ABSTRACTS OF VOLUME 6:
Journal of the Nigerian Association of Mathematical Physics(2002)
ISBN: 1116-4336


TOPICS & CONTRIBUTORS :
(please click on the hyperlinked title of each article to go to the abstract)

1) Transformation Properties of Pseudoscalar and Pseudovector Bilinear Forms
by ; O. Adetunji Odundun, Department of Physics, Obafemi Awolowo University, Ile-Ife, Nigeria

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2) A Tensor Identity in Quantum Field Theory
by ; O. Adetunji Odundun, Department of Physics, Obafemi Awolowo University, Ile-Life Nigeria.

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3) Classicalization of the Non-linear Schrodinger Equation
by ; A. N. Njah, Department of Physics, University of Agriculture, Abeokuta, Nigeria.
and R. Akin-Ojo, Department of Physics, University of Ibadan, Ibadan, Nigeria

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4) Feynman Paths in the Quantum Mechanics of a Simple Harmonic Oscillator
by ; Etim Eno Ituen, Department of Physics, University of Uyo, Uyo, Nigeria

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5) Exact Eigenenergies and eigenfunctions of the KP Anharmonic Oscillator
by ; S. X. K. Howusu, Department of Physics, University of Jos, Jos, Nigeria.

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6) A variational Approach to the Study of Strongly Correlated Electron Systems
by ; Edison A. Enaibe, Department Physics, University of Benin Benin City, Nigeria
and John O. A. Idiodi, Department of Physics, University of Benin Benin City, Nigeria

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7) Critical field/Critical Temperature Correlation in Conventional Superconductors
by ; Awele Maduemezia, F.A.S P. O. Box 9598, University of Ibadan Post Office, Ibadan, Nigeria. E-mail: awele@alum.mit edu.

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8) A Least Squares fit of Meson Spectra in the Dirac Equation with a Power –law Potential Model
by ; J. O. Fiase and L. K. Sharma, Department of Physics, University of Botswana
Private Mail Bag 0022, Gaborone, Botswana. E--mail:fiasejo@mopipi.ub.bw

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9) Missing ideas: Self-consistency problem in the Derivation of the one-and two-body effective interactions for SD Shell-Model Calculations
by ; J. O. Fiase and L. K. Sharma, Department of Physics, University of Botswana
Private Mail Bag 0022, Gaborone, Botswana E-mail:fiasejo@mopipi.ub.bw

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10) One- Dimendional Electrostatic (esi) Simulation of the Ionospheric Electron Beam- plasma Interaction
by ; Salihu S. Duwa, Department of Physics, Bayero University, Kano,Kano State, Nigeria

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11) Excitation of Lower Hybrid waves by Electron Beams In a Generalized lorentzian Distribution
by ; Salihu S. Duwa, Department of Physics, Bayero University, Kano, Kano State, Nigeria

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12) On the Fractal Measure and the Sojourn Time for the Path Of a Levy Process in n- Space
by ; Chukwuemeka A. Okoroafor, Department of Mathematics, Abia state University, Uturu, Nigeria

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13) Phase Synchronization of Coupled Oscillators
by; Ibiyinka .A. Fuwape, Department of Physics, Federal University of Technology Akure, Nigeria

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14) On the progressive oscillations in a solid with internal friction
by; E. O. Okeke, Department of Mathematics, University of Benin, Benin City, Nigeria

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15) On Quasi Linear Kinematics Waves
by ; Vincent E. Asor , Information Technology, Shell Nigeria, Warri
and Jane Gore, Department of Physics, University of Zimbabwe, Harare

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16) Longitudinal shear Deformation of a Composite Cylinder Sectionally Loaded Across Interface Edges
by ; James N. Nnadi, Department of Mathematics, Abia state University, Uturu Nigeria

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17) On the Existence and Uniqueness of a Power-Law Fluid Flowing in a Cylinder
by ; B. I. Olajuwon and R. O. Ayeni, Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso.

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18) Effects of the Geometry of Vessel on Detonations
by ; B. I. Olajuwon and R. O. Ayeni, Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso

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19) Asymptotic Analysis of Imperfection Sensitivity of Toroidal shell Segment with Modal Imperfection.
by; M. O. Oyesanya, Department of Mathematics, University of Nigeria, Nsukka, Nigeria

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20) Computation of Resistivity Transform Derivatives in Geophysical Sounding
by ; J. C. Egbai, Department of Physics, Delta State University, Abraka Nigeria

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21) Ionospheric Investigation using Analog Bottom Side Sounder Ionograms
by; O. S. Oyekola, Department of Physics, University of Ibadan, Ibadan, Nigeria
and E. E. Iheonu, Nigeria Building and Road Research Institute, Building Research Division, Otta, Ogun State,Nigeria

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22) A Simple Correction to Absorption Theory in the Region of Quasi-Transverse Propagation of Radio Waves Through the Ionosphere
by ; O. S. Oyekola, Department of Physics, University of Ibadan, Ibadan, Nigeria
E. E. Iheonu, Nigeria Building and Road Research Institute, Building Research Division
Otta, Ogun State, Nigeria.
and J. Akinrimisi, Department of Physics, University of Lagos, Lagos, Nigeria

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23) Calculation of Hyperfine Fields of 3d and 4d Impurities in Nickel.
by ; J. O. Ononiwu, Department of Physics, Federal University of Technology, Owerri Imo State, Nigeria.

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24) Application of Equivalent Crystal Theory to BCC Metal Surfaces: Surface Relaxation Calculation
by ; E. Aghemenloh, Department of Physics, Ambrose Alli University, Ekpoma, Nigeria
and J. O. A.. Idiodi, Department of Physics, University of Benin, Benin City, Nigeria

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25) An algorithmic Collocation Approach for Direct Solution of Special and General Fourth-Order Initial Value Problems of Ordinary Differential Equations
by ; D O. Awoyemi, Department of Industrial Mathematics and Computer Science, Federal University of Technology, Akure, Nigeria.

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26) An optimal Order Continuous Multistep Algorithm For Initial value Problem of Special Second Order Differential Equations
by; D. O. Awoyemi and S. J. Kayode, Department of Industrial Mathematics and Computer Science, Federal University of Technology, Akure, Nigeria.

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27) Interval Methods for Simultaneous Inclusion of all Zeros of a Polynomial
by ; M. N. O. Ikhile. and F. O. Otunta, Department of Mathematics, University of Benin, Benin city, Nigeria.

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28) On the Discrete Fourier Transform: The Colley-Tukey Fast Fourier Transform Algorithm
by ; A. O. Atonuje and P. N. Okonta, Department of Mathematics, Faculty of Science, Delta state University, Abraka, Nigeria.

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29) On Distance Between Nodes in Partitioned Networks
by ; E. D. Nwanze, and G. O. Abada, Department of Computer Science, University of Benin, Benin City, Nigeria

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30) An Application of Homogeneous and Non-Homogeneous Markov Chains
by ; A. A. Osagiede and S. E. Omosigho, Department of Mathematics, University of Benin, Benin city, Nigeria

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31) Work Force Stability and Suitability
by ; S. E. Omosigho and A. A. Osagiede, Department of Mathematics, University of Benin, Benin City, Nigeria

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32) Replacement Model Using Subjective Data
by ; Bashir M. Yakasai, Department of Mathematical Sciences, Bayero University Kano, Nigeria

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1)

Transformation Properties of Pseudoscalar and Pseudovector Bilinear Forms

( page 1 – 10 of Vol 6 Namp Journals )

by O. Adetunji Odundun
Department of Physics, Obafemi Awolowo University, Iie-Ife,
Nigeria: e-mail:oodundun@oauife.edu.ng

Abstract
By using spinor calculus the following Lorentz transformation properties of pseudeoscalar and pseudovector bilinear forms are proved:
and
Keywords: supersymmety, pseudoscalar, pseudovector, spinor calculus, quatum field theory.

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2)

A Tensor Identity in Quantum Field Theory

( page 11 –18 of Vol 6 Namp Journals )

by O. Adetunji Odundun
Department of Physics, Obafemi Awolowo University, Ile-Life Nigeria.
e: mail:oodundun@oauife.edu,ng.

Abstract
Using the methods of spinor calculus, we prove the identity .

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3)

Classicalization of the Non-linear Schrodinger Equation

( page 19 – 30 of Vol 6 Namp Journals )

by A. N. Njah
Department of Physics, University of Agriculture, Abeokuta, Nigeria.
and R. Akin-Ojo
Department of Physics, University of Ibadan, Ibadan, Nigeria.

Abstract
The Non-linear Schrodinger Equation (NLSE), (in units of where is a positive real constant, and is a real constant, E is the energy, is known to be integral for infinite X space. A Fourier analysis in a bounded interval , i.e. shows that the NLSE is a nonlinear Hamiltonian system of N degrees of freedom. The effect of truncating the degrees of freedom to a finite number N and the fact that L is finite are investigated for the case and . The results show that chaos sets in at certain value of the energy as the energy – increases for fixed N. Hence the NLSE is not integrable for finite N, and L. However, the integrability increases with increase in N implying that as N tends to infinity the NLSE becomes completely integrable as expected.

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4)

Feynman Paths in the Quantum Mechanics of a Simple Harmonic Oscillator

( page 31 – 44 of Vol 6 Namp Journals )

by Etim Eno Ituen
Department of Physics, University of Uyo, Uyo, Nigeria

Abstract
The propagator in path- integral quantum mechanics is as versatile as a wave function in Schroedinger’s formulation. The main challenge in this work is in computing the quantum propagator, Ks of a simple harmonic oscillator, as is entails summation over infinite number of paths. Using Van Vleck’s formula, the classical propagator, Kcl, is computed as the analytical results. The graphical display of the result with Feynman-Schullman’s checkerboard model used to enumerate the paths gives a reasonable comparison between Ks and Kcl. This work further shows that instead of instead of infinite number of paths uniformly weighted, Ks, can be reasonably computed by windowing off a large number of the paths and then weighting the rest non- uniformly. The weights used are Gaussian and velocity window functions: Wg and Wv respectively.

Keywords: path –integral, propagator, checkerboard model, windowing weights

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5)

Exact Eigenenergies and eigenfunctions of the KP Anharmonic Oscillator

( page 45 – 62 of Vol 6 Namp Journals )

by S. X. K. Howusu,
Department of Physics, University of Jos, Jos, Nigeria.
email:howusus@yahoo.co.uk

Abstract
In this paper we derive the exact analytic eigenenergies and eigenfunctions for the relativistic linear harmonic oscillator for comparison with the corresponding results obtained earlier by perturbation theoretic schemes.

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6)

A variational Approach to the Study of Strongly Correlated Electron Systems

( page 63 – 74 of Vol 6 Namp Journals )

by Edison A. Enaibe
Department Physics, University of Benin Benin City, Nigeria
And John O. A. Idiodi
Department of Physics, University of Benin Benin City, Nigeria
e-mail: idijohn@uniben.edu

Abstract
An investigation of the dynamic behavior of two electrons interacting under an extended Hubbard - type potential (t - t– U model) is presented., employing a variational analytic approach. The role of the next – nearest neighbour hopping parameter t is discussed and the results obtained form the extended Hubbard model are compared with those emerging from the usual t - u Hubbard model which contains only a nearest neighbour hopping parameter t.

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7)

Critical field/Critical Temperature Correlation in Conventional Superconductors

( page 75 – 80 of Vol 6 Namp Journals )

by Awele Maduemezia, F.A.S
P. O. Box 9598, University of Ibadan Post Office, Ibadan, Nigeria.
e-mail: awele@alum.mit edu

Abstract
In this paper we report a curious analytical relationship between the critical field at absolute zero, Bc(0) , and the critical temperature, Tc for elemental superconductors. We show that the correlation between the two variables is given by the quadratic curve: (units in Tesla), augmented with a sequence of Gaussian exponential ripples.

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8)

A Least Squares fit of Meson Spectra in the Dirac Equation with a Power –law Potential Model

( page 81 – 92 of Vol 6 Namp Journals )

by J. O. Fiase and L. K. Sharma
Department of Physics, University of Botswana
Private Mail Bag 0022, Gaborone, Botswana
e-mail:fiasejo@mopipi.ub.bw

Abstract
The recent discovery of the top quark and the huge amount of data generated among various particle physics data groups has generated a lot of interest among researchers. This calls for an update of our potential models describing these systems using a single power-law potential of the form: V(r) = Ar- V0 where A, V0 and ( > 0) are parameter to be fitted we have performed a least squares fit by fitting all the spectra of both light and heavy mesons (including leptonic decay–widths) in the Dirac equation. We have found for each meson type the optimum values of the parameters of our potential model described above that are required to give a good description of the meson spectra through a least squares fit. We next used the same potential model to predict the mass- spectra of the toponium (tt) system. The experimental data for this system is still in its infancy but we hope our potential model developed here will help in the further understanding of this meson structure.

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9)

Missing ideas: Self-consistency problem in the Derivation of the one-and two-body effective interactions for SD Shell-Model Calculations

( page 93 – 104 of Vol 6 Namp Journals )

by J. O. Fiase and L. K. Sharma
Department of Physics, University of Botswana
Private Mail Bag 0022, Gaborone, Botswana
e-mail:fiasejo@mopipi.ub.bw

Abstract
The input data to the shell model for nuclear energy level calculations consists of a set of single-particle energies on the one hand and a set of two-body matrix-elements on the other. The single-particle energies are usually extracted from experimental data, whereas, various empirical and theoretic techniques are used in the determination of the two-body matrix elements. Thus, there is no self-consistent approach in the determination of these quantities. Using the method of lowest order constrained variational approach (LOCV) with a set of two-body correlation operators, we calculated a set of single-particle energies together with a set of two-body matrix elements self-consistently. We have used the results to calculate the energy spectra of O and F nuclei and have found that the calculated spectra are rather compressed. However, on keeping our single-particle energies fixed at their calculated values and replacing some our calculated two-body matrix elements with the Chung-Wildenthal empirically fitted two-body interaction, we have found a reasonable agreement with experiment. These results demonstrate that shell-model calculations can be done quite successfully with the single-particle energies derived from the interaction but that there is a self-consistency problem in determining the nuclear spectra entirely from the microscope theory.

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10)

One- Dimendional Electrostatic (esi) Simulation of the Ionospheric Electron Beam- plasma Interaction

( page 105 – 110 of Vol 6 Namp Journals )

by Salihu S. Duwa
Department of Physics, Bayero University, Kano, Nigeria

Abstract
The 1-D Electrostatic. ESI code, developed by Langdon and Birdsall is used here to observe the effects of ionospheric electron beams on the plasma properties. The diagnostics include the displays of the kinetic energy of the particle species, the electrostatic energies of the excited modes and the total energy of the system, as functions of time. It is observed that the linear instabilities developed fully in a very short time and a nonlinear stage, in the form of amplitude fluctuations, quickly sets in. The rate at which the electron beam and the ionospheric electrons lose their (kinetic) energies, to ions and the wave modes (in form of growth rates) are estimated.

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11)

Excitation of Lower Hybrid waves by Electron Beams In a Generalized lorentzian Distribution

( page 111 – 115 of Vol 6 Namp Journals )

by Salihu S. Duwa
Department of Physics, Bayero University, Kano, Kano, Nigeria

Abstract
A theory of lower hybrid wave instability by electron beams with generalized Lorentzian (kappa) drift distributions is presented. The system is one where a super- thermal electron beam with temperature Tb and drift velocity vb, streams through plasma containing electrons and ions with temperature Te and Ti, respectively. The electrons and ions are both modeled by isotropic kappa distributions. The electrons appear as magnetized, and therefore treated using the drift kinetic equation while the ions appear as un-magnetized and hence obey the electrostatic Vlasov equation. The frequency of the wave mode, w0 and the linear growth rate of the excitation , are then derived, under any arbitrary temperature ratios, Ti/Te,, Tb/Te, but equal spectral index, k., for the three particle distribution functions. This study would be useful in computing beams generated instabilities in space and laboratory plasmas.

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12)

On the Fractal Measure and the Sojourn Time for the Path Of a Levy Process in n- Space

( page 116 – 130 of Vol 6 Namp Journals )

by Chukwuemaeka A. Okoroafor,
Department of Mathematics, Abia state University, Uturu, Nigeria

Abstract
After a brief survey of the technique for sojourn time in determining the fractal measure properties of a path of levy process in n-space, an integral test is established for the maximum difference in order of magnitude between one- side and two sided lower asymptotic growth for sojourn time process.

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13)

Phase Synchronization of Coupled Oscillators

( page 131 – 136 of Vol 6 Namp Journals )

by .Ibiyinka .A. Fuwape
Department of Physics, Federal University of Technology Akure, Nigeria

Abstract
The behaviours of coupled Oscillators, each of which has periodic motion with random natural frequency in the absence of coupling are investigated. Some novel collective phenomena are revealed subject to the boundary conditions applied. By increasing the coupling a bifurcation tree from high dimensional quasi-periodicity to chaos to quasi periodicity an periodicity is found.

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14)

On the progressive oscillations in a solid with internal friction

( page 137– 142 of Vol 6 Namp Journals )

by E. O. Okeke
Department of Mathematics, University of Benin, Benin City, Nigeria.

Abstract
A Theoretical consideration is presented. It concerns the progressive waves significantly modified by the dissipation induced by internal friction in the solid. The frictional term is consequently introduced in the formulation through a generalization of the elastic constants. These constants are then assumed to be proportional to the nth power of the frequency related to the dominant mode of the solid. In the foregoing consideration, the crucial term through which all parameters depend is the Poisson’s ratio . The ratio is also expressed in terms of the same viscous parameters associated with the solid. Calculations were performed using a range of positive values of n. The case n = 0 corresponds to that of purely elastic solid. For , the range of values within which v gives progressive wave solution shrinks with increasing n. Interestingly, this result completely agrees with that which we obtained by using Sturm’s theorem method.

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15)

On Quasi Linear Kinematics Waves

( page 143 – 170 of Vol 6 Namp Journals )

by Vincent E. Asor
Information Technology, Shell Nigeria, Warri
e.mail: vincent.asor@.shell.com
and Jane Gore
Department of Physics, University of Zimbabwe, Harare
e-mail:jgore@ science.uz.ac.zw

Abstract
We present results of a selective study of the asymptotic solution of wave equation satisfying certain initial value conditions for kinematic waves. Furthermore, the characteristics for the equation and the transition from stable to unstable solutions were discussed illustrating the results obtained with relevant and initial problems (IVP). Development of shock governed by the same IVP and initial data was evaluated with is characteristic equation. It was shown the displacement, u(x, t) is constant along characteristics which propagates with speed c(u). The dependence of on u produces a gradual nonlinear distortion of wave profile as it propagates through the medium. It is also follows that c(u) must be constant along characteristics, thus characteristics must be straight lines in the x-t plane.

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16)

Longitudinal shear Deformation of a Composite Cylinder Sectionally Loaded Across Interface Edges

( page 171 – 186 of Vol 6 Namp Journals )

by James N. Nnadi
Department of Mathematics, Abia state University, Uturu Nigeria

Abstract
The study concerns the effect of subjection of a cylinder of radius r = a to shear loads that can be adjusted to spread or over a subsection of the lateral surface by variation of an angle situated at the center of a typical cross section of the cylinder. The interface is perpendicular to the real axis and constitutes a line about which the loaded segments are symmetric. The general forms of the stress along the interface are shown to depend on material constants/. The stresses which can induce cracks, are analysed in a graph to understand their distribution as the length of a load site is compared with the semi – interface length, a .it is deduced that results for the special case when agrees with those obtained when the entire lateral surface is loaded.

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17)

On the Existence and Uniqueness of a Power-Law Fluid Flowing in a Cylinder

( page 187 – 190 of Vol 6 Namp Journals )

by B. I. Olajuwon and R. O. Ayeni
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso.

Abstract
In this paper we examine the flow of power–law fluid in a cylindrical vessel. We investigate the appropriate conditions for a similarity. Of particular interest is the questions of existence and uniqueness of solution and we include the criteria for both.

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18)

Effects of the Geometry of Vessel on Detonations

( page 191 – 196 of Vol 6 Namp Journals )

by B. I. Olajuwon and R. O. Ayeni
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso.

Abstract
We examine the effect of geometry of vessel on detonations. It is shown that in a non-uniform vessel, maximum temperature occurs towards the end of the tube. Whereas, in a uniform tube maximum temperature occurs at the center. Also maximum temperature for diverging or converging channel is greater than that of a uniform vessel.

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19)

Asymptotic Analysis of Imperfection Sensitivity of Toroidal shell Segment with Modal Imperfection.

( page 197 – 206 of Vol 6 Namp Journals )

by M. O. Oyesanya
Department of Mathematics, University of Nigeria, Nsukka, Nigeria

Abstract
We consider a multimode analysis of imperfection sensitivity of the toroidal shell segment with modal imperfection. We derive an asymptotic formula for the loss in buckling strength. We compare our results with known analysis in the literature.

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20)

Computation of Resistivity Transform Derivatives in Geophysical Sounding

( page 207 – 222 of Vol 6 Namp Journals )

by J. C. Egbai
Department of Physics, Delta State University, Abraka Nigeria

Abstract
The resistivity transform derivative deals with the computation of resistivity transform data for an assumed model of the earth. It can be calculated readily form theoretical models.
Some of the difficulties in the interpretation process may be reduced if each field apparent resistivities curve is converted into an equivalent resitivities transform curve. The theory based on an earth model of n layers was analysed. Interpretation which operates in the resistivity transform domain benefit form the use of forward linear filter to effect a quick transformation from the domain of measured apparent resistivities. Data were collected from about 57 vertical soundings. These data were incorporated into a computer programme where theoretical as well as field curves were generated sand analysed.

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21)

Ionospheric Investigation using Analog Bottom Side Sounder Ionograms

( page 223 – 232 of Vol 6 Namp Journals )

by O. S. Oyekola
Department of Physics, University of Ibadan, Ibadan, Nigeria
and E. E. Iheonu
‘Nigeria Building and Road Research Institute, Building Research Division, Otta, Ogun State,Nigeria
(Correspondence author, e-mail: osoyekola@yahoo.com)

Abstract
The five-point Kelso analysis, for calculating the real height of reflection corresponding to the ordinary (O) mode trace at any frequency in terms of the virtual heights at any five–lower frequencies, is compared with ten–point. Kelso analysis using the same frequencies in order to investigate electron density profile over Ibadan. The bottom- side ionograms obtained at Ibadan (7.26°N, 3.54°E) is then reduced to vertical electron–density profiles. The two methods are found to give the same result. A topside–bottom-side profile of electron concentration obtained form satellite-borne digital sounder at other low latitude station Chung-Li, Taiwan, 24.9°N, 121.24°E is given for comparison. The result suggests that manually scaled and calculated O-mode trace in the frequency regions where a scaled O–mode trace was available provides a degree of confidence in electron density profile obtained by the method of Kelso (1952)

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22)

A Simple Correction to Absorption Theory in the Region of Quasi-Transverse Propagation of Radio Waves Through the Ionosphere

( page 233 – 238 of Vol 6 Namp Journals )

by O. S. Oyekola,
Department of Physics, University of Ibadan, Ibadan, Nigeria
e-mail: osoyekola@yahoo.com,

*E. E. Iheonu Nigeria Building and Road Research Institute, Building Research Division
Otta, Ogun State, Nigeria (*author for correspondence)
e-mail: eeiheonu@yahoo.com,

and J. Akinrimisi
Department of Physics, University of Lagos, Lagos, Nigeria
e-mail: jakinrimisi@yahoo.com

Abstract
This paper presents a simple model correction to absorption theory in the quasitransverse region of propagation of radio waves through the ionosphere using the Appleton-Hartree equation. It is shown that if the computations of the refractive index are done as derived here and applied in the expression for absorption coefficient for attenuation of HF radio waves traversing an absorption regime, then the total absorption can be determined to a reasonably high degree of accuracy an may be relevant at different strata of the ionosphere, for HF signal prediction purposes.

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23)

Calculation of Hyperfine Fields of 3d and 4d Impurities in Nickel.

( page 239 – 252 of Vol 6 Namp Journals )

by J. O. Ononiwu.
Department of Physics, Federal University of Technology, Owerri Imo State, Nigeria.

Abstract
Detailed calculations of the electronic, magnetic and hyperfine fields of 3d and 4d impurities in Ni are here presented. We base the calculations on the local spin density approximation of density functional theory and the Korringa-Kohn–Rostoker Greens function method for impurity methods of calculation. The local moments and hyperfine fields of the impurities and their nearest neighbours are self-consistently calculated. We used the formulas derived by Blugel el al 1987 [1] for the paper relativistic generalization of the contact orbital and dipolar contributions to the hyperfine field and explicitly calculate relativistic corrections to the contact interaction, which are important for 4d impurities. The hyperfine fields can be split up into local and transferred contributions. The later are directly related to the local moments and to the moments of the neighbouring atoms. We report about calculations for dilute alloys using the KKR - Green’s function method and for concentrated disordered alloys using; the charge-self consistent KKR - CPA method. The values of calculated hyperfine fields are in agreement with the values obtained from experiments.

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24)

Application of Equivalent Crystal Theory to BCC Metal Surfaces: Surface Relaxation Calculation

( page 253 – 270 of Vol 6 Namp Journals )

by E. Aghemenloh
Department of Physics, Ambrose Alli University, Ekpoma, Nigeria
and J. O. A.. Idiodi
Department of Physics, University of Benin, Benin City, Nigeria
e-mail: idijohn@uniben.edu

Abstract
The surface energy and surface relaxation for three low – index surfaces of nine BCC metals are calculated using the equivalent crystal theory. The results for changes in the first interlayer spacing and the ensuing surface energies are discussed and then compared with other theoretical results and available experimental data.

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25)

An algorithmic Collocation Approach for Direct Solution of Special and General Fourth-Order Initial Value Problems of Ordinary Differential Equations

( page 271 – 284 of Vol 6 Namp Journals )

by D O. Awoyemi
Department of Industrial Mathematics and Computer Science,
Federal University of Technology, Akure, Nigeria.

Abstract
This paper discusses a Multiderivative Collocation method for direct solution of general initial value problems in ordinary differential equations of the form:
Our approach for the development of the method is based essentially on collocation of the differential system obtained from the basis function of degree n = 6 at the selected equidistant grid points. This is necessary in order to ensure symmetry in the method, which is essential for solving oscillatory initial value problem. Furthermore, a predictor for the calculation of the value of yn+k for k = 4, and its derivatives that appear in the main method is developed. Taylor series expansion is used to calculate the values of yn+i i =1,2,3 and their derivatives which also appear in the main method. The interval of periodicity and the error constant of the method at x = xn+4 are calculated. Evaluation of the proposed method at x = xn+4 gives a particular discrete scheme as a special case of the method. Finally the efficiency of the method is tested on non-stiff initial value problems.
Keywords: multiderivative method, numerical integrator, collocation, Predictor, equidistant grid points, interval of periodicity, error constant C.R. CATEGORIES: G1.7

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26)

An optimal Order Continuous Multistep Algorithm For Initial value Problem of Special Second Order Differential Equations

( page 285– 292 of Vol 6 Namp Journals )
by *D. O. Awoyemi and S. J. Kayode
Department of Industrial Mathematics and Computer Science,
Federal University of Technology, Akure, Nigeria.
(*Author to communicate concerning this paper.)

Abstract
An optimal symmetric continuous multi-step method is proposed in the paper of the solution of initial value problems of special; second order ordinary differntial equation. The method is based on collocation of the differential system at all the grid points and interpolation of the approximate solution at xn+j, j=0,1,2,3. The procedure yields a consistent scheme of order eight with moderately large interval of absolute stability for non-stiff special second order odes. Also, a number of explicit scheme s are developed for evaluation of yn+j, j =1,2,3,4, in the main method. The efficiency of the scheme is compared with the work of Awoyemi [1993].
Keywords: collocation, differential system, grid points, interval of absolute stability, explicit schemes. CR. Categories: G1.7

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27)

Interval Methods for Simultaneous Inclusion of all Zeros of a Polynomial

( page 293 – 302 of Vol 6 Namp Journals )

by M. N. O. Ikhile. and F. O. Otunta
Department of Mathematics, University of Benin, Benin city, Nigeria.

Abstract
In this paper, we present some interval methods for simultaneous determination of polynomial zeros in the spirit of Petkovic [1979]. The convergence of the methods is illustrated with numerical examples. It is our desire also to identify several new directions of modifications from which significant improvements in terms of convergence, accuracy, efficiency can be made possible, although with little overhead computational complexity.

Keywords: polynomials, zeros, disks, circular arithmetic, convergence
CR. Categories: G1.5

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28)

On the Discrete Fourier Transform: The Colley-Tukey Fast Fourier Transform Algorithm

( page 303 – 312 of Vol 6 Namp Journals )

by A. O. Atonuje and P. N. Okonta
Department of Mathematics, Faculty of Science,
Delta state University, Abraka, Nigeria.

Abstract
In this paper we look at the Cooley-Tukey Fast Fourier Transform (C-TFFT) algorithm and its application to the Fourier transform of discretely sampled data. We apply the C-TFFT algorithm to the computation of a discrete Fourier transform and show that the number of complex multiplications followed by the number of additions in the computations of the discrete Fourier transform can be reduced from N and N(N - 1) to Ny/2 and Ny respectively. Here y is a power 2 to which N is expressed and N is the number of sampled points over, which the discrete Fourier transforms, is computed

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29)

On Distance Between Nodes in Partitioned Networks

( page 313 – 322 of Vol 6 Namp Journals )

by E. D. Nwanze, and G. O.Abada
Department of Computer Science, University of Benin, Benin City, Nigeria

Abstract
In this paper we describe network partition from the viewpoint of recursive trees, which result as computer networks are exposed to series of degradations. Our attempt here to establish that the mean and variance of the distance between nodes over the set (n - 1)! recursive trees also occurs in partitioned networks. The operational approach adopted is a model-theoretic analogue of the notion of random recursive trees as they apply to computations that occur forever.

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30)

An Application of Homogeneous and Non-Homogeneous Markov Chains

( page 322– 332 of Vol 6 Namp Journals )

by A. A. Osagiede and S. E. Omosigho
Department of Mathematics, University of Benin, Benin city, Nigeria

Abstract
The present in application homogeneous and non-homogeneous Markov chain models to projecting school enrolment structures. These models are similar to Markov chain models used in manpower planning .the methods used in estimating the parameters of manpower planning models are adapted to the data available on the flow of pupils into, through and out of the system. The work is illustrated with a case study.

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31)

Work Force Stability and Suitability

( page 333 – 340 of Vol 6 Namp Journals )

by S. E. Omosigho and A. A.. Osagiede
Department of Mathematics, University of Benin, Benin City, Nigeria

Abstract
The paper examines workforce stability and suitability. The current measure of the stability of workforce is entropy. There are various versions of this measure. The various versions of entropy assume that the size of the workforce is constant. However, this assumption is difficult to attain in practice. Besides, entropy does not consider the desired size of workforce for an organization. Hence, the present paper proposes augmented ratio of squares and the recalibrated augmented ratio of squares to determine the stability and desirability of an organizational workforce. These two new measures have major advantages over the entropy measure.
Keywords: workforce stability, augmented ratio of squares, entropy.

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32)

Replacement Model Using Subjective Data

( page 341 – 346 of Vol 6 Namp Journals )

by Bashir M. Yakasai
Department of Mathematical Sciences, Bayero University Kano, Nigeria

Abstract
In the absence of reliable information on the system failure-time history and defects arrival, various authors have suggested use of subjective data; which can be obtained from expert opinions and judgments. In this short communication, we present a replacement model for a component using subjective information on the life history of the component in view.
Keywords: subjective information, replacement, renewal process, failure-time.

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