International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 12 No. 1or Keyword in Title:
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Table of Content for Vol. 12 No. 1, 2014

Variational Finite Element Approach to Estimate the Behaviour of Oxygen Diffusion in the Biological Tissue via Plasma and Capillary Layers
M. A. Khanday, Aijaz Najar
      
 PP. 1 - 9
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ABSTRACT: The respiratory system is responsible for gas transfer between the tissue and the outside air. The oxygen that is supplied to the tissues must be extracted from the outside air by the lungs. Erythrocytes are responsible for the oxygen exchange with the living tissue through capillary bed. To understand the transport of oxygen across the Plasma layer through capillary wall and cell membrane to the spherical tissue, we have established a mathematical model based on diffusion equation and Variational Finite Element Method has been employed for the numerical results. The study reveals the fact that the amount of oxygen supply retards from the plasma layer to the tissue layer via capillary layer and cell membrane. The results obtained are closer and refinement to the results in the models developed by Simpson et al [4] and Sharan et al [1]. The main observation of this study is that the plasma layer shows a significant change in the diffusion process of oxygen and its concentration is maximum between capillary layer and a cell membrane.


A New Method for Finding an Optimal Solution of Assignment Problem
A.Ahmed and Afaq Ahmad
      
 PP. 10 - 15
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ABSTRACT: In this paper a new method is proposed for finding an optimal solution of a wide range of assignment problems, directly. A numerical illustration is established and the optimality of the result yielded by this method is also checked. The most attractive feature of this method is that it requires very simple arithmetical and logical calculations. The method is illustrated through an example.


Bayesian Analysis of Size Biased Exponential Distribution
J.A.Reshi, A.Ahmed, K.A.Mir
      
 PP. 16 - 29
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ABSTRACT: In this paper, we have considered a size biased Exponential distribution (SBED), a particular case of the weighted exponential distribution, taking the weights as the variate values. Moments of the distribution are derived. Maximum likelihood estimation is also discussed. We also present Bayes’ estimator of the parameter of Size biased exponential distribution (SBGMD), that stems from an extension of Jeffery’s prior (Al-Kutubi (2005)) with a new loss function (Al-Bayyati (2002)). We are proposing four different types of estimators. Under squared error loss function, there are two estimators formed by using Jaffrey prior and an extension of Jaffrey’s prior. The two remaining estimators are derived using the same Jeffrey’s prior and extension of Jeffrey’s prior under a new loss function. We are also deriving the survival functions of the size biased exponential distribution under the Jaffrey’s prior and an extension of the Jaffrey’s prior. These methods are compared by using mean square error through simulation study with varying sample sizes.


New Exact Solutions of Some Nonlinear Partial Differential Equations via the Bernoulli Sub-ODE Method
M. F. El-Sabbagh, R. Zait and R. M. Abdelazeem
      
 PP. 30 - 42
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ABSTRACT: In this paper, we obtain new exact solutions of some nonlinear partial differential equations such as the (1+1)–dimensional travelling regularized long wave (TRLW) equation, the (2+1)-dimensional Calogero equation, the (3+1)-dimensional Jimbo–Miwa equation, and the variant shallow water wave equations via the Bernoulli sub-ODE method.