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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