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16. A Discrete Time EOQ Model For Delayed Deteriorating Items With Shortages

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by 1Yakubu M.I. and 2Sani B.
Department of Mathematics, Ahmadu Bello University, Zaria-Nigeria

Abstract
In this work, a discrete time Economic Order Quantity (EOQ) inventory model was developed for delayed deterioration items with shortages. The model consist of three stages in its cycle. In the first stage, the inventory depletes to a certain level due to market demand only while the second stage depletion occurs due to combined effect of market demand and deterioration. In the final stage, shortage time is assumed by the stockist and are fully backlogged. In the first two stages, the demand rates are different but are all constants. The model is used to determine the optimal ordering quantity and replenishment cycle. Numerical example is given to illustrate the application of the model and sensitivity analysis carried out to see the effect of parameter changes.

Keywords: Stockist; Backlogged; Lost sale; Deterioration; Discrete

15. Three-Dimensional Stability Analysis of A Uniaxially Compressed Polynomially Thick Rectangular Plates Using Energy Method

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by Onyeka F C.1, 3, Nwa-David C D.2 and Okeke T E.3*
1 Department of Civil Engineering, Edo State University Uzairue, Edo State.
2Department of Civil Engineering, University of Nigeria, Nsukka.
3Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike.

Abstract
This study presents the three-dimensional (3-D) stability analysis of a uniaxially compressed thick rectangular isotropic plate that is clamped in one edge and the other three edges simply supported (CSSS). The energy method was applied in the coupling the three dimensional kinematics and constitutive relations to formulate the total potential energy equation. The formulated the total potential energy for the plate was transformed into equilibrium equation and used to obtain the shape function of the plate. The shape function derived was analysed through variational principle to get an exact polynomial displacement function which is a product of the coefficient of deflection and shape function of the plate. The expression for the critical buckling load and other formulae was obtained by the direct variation of the total potential energy equation to produce a reliable solution for stability analysis of any type of plate rectangular plate. The span to thickness ratio and aspect ratios were varied to ascertain the buckling behavior of different type of plate under uniformly distributed load. The outcome of the numerical analysis revealed that increase in the span- thickness ratio led to the increased value of the critical buckling load which implies that the plate structure is safe when the plate thickness is increased. The result showed that the critical buckling loads from the present study using the established 3-D model for both functions is satisfactory and were found to follow an identical pattern, but quite distinct in validation which shows the credibility of the derived relationships. The overall average percentage differences between the two functions recorded are 2.06%. This shows that at about 98% both approaches are the same and can be applied with confidence in the stability analysis of any type of plate with such boundary condition.

Keywords: CSSS rectangular plate, stability analysis 3-D plate, exact polynomial function, critical buckling load.

14. Solar Energy Driven-Photocatalysis: Kinetics and Sorption Studies of Cr(VI) Reduction in Paint Effluent

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by Osarumwense J. O and Chris-Abey O. F.
Department of Science Laboratory Technology, Faculty of Life Sciences,
University of Benin, Benin City.

Abstract
Solar energy driven-photocatalysis is a clean and relatively new technology adopted to assuage the environmental problems caused by industrial effluent discharge. Chromium is widely used for the production of pigments for the paint and textile industries. The hexavalent form of chromium, Cr(VI) is highly toxic to human if ingested, and it is capable of causing oxidative damages to the blood cells at low concentration which may lead to hemolysis. In this study, a mixture of titanium oxide (TiO2) and chromium contaminated effluent was irradiated under the sunlight for three hours in batch system. Some operational conditions such as catalyst dosage and exposure time were investigated during the photocatalytic process. Atomic absorption spectrophotometer (AAS) was used to determine the residual Cr(VI) ion in the mixture. The data obtained was subjected to a variety of kinetics models and adsorption equilibrium isotherms; the process was well modeled by pseudo-first kinetics order with a reaction rate constant of 0.0141 min-1.The intra-particle diffusivity model revealed that the uptake of Cr(VI) ion was more of the film diffusion than the intra-particle diffusion. The data obtained from adsorption fitted well into the Langmuir adsorption isotherm with coefficient of determination (R2) of 0.9387; while the Temkin isotherm indicates that the process was exothermic.

Keywords: Solar energy, Photocatalysis, Chromium (VI), Adsorption equilibrium, Intra-particle diffusion.

13. Investigating Trusted Routing Mechanism On A Full-Meshed Telecommunication Network Model

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by OSUOLALE A. TIAMIYU
Department of Telecommunication Science, University of Ilorin

Abstract
The article is on the study of the properties of the trusted routing mechanism via simulation experiments of a fully-meshed telecommunication network model. The description of the model, the experimental results and their interpretations are given.

Keywords: Trusted routing, routing mechanism, telecommunication network, node monitoring, trusted node,
network agent.

12. Surface Wave Dispersion in Brazil East of Andes

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by Edward O. Osagie
Benson Idahosa University, Department of Physical Science, Benin City – Edo State

Abstract
This paper presents the results of a study of the dispersion characteristics of fundamental mode surface waves propagating in Brazil, east of Central Andes in particular, the continental crust and upper mantle structure. The occurrence of several large earthquakes in South America from 1965 to 1974 permits a reconnaissance study of the continental crust and upper mantle structure of Brazil, east of the Andes using surface wave dispersion. Data from WWSSN stations NAT and LPA were used to measure fundamental mode group velocity of Rayleigh and Love waves. The average S- velocity in the lower crust was found to be 4.40 km/sec. in Brazil, east of the Andes, which is typical of stable continents. The average S- velocity beneath the upper mantle is 4.66 km/sec, a typical value for cold platform areas. Other seismological data support this observation.

Keywords: Surface waves, dispersion, continental crust, upper mantle, Brazil.

11. Evaluation of Total Dissolved Solids (TDS) In Groundwater Around A Poultry Farm Using Electrical Resistivity Method and Geochemical Method

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by M. A. Fakunle, G. I. Olatona, O. O. Alabi, J. T. Adeleke, O. F. Oladejo and W.B. Agbaje
Department of Physics, Faculty of Basic and Applied Sciences, Osun State University, Osogbo
Department of Pure and Applied Chemistry, Faculty of Basic and Applied Sciences, Osun State
University, Osogbo

Abstract
Most hands dug wells and boreholes at Isundunrin (a town) in Ejigbo Local Government Area of Osun State, South-West Nigeria were completed without physicochemical analysis of the exploited water. This study aimed at validating the electrical resistivity technique as an alternative to the geochemical technique to identify potential aquifers based on total dissolved solids (TDS). Four Schlumberger Vertical Electrical Soundings (VES) were carried out very close to four different
available hand-dug wells located within the premises of a poultry farm at Isundunrin on the longitude E04o 6ʹ 34ʺ – E04o 15ʹ 46ʺ and latitude N07o 51ʹ 52ʺ – N07o 51ʹ 56ʺ.
The apparent resistivity values obtained were later transformed to formation resistivity and layered thicknesses by curve matching and computer iteration. The formation resistivity was used to determine the TDS levels in the exploited groundwater. When the TDS of the geochemical analyses (GCA) was compared with the TDS from VES results, a strong correlation coefficient of R2 = 0.875 was obtained, which indicated that the geoelectric sounding can be an alternative technique to geochemical technique to estimate the TDS level in groundwater.

Keywords: Total Dissolved Solids, Electrical resistivity technique, geochemical technique

10. Computational Analysis Of Higher-Order Integro-Differential Equations By Canonical Polynomial Basis Functions

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by Raji M. T., Fagbemiro O. and Olajuwon B. I.
Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

Raji M. T., Fagbemiro O. and Olajuwon B. I.
Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Abstract
This paper presents the computational analysis approach to the solution of
higher order Integro- Differential Equations (IDES) via the canonical
polynomial basis function. The canonical polynomial basis function
generated by re-defining the differential part in operator form. The analytical
results of the equations have been obtained in terms of convergent series with
easily computable components. Two numerical examples were considered
with the use of Mathematical Software (MATLAB 2009b) to illustrate the
performance, efficiency and implementation of the method. Hence, the
results showing the performance and effectiveness of the technique were
presented in tabular form. The technique has approachable better
performance than variational iteration method when compared.
Keywords: Integro Differential Equations (IDEs), canonical, integral equations.Two numerical examples were considered with the use of Mathematical Software (MATLAB 2009b) to illustrate the performance, efficiency and implementation of the method. Hence, the results showing the performance and effectiveness of the technique were presented in tabular form. The technique has approachable better performance than variational iteration method when compared.

Keywords: Integro Differential Equations (IDEs), canonical, integral equations.

9. Multiswitching Double Compound Combination Synchronizaion Of 5-Dimensional Hyperchaotic System In Application to Magentohydrodynamic Systems

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by Samuel O. Ogundipe
Department of Physics, Federal College of Education, Abeokuta, Ogun State, Nigeria.

Abstract
In this paper, we proposed an integrator backstepping technique for the realization of multi switching and synchronization of double compound combination of 5-dimensional hyperchaotic systems with application to 5-dimensional hyperchaotic magnetohydrodynamic systems to verify our analytical method. Using the Runge-Kutta algorithm, our numerical results confirm the effectiveness of the proposed analytical technique.

Keywords: Multiswitching, Double Compound Combination, Synchronisation,5-Dimensional, Hyperchaotic Systems, Magnetohydrodynamic Systems

8. A Note On the Connections and Contrasts Of Some Selected Results in Groups and Multi groups

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1Pokalas P. Tal, 2Mahmud Shamsuddeen and 3Moses Mbah
1,2 Department of Mathematics and Statistics, Federal University of Kashere, Gombe State
3 Department of Mathematics, Federal University, Lafiya, Nasarawa State

Abstract
This study undertakes a comparative examination of some selected properties (results) of groups and multi groups with a view to discover their similarities and differences. We compare the nature of the order of elements, the behaviour of elements with respect to Lagrange’s theorem and homomorphisms in both structures.

Keywords: groups, multi groups, order of elements, Lagrange’s theorem, homomorphisms

7. Quantum Mechanical Calculation Of OPtical Properties of Silicon-Oxide Nanoparticles Using Born-Mayer Potential

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by *Iorngbough I.O., Echi I.M., Onoja A.D. and Tikyaa E.V.
Department of Physics, Joseph Sarwuan Tarka University, Makurdi, Nigeria.

Abstract
In this work, the basic postulates of quantum mechanics are applied to calculate the optical properties of silicon oxide nanoparticle using Born-Mayer potential. The Born-Mayer potential was inputted into the time independent Schrödinger equation and the radial wave function was obtained by solving the equation using Runge-Kutta fourth and fifth order method.. The radial wave functions were then used to evaluate the expectation values of the energy of the system. The energies were used in the calculation of the optical properties such as, absorption coefficient extinction coefficient, real and imaginary dielectric constant and optical conductivity of the system. The accuracy of the theoretical model used for calculating the optical properties of silicon oxide nanoparticles was validated by comparing the results with experimental values using the Tauc plot which was used to determine the energy band gap (Eg) of silicon oxide nanoparticles and its optical properties empirically. The results obtained shows an oscillating radial wave function which decays exponentially in amplitude along the direction of propagation due to the core-shell nature of silicon-oxide nanoparticles The curve of the absorption coefficient shows a band gap value of 9.0 eV which is the theoretical band gap value of silicon oxide nanoparticle. The calculated and experimental curves of the absorption, extinction coefficients and the optical conductivity almost ride on each other and also showed good agreement between the theoretical calculation and experimental data.

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