iosr-Jm   Volume-6 ~ Issue-5

Abstract: Bayesian approach for parameter estimation has the capacity to yield more precise estimates than methods based on sampling theory. There are several common Bayesian models; in this study we applied Empirical Bayes (EB) model called Beta-binomial model. The study is motivated by the need to beam searchlight on universities, faculties or fields of study with graduates who may not be eligible for further educational pursuits. This study provides means of assessment or a basis of evaluation of students' performances among faculties or fields of study and overall performance of a university. This study uses Bayesian methods of inference to estimate the proportion of above-average performance of graduates from the various faculties in University of Lagos. The model adopted generated results which are of smaller variances compared with variances of sample Proportions, showing that the posterior proportions generated are more efficient estimators. This is further evidenced in narrow widths of the computed confidence intervals. The overall result shows that the proportion of above-average performance of graduates of University of Lagos, who are eligible for further educational pursuits (i.e. higher degrees), is approximately 72% of the university graduates.

Keywords: Empirical Bayes Models, Beta-Binomial Model, Cumulative Grade Point Average, Posterior Proportion, Sample Proportion, University of Lagos-Nigeria.

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Abstract: This paper is conducted to investigate mixed convection flow within triangular enclosures having heatline concept. Here the left vertical wall which is moving from the bottom corner of the enclosure is also kept at a uniform constant cold temperature and the bottom wall is heat generating, while the other inclined wall is adiabatic. A finite element analysis is performed for solving the governing equations which are discretized by Galerkin weighted residual method of finite element formulation. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters Prandtl number, Pr (Pr = 0.71 - 6) varying Rayleigh number (Ra) from 103 to 104 while Reynolds number, Re (Re = 50) is fixed. The Result also indicates streamlines, isotherms, average Nusselt number along the hot wall, average temperature of the fluid in the enclosure. The computational results also indicate that the average Nusselt number at the hot wall of the Enclosure is depending on the dimensionless parameters.

Keywords: Mixed convection, Finite element method, Triangular enclosure, Heatline.

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Abstract: We consider the second order matrix differential equation M    0, 0  x   . Where M is a second-order matrix differential operator and  is a vector having two components. In this paper we prove a convergence theorem for the vector function 1 2 ( ) ( ) ( ) f x f x f x       which is continuous in 0  x   and of bounded variation in 0  x  , when p(x) and q(x) tend to  as x tend to  .

Key Words: Matrix differential operator, convergence theorem, bounded variation.

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Abstract: This paper presents an inventory model for deteriorating products with constant demand and time varying deteriorating rate, under permissible delay in payments. It discussed in two cases whether the permissible periods are less than or equal to or greater than replenishment cycle. During the permissible period both supplier and retailer got some benefits. Shortages are allowed and are completely backlogged. This model is explained with numerical example and sensitivity analysis.

Keywords - Deteriorating Products, Economic Order Quantity, Holding Cost, Permissible delay in periods.

[1] Ajanta Roy (2008) "An inventory model for deteriorating items with price dependent demand and time-varying holding cost." AMO-Advanced Modeling and Optimization, volume 10, November 1
[2] Chaitanya Kumar Tripathy and Umakanta Mishra, "Ordering Policy for Weibull Deteriorating Items for Quadratic Demand with Permissible Delay in Payments", Applied Mathematical Sciences, Vol.4, 2010, no.44, 2181-2191.
[3] Hardik Soni, Nita H.Shan and Chandra K.Jaggi, "Inventory models and trade credit: a review", Control and Cybernetics, Vol39, (2010) No.3.
[4] Hesam Saiedy, Mohammed Bamani Moghadam, "Inventory Model with Composed Shortage and permissible delay in payment linked to order quantity", J. Ind. Engg. Int.7(15) 1-7, Fall 2011, ISSN: 1735-5702
[5] Jamal AMM, BR Sarker and S Wang, "An ordering policy for deteriorating items with allowable shortage and permissible delay in payment", Journal of the Operational Research Society (1997), 48, 826-833.
[6] Khanr.S, K.S.Chaudhuri, "A Production – Inventory Model for a Deteriorating Item with Shortage and Time- Dependent Demand", Yugoslav Journal of Operations Research 21 (2011), Number 1, 29-45.
[7] Kumar Arya.R, and S.Kumar Shakya, "An Inventory Model for Deteriorating Items with Time Dependent Demand and Partial Backlogging", Int.J.of Appl.Math and Mech. 8 (8): 55-71, 2012.
[8] Kun –Shan Wu "An Ordering Policy for Items with Weibull distribution Deterioration under permissible Delay in Payments." Tamsui Oxford Journal of Mathematical Science 14 (1998) 39-54.
[9] Manisha Pal and Sanjoy Kumar Ghosh, " An Inventory Model with Shortage and Quantity Dependent Permissible Delay in payment",
[10] Manoj Kumar Meher , Gobinda Chandra Panda, Sudhir Kumar Sahu," An Inventory Model with Weibull Deterioration Rate under the Delay in Payment in Demand Decling Market" Applied Mathematical Sciences,Vol.6, 2012, no.23, 1121 -1133.

Abstract: There are many elastoviscous fluids that can be characterised neither by Maxwell's constitutive relations nor by Oldroyd's constitutive relations. One such class of viscoelastic fluids is the Rivlin– Ericksen's fluid. RIVLIN and ERICKSEN] have proposed a theoretical model for such viscoelastic fluid. The behaviour of surface waves propagating between two Rivlin–Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients.

Index terms- viscoelastic effects; perturbation; permeability; elastoviscous fluids; porous medium; thermosolutal instability; thermohaline convection; convecting layers hydrothermal circulation; oscillatory modes; non-Newtonian fluids

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Abstract: It is a well-experienced fact that whenever one tries to detect a weak object point in the vicinity of an intense point object, viz., a binary star-SIRUS and its companion weak satellite star, there is always loss of resolution of the optical system. In other words, one wants to improve the defectively of the system, there is always a loss of resolution capabilities of the system. Thus, there is a trade-off between Detection and Resolution of optical systems under various imaging situations. In this first paper of discussion of this trade-off, we have derived the Fourier analytical formulation of this problem. This formulation will be used to find out a compatible trade-off between Detection and Resolution in our further publications.

Key words: Fourier Optics, Mathematical Optics, Super-Resolution, etc.-

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Abstract: The maiin objjectt off tthiis paper tto iinttroduce T--pre--operattor,,T--pre--open sett,, T--pre--monottone,,pre-- subadiittiive operattor and pre--regullar operattor.. As wellll as we iinttroduce ((T,,L))pre--conttiinuiitty..

Keywords:: T--pre--operattor,, T--pre--open sett,, ((T,,L))pre--conttiinuiitty

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Abstract: This article deals with a study of two dimensional free convective flow of a polar fluid through a porous medium due to combined effects of thermal and mass diffusion in presence of a chemical reaction of first order. The objective of the present investigation is to analyze the free convective flow in the presence of prescribed wall heat flux and mass flux condition. The governing partial differential equations are non-dimensionalized and transformed into a system of non-similar equations. The resulting coupled nonlinear partial differential equations are solved numerically under appropriate transformed boundary conditions using an implicit finite difference scheme in combination with quasilinearisation technique. Computations are performed for a wide range of values of the various governing flow parameters of the velocity, angular velocity, temperature and species concentration profiles and results are presented graphically. The numerical results for local skin friction coefficient, couple stress coefficient, local Nusselt number and local Sherwood number are also presented. The obtained results are compared with previously published work and were to be in excellent agreement. The study reveals that the flow characteristics are profoundly influenced by the polar effects.

Keywords: Free convection; polar fluid; porous medium; chemical reaction; quasilinearisation.

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