International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 14 No. 2or Keyword in Title:
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Table of Content for Vol. 14 No. 2, 2016

Coupling of Exact Lagrange Multipliers with Various Analytical Techniques for Higher Order Initial Value Problems
Muhammad Hamid, Muhammad Usman, Nida Mehmood, and Syed Tauseef Mohyud Din
 PP. 123 - 133
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ABSTRACT: Solutions of higher order differential equations are of great importance for scientists and mathematicians. In this work, we likewise calculate exact langrage multiplier and it progressively connects to the definite results of higher order initial value problems. This study witnesses the advantages of Exact Lagrange multipliers and their coupling with Variational Iteration Method and Homotopy Analysis Method (H-HAM). Work witnesses a new modification in Homotopy Analysis method. Computational work reflects that use of exact Lagrange multipliers reduces the computational work to a tangible level and also increase the level of accuracy. Moreover, exact Lagrange multiplier reduce the successive application of integral operator and are more user friendly.

The Inverse Weibull-Geometric Distribution
Adil H. Khan, T.R. Jan
 PP. 134 - 146
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ABSTRACT: Inverse Weibull-Geometric Distribution which generalizes the Inverse Exponential-Geometric distribution, Inverse Weibull distribution, Inverse Exponential distribution and Inverse Rayleigh distribution has been introduced in this paper. The model can be considered as another useful 3-parameter distribution. Model characterization is studied, we derive the cumulative distribution and hazard functions, the density of the order statistics and calculate expressions for its moments and for the moments of the order statistics. Mixture model of two Inverse Weibull-Geometric distributions is investigated. Estimates of parameters using method of maximum likelihood have been obtained through simulations. Two real life example are provided one for complete data another for censored data to show the flexibility and potentiality of the proposed distribution and comparison with Inverse Weibull distribution, Inverse Exponential Geometric distribution, Inverse Exponential distribution and Inverse Rayleigh distribution is also discussed. The proposed model compares well with other competing models to fit the data.

Bayesian Estimation of Length Biased Nakagami Distribution
Sofi Mudasir, S.P Ahmad1 and A.Ahmad
 PP. 147 - 159
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ABSTRACT: In this paper, two parameter length biased Nakagami distribution is introduced. We obtain Bayesian estimators of scale parameter of the distribution under square error loss function, quadratic loss function and entropy loss function using quasi and Jeffrey’s priors.

Analytical Expressions of Non-linear Boundary Value Problems in MHD Boundary Layer Flow
V. Ananthaswamy, B. Seethalakshmi
 PP. 160 - 182
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ABSTRACT: A theoretical model of MHD boundary layer forced convection flow along a shrinking surface with the variable heat flux in the presence of the heat source is presented. A new approach to Homotopy Analysis Method (NHAM) is employed to solve the system of nonlinear dimensionless stream function and temperature profile equations. The effect of magnetic parameter, suction parameter, prandtl number, heat source parameter and heat flux parameter over a flow and other physical quantities are discussed with help of analytical solutions by means of graphs. The analytical results are compared with recently presented digital numerical simulation results for MHD boundary layer flow and are found to be in excellent agreement. Tabular compilations of skin friction and wall temperature are also explored for typical values of the governing parameters are reported.

Bayesian Analysis of Generalized Inverse Weibull Distribution
Saima Naqash, S.P. Ahmad1 and A. Ahmed
 PP. 183 - 196
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ABSTRACT: In this paper, we propose to obtain the Bayesian estimators of unknown scale parameter of a three parameter generalized inverse Weibull distribution, based on non-informative and informative priors using different loss functions. A real life example has been used to compare the performance of the estimates under different loss functions.

On Relating Vertex Covers and Dominating Sets in Simple Connected Graphs
R. Dharmarajan and V. Ananthaswamy
 PP. 197 - 203
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ABSTRACT: In any graph, each vertex cover is a dominating set, but the converse is not true. This article characterizes the simple loop-free connected graphs for which each dominating set is a vertex cover. This characterization holds for all simple graphs since a disconnected graph is a union of its components.

Improved Ratio Estimation under Rank Set Sampling
M.Iqbal Jeelani, S.E.H.Rizvi, Manish.K.Sharma, S.A.Mir, T.A.Raja, S.Maqbool, Nageena Nazir, Faheem Jeelani
 PP. 204 - 211
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ABSTRACT: In this article we have proposed ratio estimators of population mean using the linear combinations of known values of Deciles and Coefficient of Skewness of the auxiliary variable under Rank set sampling and Simple random sampling. Mean square error of the proposed estimators under rank set sampling is calculated and compared with Simple random sampling estimators. By this comparison, we demonstrate theoretically and numerically that the proposed estimators under Rank set sampling are more efficient than similar ratio estimators based on Simple random sampling.