Delta University, Wilberforce Island,
Amasoma, Nigeria.
e-mail-preboj@yahoo,com
Abstract
In this paper we established sufficient conditions for the relative controllability of the nonlinear neutral volterra integro-differential systems with distributed delays in the control. The results were established using the Schauder’s fixed point theorem which is an extension of known results.
Pg 543 – 546
Stability of discrete control systems
by
Celestin. A. Nse
Department of Mathematics and Computer Sciences, Federal University of Technology, Owerri, Nigeria.
Abstract
(*)
We implore the notion of asymptotic controllability to show
that, a system which can be stabilized by an arbitrary feedback
can
also be stabilized by a linear feedback
.
Pg 547 - 548
Necessity and sufficiency conditions for the absolute null controllability for Linear delay perturbations
by
Department of Mathematics and Computer Sciences
Federal University of Technology, Owerri, Nigeria.
Abstract
We are inspired by the works of Chukwu [1], Eke [2], Schinterdorf and Barmish [4] to unveil necessary and sufficient conditions for the absolute null controllability of a linear delay perturbed system with zero in the domain of null controllability.
Pg 549- 552
Euclidean null controllability of linear systems with delays in state and control
By
Department of Mathematics and Computer Science,
Rivers State University of Science and Technology, Port Harcourt, Nigeria.
email: davsdone@yahoo.com
Abstract
Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable.
Keywords: Admissible controls, Controllability, Delayed systems,Linear systems, Null controllability.
Pg 553 - 558
Relative controllability of nonlinear neutral systems with multiple delays in state and control
by
Department of Mathematics and Computer Sciences
Federal University of Technology, Owerri, Nigeria.
Abstract
Sufficient conditions are developed for the relative controllability of nonlinear neutral systems with time-varying multiple delays in both state and control. The results are obtained by using Schauder’s fixed-point theorem.
Pg 559 -564
Relative controllability of nonlinear neutral systems with distributed and multiple lumped delays in control
by
Department of Mathematics and Computer Sciences
Federal University of Technology, Owerri, Nigeria.
Abstract
In this paper we study the relatie controllability of nonlinear neutral system with distributed and multiple lumped time varying delays in control. Using Schauder’s fixed point theorem sufficient conditions for relative controllability in a given time interval are formulated and proved.
Pg 565 - 570
by
Henry O. Omokaro
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
In [2] and [3] spaces in which every bounded subset is a compactoid was studied. Every compactoid set is limited but the converse is not true [3]. In this paper, we shall study some spaces in which every limited set is compactoid.
Pg 571 - 574
The direct product of right zero semigroups and certain groupoids
by
*E. E. David and †Adewale Oladipo Oduwale
*Department of Mathematics and Statistics, University of Port-Harcourt, Port-Harcourt, Nigeria.
†Department of Mathematics, University of Benin, Benin City, Nigeria.
e-mail:adeoduomoba@yahoo.com
Abstract
This paper investigates first the structure of semigroups which are direct products of right zero semigroups and cancellative semigroups with identity. We consider the relationship of these semigroups to right groups (the direct products of groups and right zero semigroups). Finally, we consider groupoids which are direct products of right singular semigroups and unipotent (one-idempotent) groupoids with identity.
Pg 575 - 578
A study of the Hubbard-Hirsch model within the Hartree-Fock Approximation (HFA)
by
Ben E. Iyorzor1, Robinson Okanigbuan2 and John O.A. Idiodi3
1,3Department of Physics, University of Benin, Benin City.
2Department of Physics, University of Mkar, Gboko, Benue State.
Based on the Hubbard-Hirsch model, we studied the dynamical susceptibility and spin excitation of an itinerant electron system within the Hartree-Fock Approximation (HFA) by using a Green’s function technique. We are able to arrive at the same results obtained by Zhang et al [1] who employed a Random-Phase Approximation (RPA).
Pg 579 - 582
Correlation between perturbation and variation methods in the study of strongly correlated electron systems
by
Robinson O. Okanigbuan
Department of Physical Sciences University of Mkar, Mkar, Nigeria.
John O.A. Idiodi
Department of Physics, University of Benin, Benin City, Nigeria.
Abstract
The ground–state wave function and energy are calculated for two electrons subject to a one-band Hubbard Hamiltonian on a one dimensional lattice containing N electronic sites, N = 2,3,4,5,6, and a 3 x 3 cluster of the square lattice, using perturbation and variational methods. The results from these two approximation methods are then compared with the result from exact calculational method.
Pg 583 - 594
Logarithmic perturbation theory: Applications and limitations
by
G. Y. Ndefru and S. Duwa
Department of Physics, Bayero University, Kano, Nigeria
Abstract
The time independent, non-degenerate standard perturbation theory is compared with the alternate treatment of perturbation theory called logarithmic perturbation theory (LPT). For determining the non-degenerate ground state the LPT is, in principle, easier to apply than standard perturbation theory. This is because, as opposed to the standard perturbation method which requires the knowledge of the complete set of eigenvalues and eigenfunctions of the unperturbed system, for the LPT one only needs to know the ground state wave function of the unperturbed system, the energy correction to the next lower order and some easily computable coupling constants. However, in reality, the LPT is a simpler method to apply when the ground state wavefunction is exponential in nature. But as shown here for trigonometric unperturbed wave function the LPT leads to integrals which have no analytical solutions thereby making LPT more difficult and less accurate method than the standard perturbation approach.
Pg 595 - 600
Streaming instability in a velocity–sheared dusty plasma
by
Salihu S. Duwa
Department of Physics, Bayero University, Kano, Nigeria
e-mail: duwass@yahoo.co.uk;
Abstract
A two-stream
instability, obtained from kinetic theory, of strongly velocity-sheared
inhomogeneous streaming electron in a magnetized plasma in the presence of
negatively charged dust is discussed. Various cold plasma approximations were
considered and it is shown that when the diamagnetic effect of ion can be
ignored, the excited mode could be dust lower hybrid-like. On other hand, if the
dust is treated as immobile background, the excited wave is ion lower
hybrid-like. In both cases, the growth rate is reduced due to the presence of
the dust particles and the velocity shear scale length,
,
is on the order of 
(where
k is wave vector) for the most unstable mode. An example is given from the
plume.
Keywords: Ionosphere, Space, Dusty plasma.
Pg 601 - 606
Excitation of low-frequency electrostatic instability on the auroral field lines due to precipitation electron beam
by
*L. E. Akpabio and +E. J. Uwah
*Department of Physics, University of Uyo, Uyo, Nigeria.
+Department of Physics University of Calabar, Calabar, Nigeria.
e-mail: leabio 2002 @yahoo. Com
Abstract
Low-Frequency Electrostatic Instability That Is Observed By Both Ground Facilities And Satellites Have Been Studied In The Auroral Acceleration Region Consisting Of Hot Precipitating Electron Beam From The Magnetosphere, Cold Background Electron And Ion Beam Moving Upward Away From The Earth Along The Auroral Field Lines. The Model Distribution For Both The Electron And Ion Are Taken, As Drifting Maxwellians While The Cool Background Electron Is Maxwellian. The Excited Mode And Growth Rate For The Resonant Instability Driven By The Precipitating Electron Beams Are Derived. We Also Discuss The Growth Rate And The Real Frequency Of The Resonant Instability. It Is Also Shown That, The Precipitating Electrons Can Generate Low-Frequency Electric Field Fluctuations (Lefs) Within The Frequency Range 55.4Hz To About 174.7Hz.
Pg 607 - 610
On iterative solution of non-linear equation
by
*O. Ogbereyivwe
Department of Natural and Applied sciences, Federal polytechnic, Auchi, Nigeria.
and
O. Izevbizua.
Department of Mathematics, University of Benin, Benin City, Nigeria.
Abstract
In solving non – linear equations by iterative method, Ohirhian (1994), (2005) [4],[5] developed a new algorithm based on cubic interpolation for solving non- linear equations of degree 1 to 3. The algorithm was found to be faster than the Regular falsi and the Newton Raphason method. This paper extend the algorithm to solving non linear equations of degree n by deriving a general formular, also some of the iteration procedures are reviewed for ease in computation
Pg 611 - 615