Volume-6 , Issue-1 , Feb 2019, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Analysis of a Three Unit System with Demand Dependent Operability of Units

  Rachna Khurana, A.K.lal, S.S. Bhatia, R.K.Tuteja, Shakuntla

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.1-24, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.124

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  Abstract
  In this paper we develop a stochastic model for a three dissimilar unit standby system wherein the units may be made operative depending upon the load/demand. The system under consideration is assumed to have two shifts of working and the whole system undergoes for scheduled preventive/corrective maintenance before starting the second shift. Mathematical formulation of the problem determining the transition probabilities of various states is developed considering two types of failure for each unit (Type -I which has no standby and the Type – II which has standby). Various reliability metrics such as mean time to system failure (MTSF), availability, busy period and profit have been discussed for measuring the system effectiveness by using semi-Markov process and regenerative point technique. Graphical study of the behavior of MTSF, availability and profit analysis has also been done.

  Key-Words / Index Term
  Availability, Busy Period, MTSF, Regenerative point technique, Semi-Markov Process

  References
  [1]. Attahiru Sule Alfa W.L. and Zhao, Y.Q, “Stochastic Analysis of A Repairable System With Three Units And Repair Facilities”, Microelectron Reliability, 38(4), pp. 585-595, 1998.
  [2]. Gupta, P.,Lal, A. K., Sharma R. K. and Singh, J., “Numerical Analysis of Reliability And Availability of The Serial Processes in Butter Oil Processing Plant”, International Journal of Quality and Reliability Management, Vol. 22(3), pp. 303-316, 2005.
  [3]. Gupta, R., Chaudhary, A. and Goel, R., “Profit Analysis of A Two Unit Priority Standby System Subject To Degradation And Random Shocks”, Microelectronic and Reliability, Vol. 33 (80), pp. 1073-1080, 1993.
  [4]. Malhotra Reetu and Taneja Gulshan, “Reliability and Availability Analysis of A Single Unit System With Varying Demand”, Mathematical Journal of Interdisciplinary Sciences, 2(1), pp. 77-88, 2013.
  [5]. Malhotra Reetu and Taneja Gulshan, “Cost-Benefit Analysis of A Single Unit System With Scheduled Maintenance And Variation in Demand”, Journal of Mathematics and Statistics, Vol. 9(3), pp. 155–160, 2013.
  [6]. Minocha Amit, “Profit Evaluation of Some Reliability Models For Technological System”, Ph.D Thesis, National Instiute of Technology Kurukshetra, 2007.
  [7]. Nakagawa, T., “Optimum Preventive Maintenance Policies for Repairable Systems”, IEEE Transactions on Reliability”, Vol.R-26(3), pp. 168-173, 1977.
  [8]. Parashar, B. and Bhardwaj, N., “A Comparative Study of Profit Analysis of Two Reliability Models on A Two Unit PLC System”, International Journal of Scientific and Engineering Research, Vol 4(4), pp. 400-409, 2013.
  [9]. Sarhan, A.M., “Analysis of Incomplete, Censored Data in Competing Risks Models With Generalized Exponential Distributions”, IEEE Transactions. on Reliability, Vol. 56(1), pp. 132-139, 2007.
  [10]. Taneja, G. Nanda, J. and Sharma, H.R. “Profit Evaluation of A System Wherein Instructions Imply Perfect Repai”r, Pure and Applied Mathematika Sciences, Vol. 60 (1-2), pp. 37-54, 2004.
  [11]. Tuteja, R.K. and Taneja, Gulshan “Proper Utilization of A System With Two Identical Repairmen’’, International Journal of Management and Systems”, Vol. 7, pp. 273-281, 1991.
  [12]. Yusuf, I., “Comparative Analysis of Profit Between Three Dissimilar Repairable Redundant Systems Using Supporting External Device for Operation”, Journal of Industrial Engineering International, Vol 10, pp. 199-207, 2014.
  [13]. Praveen Gupta and Pooja Vinodiya, “ Analysis of Reliability of a Two Non Identical Units Cold Standby Repairable System Has Two Types of Failures”, International Journal of Computer Science and Engineering, Vol. 6(11), pp. 907-913, 2018.
  

  Citation
  Rachna Khurana, A.K.lal, S.S. Bhatia, R.K.Tuteja, Shakuntla, "Analysis of a Three Unit System with Demand Dependent Operability of Units," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.1-24, 2019

• Open Access   Article

  A New Generalization of Pranav Distribution Using Weighting Technique

  Anwar Hassan, Mohd Altaf Dar, Peer Bilal Ahmad, Bilal Ahmad Para

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.25-32, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.2532

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  In this paper, we introduce a new generalization of Pranav distribution called as Weighted Pranav Distribution (WPD). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Finally, an application to real data set is presented to examine the model performance.

  Key-Words / Index Term
  Pranav Distribution, Weighting Technique, Structural Properties and Maximum Likelihood Estimation

  References
  [1]. Akaike, H. (1976). A new look at the statistical model identification. IEEE Trans. Autom.Control , 19 , 716–723.
  [2]. Ayesha, A. (2017). Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution. Applied Mathematics, 08(06), 808-819.
  [3]. Fisher, R.A. (1934). The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics, 6, 13-25.
  [4]. Hassan, A., Dar, S. A., & Para, B. A. (2018), On three Parameter Weighted Quasi Akash Distribution: Properties and Applications, IOSR Journal of Engineering (IOSRJEN), 08(11), 01-10.
  [5]. Hassan, A., Wani, S.A., & Para, B. A. (2018). On three Parameter Weighted Quasi Lindley Distribution: Properties and Applications, International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(5), pp. 210-224 DOI: https://doi.org/10.26438/ijsrmss/v5i5.210224.
  [6]. Hinkley, D. On quick choice of power transformation. Applied Statistics, 67-69 (1977).
  [7]. Jing (2010) Weighted Inverse Weibull and Beta-Inverse Weibull Distribution, Georgia Southern University Digital Commons@Georgia Southern.
  [8]. Para, B.A., & Jan, T. R. (2018). On three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences. Applied Mathematics and Information Sciences Letters, 6 (1), 13-26.
  [9]. Rao, C.R (1965). On discrete distributions arising out of method of ascertainment, in classical and Contagious Discrete, G.P. Patil .ed ;Pergamon Press and Statistical publishing Society, Calcutta, pp-320-332.
  [10]. Schwarz, G. (1987). Estimating the dimension of a model. Ann. Stat., 5, 461–464.
  [11]. Shanker, R., & Shukla, K. K. (2018). A Generalized Size-Biased Poisson-Lindley Distribution and Its Applications to Model Size Distribution of Freely-Forming Small Group. Journal of Scientific Research, 10(2), 145-158.
  

  Citation
  Anwar Hassan, Mohd Altaf Dar, Peer Bilal Ahmad, Bilal Ahmad Para, "A New Generalization of Pranav Distribution Using Weighting Technique," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.25-32, 2019

• Open Access   Article

  Exploring the Effect of Varying Volatility in the Black-Scholes Option Pricing Model

  V. A. Vaghela, R. M. Gor

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.33-40, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.3340

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  Abstract
  Derivatives trading are a core part of the Stock Market in the current era. Trading volumes in stock options have grown up tremendously during recent years. Black-Scholes is a pricing model used to determine the fair price or theoretical value for a European call or a put option. The objective of this paper is to price the derivatives by incorporating volatility which is assumed to be constant in the Black-Scholes model. We observe through a case study that we can price the options better by change in volatility due to change in stock price.

  Key-Words / Index Term
  Black-Scholes model, European call &put option, volatility

  References
  [1] K. Sasidharan, A. K. Mathews. “Option Treading Bear Market Strategies”, Tata McGraw Hill Education Private Ltd, New Dehli, India, 2010.
  [2] J.C.Hull, “Options, Future, and Other Derivatives”, New Jersey, Prentice Hal, USA, 1999.
  [3] F.Black, M. Scholes, “The Pricing of Options and Corporate Liabilities”. Journal of Political Economy, Vol.81, Issue.3, pp.637-654, 1973.
  [4] R. Merton, “Theory of Rational Option Pricing”, Bell Journal of Economics and Management Science Vol.4, Issue.1, pp.141-183, 1973.
  [5] R. C. Blattberg, J.Gonedes, “A comparison of the stable and student distributions as statistical models for stock prices”, Journal of business, Vol.47, Issue.2, pp.244-280, 1974.
  [6] F. Black, “Fact of fantasy in the use of options”. Financial analysis journal, Vol.31, Issue. 4, pp. 36-41, 61-72, 1976.
  [7] J. D.MacBeth, L. J. Merville, “Tests of the Black-Scholes and Cox call option valuation models”, Journal of finance, Vol.35, Issue.2, pp.285-301, 1980.
  [8] S. Beckers, “The constant elasticity of variance model and its implications for option pricing”, Journal of finance, Vol.35, Issue.3, pp.661-673, 1980.
  [9] A.Frino, E. Khan, S.Lodh, “The Black Scholes Call Option Pricing Model and the Australian Options Market: Where Are We After 15 Years”, Faculty of Business-Accounting & Finance Working Papers, No. 24, pp.1-21,1991.
  [10] G. Bakshi, C. Cao, Z. Chen, “Empirical performance of alternative option pricing models”. Journal of Finance, LII, December, Vol. 52, Issue.5, pp.2003–2049, 1997.
  [11] G.Ramazan, S.Aslihan, “Degree of mispricing with the Black-Scholes model and nonparametric cures”, Annals of Economics and Finance, Vol.4, Issue.1, pp.73–101, 2003.
  [12] A.Angeli, C. Bonz, “Changes in the Creditability of the Black-Scholes Option Pricing Model Due to Financial Turbulences”, Master’s thesis, Umeå School of Business and Economics, 2010.
  [13] V. Panduranga, “Relevance of Black-Scholes option pricing model in Indian derivatives markets – a study of cement stock options”, International Journal of Multidisciplinary Research in Social and Management Sciences, Vol.1, Issue.4, pp.91–95, 2013.
  [14] K. Arora, M. Sharma, “Analysis of option pricing using implied volatility of equity option contracts”, Emerging Trends in Business and Economy, Excel Books, pp.13–28, 2013.
  [15] R. Kumar, R. Agrawal, “An empirical investigation of the Black-Scholes call option pricing model with reference to NSE”, International Journal of BRIC Business Research (IJBBR), May, Vol.6, Issue.2, pp.1–11, 2017.
  [16] Dr.N R Parasuraman, Dr.P.JanakiRamudu, “Historical and Implied Volatility: An Investigation into NSE Nifty Futures and Options”, Australian Journal of Business and Management Research, Vol.1, Issue.7, pp.112-120, October-2011.
  

  Citation
  V. A. Vaghela, R. M. Gor, "Exploring the Effect of Varying Volatility in the Black-Scholes Option Pricing Model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.33-40, 2019

• Open Access   Article

  Statistical Model Differences in Hepatic or Renal Impairment Trials – All Impaired Categories

  C. Bhupathi, V.V. Haragopal

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.41-45, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.4145

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  Abstract
  The statistical analysis for organ impairment studies are performed using the mixed model techniques. The analysis is carried out by considering the impairment categories as fixed effects and/or the matched pair as random effect. By using simulated data for mild, moderate and severe impaired categories and the corresponding matched healthy volunteer groups, we have attempted to compare the results of these two models in multiple situations. We have used a pool of healthy volunteers group to execute the model without random effects. Since the organ impairment trials are conducted on a very small number of subjects, the aim of this research paper is to avoid the use of complicated models on such small data.

  Key-Words / Index Term
  Mixed models, Parallel designs, Clinical trials, Hepatic or Renal impairment

  References
  [1] FDA Guidance for industry, “Pharmacokinetics in Patients with Impaired Hepatic Function: Study Design, Data Analysis, and Impact on Dosing and Labeling”, Food & Drug Administration, 2003.
  [2] FDA Guidance for industry, “Pharmacokinetics in Patients with Impaired Renal Function: Study Design, Data Analysis, and Impact on Dosing and Labeling”, Food & Drug Administration, 2010.
  [3] D. McNeish, K. Kelly, “Fixed effects models versus mixed effects models for clustered data: Reviewing the approaches, disentangling the differences, and making recommendations”, Psychological Methods, 2018.
  [4] R. C. Littell, G. A. Milliken, W. W. Stroup, D. Wolfinger R. “SAS for mixed models (2nd ed.)” SAS Institute Inc., Cary, NC, 2006.
  [5] R. Urso, P. Blardi, G. Giorgi, “A short introduction to pharmacokinetics”, Eur. Rev. Med. Pharmacol. Sci, 6, pp.33, 2002.
  

  Citation
  C. Bhupathi, V.V. Haragopal, "Statistical Model Differences in Hepatic or Renal Impairment Trials – All Impaired Categories," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.41-45, 2019

• Open Access   Article

  Prediction of HIV Replication in the Human Immune System using Multinomial Distribution by Bayesian Methodology

  G. Meenakshi, P.R. Maheswari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.46-52, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.4652

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  Abstract
  For the last four decades the treatment of the HIV infection is very complicated. There are many Statistical and Mathematical models have been developed for the HIV replication. Most of them are system of linear differential equations. But parameter estimation and analytical solution of the differential equations is not easy to obtain. So, this paper concentrated to predict the viral replication based on the determination of the four categories of CD_4^+ T cells classification as multinomial distribution and also used the Bayesian methodology with conjugate prior of Dirichlet distribution.

  Key-Words / Index Term
  Bayesian Methodology,〖CD〗_4^+ T cells, Dirichlet Distribution, HIV Replication, Multinomial Distribution

  References
  [1] M. Eigen and R. Winkler – Oswatitsch, “Steps towards life: A perspective on evolution”,Oxford University Press, Oxford, pp 173, 1992.
  [2] M.Eigen, “ The origin of genetic information : viruses as models”, Elsevier,vol.135,issue.1-2 pp 37-47,1993.
  [3] J. M. Coffin. “HIV population dynamics in vivo: implications for genetic variations, pathogenesis, and therapy”, Science,vol.267,pp 483 – 489, 1995.
  [4] A. J. Leigh Brown, and D. D. Richman, “HIV – 1: gambling on the evolution of drug resistance”, Nature Medicine 3,pp 268 – 271, 1997.
  [5] A. J. Leigh Brown, “Analysis of HIV – 1 env gene sequences reveals evidence for a low effective number in the viral population”, Proc.Natl.Acad.Sci USA,vol. 97,pp 1862 – 1865,1997.
  [6] O.Davidov, “The steady state probabilities for a regenerative semi – Markov processes with application to prevention and screaming”, Applied Stochastic Models and Data Analysis, Vol.15, No.1, pp. 55 – 63, 1999.
  [7] O.Davidov and M. Zelen, “Designing Cancer Prevention Trials: a Stochastic model approach”, Statistics in Medicine, Vol.19, issue.15, pp. 1983 – 1995, 2000.
  [8] G.D. Biase and et.al, “A Stochastic model for the HIV/AIDS dynamic evolution”, Hindawi Publishing Corporation Mathematical problems in Engineering, vol.2007, Article ID.65636, 14 Pages doi: 10.1155/2007/65636,2007.
  [9] R. Lakshmajayam and G.Meenakshi “HIV Replication Model for the Succeeding Period of Viral Dynamic Studies In Aids Clinical Trials” International Journal Of Mathematics And Statistics Invention (IJMSI) Volume 2 Issue 10 PP-28-36, 2014.
  [10] S.Sharma et.al “Predictive analysis using classification techniques in healthcare domain” International Journal of Computer Sciences and Engineering,vol. 6,issue.2 ,pp 206 -212,2018.
  

  Citation
  G. Meenakshi, P.R. Maheswari, "Prediction of HIV Replication in the Human Immune System using Multinomial Distribution by Bayesian Methodology," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.46-52, 2019

• Open Access   Article

  An investigative resolution of collinearity through location shift and partial regression splines with an application to crime-data modeling

  P. Sangli Therasanathan, Martin L. William

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.53-60, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.5360

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  Abstract
  Collinearity is an issue that plagues any regression model primarily built to explain the effect of regressors on a response variable. Various solutions have been attempted in the literature on addressing the collinearity issue, like taking non-linear transformations and dropping a regressor that has a collinear relation with another. But, there are situations where a regressor is affected by collinearity but not exactly in relation to another. Dropping of such a variable leads to complete loss of information of an ‘important` factor and so a different solution is called for in such situations. This paper explores a heuristic approach to resolve collinearity by making a location shift on the affected variable(s) and creating a regression spline. This approach is illustrated for modeling district-wise data on crime against women recorded in 2011 across the districts of the South Indian states, using regressors available from the 2011census data and from data sources on the presence of schools and police stations.

  Key-Words / Index Term
  Collinearity, Location shift, Regression splines

  References
  [1] D.C. Montgomery, E.A. Peck and G.G. Vining. “Introduction to Linear Regression Analysis”, John Wiley & Sons, New Jersey, USA, pp. 325-381, 2012
  [2] D.E. Farrar and R.R. Glauber. “Multicollinearity in regression analysis: the problem revisited”, Review of Economics and Statistics, Vol. 49, pp. 92-107, 1967
  [3] R. Mason and J.T. Webster. “Regression Analysis and Problems of Multicollinearity”, Communications in Statistics, Vol. 4, Issue 3, pp. 277-292, 1975
  [4] A.C. Harvey. “Some Comments on Multicollinearity in Regression”, Journal of the Royal Statistical Society, Series C (Applied Statistics), Vol. 26, Issue 2, pp. 188-191, 1977
  [5] G.W. Stewart. “Collinearity and Least Square Regression”, Statistical Science. Vol. 2, Issue 1, pp. 68-94, 1987
  [6] J. Fox and G. Monette. “Generalized Collinearity Diagnostics”, Journal of the American Statistical Association, Vol. 87, pp. 178-183, 1992
  [7] C.F. Mela and P.K. Kopalle. “The impact of collinearity on regression analysis: the asymmetric effect of negative and positive correlations”, Applied Economics, Vol. 34, pp. 667-677, 2002
  [8] M. Shacham and N. Brauner. “Minimizing the effects of collinearity in polynomial regression”, Ind. Eng. Chem. Res. Vol. 36, pp. 4405–4412, 1997
  [9] J.H. Friedman. “Multivariate Adaptive Regression Splines”, The Annals of Statistics, Vol. 19, Issue 1, pp.1-67, 1991
  

  Citation
  P. Sangli Therasanathan, Martin L. William, "An investigative resolution of collinearity through location shift and partial regression splines with an application to crime-data modeling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.53-60, 2019

• Open Access   Article

  A New Generalization of Ailamujia Distribution with Applications in Bladder Cancer Data

  B. Jayakumar, R. Elangovan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.61-68, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.6168

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  Abstract
  In this paper, a new probability model called as Area Biased Weighted Ailamujia Distribution (ABAD) with applications in bladder cancer data has been derived. Structural properties of this new distribution are discussed comprehensively and the parameters have been estimated using maximum likelihood method. Finally, the model is examined with bladder cancer data set for significance purpose and the fit has been found to be good.

  Key-Words / Index Term
  Ailamujia distribution, Reliability Analysis, Order Statistics, Maximum Likelihood Estimation, Bladder Cancer data.

  References
  [1] B. Long, (2015) Bayesian estimation of parameter on Эрлангa distribution under different prior distribution. Mathematics in Practice & Theory. (4), 186-192.
  [2] Fisher, R. A., (1934), The effects of methods of ascertainment upon the estimation of frequencies. Annals of Eugenics, 6, 13-25.
  [3] G. T. Pan, B. H. Wang, C. L. Chen, Y. B. Huang & M. T. Dang, (2009), The research of interval estimation and hypothetical test of small sample of Эрланга distribution. Application of Statistics and Management, 28(3), 468-472.
  [4] H. Q. Lv, L. H. Gao & C. L. Chen, (2002)., Эрланга distribution and its application in supportability data analysis. Journal of Academy of Armored Force Engineering. 16(3), 48-52.
  [5] L. P. Li, (2016) Minimax estimation of the parameter of ЭРланга distribution under different loss functions, Science Journal of Applied Mathematics and Statistics. 4(5), 229-235.
  [6] Lappi J, Bailey RL., (1987), Estimation of diameter increment function or other tree relations using angle-count samples, Forest science 33: 725-739.
  [7] Lee, E. T. and Wang, J. W(2003). Statistical Methods for Survival data Analysis, 3 ed, John Willey, New York.
  [8] Para, B. A., & Jan, T.R., (2018), On Three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences. Applied Mathematics & Information Sciences Letters, 6(1), 13-26.
  [9] Rao, C. R., (1965), “On discrete distributions arising out of method of ascertainment, in classical and Contagious Discrete”, G.P. Patiled; Pergamum Press and Statistical publishing Society, Calcutta. 320-332.
  [10] Rather, A. A., and Subramanian, C., (2018), Transmuted Mukherjee-Islam failure model, Journal of Statistics Applications & Probability, 7(2), 343-347.
  [11] 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.
  [12] Uzma Jan, Kawsar Fatima and S. P. Ahmad., (2017) On Weighted Ailamujia Distribution and Its Applications to Lifetime Data, J. Stat. Appl. Pro. 6, No. 3, 619-633.
  [13] Van Deusen P.C., (1986), Fitting assumed distributions to horizontal point sample diameters. For Sci 32(1): 146-148.
  

  Citation
  B. Jayakumar, R. Elangovan, "A New Generalization of Ailamujia Distribution with Applications in Bladder Cancer Data," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.61-68, 2019

• Open Access   Article

  Analysis of Transport Phenomena in Air Contaminants with Chemical Reaction in the Presence of Electric Field

  P. Meenapriya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.69-75, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.6975

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  Abstract
  An attempt had made to understand the dynamics of dust particles in the atmosphere. Generalised dispersion model is used to describe the transport of chemically reactive pollutant in the couple stress fluid and in the presence of electric field. The analytical results obtained for the concentration as a function of time and the dispersion coefficient for various values of electric number, couple stress parameter and reaction rate parameter. The obtained analytical results are illustrated by graphs and conclusions are made. It is noted that dispersion increases with increase in electric number and couple stress parameter but decreases with increase in reaction rate parameter.

  Key-Words / Index Term
  Couple stress fluid, Electric number, Reaction rate parameter

  References
  [1] K. Abdella and H. Rasmussen, “Electrohydrodynamic instability of two superposed fluids in normal Electric fields”, Journal of Computational and Applied Mathematics, Vol. 78, pp. 33-61, 1997.
  [2] Anju Saini, V.K. Katiyar and Pratibha, “Effect of first order chemical reactions on the dispersion coefficient associated with Laminar flow through lungs”, International Journal of Biomathematics, Vol.7 No. 2, 2014.
  [3] Chairat Siripatana, Hathaikarn Thongpan and Arwut Promraksa, “Generalised volumetric dispersion model for a class of two phase reaction”. In the proceedings of the 2017 5th International Conference on science & Engineering in Mathematics, Chemistry and Physics, Indonesia. Vol.820, pp. 1-11, 2017.
  [4] Dulal Pal, “Effect of chemical reaction on the dispersion of a solute in a Porous medium”, Journal of Applied Mathematical modeling, Vol. 23, No.7, pp.557-566,1999.
  [5] H.G. Georgiadis, E.G Velgaki , “High-frequency Rayleigh waves in materials with micro - structure and couple stress effects”, International Journal of Solids and Structures, Vol. 40 No. 10, pp. 2501-2520, 2003.
  [6] W.N. Gill, V. Ananthakrishnan and Allen J. Barduhn, “Laminar dispersion in Capillaries Part 4, The slug stimulus”, An official publication of the American institute of chemical Engineers, Vol. 13, pp. 801, 1967.
  [7] W.N. Gill and R. Sankarasubramanian, “Dispersion of a non-uniform slug in time-dependent flow”, Proc. Roy. Soc. London. Series, Vol. A 322, pp. 101,1971.
  [8] W.N. Gill and R. Sankarasubramanian , “ Dispersion of a non-uniformly distributed time-variable continuous sources in time-dependent flow”, Proc. Roy. Soc. London. Series, Vol. A 327, pp. 191-208, 1972.
  [9] W.N. Gill and R. Sankarasubramanian, “Exact analysis of unsteady convective diffusion”, Proc. Roy. Soc. London. Series, Vol. A 316, pp. 341, 1970.
  [10] W.N. Gill , “A note on the solution of Transient dispersion problems”, Proc. Roy. Soc. London, Vol. A 298, pp. 335, 1967.
  [11] Kazuhide Ito and Hiroshi Harashima, “Coupled CFD analysis of size distributions on indoor Secondary organic Aerosol derived from Ozone reactions”, Building and Environment, Vol. 46, No. 3, pp. 711-718, 2011.
  [12] K.S. Mallika and N. Rudraiah, “Generalized dispersion of unsteady convective diffusion in Couple stresses poorly conducting Fluid bounded by Porous layer in the presence of an Electric field”, World Journal of Engineering, Vol. 8 No.4, pp. 335-346,2011.
  [13] Runzhang Xu, Yacheng Liu and Tau Yu, “Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations”, Nonlinear Analysis: Theory, Methods and Applications, Vol. 71, No.10, pp. 4977-4983, 2009.
  [14] D.S. Sankar , Nurul Aini Binti Jaafar and YazariahYatim, “ Non-linear Analysis of Shear augmented dispersion of solutes in Blood flow through narrow Arteries”, Journal of Applied Mathematics, pp. 1-24, 2012.
  [15] Sanjeev Kumar Sharma, Jyoti Singh, Anil Kumar, “Modeling of Blood flow through Artery with Magnetic effects”, International Journal of Computer Sciences and Engineering, Vol.6, No. 7 pp. 28-36, 2018.
  [16] Anil Kumar and G.C. Sharma, “Performance and analysis of flow between Annular Space Surrounded by a Rotating Coaxial cylinder with Co-axial Cylindrical Porous Medium”, International Journal of Scientific Research in Computer Sciences and Engineering, Vol. 5, No.3, pp. 1-6, 2017.
  

  Citation
  P. Meenapriya , "Analysis of Transport Phenomena in Air Contaminants with Chemical Reaction in the Presence of Electric Field," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.69-75, 2019

• Open Access   Article

  Time Series Analysis on Rainfall and Ground Water Levels Data – A Case Study

  Raju Sake, P. Mohammed Akhtar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.76-85, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.7685

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  Abstract
  In this paper we have done the Time Series Analysis on the data related to Rainfall and Ground water levels collected from Anantapur district in Andhra Pradesh, and the data is divided into five zones we have seen the relation between Rainfall and Ground water levels in the specified zones. We have estimated the trend line using linear and non-linear models and also compared among them by using critical deference test and diagnostic checking. We identified the best suitable Time series model for the data collected. Finally we have given conclusions about the results evaluated.

  Key-Words / Index Term
  Rainfall, Ground Water Level, Linear and Non-Linear, diagnostic checking ,forecasting

  References
  [1]. A.H. Nury, M. Koch and M.J.B. Alam, “Time Series Analysis and Forecasting of Temperatures in the Sylhet Division of Bangladesh”, Proceedings of 4th International Conference on Environmental Aspects of Bangladesh, Fukoka, Japan, 2013.
  [2]. D. Machiwal and M.K. Jha, “Time Series Analysis of Hydrologic Data For Water Resources Planning and Management“ : A Review. J. Hydrol, Hydromech, 54(3): 237-257, 2006.
  [3]. D.C Montgomery, L.A Johnson,” Forecasting and time series analysis”. McGraw-Hill; 1976.
  [4]. G.E.P Box, G.M. & G.C Reinsel, “Time series analysis and forecasting and control”, 3rd ed., Englewood Cliffs, N.J. Prentice Hall, 1994.
  [5]. G.E.P Box, G.M Jenkins, “Time Series Analysis, Forecasting and Control”, Holden-Day: San Francisco, 1976.
  [6]. G.E.P Box, G.M Jenkins, G.C Reinsel, ”Time series analysis: Forecasting and Control”. John Wiley and Sons; 2008.
  [7]. J.D Hamilton , “Time series analysis”. Princeton University Press; 1994.
  [8]. Otnes RK, Enochson L. “Applied Time Series Analsis”, Vol. 1. New York: Wiley; 1978.
  [9]. S. Soltani, R. Modarres and S.S. Eslamian, “ The use of time series modeling for the determination of rainfall climates of Iran”. International Journal of Climatology, 27: 819-829, 2007.
  [10]. S.A. Shamsnia, N. Shahidi, A. Liaghat, A. Sarraf and S.F. Vahdat, “ Modelling Of Weather Parameters ( Temperature, Rainfall And Humidity) Using Stochastic Methods. Internat. Conference on Environment and Industrial Innovation, IPCBEE, Singapore, 282-285, 2011.
  [11]. S.C Gupta,” Fundamentals of Statistics”, Himalaya Publishing House, 2004.
  [12]. S.M. Ali, “Time Series Analysis of Baghdad Rainfall Using ARIMA method “Iraqi Journal of Science,54(4):1136-1142,2013.
  

  Citation
  Raju Sake, P. Mohammed Akhtar, "Time Series Analysis on Rainfall and Ground Water Levels Data – A Case Study," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.76-85, 2019

• Open Access   Article

  Prime labeling of Union Graphs

  S K Patel, A N Kansagara

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.86-93, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.8693

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  Abstract
  A graph with n vertices is called prime graph if its vertices can be labeled with first n positive integers such that each pair of adjacent vertices have relatively prime labels. Such a labeling is called prime labeling. It is known that graphs like gear graphs, crown graphs, helm graphs, book graphs and C_n (C_n) are prime. In this paper, we study the prime labeling of union of these graphs.

  Key-Words / Index Term
  Prime labeling, union of graphs, Corona product, Cartesian Product

  References
  [1] J. A. Gallian, A dynamic survey of graph labeling. The Electronic Journal of Combinatronics 2017.
  [2] M. A. Seoud, A. T. Diab, and E. A. Elsahawi, On strongly-C harmonious, relatively prime, odd graceful and cordial graphs, Proc. Math. Phys. Soc. Egypt, no. 73, pp 33-55, 1998.
  [3] M. A. Seoud and M. Z. Youssef, On prime labelings of graphs, Congr. Numer.,141, pp 203-215, 1999.
  [4] A. Tout, A. N. Dabboucy, and K. Howalla, Prime labeling of graphs, Nat. Acad. Sci. Letters, 11 pp 365-368, 1982.
  [5] S. K. Vaidya, K. Kanani, P. Vihol, and N. Dani, Some cordial graphs in the context of barycentric subdivision, Int. J. Comtemp. Math. Sciences, 4 pp 1479-1492, 2009.
  

  Citation
  S K Patel, A N Kansagara, "Prime labeling of Union Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.86-93, 2019