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52) On the kinetics of martensite formation in a duplex stainless steel

by O. U. Osuoji Department of Physics, University of Benin, Benin City, Nigeria

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53) The effect of deformation on the sigma phase occurrence in some stainless steels

by O. U. Osuoji Department of Physics, University of Benin, Benin City, Nigeria

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54) Tidal flow in the Escravos Bar, Warri, Nigeria
by E. O. Oghre and E. O. Okeke Department of Mathematics University of Benin, Benin City, Nigeria

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.55) On strongly correlated N-electron systems

by E. A. Enaibe¹, G. E. Akpojotor², E. Aghemenloh³ and J. O. Fiase⁴, J. O. A. Idiodi¹

¹Department of Physics, University of Benin, Benin City, Nigeria ²Department of Physics, Delta State University, Abraka, Nigeria ³Department of Physics, Ambrose Alli University, Ekpoma, Nigeria ⁴Department of Physics, University of Botswana, Gaborone, Botswana

Click here for Abstract

 

56) An application of the extended RSA congruence

by Henry Osaretin Omokaro Department of Mathematics University of Benin, Benin City.

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1.                 

The Construction of an automorphism with a continuous spectrum and no square root
by

O. Izevbizua and I. C. Alufohai, Department of Mathematics, University of Benin, Benin City, Edo state Nigeria

 Abstract

An automorphism S is called a square root of an automorphism T if S² = T.  The Problem of describing the square root of a given automorphism T is completely solvable only when T has a discrete [1], [2] or guasi-discrete spectrum.  Katok and Stepin [3] gave a general construction of an automorphism with a continuous spectrum but no square root.  In this work, we construct a particular example of this kind of automorphisms using the following result.

pp 1 – 4

2.     

On the existence of weak solutions of quantum stochastic differential equations
by

 E. O. Ayoola, Department of Mathematics, University of Ibadan, Nigeria and A. W. Gbolagade Department of Mathematical Sciences Olabisi Onabanjo University, Ago-Iwoye, Nigeria

Abstract

We establish further results concerning the existence, uniqueness and stability of weak solutions of quantum stochastic differential equations (QSDEs). Our results are achieved by considering a more general Lipschit condition on the coefficients than our previous considerations in [1].  We exhibit a class of Lipschitzian QSDEs in the formulation of this paper, whose coefficients are only continuous on the locally convex space of the weak solution.

Key words QSDEs, Fock space Exponential vectors, Lipschitzian, Quantum stochastic processes

 pp 5 - 8

3.   

   On the numerical solution of the Gross–Pitaevskii equation
by

 J.A. Laoye¹, M. A. Liadi² and R. K. Odunaike^{1 1}Department of Physics, Nasarawa State University, Keffi, Nigeria, ²Department of Physics, University of Jos, Nigeria

Abstract

The Gross–Pitaevskii equation is solved using an approach developed for the solution of the Bogoliubov–de Gennes equations for type II superconductivity.  The solution is compared with others in the literature and is shown to be easily adapted to the study of an isolated vortex recently discovered in Bose-Einstein Condensation in trapped gases.

4.  

    Relative deviation between a uniformly weighted propagator and windowed propagator of a simple Harmonic Oscillator–2
by

E. E. Ituen, G. T Akpabio and A. A. Okon
Department of Physics, University of Uyo, Nigeria

Abstract

  A further processing of windowing in the computation of the quantum propagator, k_s, for a simple harmonic oscillator is performed with variation in space; instead of time as in Ituen (2003b).  All the four window functions are analysed as before, namely, random, W_r, exponential, W_e, gaussian, W_g and velocity, W_v window functions. Again the values of the propagator as Kw_r, Kw_e, Kw_g, Kw_v, in space, compare reasonably with K_s and hence K_cl.  The quantities s_r, s_e, s_g, s_v are the respective slight relative deviations measured with variation in space as expected in this case.

Keywords: Action, propagator, window function, relative deviation.

 pp 13 -18

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5..     

Combined effects of perturbations, radiation and oblateness on the location of equilibrium points in the restricted three-body problem.
  by

AbdulRazaq AbdulRaheem and Jagadish Singh, Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria

Abstract

 We have studied the effect of small perturbations in the coriolis and the centrifugal forces together with oblateness and radiation pressure forces of the primaries on the locations of equilibrium points in the restricted three-body problem.  We have found that oblate-ness and radiation pressure forces affect the locations of equilibrium points.  We have further seen that the positions of equilibrium points are not affected by the change in the coriolis force. They are only affected by the change in the centrifugal force.  It is also observed that the triangular points form triangles with the primaries and lie on the line joining the primaries.

Key words: equilibrium points, oblate-ness, perturbations, radiation, and restricted three- body problem.

 pp 19 - 24

6.     

Power series like relation of power law and coupled creep constrained grain boundary cavitation under strain gradient plasticity analysis.
by

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

Abstract

The continuum damage theory of Kachanov and Rabotnov has limitations since the mechanical properties of a material (especially plastic deformation and fracture) are determined by its microstructure.  When a solid deforms at high temperature its microstructure may in some sense be altered- holes and cracks may nucleate and grow inside the solid by various mechanism controlled by diffusion and by power law creep or by a combination of these mechanisms.  Considering a coupled diffusion power law creep mechanism using a mechanistic model approximate analytical equations for the growth rate under multi-axial stress states are developed.  These results are related to the power law mechanistic results in a power series like form, which are used to analyze the crack, tip fields for the coupled mechanism using a strain gradient plasticity analysis.  The Kachanov-Rabotnov results and the HRR results are shown to be special cases of these results. 

Key words: diffusion, power law, creep, microstructure, strain gradient plasticity,

 pp 25 -34

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7.

On the dynamic buckling of stochastically imperfect finite cylindrical shells under step loading
by

A. M. Ette, Department of Mathematics and Computer Science, Federal University of Technology, Owerri, Imo State, Nigeria

Abstract

The dynamic buckling load of stochastically imperfect finite right circular cylindrical shells subjected to step loading is determined by means of regular perturbation procedures .The imperfection is assumed to be a Gaussian random function of position and consequently is homogeneous. The result obtained is implicit in the load parameter and is asymptotically valid for small magnitude of the random imperfection, which is itself taken as the first term in a Fourier sine expansion.

 pp 35 - 46

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8.    

  Deformation fields due to sheared semicircular edge notch in a non-homogeneous elastic material
by

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

Abstract

 A non-homogeneous semi-infinite elastic material containing a semicircular edge notch of radius a, is studied for determination of deformation fields and maximum anti-plane shear concentration.  The mode of loading on variable intervals [a_i,b_i], i =1,2, leads to expression for the maximal stress, (a, 0) as a product of two terms; the first is analogous to a known anti-plane stress concentration term for a circular hole in an infinite body while the other term is a measure of the contribution of material constants and changes at load site to the high stress concentration. The special case of our result for (r, 0) when the notch is absent (a = 0) is in agreement with known results.  The variations (a, 0) with  are displayed on graphs

 pp 47 - 56

9.     

 Dynamic analysis of a thermal–induced stress in an elastic circular plate
by

Y. M Aiyesimi, Department of Mathematics and Computer Science, Federal University of Technology, Minna, Nigeria.

Abstract

Stress is a phenomenon that could cause a lot of destruction to engineering structures if there are no adequate in-built absorbers in such structures.  Buildings, bridges and such other structures must therefore be protected from excessive stress in other to maintain their shapes and forms and hence to guarantee the life span of these structures because of the negative effects this phenomenon may have on them if left unchecked.  In this work we study the magnitude of a thermal-induced stress in a circular elastic plate of radius b with an indented circular hole of radius a at the center.  The magnitudes of the normal and tangential components for various span ratio are computed. The results of this analysis show a definitive relationship between the stress profile and variability in span ratio.

 pp 57 - 60
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10. 

 Collisional effect on lower hybrid waves instability in a dusty plasma
by

Lawan S. Taura, Department of Physics, Bayero University, Kano, Nigeria
Abstract

 The effect of particle collisions on lower hybrid modes in a dusty plasma is studied.  The dispersion relation derived from fluid theory is numerically solved for plasma parameters relevant to determine the modification in wave propagation due to collisions.  This study is relevant to the earth’s lower atmosphere, in particular, the mesosphere, where charged dusts and excitation of low frequency waves have been observed

 pp 61 - 62

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11. 

A review of ²⁰Ne structure in a full microscopic self-consistent shell–model calculation with tensor correlations
  by

J. O. Fiase^++, H . E Agba⁺, A. A. Akombor⁺ and Frederick Gboarun ^+
++ Department of Physics, University of Botswana,
⁺Department of Physics, Benue State University, Makurdi, Nigeria.

Abstract

A set of single-particle energies together with a set of two-body matrix- elements derived in a self –consistent manner from the Reid soft–core potential are used to calculate the energy levels of ²⁰Ne.  We used a harmonic oscillator wave function folded with two-body correlation functions in our calculation. It is found that the calculated spectra agree very well with experiment and the best available shell-model calculations by other workers. As a result we have demonstrated that it is possible to calculate the spectroscopy of nuclei microscopically and self-consistently in such a way that both the single –particle energies and the effective two-body interactions are derived from the same procedure.

Keywords: single-particle energies, shell-model, two-body correlation functions, effective two-body interactions.

PACS numbers (s): 21.60. -n,21,.60.Cs

 pp 63 -68

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12. 

Numerical simulation of hole injection in high barrier metal-semiconductor short diodes
by

M. G. Zebaze Kana , R. K. Odunaike and A. A. Oberafo , Physics Advanced Laboratory, Sheda Science and Technology Complex, Garki, Abuja.

Abstract

A numerical investigation is carried out on effects of minority carriers on the transport parameters of one-dimensional metal-semiconductor short diodes under highly injecting conditions.  The results show that at a donor concentration N_d=10¹⁴ cm^-3 and total current density J=0.1 mAcm^-2, the hole injection ratio,g_h , decreases rapidly by a factor of more than 80% within 2mm semiconductor layer from the interface.  Furthermore, a comparison of the two-carrier model adopted in this work with the Schottky model reveals a discrepancy of 30% in the lnJ-V characteristics of a diode of 0.92 eV barrier height.

          pp 69 - 74

13. 

Pressure transient analysis of a horizontal well subject to four vertical well injectors
by

E. S. Adewole and K .O. Bello, Department of Petroleum Engineering, University of Benin, Benin City, Nigeria

Abstract

Reservoir characterization is essential for effective reservoir and wellbore management. But when a horizontal well is subject to constant-pressure external boundaries, the extent of reservoir characterization that is possible depends on the flow regimes that are encountered in a given flow time. In this paper dimensionless pressure distribution of a horizontal well oil producer, subject to four vertical well fluid injectors, is utilized to identify the possible flow regimes in the horizontal well.  The study shows that the number of flow regimes identifiable depends on the permeability distribution and geometry of the reservoir. In particular, for a square shaped reservoir with central horizontal well location, only two major flow regimes are identifiable. More flow regimes may occur if the reservoir length is at least one log cycle greater than the breadth, and the horizontal permeability is substantially high.

 pp 75 - 82

14.  The Mathematical modelling of environmental pollution using the Freundlich non-linear contaminant transport formulation

by Y. M Aiyesimi Department of Mathematics and Computer Science

Federal University Of Technology, Minna, Nigeria

Abstract 

In this paper environmental pollution has been modeled mathematically using the Freundlich non-linear contaminant transport formulation.  An analytical solution of lower order perturbation of the concentration Cis obtained.  Flow profiles for various values of molecular diffusion D and the velocity U are studied and the effects of these parameters on the flow regimes highlighted.

  pp 83 -86

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15.             

Higher Order Bootstrap likelihood

By

S. M. Ogbonmwan

Department of Mathematics, University of Benin

Benin City, Nigeria

Abstract

In this work, higher order optimal window width is used to generate bootstrap kernel density likelihood.  A simulated study is conducted to compare the distributions of the higher order bootstrap likelihoods with the exact (empirical) bootstrap likelihood.  Our results indicate that the optimal window width of orders 2 and 4 perform better than those of higher orders.  The higher order kernels () provided window widths, which obscured the details of the distribution when the exact bootstrap likelihood was taken to be the true density.

Keywords: Higher order kernels, exact bootstrap empirical likelihood, Bootstrap kernel likelihood, optimal window width.

pp 87 - 92

16. 

Gravitational fields of prolate spheroidal bodies extension of gravitational fields of spherical bodies.

by¹E. F. Musongong and ²S. X. K. Howusu¹Department of Physics, Nasarawa State University, Keffi, Nigeria.e-mail: musongong @yahoo.co.uk²Department of Physics, University of Jos, Nigeria .e-mail: howusus@yahoo.co.uk  

Abstract

The expressions for the gravitational fields of spherical bodies are well known. In this paper we derive the exact expressions for a homogenous massive prolate spheroidal, an extension of the gravitational fields of spherical body for investigations and applications.

pp 93 - 96

17. 

Gravitational time dilation and spectral shift in the field of a massive oblate spheroidal body.

by ¹E. F. Musongong and ²S. X. K. Howusu ¹Department of Physics, Nasarawa State University , Keffi, Nigeria. e-mail: musongong @yahoo.co.uk ²Department of Physics, University of Jos, Nigeria . e-mail:howusus@yahoo.co.uk

Abstract

In this paper, we derive expressions for the time dilation and spectral shift in terms of proper time and proper frequency in the field of a massive oblate spheroidal body using an approximate value of

pp 97 -100

18. 

Compactness of cores of targets for nonlinear delay systems

by V. A. Iheagwam and C. A. Nse Department of Mathematics and Computer Science, Federal University of Technology Owerri, Imo State, Nigeria.  

Abstract

The purpose of this study is to investigate the compactness of cores of targets for nonlinear delay systems.  Our results are obtained by exploiting the non-singularity of the fundamental matrix for the homogeneous part of the system and its “conjugate” equation.  Hajek's arguments in [4] of the notion of asymptotic direction and other concepts of convex set theory stand monumental in the development of this study.  With a perturbation function, satisfying a smoothness condition – growth condition.  A relationship is established between the boundedness of cores of targets and the Euclidean controllability of the nonlinear system.  This relationship gives vent to the establishment of the compactness of cores of target for the system.  We complement Ukwu [9] and Chukwu [1] by answering in the affirmative that under certain smoothness conditions, the compactness of cores of targets for a linear system guarantees the compactness of cores of target for the linear perturbation.

pp. 101 – 104

19. 

Combination methods for numerical inclusion of the zeros of a polynomial

by

M. N. O. Ikhile

Department of Mathematics, University of Benin, Benin City, Nigeria. E-mail: mnoikhilo@yahoo.com

Abstract

In the numerical inclusion and isolation of the zeros of a polynomial in an interval on the plane, hybrid combination methods have been found quite useful for their virtue of easy construction and reduced computational cost with respect to interval arithmetic operations, while still providing restrictive inclusion for the respective zeros simultaneously. In what now follows, consider a collection of combination methods arising from efficient enhancement of a class of basic simultaneous numerical inclusion methods under two different updating procedures of the generated iterates. The accuracy of the methods will be illustrated by insightful numerical experiments.

Keywords: combination methods, zeros of a polynomial, correction, R-order of convergence, interval methods, efficiency index C.R. Category: G1.5

pp 105 – 120  

20. 

On the Cooley-Turkey Fast Fourier algorithm for arbitrary factors

byA.O. Atonuje and I. N. NjosehDepartment of Mathematics,Delta State University, Abraka, Nigeria  

Abstract

Atonuje and Okonta in [1] developed the Cooley-Turkey Fast Fourier transform algorithm and its application to the Fourier transform of discretely sampled data points N, expressed in terms of a power y of 2.  In this paper, we extend the formalism of [1] Cookey-Turkey Fast Fourier transform algorithm.  The method is developed in this paper to guarantee the application of (C-TFFT) algorithm for arbitrary factors say .

pp 121 - 124

21. 

Some example of modelling with super-diagonal bilinear moving average time series

by

Iheanyi S. Iwueze

Department of Statistics, Faculty of Biological and Physical Sciences Abia State University, Uturu, Nigeria.  

Abstract

In this paper the modeling of super diagonal bilinear moving average time series models are considered.  Other determination of bilinear models based on the observed covariance structure of the data is pointed out.  Linear and bilinear moving average models that have identical covariance structure are fitted to both simulated and real-time series data.  Forecasts obtained for stationary and invertible linear and bilinear models are compared

Keywords and Phrases: Super-diagonal bilinear moving average time series; stationarity; ergodicity; invertibility; covariance structure.

pp 125 -130

22. 

The critical role associated with beach slope and its width in evolution of swell near the shoreline

by Vincent E. Asor[1] Shell International, Port Harcourt, Nigeria e-mail: Vincent.Asor@shell.com and Ezekiel O. Okeke Department of Mathematics, University of Benin, Benin City, Nigeria e-mail: Okeke69@yahoo.com  

AbstractUsing perturbation method, the shallow water wave equation is investigated.  We are, however, interested in the case in which the incident wave train propagate in the radial direction towards the shoreline.  This is rather more general than the case in which the trains of progressive waves propagate strictly in x–direction.  The essential part of this study is the determination of the critical role associated with the width of the shelf and the beach gradient in relation to the transformation of the beach waves.  There from, it is deduced that the wave energy is an increasing function of the beach bottom gradient and the shelf width. The later should, however, be finite.  Further, the nonlinear interactions between the wave trains and the resulting excitations of the seabed are also discussed.

pp 139 - 144

23. 

Multi-valued solution of the Burgers’ equation and shock Determination I.

by Vincent E. Asor Information Technology, Shell International, Port Harcourt. e-mail: Vincent.Asor@Shell.com  

Abstract

We present the Burgers’ equation as a balance between time evolution, non-linearity and dissipation and use these properties to examine the vanishing behaviour of the dissipation coefficient.  Furthermore, we undertake a rigorous mathematical analysis which gives rise to multi-valued solutions after sufficient time and discontinuities.  Though the complete solution is single-valued for all time, t, revelations from the equation of shock determination is interesting in the determination of the random properties of the wave.

  Keywords: Burgers’ equation, time evolution, non-linearity, dispersion, dissipation, discontinuity, shock, hump. 

pp 145 - 148

24.  Dynamic stability of a lightly damped column trapped by a harmonically slowly varying explicitly time dependent load

by A. M Ette Department of Mathematics and Computer Science Federal University of Technology Owerri, Imo State e-mail: tonimonsette@yahoo.con

Abstract 

In this paper we initiate an analytical approach for determining the dynamic buckling load of a finite viscously damped column acted upon by a harmonically slowly varying explicitly time dependent load.  The viscous damping is considered light and the column rests on an elastic foundation that produces a nonlinear restoring force per unit length.  Unlike most similar analyses, the time variable appears explicitly making the problem non-autonomous the formulation contains two small but unrelated parameters upon which asymptotic expansions are initiated.  The coefficients are sinusoidally slowly varying and problem is solved using a generalization of Lindsted-Poincare method in a mulit-timing regular perturbation technique.  Simple asymptotic results implicit in the load parameter are obtained. 

pp 149 – 156  

25. 

On the convergence of the dynamic series solution of a constrained elastic column subjected to wind gust.

by J. A. Gbadeyan and E. O. Titiloye Mathematics Department, University of Ilorin, Ilorin. Nigeria.

Abstract

The one dimensional problem of analysing the dynamic behaviour of an elevated water tower with elastic deflection–control device and subjected to a dynamic load was examined in [2].  The constrained elastic system was modeled as a column carrying a concentrated mass at its top and elastically constrained at a point along its length.  A new solution technique, which yielded a series solution to the problem, was then developed.  This paper is basically concerned with establishing the convergence of the series solution obtained in [2] and hence, the acceptance of this solution as the actual solution of the constrained elevated water tower vibration problem.  Damping is neglected.

pp. 157 - 160

26. 

Flow of a power-law fluid with memory past an infinite plate

by

B. I. Olajuwon and R. O. Ayeni Department of Pure and Applied Mathematics Ladoke Akintola University of Technology Ogbomoso, Nigeria e-mail: ishola_1@hotmail.com

Abstract

            We examined the flow of a power law fluid with a non-constant relaxation lt^b past an infinite plate.  When l is zero the fluid is pseudoplastic and when the power law exponent is 1, the fluid is a Maxwell fluid.  It is shown that the problem has a solution when 0 < n £ 1.  Moreover, we show that momentum penetration decreases with l.

pp. 161-162  

27. 

 Higher order MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and chemical reaction

by

R.O. Ayeni, A.M. Okedoye, F.O. Balogun and T.O. Ayodele

Department of Pure and Applied Mathematics

Ladoke Akintola University of Technology

Ogbomoso,