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• Open Access   Article

  On Concomitants of Upper Record Statistics and Survival Analysis for a Morgenstern Type Bivariate Transmuted Exponentiated Gumbel Distribution

  Deepshikha Deka, Bhanita Das

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.239-251, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.239251

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  Abstract
  This paper presents upper record statistics and their concomitants for a Morgenstern Type Bivariate Transmuted Exponentiated Gumbel Distribution. Survival Functions of the Concomitants of Upper Record Statistics are derived for the distribution. The numerical values of the survival functions are displayed for some selected values of the parameters.

  Key-Words / Index Term
  Record values, Concomitants, Morgenstern Family, Survival function, Numerical Study

  References
  [1] Ahsanullah, M., (1982). Characterization of the Exponential Distribution by Some Properties of the Record Values. Statist. Hefte, 23, 326-332.
  [2] Ahsanullah, M. & Kirmani, S.N.U.A., (1991). Characterization of the Exponential Distribution through a Lower Record. Comm. Statist. Theory Methods, 1293-1299.
  [3] Ahsanullah, M., (1995). Record Statistics. Nova Science, USA.
  [4] Ahsanullah, M. & Nevzorov, V.B., (2000). Some Distributions of Induced Record Values. Biometrical Journal, 42, 1069-1081.
  [5] Amini, M. & Ahmadi, J., (2005). On Moments of Concomitants of Classic Record Values and Nonparametric Upper Bounds for the Mean Under the Farlie-Gumbel-Morgenstern Model. Journal of Statistical Research of Iran, 123-125.
  [6] Arnold, B.C., Balakrishnan, N. & Nagarajah, H.N., (1998). Records. Wiley, New York.
  [7] Candler, K.N., (1952). The Distribution and Frequency of Record Values. Journal of Royal Statistical Society, Series B14, 220-228.
  [8] Chacko, M., (2007). On Concomitants of Order Statistics. Ph.D. Thesis, University of Kerala, Trivandrum, India.
  [9] Chacko, M. & Thomas, P.Y. (2008). Estimation of Parameters of Binomial Normal Distribution Using Concomitants of Records Values. Statistical Propers, 49(2), 263-275.
  [10] David, H.A. & Nagaraja, H.N. (2003). Order Statistics, Third Ed; John Wiley & Sons.
  [11] Deka, D., Das, B. & Baruah, B.H., (2017). Transmuted Exponentiated Gumbel Distribution (TEGD) and its Application to Water Quality Data. Pak.J.Stat.Oper.Res. 17(3), 115-126.
  [12] Houchens, R.L., (1984). Record value theory and inference. Ph.D. Dissertation, University of California, Riverside, California.
  [13] Kirmani, S.N.U.A. & Beg, M.I., (1984). On Characterization of Distribution by Expected Records. Sankhya, A 46(3), 463-465.
  [14] Morgenstern, D., (1956). Einfeche beispiele Zweidimensionder Venteihengen. Mitteingsblatt fu ̈r Mathematishe Statistik, 8, 234-238.
  [15] Resnick, S.I., (1987). Extreme Values, Regular Variation and Point Processes. Springer Verlag.
  [16] Thomas, P.Y. & Veena, T.G., (2011). On an Application of Concomitants of Order Statistics in Characterizing a Family of Bivariate Distributions. Comm. Stat. Theory Methods, 40, 1445-1452.
  [17] Thomas, P.Y. & Veena, T.G., (2014). Characterization of Bivariate Distributions Using Concomitants of Record Values. Metrika, 77, 947-963.
  [18] Veena, T.G. & Thomas, P.Y., (2008). Characterization of Bivariate Distributions by Properties of Concomitants of Order Statistics. Stat. Prob. Lett. 78, 3350-3354.
  

  Citation
  Deepshikha Deka, Bhanita Das, "On Concomitants of Upper Record Statistics and Survival Analysis for a Morgenstern Type Bivariate Transmuted Exponentiated Gumbel Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.239-251, 2019

• Open Access   Article

  Survival Modeling and Analysis for Time to Failures of Aircraft Glass

  J. Vijay Anto, Lilly George

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.252-257, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.252257

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  Abstract
  Assuring the reliability of components of an aircraft is very essential, as even a minor problem in the aircraft leads to major risk to the passengers. In this study, the lifetime of aircraft glass is assessed through survival modeling. The aircraft glass failure data has been taken from the National Institute of Standards and Technology (NIST), and it is assumed to follow the lifetime distributions. Kolmogorov-Smirnov test statistic clearly reveals that the empirical data is fitted with the following theoretical distributions: gamma, Weibull and lognormal. The Maximum Likelihood Estimation method is used to estimate the parameters of the theoretical distributions. With the assistance of AIC and BIC statistics, the best model has been chosen among the three distributions. Lognormal distributed empirical data has the lowest AIC and BIC statistic compared with Weibull model and gamma model. Therefore, time to failure of the aircraft glass data best fitted with the lognormal survival model. Once the best model had been identified, the reliability measures like cumulative hazard rate, reliability function and mean time to failure are estimated in the paper. The hazard rate of aircraft glass is maximum during the period of 18.83-23.83 months. The aircraft glass has a decreasing failure rate (DFR) over time. The expected lifetime of aircraft glass is 31 months based on MTTF. The total amount of risk to aircraft glass failure until 48.83 months is 65 percent.

  Key-Words / Index Term
  Lifetime distributions, KS test, AIC, BIC, cumulative hazard rate, reliability function, MTTF

  References
  [1] David J Smith, “Reliability, Maintainability and Risk”, Butterworth-Heinemann Ltd 1993 publisher, Massachusetts, pp.4-5, 1993.
  [2] R.A. Bakoban, Hanaa H. Abu-Zinadah, “The beta generalized inverted exponential distribution with real data applications” REVSTAT – Statistical Journal, Vol.15, No.1, pp.65–88, 2017.
  [3] Bianca Schroeder, Garth A. Gibson, “A large-scale study of failures in high-performance computing systems” In the Proceedings of the International Conference on Dependable Systems and Networks (DSN2006), Philadelphia, PA, USA, June 25-28, 2006.
  [4] Maydeu-Olivares, C.G. Forero, “Goodness-of-Fit Testing”, International Encyclopedia of Education, vol.7, pp. 190-196, 2010.
  [5] Khaled Haddad, Ataur Rahman, “Selection of the best fit flood frequency distribution and parameterestimation procedure: a case study for Tasmania in Australia” Springer-Verlag, Vol.25, pp.415-428, 2010.
  [6] J. G. Elerath, “AFR: problems of definition, calculation and measurement in a commercial environment” In the Proceedings of the 2000 international symposium on product quality and integrity, Los Angeles, CA, USA, pp. 71-76, 2000.
  [7] Milena Krasich, “How to Estimate and Use MTTF/MTBF Would the Real MTBF Please Stand Up?”, In the Proceedings of the 2009 Annual Reliability and Maintainability Symposium, Fort Worth, TX, USA, pp.353-359, 2009.
  [8] Dong Shang Chang, “Optimal burn-in decision for products with an unimodal failure rate function”, European Journal of Operational Research, Vol.126, Issue.3, pp.534-540, 2000.
  [9] Nezih Yigitbasi et al., “AnalysisandModelingofTime-CorrelatedFailuresinLarge-ScaleDistributed Systems”, In the Proceedings of the 2010 11th IEEE/ACM International Conference on Grid Computing, Brussels, Belgium, pp.65-72, 2010.
  [10] Akaike H, “A new look at the statistical model identification. Automatic Control 19” in IEEE Transaction on Automatic control, Vol.19, No.6, pp.716-723, 1974.
  [11] Emad A. Mohammed, Christopher Naugler, Behrouz H. Far “Emerging Business Intelligence Framework for a Clinical LaboratoryThrough Big DataAnalytics” Elsevier Publisher, pp.577-602, 2015.
  [12] Stone M, “Comments on model selection criteria of Akaike and Schwarz”, Journal of the Royal Statistical Society. Series B (Methodological), Vol.41, No.2, pp.276-278, 1979.
  [13] Michael Todinov, “Reliability and risk models: setting reliability requirements”, John Wiley & Sons publisher, pp.33-34, 2005.
  [14] Jerald F. Lawless, “Statistical models and methods for lifetime data”, A John Wiley & Sons, Inc., publication, USA, pp.9-10, 2003.
  [15] L. E. Wagner, D. Ding, “Representing aggregate size distributions as modified lognormal distributions”, American society of agricultural and biological engineers, Vol.37, No.3, pp.815-821, 1994.
  

  Citation
  J. Vijay Anto, Lilly George, "Survival Modeling and Analysis for Time to Failures of Aircraft Glass," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.252-257, 2019

• Open Access   Article

  Common Fixed Point Theorems in Complex Valued b- Metric Spaces

  Neelu Rajput, Naval Singh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.258-261, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.258261

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  Many authors prove several fixed point results for mappings satisfying certain contraction conditions. b- metric spaces in fixed point has attracted much attention in recent times. In this paper, we prove the existence and uniqueness of fixed point for two self mappings satisfying rational expressions in Complex Valued b –metric spaces. These theorems generalize many previously obtained fixed point results. An example is given to illustrate the main result.

  Key-Words / Index Term
  Fixed point theorem, Complex valued metric spaces,𝑏− metric spaces

  References
  [1] A zam A.,Fisher B.and Khan M.,“ Common fixed point theorems in complex valued metric spaces”. Numer. Funct. Anal. Optim. 32(3), 243-253 (2011)
  [2] Bakhtin I.A.“ The contraction principle in quasi metric paces”,Functional analysis,vol.30,pp. 26-37 ,1989.
  [3] Banach S.“ Sur les operations dans les ensembles abstraits ef leur application aux equations integrals”, Fundamenta mathematicae,vol. 3 ,pp. 133-181,1922.
  [4] Mukheimer A.A.,“Some common fixed point theorems in complex valued b- metric spaces ,”The scientific world journel ,vol, 2014 ,article ID 587825,6 pages ,2014.
  [5] Rao K.,Swamy and Prasad J. ,“A common fixed point theorem in complex valued b-metric spaces,”Bulletin of Mathematics and statistics Research ,vol. 1 ,no. 1.2013
  Author Profile: Neelu Rajput is a PhD scholar in pure Mathematics. Her research interests are in the areas of Functional analysis and complex analysis. She has published research papers in reputed international journals of mathematics and also presented papers in international conferences.
  

  Citation
  Neelu Rajput, Naval Singh, "Common Fixed Point Theorems in Complex Valued b- Metric Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.258-261, 2019

• Open Access   Article

  Linear estimation models by polynomial hazard functions

  S.G. Parekh, D.K. Ghosh, S.R. Patel

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.262-266, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.262266

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  The paper deals with the estimation of survival function with the use of polynomial hazard function as frailty and general baseline distribution. Considering Cox PH regression model with some frailty distribution the estimation of regressors and frailty parameter is done. Particular cases for parabolic hazard function have been considered with different base line distributions. Further with linear hypothesis of regressors and frailty parameter the linear estimation is carried out by Gauss-Marcoff model. Theory has been supported by suitable example illustrated by taking kidney infection data.

  Key-Words / Index Term
  Linear Models; Polynomial Hazard; Frailty variable; Gauss-Markov model; kidney infection

  References
  [1] Cox, D., "Regression models and life tables (with discussion)". Journal of the Royal Statistical Society,Series B, Vol.34 , pp.187-200, 1972.
  [2] Vaupel, J. S., "The impact of heterogeneity in individual frailty on the dynamics of mortality", Demography , Vol. 16, pp.439-454, 1979.
  [3] Clayton, D, "A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence," Biometrica ,Vol.65, pp.141-151, 1978.
  [4] Ibrahim, J. G., Chen, M., and Sinha, D., "Bayesian Survival Analysis", New York: Springer, 2001.
  [5] Sahu, K.S., Dey, D.K., Aslanidou, H., Sinha, D., "A Weibull regression model with Gamma frailties for multivariate survival data", Lifetime Data Analysis, Vol.3, pp.123 – 137, 1997.
  [6] Yu, B.,"Estimation of shared gamma frailty models by a modified EM algorithm" Computational Statistics and Data Analysis , Vol. 50, pp.463-474, 2006.
  [7] Santos dos, C. A. and Achcar, J. A. "A Bayesian analysis for multivariate survival data in the presence of covariates" Journal of Statistical Theory and Applications, Vol. 9, pp.233-253, 2010.
  [8] Hangal, D., "Modeling survival data using frailty models", CRC Press, 2011.
  [9] Parekh S.G. and Patel S.R., "Some Univarite Continuous Frailty Models", International Journal of Computational and Theoretical Statistics, Vol.5, Issue.1, pp.29-37, 2018a.
  [10] Parekh S.G. and Patel S.R., "On estimation of Univariate Bayesian frailty models," International Journal of Statistics and Applied Mathematics, Vol.3, Issue.2, pp.199-205, 2018b
  [11] McGilchrist, C.A., Aisbett, C.W., "Regression with frailty in survival analysis" Biometrics, Vol.47, pp.461 - 466, 1991.
  

  Citation
  S.G. Parekh, D.K. Ghosh, S.R. Patel, "Linear estimation models by polynomial hazard functions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.262-266, 2019

• Open Access   Article

  Restricted linear models and their applications

  S.G. Parekh, S.R. Patel

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.267-271, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.267271

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  Abstract
  In this paper we have considered the usual Gauss-Marcoff model with some restrictions on parameters. Usually Gauss-Marcoff model has been discussed by many authors. Further some of the applications have been applied to the real life data on kidney infection. Unified theory for both types of models has been developed.

  Key-Words / Index Term
  Linear models; Gauss-Markov model; Unified theory; kidney infection

  References
  [1] Rao, C. R., “Linear models, least squares and alternatives”, Springer, 1995.
  [2] John P. Hoffmann,“Generalized linear models and Applied Aproach”, 2004.
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  [4] Rao, C. R., “Estimation in linear models with mixed effects: A Unified theory”. Prac. Second international tam pore conference in Statistics, ed., T.pukkila and S. Puntanen, pp. 79-98, 1988
  [5] Yau, K.K.W., McGilchirst, C. A.,“Use of generalized linear mixed models for the analysis of clustered survival data”, Biometrical Journal, Vol. 39, pp.3-11, 1997.
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  [7] Cankaya S, Kayaalp GT, Sangum L, Tahtali Y, Akar M., “A Comparative study study of estimation methods for parameters in multiple linear regression model”, J.Appl Anim Res,Vol. 29, Issue.1, pp.43-47, 2006.
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  [11] McGilchrist, C.A., Aisbett, C.W., “Regression with frailty in survival analysis,” Biometrics, Vol. 47, pp.461 – 466, 1991.
  

  Citation
  S.G. Parekh, S.R. Patel, "Restricted linear models and their applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.267-271, 2019

• Open Access   Article

  Time series analysis of Rainfall data and its Geo-environmental inferences on Girja Basin, Aurangabad District of Maharashtra, India

  M.L. Dhumal, K.R. Aher

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.272-283, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.272283

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  Abstract
  An attempt has been made to find the outcomes of rainfall data analysisof groundwater system of Girja Basin, Aurangabad district of Maharashtra, India, which is one of the most important hydrometerological parameter, and which also directs the recharge event. Data analysis of rainfall records for a period of 29 years (1990 to 2018) of Girja basin and geo-environmental inferences on groundwater system have been detailed and exhibited. Mathematical investigation of rainfall data displays a variation range from 341.35 to 1362.6 mm with annual average of 649.28. The 341.35 mm rainfall occurred during 2012 and 1362.6mm rainfall occurred in 2000. Departures and Cumulative departure from the average annual rainfall have been measured. Computed values of statistical parameters indicate a positive trend of rainfall. Estimation of Standard Precipitation Index (SPI) indicates that out of last 29 years, one was extremely wet (SPI 2.0+); two were very wet (SPI 1.5 to 1.99); one moderately wet (SPI 1.0 to 1.49); 22 near normal (SPI 0.99 to -0.99); three moderately dry (SPI -1.0 to -1.49) years, one severely dry (SPI -1.5 to -1.99); and two were extremely dry (SPI-2 and less), Estimations also indicates that post 1996, both severity and occurrence of drought events has increased. Prediction of predictable rainfall trend for 5 years has been envisaged. Geo-environmental inference of rainfall trends on the recharge of groundwater system erstwhile discussed. It is suggested that the climb of rainfall on the precedence beginning need to determine the on-hand water problem by adopting creating of various groundwater recharge structures in the study area.

  Key-Words / Index Term
  Rainfall Data analysis, Standard Precipitation Index, Geo-environmental inferences, Phulambri area, Aurangabad District.

  References
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  Citation
  M.L. Dhumal, K.R. Aher, "Time series analysis of Rainfall data and its Geo-environmental inferences on Girja Basin, Aurangabad District of Maharashtra, India," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.272-283, 2019

• Open Access   Article

  A Comparison of Statistical Discriminant Analysis and Artificial Neural Network Model for the prediction of breast cancer

  R Jaisankar, D Victorseelan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.284-289, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.284289

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  Abstract
  Artificial Neural Network (ANN) is one of the widely used statistical learning techniques in machine learning and cognitive science which is inspired by biological neural networks and basically consists of several non-linear processing units, called neurons or nodes. Though Artificial Neural Network has a wide variety of applications, it can also be used for discrimination of subjects. Statistical Discriminant analysis developed by R.A. Fisher (1936) is still prevailing as a novel methodology for discrimination. This paper presents the results of an experimental comparison of Statistical Discriminant Analysis and Artificial Neural Network (ANN) for predicting the patients affected by breast cancer. Samples of 116 patient’s profiles collected from various private and government hospitals in Coimbatore, India, were used. The power of the model is measured by correct prediction rate. The study reveals that higher accuracy is provided by Neural Network analysis than Discriminant analysis in terms of prediction.

  Key-Words / Index Term
  Discriminant Analysis, Machine learning, Artificial Neural Networks, Back propagation algorithm, Training and testing.

  References
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  [10] Gardner, M.W. and Dorling, S.R. “Artificial Neural Network (Multilayer Perception)- A review of applications in atmospheric sciences”, Atmospheric Environment, 32, pp.2627-2636, 1998.
  [11] Hsieh, W.W, and Tang.T.“Applying Neural Network Models to prediction and Data Analysis in Meteorology and Oceanography”, Bulletin of the American Meteorological Society,79, pp.1855-1869,1998.
  [12] Nukala V V Pravallika1and P Suresh Varma, “Prediction of Heart Disease Using Machine Learning Algorithms”, International Journal of Computer Sciences and Engineering, Vol.-7, Issue-3, March 2019.
  

  Citation
  R Jaisankar, D Victorseelan, "A Comparison of Statistical Discriminant Analysis and Artificial Neural Network Model for the prediction of breast cancer," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.284-289, 2019

• Open Access   Article

  Some Improved Exponential Ratio Type Estimators in Presence of Auxiliary Attributes

  B. Mahanty, G. Mishra

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.290-294, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.290294

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  Abstract
  In this paper some improved exponential ratio type estimators of finite population mean have been suggested in presence of auxiliary attributes. For construction of estimator for population mean, we have used the technique of using a priori and a posteriori information on coefficient of variation and auxiliary attributes .The efficiencies of these estimators are compared with the existing estimators and among themselves with regard to biases and mean square errors both theoretically and numerically.

  Key-Words / Index Term
  Auxiliary attributes, Population proportion, Simple random sampling, Exponential ratio type estimators, Bias, Mean square error, Percent relative bias, Efficiency

  References
  [1] Cochran,.W.G., “Sampling Techniques”,. New York,. 3rd Edition John Wiley and Sons, 1977
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  [5] Shabbir, J. and Gupta, S. “Estimation of the finite population mean in two phases sampling when auxiliary variables are attributes”, Hacett. J. Math. Stat., 39(1), p. 121-129., 2010.
  [6] Singh, H. P. and Vishwakarma, K.” Modified exponential ratio and product estimators for finite population mean in Double sampling”, Austral. J. Statist., 36, p. 217-225, 2007.
  [7] Koyuncu, N. “Efficient estimators of population mean using auxiliary attributes”, Appl. Math. Comp. `218, p. 10900-10905, 2012.
  [8] Singh, H. P. and Solanki, R. S. “Improved estimation of population mean in simple random sampling using information on auxiliary attribute”, Appl. Math. Comp., 218, p. 7798-7812, 2012.
  [9] Malik, S. and Singh, R. “An improved estimator using two auxiliary attributes”, Applied Mathematics and Computation, 219, p. 10983-10986., 2013.
  [10] Sinha, R. R. and Kumar, V. “Improved estimators for population mean using attributes and auxiliary characters under incomplete information”, Int. J. of math. And Stat., 14, p. 43-54, 2013.
  [11] Sinha, R. R. and Kumar, V. “Improved classes of estimators for population mean using information on auxiliary character under double sampling the non-respondents”, Nat. Acad. Sci. Lett., 37(1), p. 71-79, 2014.
  [12] Sharma, P. and Verma, H.K., Sanaullah, A., Singh, R: “Some Exponential Ratio –Product Type Estimators using Information on Auxiliary Attributes under Second Order Approximation”, Int. Jour. Stat. and Econ, 12(3), p. 58-66, 2013.
  [13] Khare, B. B., Jha, P. S. and Khare, S. “Estimation of population proportion using two phase sampling scheme in the presence of non-response”, International Journal of Applied Mathematics & Statistical Sciences (IJAMSS)., Vol. 6,Issue 1,19-32, Dec – Jan 2017.
  [14] Searls D. T.: “The utilization of known coefficient of variation in the estimation procedure”, Journal of American Statistical Association, 59, 1125-1226, 1964.
  [15] Bahl, S. and Tuteja, R.K.:” Ratio and Product type exponential estimator, Information and Optimization sciences”, Vol. XII, I, p. 159-163, 1991.
  [16] Upadhyaya, L.N. and Srivastava, S.R., “A note on the use of coefficient of variation in estimating mean,” Jour. Ind. Soc. Agri. Statist., 28(2), p. 97‐99. 1976(a).
  [17] L. N. Upadhyaya and S. R. Srivastava,: “An efficient estimator of mean when population variance is known,” Jour. Ind. Soc. Agrl. Stat., vol. 28(1),, pp. 9-10,. 1976 (b).
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  Citation
  B. Mahanty, G. Mishra, "Some Improved Exponential Ratio Type Estimators in Presence of Auxiliary Attributes," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.290-294, 2019

• Open Access   Article

  Numerical analysis of Non-Darcy MHD flow of a Carreau fluid over an exponentially stretching/shrinking Sheet in a porous Medium

  Bhim Sen Kala, Madan Singh Rawat, Nimisha Rawat, Ajay Kumar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.295-303, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.295303

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  Abstract
  In this paper, we have analysed numerically the non-Darcy MHD flow of a Carreau fluid over an exponentially stretching/shrinking sheet in a non- Darcy porous medium. In the mathematical model, using similarity variables, the momentum equation is transformed to non-dimensional ordinary differential equation . And then it is solved numerically using the MATLAB in-built numerical solver bvp4c-programm. A discussion for the effects of the parameters involved on the boundary layer thickness and the magnitude of the velocity and skin friction has been done graphically and numerically using figures and tables.

  Key-Words / Index Term
  Magnetic field, Porous medium, Exponentially stretching sheet, Carreau fluid. Mathematics Subject Classification: 35A22, 35A35, 35A99, 35G20, 35G30

  References
  [1] Lawrence J Crane, ‘‘Flow Past a Stretching Plate’’, Kurze Mitteilungen , Brief Report- Communications breves, Vol.21,1970.
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  [4] H.L.Andersson, ‘‘Note: MHD flow of a viscoelastic fluid past a stretching surface’’, Acta Mechanica 95,227-230 (1992).
  [5] B.S.Dandapat,L.E.Holmedal, and H.L.Andersson, ‘‘Note: on the stability of MHD flow of a viscoelastic fluid past a stretching sheet’’, Acta Mechanica 130,143-146, (1998).
  [6] Tiegang Fang, Fang Guo, Chia-fon F. Lee. ‘‘A note on the extended Blasius equation’’, Applied Mathematics Letters 19 , 613–617,(2006).
  [7] Anuar Ishak, Roslinda Nazar_ and Ioan Pop, ‘‘Falkner-Skan equation for flow past a moving wedge with suction or injection’’, J. Appl. Math. & Computing Vol. 25, No. 1 - 2, pp. 67 – 83,(2007).
  [8] Ch. Mamaloukas, S. Spartalis, Z. Manussaridis, ‘‘Similarity Approach to the Problem of Second Grade Fluid Flows over a Stretching Sheet’’, Applied Mathematical Sciences, Vol. 1, no. 7, 327 – 338, (2007).
  [9] Rafael Cortell Bataller , ‘‘Numerical Comparisons of Blasius and Sakiadis Flows’’ ,Matematika, Volume 26, Number 2, 187-196, (2010).
  [10] S. S. Motsa, T. Hayat, O. M. Aldossary, ‘‘MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method’’, Appl. Math. Mech. -Engl. Ed., 33(8), 975–990 (2012). DOI 10.1007/s10483-012-1599-x
  [11] S. Nadeem, Rizwan Ul Haq, C. Lee, ‘‘Research note: MHD flow of a Casson fluid over an exponentially shrinking sheet’’ , Scientia Iranica B 19 (6), 1550–1553,(2012).
  [12] Sandile Sydney Motsa , Precious Sibanda, “On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi-analytical technique’’, Article in International Journal for Numerical Methods in Fluids • April 2012, DOI: 10.1002/fld.2541.
  [13] A. Rosca, ‘‘MHD boundary-layer flow over a permeable shrinking surface’’, Acta Universitatis Apulensis ,No. 36, pp. 31-38, ( 2013). ISSN: 1582-5329.
  [14] S. Nadeem, S. T. Hussain and Changhoon Lee, ‘‘Flow of a williamson fluid over a stretching sheet’’, Brazilian Journal of Chemical Engineering, Vol. 30, No. 03, pp. 619 - 625, (2013).
  [15] Swati Mukhopadhyay, ‘‘MHD boundary layer slip flow along a stretching cylinder’’, Ain Shams Engineering Journal 4, 317–324, (2013).
  [16] N.S. Akbar, S. Nadeem, Rizwan Ul Haq , Ye .Shiwei, ‘‘MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions’’, Ain Shams Engineering Journal 5, 1233–1239, (2014).
  [17] Khidir Ahmed , ‘‘A note on the solution of general Falkner-Skan problem by two novel semi-analytical techniques’’, Propulsion and Power Research;4(4):212–220,(2015).
  [18] N.S. Akbar, S. Nadeem, ‘‘Combined effects of heat and chemical reactions on the peristaltic flow of Carreau fluid model in a diverging tube’’, Int J Numer Methods Fluid;67:1818–32,(2011).
  [19] Sumit Kushwaha, Rabindra Kumar Singh ,‘’Study and Analysis of Various Image Enhancement Method using MATLAB ‘’, International Journal of Computer Sciences and Engineering Vol.-3(1), PP(15-20) Jan 2015.
  [20] S.P. Dahake and A.V.Dubewar , ‘’Effects of Radiation on Magnetohydrodynamic Convection Flow past an Impulsively Started Vertical Plate Submersed in a Porous Medium with Suction’’, International Journal of Computer Sciences and Engineering Vol.-5(2), Feb 2017.
  [21] E.O Anyanwu, D. Raymond , C.E Okorie , F.E James , E.O Ogbaji ,’’Slip Boundary Condition Effects on the Rate of Heat Transfer in A Micro channel Including Viscous Dissipation’’ ,International Journal of Scientific Research in Mathematical and Statistical Sciences,Volume-5, Issue-4, pp.09-21, August (2018).
  
  

  Citation
  Bhim Sen Kala, Madan Singh Rawat, Nimisha Rawat, Ajay Kumar, "Numerical analysis of Non-Darcy MHD flow of a Carreau fluid over an exponentially stretching/shrinking Sheet in a porous Medium," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.295-303, 2019

• Open Access   Article

  A Study on the Kudumbashree Self Help Group(SHG) and the Pradhan Manthiri Awas Yojana(PMAY)

  Haridoss Venugopal, Reshma George, Sharukkhan Mubarrak

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.304-309, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.304309

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  Abstract
  “Kudumbashree” is a word in Malayalam which means prosperity of the family. One of the role was played by the Self Help Groups (SHG’s). In Kerala Kudumbashree programme was implemented by the Government of Kerala primarily for eradication of Poverty and empowerment of women. The slogan of the mission is “Reaching out to families through women and reaching out to community through family”. Kudumabashree has now become the benchmark for all other Self Help Groups (SHG’s). This paper focuses on the effectiveness of Kudumbashree for the implementation of the housing scheme Pradhan Manthri Awas Yojana (PMAY) in Kerala. A comparative study is made between the housing schemes Pradhan Manthri Awas Yojana (PMAY) and Livelihood Inclusion and Financial Empowerment (LIFE). Through this paper we have analysed the impact of the recent floods that hit Kerala in 2018 and the destruction caused to the houses constructed through PMAY and non-PMAY.

  Key-Words / Index Term
  Kudumbashree, Pradhan Manthri Awas Yojana, Livelihood Inclusion and Financial Empowerme, Cluster Ananlysis and Hotelling’s T-square statistic

  References
  [1] C.Saravana Selvi and Dr.K.S.Pushpa, “Sustainability of Women Empowerment through Kudumbashree”, International Journal of Research-Granthaalayah, Vol.5,Issue.12,pp.155-163, 2017.
  [2] Mercy Varghese, “Women Empowerment through Kudumbashree”, Mahatma Gandhi University, Ref.No.Ac>AII/3/851/COM/JULY/2004.
  [3] R.Reshmi, “Role of Kudumbashree Micro Enterprises in alleviation of poverty with special References to their Marketing Strategies”, International Journal of Social Science & Interdisciplinary Research, Vol.1,Issue.12,pp.173-187, 2012.
  [4] M.B.Krishna, B.Keerthi and A.Saisree, “Impact of Kudumbashree on Financial Inclusion with special reference to Alappuzha District”, International Research Journal of Management Sociology & Humanity, Vol.8,Issue.11,pp.72-81, 2017.
  [5] Pragabhal Das K.V (2017) “Financial Inclusion through Kudumbashree”
  [6] C.Saravana Selvi and Dr.K.S.Pushpa, “Kudumbashree –A Keystone for Economic Empowerment of Women”, Intercontinental Journal of Human Resource Research Review, Vol.4,Issue.3,pp.118-126, 2016.
  [7] Ansa Salim and M.M.Sulfy, “Kudumbashree Story :Critique on Kudumbashree”, International Journal of Scientific Research and Management,Vol.3, Issue.8,pp.3469-3473, 2015.
  [8] Raji,K.Paul, Dr.T.Sudha and Dr.Giji Elias ,“ A Study on the Role of Extension Education On Kudumbashree activities”, International Journal of Recent Research and Applied Studies,Vol.4,Issue.4,pp.28-33, 2017.
  [9] Meenakshi Malhotra (2004) “ Empowerment of women”(in 3 volumes)
  [10] Ashraf, Karlin and Yin (2006) “ Household decision making and Savings Impact”, Economic Growth Center Yale University,pp.1-18, 2006
  [11] K.V Varghese (1987) “Housing Problem in India :Economic and Social Aspects”
  [12] K.P Bhattacharya (1998) “Affordable Housing and Infrastructure in India”
  [13] A.K.Lal, “Hand Book of Low Cost Housing”, New Age International ,New Delhi ,pp.1-172,1995
  [14] N.Sundaram & M.Sriram , “Financial Inclusion in India: A Review”, International Journal of Applied Engineering Research, Vol.11,Issue.3,pp.1575-1578, 2016.
  

  Citation
  Haridoss Venugopal, Reshma George, Sharukkhan Mubarrak, "A Study on the Kudumbashree Self Help Group(SHG) and the Pradhan Manthiri Awas Yojana(PMAY)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.304-309, 2019