International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 15 No. 1or Keyword in Title:
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Table of Content for Vol. 15 No. 1, 2017

Decision Support System through Data Envelopment Analysis & Stochastic Frontier Analysis
Qaiser Farooq Dar, Tirupathi Rao Padi and Arif Muhammad Tali
 PP. 1 - 13
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ABSTRACT: The two principal methods that have been used for estimating the Frontiers in the production theory are Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), which involve mathematical programming and Econometric Methods respectively. DEA is a nonparametric linear Programming approach for measuring the relative efficiency of a Set of decision-making units (DMUs), which are using multiple inputs to produce multiple outputs. There are two different orientations of objectives in DEA namely input-orientation and output-orientation; two different DEA models based on scales namely Constant Returns to scale (CRS) and variable Returns to scale (VRS). Stochastic Frontier Analysis is the technique that has been used for estimating the frontier parametrically. This approach was used by Aigner and Chu (1968) who considered a Cobb-Douglas production frontier for estimating the Economic efficiency. Computing the efficiency measures involves estimating the unknown production frontier. This study has proposed the validity verification procedures through DEA & SFA for developing suitable Decision Support Systems (DSS) in the frontier Analysis. For the said objective, the study has considered the basic approaches of DEA like classical Charnes-Cooper-Rodes (CCR) model, classical Banker-Charnes-Cooper (BCC) model and Slack Based Measure (SBM) models along with different production functioning approaches like SFA.

Structural properties and parameter estimation of Length Biased Weibull Distribution
Sofi Mudasir, S.P Ahmad
 PP. 14 - 29
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ABSTRACT: In this paper, two parameter length biased Weibull distribution is derived. We study some structural properties of this distribution. Maximum likelihood estimator of length biased Weibull distribution is obtained. Also, Bayesian estimators of scale parameter of the distribution under square error loss function, quadratic loss function and entropy loss function by using Jeffrey’s and extension of Jeffrey’s priors are obtained.

Approximation Solvability for a System of Variational-like Inclusions Involving Generalized (H,φ)-η-Monotone Operators
Mohd Iqbal Bhat and Bisma Zahoor
 PP. 30 - 49
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ABSTRACT: In this paper, we consider a system of variational-like inclusions involving generalized (H,φ)-η-monotone operators in real Banach spaces. Further, we define the proximal operator associated with the generalized (H,φ)-η-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal-point operator technique, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of variational-like inclusions. Furthermore, we discuss the convergence criteria of the iterative algorithms under some suitable conditions. Our results can be viewed as a refinement and improvement of some known results in the literature.

Oscillation Criteria for Fourth-order Nonlinear Differential Equations
 PP. 50 - 57
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ABSTRACT: In this paper, we study the Oscillation Criteria for Fourth-order Nonlinear Delay Differential Equations. Some interesting results are obtained and some examples are provided to illustrate the main results.

Finite Element Model to Study Calcium Signalling in Oocyte Cell
Parvaiz Ahmad Naik and Kamal Raj Pardasani
 PP. 58 - 71
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ABSTRACT: Calcium dynamics in oocytes plays an important role in oocyte maturation. During fertilization in all animals investigated, fully developed eggs or meiotically immature oocytes must generate a proper change in their intracellular free calcium concentrations ([Ca2+]i) to develop normally. Eggs acquire the competence to produce this specialised calcium transient during oocyte maturation. In view of the importance of calcium signalling, a fundamental objective is to understand the mechanisms that underlie the spatiotemporal behaviour of calcium signalling. In this paper, a finite element model of cytosolic calcium signalling in oocyte cell has been developed for a one dimensional unsteady state case. The parameters such as buffers, ryanodine receptor (RyR) and Serca pump are incorporated in the model. Based on the biophysical conditions the initial and boundary conditions have been framed. The model is transformed into variational form and Ritz finite element method has been employed to obtain the solution. A program has been developed in MATLAB 7.10 for the entire problem and executed to obtain numerical results. The numerical results have been used to study the effect of buffers, RyR and Serca pump on calcium distribution in oocyte.

Study of Aleph-Function and Recurrence relations for the Aleph-Function
Altaf Ahmad, D.K.Jain, Renu Jain and Farooq Ahmad
 PP. 72 - 80
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ABSTRACT: In the present paper, the authors approach is based on the concept of Saxena used in I-function and derived number of recurrence relations for I-function. In the same manner the authors have derived certain recurrence relations of more generalized hypergeometric function named as Aleph function which are more useful and generalize in nature. Some special cases have also been discussed in the lost section of paper.

New Generalization of Fractional Kinetic Equation Using Multivariable I-Function
F. Ayant
 PP. 81 - 91
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ABSTRACT: Recently A. Choudhary et al [7] use the multivariable H-function for solving generalized fractional kinetic equation. Motivated by the recent work, we present a new generalization of fractional kinetic equation by using multivariable I-function. The new generalization can be used for the computation of the change of chemical composition in stars like the sun. The solution of the generalized fractional kinetic equation involving multivariable I-function is obtained with help of the Laplace transform method. Further, the same generalized fractional kinetic equation is solved by using the Sumudu transform method. The solution of the proposed problem is presented in a compact form in term of the multivariable I-function. Some special cases, involving the multivariable H-function, the H-function of two variables and the Fox"s H-function, are also considered.

Reliability of Random Numbers in 3-Dimensional Numerical Integration by Monte Carlo Method
Saurabh Saxena, A.K.Saxena
 PP. 92 - 104
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ABSTRACT: In today’s era Monte Carlo Method is one of the most powerful methods in the fields that relies on statistical properties of random variables and random sampling. On the basis of this method Monte Carlo Integration estimates the integrals or other quantities that can be expressed as an expectation by averaging the results of a high number of statistical trials. Role of random numbers in case of one and two dimensional Monte Carlo Integration has already been discussed with several satisfactory conclusions. Here we are proposing the same method for three dimensional numerical integration using the equispaced numbers as well as random numbers. The proposed research work deals with the test of reliability of random numbers for Numerical Integration using Monte Carlo Method in case of three dimensions. Different parameters are taken into consideration (Error propagation, Source of random numbers, Types of integral etc.) to conclude about the reliability of random numbers.