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• Open Access   Article

  Influence of Vertical Magnetic Field on the Onset of Rayleigh-Benard-Marangoni Convection in Superposed fluid and Porous Layers with Deformable Free Surface

  Ananda, K, Gangadharaiah, Y.H.

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.1-18, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.118

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  Abstract
  When a thin horizontal fluid layer overlying a porous layer is heated from below, convection starts after that the temperature difference between the lower and upper surfaces has reached a critical value. Two effects are responsible for this motion: buoyancy and variation of the surface tension with temperature; the first effect is usually referred to as Rayleigh-Benard instability, the second as Marangoni instability. In the present work, we examine the role of the application of a vertical magnetic field on a thin horizontal electrically conducting fluid layer overlying a porous layer. An analytical solution is obtained for constant-flux thermal boundary conditions, for which the onset of supercritical cellular convection occurs at a vanishingly small wave number and can thus be predicted by the present theory. The critical Rayleigh number, , and critical Marangoni number, , are found to depend on the Chandrasekhar number, ,the depth ratio, , the Darcy number, , the Bond number, , and the Crispation number, Results are presented for a wide range of each of the governing parameters. The results are compared with limiting cases of the problem and are found to be in agreement.

  Key-Words / Index Term
  Bernard-Marangoni convection; Magnetic field; Two-layer System

  References
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  Citation
  Ananda, K, Gangadharaiah, Y.H., "Influence of Vertical Magnetic Field on the Onset of Rayleigh-Benard-Marangoni Convection in Superposed fluid and Porous Layers with Deformable Free Surface," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.1-18, 2018

• Open Access   Article

  Designing of Modified Tightened 3 Levels Continuous Sampling Plan Indexed through Maximum Allowable Average Outgoing Quality

  V. Nirmala and K.K. Suresh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.19-24, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.1924

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  Abstract
  The principal objective of this paper is to propose a novel determination of the quality measures for maximum allowable average outgoing quality in final products in manufacturing industries. In this paper presents a procedure for designing continuous sampling plan - MLP-T-3 indexed through maximum allowable average outgoing quality (MAAOQ). Tables and procedures are also provided for the selection of the parameters for the plan with specified Average outgoing quality level (AOQL), Maximum allowable percent defective (MAPD), MAAOQ and operating ratio. Numerical illustrations are also provided for the shop floor applications of this plan. MAAOQ indexed plan provides a method for designing sampling plan based on quality, instead of AOQL description in operating characteristic (OC) curve about quality.

  Key-Words / Index Term
  Skip-lot sampling plan, Quality Region, Final Product, Quality, Manufacturing Industries

  References
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  Citation
  V. Nirmala and K.K. Suresh, "Designing of Modified Tightened 3 Levels Continuous Sampling Plan Indexed through Maximum Allowable Average Outgoing Quality," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.19-24, 2018

• Open Access   Article

  Transmuted Generalized Uniform Distribution

  C. Subramanian and A.A. Rather

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.25-32, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.2532

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  Abstract
  In this paper we have introduced a new probability model called as transmuted generalized Uniform distribution (TGUD) by using the quadratic rank transmutation map studied by Shaw and Buckley (2007). The moments, survival function, failure rate and reverse hazard rate of the distribution have been derived. The parameters have been estimated by the maximum likelihood method. Also we have obtained the pdf of rth, 1st and nth order statistics.

  Key-Words / Index Term
  Transmuted generalized Uniform distribution, Moments, Reliability analysis, Parameter estimation, Order statistics

  References
  [1] Afify, A.Z., Nofal, Z.M. and Yousuf, H.M. (2015). The transmuted weibull Lomax distribution: properties and applications. Pak.J.Stat.Oper.res., 11, 135-152.
  [2] Aryal, G. R. and Tsokos, C. P. (2009). On the transmuted extreme value distribution with applications. Nonlinear Analysis, 71, 1401–1407.
  [3] Bhatt, M. B. (2014), Characterization of Generalized Uniform Distribution through Expectation.Open Journal of Statistics, 4, 563-569.
  [4] Deepshikha Deka, Bhanita Das and Bhupen K. Baruah (2017),“Transmuted Exponentiated Gumbel Distribution and its applications to water quality data”, Pak.J.Stat.Oper.res., 13 (1), pp. 115-126.
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  [8] Rather, A. A., Subramanian, C., Shafi, S., Malik, K. A., Ahmad, P. J., Para, B. A., and Jan, T. R. (2018), "A new Size Biased Distribution with applications in Engineering and Medical Science", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.75-85.
  [9] Shaw, W. T. and Buckley, I. R. C. (2007). The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. UCL Discovery Repository, pages 1–16.
  

  Citation
  C. Subramanian and A.A. Rather, "Transmuted Generalized Uniform Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.25-32, 2018

• Open Access   Article

  On the General Product-connectivity Index of Transformation Graphs

  B. Basavanagoud and C.S. Gali

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.33-40, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.3340

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  Abstract
  The general product-connectivity index is a molecular structure descriptor of a molecular graph, which generalizes both Randi index and second Zagreb index. In this paper, we obtain general product-connectivity index of subdivision graph, partial complement of subdivision graph, semitotal-point graph, semitotal-line graph and total graph. Also bounds for general product-connectivity index of some transformation graphs.

  Key-Words / Index Term
  General product-connectivity index, Semitotal-point graph, Semitotal-line graph, Total transformation graphs, First and second Zagreb indices

  References
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  Citation
  B. Basavanagoud and C.S. Gali , "On the General Product-connectivity Index of Transformation Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.33-40, 2018

• Open Access   Article

  Effects of Temperature dependent viscosity on Penetrative Convection in a Fluid Layer Bounded by Slabs of Finite Thermal Conductivity and Finite Thickness

  Gangadharaiah Y.H., Ananda K.

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.41-50, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.4150

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  Abstract
  The onset of penetrative convection in a variable-viscosity flow bounded by slabs of finite thermal conductivity and finite thickness has been investigated by means of linear stability analysis. The relationship between the viscosity and the temperature is assumed of exponential type. The asymptotic solutions of the long wavelength, for small values of the conductivity and thickness of the solid, are achieved. The values of critical Rayleigh numbers for different values of thermal conductivity ratio and viscosity parameters and, consequently the critical Rayleigh numbers at which the onset of convection starts, are computed analytically. The effects of various parameters (namely, viscosity parameter, thermal conductivity ratio , depth ratio and the presence of internal heat source strength on the onset of stationary convection) are computed analytically and depicted graphically. It is observed that both stabilizing and destabilizing factors can be enhanced because of the presence of a heat source, thermal conductivity ratio, depth ratio, and variable viscosity .As a result, it is possible so that to postpone (or advance) significantly the onset of motion.

  Key-Words / Index Term
  variable viscosity: internal heat source: thermal conductivity: Stability

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  Citation
  Gangadharaiah Y.H., Ananda K., "Effects of Temperature dependent viscosity on Penetrative Convection in a Fluid Layer Bounded by Slabs of Finite Thermal Conductivity and Finite Thickness," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.41-50, 2018

• Open Access   Article

  South Indian River Ranking using Fuzzy Analytic Hierarchy Process

  A. Rajkumar, M.Chandramohan

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.51-59, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.5159

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  Abstract
  Nowadays, water resource management should be managed in integrated manner including water quality, water quantity, land use and economy, especially when we wanted to find the highest potential river to be developed for efficient use of water systems. Water resources planning and management should consider various aspects of river basins. Current river ranking techniques namely, water quality index, and national water quality standard were found to only consider water quality aspects. In this study a special focus is given on the method that deals with vague data which the decision making accounted during data acquisition. The river ranking problem is a strategic issue and has significant impact on the efficiency of a river system. On the other hand, the river ranking among many alternatives presents a multi-criteria decision Making (MCDM) problem. Hence, fuzzy set theory can be applied. Fuzzy Analytic Hierarchy Process (FAHP) technique is used to rank alternatives to find the efficient use of the river system. Fuzzy number and linguistic variable are used to in-currently vague data. Four criteria and twenty sub criteria and identify, tested and applied to real data. The FAHP is used to analyze the structure of the river ranking problem. A real world application is conducted to illustrate the utilization of the model using the valuable data pertaining to a six south Indian rivers. The application can interpreted as demonstrating the effectiveness and feasibility of the FHAP model.

  Key-Words / Index Term
  FAHP, MCDM, WQI, Triangular fuzzy Number

  References
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  Citation
  A. Rajkumar, M.Chandramohan, "South Indian River Ranking using Fuzzy Analytic Hierarchy Process," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.51-59, 2018

• Open Access   Article

  A Bivariate Binomial Distribution

  S. R. Supanekar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.60-64, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.6064

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  Abstract
  In this paper, we introduce a bivariate binomial distribution that allows positive, zero or negative correlation between two variables which depends on multiplicative factor parameter. The marginal distributions of the bivariate binomial distribution are the univariate binomial distributions. Moment estimators and maximum likelihood estimators of parameters involved in this distribution are discussed. Sample observations are simulated from bivariate binomial distribution using the conditional distribution technique and test of the goodness of fit is carried out.

  Key-Words / Index Term
  Bivariate binomial distribution; Maximum likelihood estimation; Test of the goonness of fit

  References
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  Citation
  S. R. Supanekar, "A Bivariate Binomial Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.60-64, 2018

• Open Access   Article

  Empirical Robust Multivariate Regression Parameter Estimation Using Median Approach

  O.K Sajana, T.A Sajesh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.65-71, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.6571

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  Abstract
  Main purpose of multivariate regression analysis is the estimation of model parameters. The use of maximum likelihood method would not be appropriate in estimation problems while data contains outlier or extreme observations. So it is necessary to find a parameter estimation method in which the value of the estimator is not much affected by small changes in the data. This paper introduces robust method for multivariate regression based on robust estimation of location and scatter matrix of predictor and response variables. In this paper Comedian method is taken as a robust estimator of location and scatter. Based on the simulations, the finite-sample efficiency and robustness of the estimator are investigated. Efficiency of proposed robust estimators is compared with maximum likelihood estimator, minimum covariance determinant estimator and orthogonalized Gnanadesikan-Kettenring estimator in terms of mean squared errors. Proposed estimator combines high robustness and high efficiency in estimation. The proposed method is illustrated on a real data set.

  Key-Words / Index Term
  Multivariate Regression, Outliers Detection, Comedian Approach, Finite Sample Efficiency

  References
  [1]. V. Barnett, T. Lewis, “Outliers in Statistical Data”, 3rd ed. Chichester, John Wiley & Sons, pp. 27-52, 1994.
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  Citation
  O.K Sajana, T.A Sajesh, "Empirical Robust Multivariate Regression Parameter Estimation Using Median Approach," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.65-71, 2018

• Open Access   Article

  Characterization and Estimation of Length Biased Weighted Generalized Uniform Distribution

  A. A. Rather and C. Subramanian

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.72-76, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.7276

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  Abstract
  In this paper, we proposed a new probability model called as the length biased weighted generalized uniform distribution (LBWGUD) and discussed its various statistical properties. The probability density function, moments, hazard rate function, reverse hazard rate function and survival function have been derived. The maximum likelihood method has been used to estimate the parameter and their asymptotics have been discussed.

  Key-Words / Index Term
  Weighted distribution, Moments, Reliability Analysis, Order Statistics, Maximum Likelihood Estimation, Fisher’s information matrix

  References
  [1] Bhatt, M. B. (2014), Characterization of Generalized Uniform Distribution through Expectation.Open Journal of Statistics, 4, 563-569.
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  Citation
  A. A. Rather and C. Subramanian, "Characterization and Estimation of Length Biased Weighted Generalized Uniform Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.72-76, 2018

• Open Access   Article

  About Edge Independent Sets in Hypergraphs

  D. K. Thakkar and V. R. Dave

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.77-81, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.7781

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  Abstract
  In this paper we have introduced maximum edge independent sets in hypergraphs where a maximum edge independent set is an edge independent set with maximum cardinality. We have proved that the edge independence number of a hypergraph (with minimum edge degree at least two) remain same or decreases when an edge is removed from the hypergraph. In particular we have proved that the edge independence number of a hypergraph (with minimum edge degree at least two and edge independence number is greater than one) decreases if and only if there is a maximum edge independent set which contains the edge. We have also considered the edge independence numbers of the subhypergraph and the partial subhypergraph obtained by removing a vertex from the hypergraph. We observe that edge independence number of the finite projective plane always increases when any vertex is removed from the hypergraph and the subhypergraph is considered and the edge independence number remains same when any vertex is removed and the partial subhypergraph is considered.

  Key-Words / Index Term
  Hypergraph, Edge Independent Set, Maximal Edge Independent Set, Maximum Edge Independent Sets, Edge Independence Number, Subhypergraphs, Partial Subhypergraphs

  References
  [1] Acharya B., Domination in Hypergraphs, AKCE J. Graphs. Combin., 4, NO. 2,pp.111 – 126, 2007
  [2] Behr A., Camarinopoulos L., On the domination of hypergraphs by their edges, Discrete Mathematics,187,pp.31 – 38, 1998.
  [3] Berge C.,Graphs and Hypergraphs, North-Holland, Amsterdam ,1973.
  [4] Berge C., Hypergraphs, North – Holland Mathematical Library, New York, Volume – 45, 1989
  [5] Haynes T., Hedetniemi S. and Slater P., Domination in Graphs Advanced Topics, Marcel Dekker, Inc., New York, 1998.
  [6] Haynes T., Hedetniemi S. and Slater P., Fundamental of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.
  [7] Thakkar D.and Dave V., Edge Domination in Hypergraph, International Journal of Mathematics & Statistics Invention. Volume 5, Issue 9,pp. 13-17, 2017
  [8] Thakkar D.and Dave V., More about Edge Domination in Hypergraph, International Journal of Statistics and Applied Mathematics Volume 3, Issue 5,pp.01-06,2018.
  [9] Thakkar D.and Dave V., Regarding Edge Domination in Hypergraph, International Journal of Mathematics Trends & Technology, Volume 44, NO. 3,pp.108 – 114, 2017
  [10] Thakkar D.and Dave V., Edge Stable Sets & Edge Independent Sets in Hypergraphs, Journal of Mathematics and Informatics,Volume 12,pp 33-39, 2018.
  

  Citation
  D. K. Thakkar and V. R. Dave, "About Edge Independent Sets in Hypergraphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.77-81, 2018