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• Open Access   Article

  Common Fixed Point Results for Generalized Contraction under the Rational Expressions in Complex Valued Metric spaces

  Garima Gadkari, M.S. Rathore, Naval Singh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.282-293, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.282293

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  Abstract
  In this paper we prove the existence and uniqueness of common fixed point theorems satisfying contractive conditions involving rational expression for two pairs of weakly compatible self-mappings and further some results using (E.A) property and (CLR) property are obtained in complex valued metric spaces. An illustrative example is provided to support the results obtained. The presented results improve and generalize the main results of Öztűrk in (Öztűrk, 2014).

  Key-Words / Index Term
  Complex valued metric space, weakly compatible mapping, (E.A) property, (CLR) property

  References
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  [7] S. Chauhan, M.A. Khan, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces satisfying ф-contractive condition with common limit range property, Abstract Applied Analysis, Vol. 2013, Article ID 735217, 14 pages,2013
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  [9] F. Rouzkard and M. Imdad, Some Common fixed point theorems in complex valued metric spaces, Computers and Mathematics with Applications, Vol.64, pp.1866-1874, 2012.
  [10] W. Sintunavarat and P. Kumam, Generalized Common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications, Vol. 2012, Article 84, 2012.
  [11] N. Singh, D. Singh, A. Badal and V. Joshi, Fixed point theorems in complex valued metric Spaces, Journal of Egyptian Mathematical Society, Vol. 24, pp. 402-409, 2016.
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  [15] M. Öztűrk, Common fixed point theorems satisfying contractive type conditions in complex valued metric spaces, Abstract and Applied Analysis, Vol. 2014, Article ID 598465, 7 pages, 2014.
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  Citation
  Garima Gadkari, M.S. Rathore, Naval Singh, "Common Fixed Point Results for Generalized Contraction under the Rational Expressions in Complex Valued Metric spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.282-293, 2018

• Open Access   Article

  Gaussian Prime Labeling of Some Cycle Related Graphs

  N.P.Shrimali, S.K.Singh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.294-300, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.294300

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  Gaussian Prime labeling is a bijection from the set of vertices of graph of order to the first ’ ’ Gaussian integers in the spiral ordering such that images of adjacent vertices are relatively prime. A graph is called Gaussian prime graph if admits Gaussian prime labeling. In this paper, we examine Gaussian prime labeling of some cycle related graphs and union of some cycle graphs.

  Key-Words / Index Term
  Gaussian integers, spiral order of Gaussian integers, Gaussian prime labeling

  References
  [1] H. Lehmann and A. Park, Prime labeling of small trees with Gaussian integers, Rose-Hulman Undergraduate Mathematics Journal, Vol. 17(1), pp.72-97, 2016.
  [2] S. Klee, H. Lehmann, and A. Park, Prime labeling of families of trees with Gaussian integers, AKCE International Journal of Graphs and Combinatorics, Vol. 13(2), pp. 165-176, 2016.
  [3] Hung-Lin Fu, Kuo-Ching Huang, On Prime labellings, Discrete Mathematics, Vol. 127, pp. 181-186, 1994.
  [4] J. Gross and J. Yellen, Graph theory and its applications, CRC press, (1999).
  [5] D.M. Burton, Elementary Number Theory, Tata McGraw Hill, 1990.
  [6] S.K. Patel, On Prime labeling of union of cycle graphs, Mathematics Today, Vol. 30, pp. 75-82, 2014.
  [7] S.K. Patel, J. Vasava, On Prime labeling of some union graphs, Kragujevac Journal of mathematics, Vol. 42(3), pp. 441-452, 2018.
  [8] J. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, Vol. 17, 2016.
  [9] S.K. Vaidya, K.K. Kanani, Prime labeling for some cycle related graphs, Journal of Mathematics research, 2(2), 98-103, 2010.
  [10] L.Robertson, B. Small, On Newman’s conjecture and prime trees, Integers, Vol. 9, pp. 117-128, 2009.
  

  Citation
  N.P.Shrimali, S.K.Singh, "Gaussian Prime Labeling of Some Cycle Related Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.294-300, 2018

• Open Access   Article

  Application of Cauchy Characteristic in General Relativity

  Noruddin Ansari

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.301-307, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.301307

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  This paper reveals the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to current 3D black hole codes that run forever. A prime application of characteristic evolution is Cauchy-characteristic matching, which is also reviewed

  Key-Words / Index Term
  Cauchy-characteristic, general relativity, 3D codes, Hypersurfaces, etc

  References
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  [15] Bishop NT. Some aspects of the characteristic initial value problem in numerical relativity. In: d’Inverno RA, editor. Approaches to Numerical Relativity. Cambridge; New York: Cambridge University Press; 1992. pp. 20–33.
  [16] Bishop NT. Class. Quantum Grav. 1993;10:333–341. doi: 10.1088/0264-9381/10/2/015.
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  [18] Bishop NT, Gómez R, Holvorcem PR, Matzner RA, Papadopoulos P, Winicour J. J. Comput. Phys. 1997;136:140–167. doi: 10.1006/jcph.1997.5754.
  [19] Bishop NT, Gómez R, Isaacson RA, Lehner L, Szilágyi B, Winicour J. Cauchy-characteristic matching. In: Bhawal B, Iyer BR, editors. On the Black Hole Trail. Dordrecht; Boston: Kluwer; 1999.
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  Citation
  Noruddin Ansari, "Application of Cauchy Characteristic in General Relativity," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.301-307, 2018

• Open Access   Article

  On t*-Generalized b-closed sets in Topological Spaces

  C. Aruna, R. Selvi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.308-312, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.308312

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  Abstract
  In this paper we introduce a new class of sets called t* generalized b closed sets in topological spaces (briefly t* gb closed set). Also we investigate the characteristics of t* generalized b closed sets and studied some of their properties. Further we introduced t* generalized b neighbourhoods in topological spaces by using the notion of t* generalized b open sets and study some of their properties.

  Key-Words / Index Term
  Topological Spaces and their properties

  References
  [1] D. Andrijevic, On b-open sets, Mat. Veosnik.,48(1-2), 59-64, 1996.
  [2] Dunham W., A new closure operator for non-T1 topologies, Kyungpook Math.J.22,55-60, 1982.
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  [5] Ahmad Al-Omari and Mohd. Salmi Md. Noorani, On Generalized b-closed sets. Bull. Malays.Math.Sci.Soc.,(2)32(1), 19-30, (2009)
  [6] Pushpalatha A. Eswaran S. and Raja Rubi P., -generalized closed sets in topological spaces,
  WCE, London, U.K., July 1-3, 2009.
  [7] MashorAbd.ElMonsef.M.EandEiDeeb.S.N.,On Precontinous and weak precontinous mapping, Proc.Math.,Phys.Soc.Egypt,53,47-53, (1982).
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  [10] . H.Maki, R.Devi and K.Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Uni., Ed.Part III,42, 13-21, (1993).
  

  Citation
  C. Aruna, R. Selvi, "On t*-Generalized b-closed sets in Topological Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.308-312, 2018

• Open Access   Article

  Selection of Bayesian Single Sampling Plan with Zero – Inflated Poisson Distribution Based on Quality Region

  M. Latha, A. Palanisamy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.313-320, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.313320

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  Abstract
  Acceptance sampling procedures are the practical tools for quality assurance application involving product control. Acceptance sampling systems are advocated when small sample size are necessary or desirable towards costlier testing for product quality. This paper is concerned with the set of tables for selection of Bayesian Single Sampling Plan with Zero – Inflated Poisson distribution on this basic of different combinations of entry parameter single sampling plan involving producer’s and consumer’s risks and probabilistic Quality Region, Indifference Quality Region for Specified AQL and LQL. Beta distributions are considered as prior distribution. Comparison is made with conventional Single Sampling Plan.

  Key-Words / Index Term
  Bayesian Single Sampling Plan, Gamma Prior, Zero – Inflated Poisson distribution, Average Quality Limit (AQL), Limiting Quality Limit (LQL), Producer`s Risk (α),Consumer Risk (β), Indifference Quality Level (IQL), Probabilistic Quality Region (PQR), Indifference Quality Region (IQR)

  References
  [1] D. Bohning, E Dietz, P. Schlattmann, “The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology”, Journal of Royal Statistical Society, Series A 162:195–209, (1999).
  [2] T.W. Calvin, 1984. “How and when do perform Bayesian Acceptance Sampling”, American Society for Quality Vol.7, 1984.
  
  [3] A. Hald, “Bayesian Single Sampling Plans for Discrete Prior Distribution”, Mat. Fys. Skr. Dan. Vid. Selsk., Vol.3, No.2, pp.88, (1965). Copenhagen, Munksgaard.
  [4] D. Lambert, “Zero-inflated Poisson regression with an application to defects in manufacturing”, Technimetrics 34:1–14, (1992)
  [5] A .Loganathan, and K. Shalini, “Determination of Single sampling plans by attributes under the conditions of Zero – inflated Poisson distribution”, Communications in Statistics – Simulation and Computation 43:3, 538-548, ,(2013)
  [6] M. Latha, and K. Subbiah, “Selection of Bayesian multiple deferred state (BMDS-1) sampling plan based on quality regions”, Internat. J. Recent Scientific Res., 6 (4): 275-282, (2015).
  [7] G. McLachlan, D. Peel, “Finite Mixture Models”, New York: John Wiley & Sons. (2000).
  [8] H. Naya, J.I Urioste, Y.M Chang, M.R Motta, R. Kremer, D. Gianola,“A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in corriedale sheep”, Genetics Selection Evolution 40:379–394, (2008).
  [9] H. Sim, M.H Lim, “Attribute charts for zero-inflated processes”, Communications in Statistics- Simulation and Computation 37:1440–1452, (2008).
  [10] K.S.Stephens, “The Handbook of Applied Acceptance Sampling Plans, Procedures and Principles. Wisconsin”. ASQ Quality Press. (2001).
  [11] K.K. Suresh and M. Latha , “Bayesian Single Sampling Plan for a Gamma Prior” Economic Quality Control, Vol.16, No.l, pp.93-107. (2001),
  [12] K.K. Suresh and M. Latha (2002), “Selection of Bayesian Single Sampling Plan with Gamma Prior Distribution”, Statistical Methods, Vol.4, No.l, pp.64-74, (2002)
  [13] J. Yang, M. Xie, T.N. Goh, “Outlier identification and robust parameter estimation in a zero-inflated Poisson model”, Journal of Applied Statistics 38:421–430, (2011).
  

  Citation
  M. Latha, A. Palanisamy, "Selection of Bayesian Single Sampling Plan with Zero – Inflated Poisson Distribution Based on Quality Region," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.313-320, 2018

• Open Access   Article

  Forecasting Analysis for Tuberculosis (TB) Incidence in Tamilnadu

  S. Poyyamozhi, A. Kachi Mohideen

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.321-327, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.321327

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  Abstract
  Tuberculosis (TB) remains a major global public health problem, especially for considered as high burden cities in Tamilnadu. It is considered by WHO as one of the high burden countries and tuberculosis incidence continues to be very high. Therefore, there is need to continue monitoring and predicting tuberculosis incidence in an effort to make the control of tuberculosis more effective. The Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the incidence of infectious diseases. This method takes into account changing trends, periodic changes, and random disturbances in time series. Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity. Holt Winters (HW) methods also play a significant role in time series forecasting and are especially effective for short term forecasting. In this study, based on the data of the tuberculosis incidence from 2005 -2017 in Tamilnadu, we establish the single ARIMA (2, 2, 1) model, the combined ARIMA (2, 2, 1)-ARCH (1) model, and the HW model, which can be used to predict the tuberculosis incidence successfully in Tamilnadu. Comparative analyses show that the ARIMA and ARIMA-ARCH models perform reasonably well, with the ARIMA model being the best in our case. To the best of our knowledge, this is the First study to establish the ARIMA model and ARIMA-ARCH model for pre-diction and monitoring the yearly incidence of tuberculosis (TB) in Tamilnadu. Based on the results of this study, the ARIMA (2, 2, 1) and ARIMA (2, 2, 1)-ARCH (1) models are suggested to give tuberculosis surveillance by providing estimates on tuberculosis incidence trends in Tamilnadu.

  Key-Words / Index Term
  Tuberculosis, Box-Jenkins approach, the autoregressive integrated moving average (ARIMA) model, Heteroscedasticity (ARCH)model, Holt Winters (HW) method

  References
  [1]. Cain, K.P., Oeltmann, J.E., Kammer er, J.S., Moonan, P.K., Ricks, P.M (2011). Estimating the burden of tuberculosis among foreign-born persons acquired prior to entering the u.s., 2005-2009. PLoS One, 6:e27405.
  [2]. Floyd, K., Raviglione, M., Glaziou, P.(2009) Global burden and epidemiology of tuberculosis. Clin. Chest Med., 30:621636.
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  [5]. Roslanb, U., Kilicmana, A. Tuberculosis in the terengganu region. Forecast and data analysis. Scie Asia.
  [6]. Willis MD, Winston CA, Heilig CM, Cain KP, Walter ND, Mac Kenzie WR. Seasonality of tuberculosis in the United States, 1993-2008.Clin Infect Dis. 2 012;54(11):1553-60.
  [7]. Zhang Y, Tang G, Wang W. Application of ARIMA Model in forecasting incidence of tuberculosis. Modern Prevent Med. 2008;9:6.
  [8]. Abdullah S, Sapii N, Dir S, Mardiah T. (2012) Aplication of univariate forecasting models of tuberculosis cases in Kelantan, in Statistics in Science, Business, and Engineering (ICSSBE). 2012 International Conference on: IEEE. Langkawi, Kedah, Malaysia.
  [9]. Engle, R.F. Autoregressive conditional heteroscedasticity with estimates of variance ofed kingdom ination. Econometrica.
  [10]. Roslanb, U., Kilicmana, A. Tuberculosis in the terengganu region. Forecast and data analysis. Scie Asia.
  [11]. Zhang, L.P., Zhang, X.L., Wang, K., Zheng, Y.J., Zheng, Y.L.(2015), Forecast model analysis for the morbidity of tuberculosis in Xinjiang,China. PLoS ONE, 10(3).
  [12]. Liu, X., Jiang, B., Yang, W., Liu, Q. Forecasting incidence of hemorrhagic fever with renal syndrome in china using arima model. BMC Infect Dis.
  [13]. Tong, L.I., Lee, Y.S. Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming. Knowl-Based. Syst.
  [14]. Central TB Division in India report Directorate General of Health Services, Ministry of Health and Family Welfare, Nirman Bhavan, New Delhi 10011(http://www.tbcindia.org)
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  Citation
  S. Poyyamozhi, A. Kachi Mohideen, "Forecasting Analysis for Tuberculosis (TB) Incidence in Tamilnadu," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.321-327, 2018

• Open Access   Article

  On the Zagreb polynomials of transformation graphs

  B. Basavanagoud, Praveen Jakkannavar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.328-335, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.328335

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  Abstract
  In the year 2009, Fath-Tabar introduced the concept of Zagreb polynomials. The novel topological indices called Zagreb indices can be derived from these polynomials. In order to find the Zagreb polynomials of transformation graphs we introduce the concept of Zagreb co-polynomials, from which one can derive the Zagreb coindices. Further, we establish the relations connecting the Zagreb polynomials of the graph G to those of the transformation graphs.

  Key-Words / Index Term
  Zagreb index, Zagreb polynomial, xyz-Point-Line transformation graph

  References
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  Citation
  B. Basavanagoud, Praveen Jakkannavar, "On the Zagreb polynomials of transformation graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.328-335, 2018

• Open Access   Article

  MHD Free convective flow of a Jeffrey fluid in a vertical channel partially filled with porous medium

  G.Kathyayani, R. Lakshmi Devi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.336-342, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.336342

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  Abstract
  MHD free convection flow of a Jeffrey fluid between vertical plates partially filled with porous medium is investigated. The momentum transfer in the porous medium has been described by the Brinkman extended Darcy model. The fluid flow in the free region is governed by Jeffrey model. The solution for the problem is obtained using a perturbation method. The effects of Darcy number, magnetic parameter and Jeffrey parameter on the velocity field and temperature distributions are discussed in detail through graphs.

  Key-Words / Index Term
  Convection, Darcy number, Jeffrey fluid, MHD, Porous medium

  References
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  Citation
  G.Kathyayani, R. Lakshmi Devi, "MHD Free convective flow of a Jeffrey fluid in a vertical channel partially filled with porous medium," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.336-342, 2018

• Open Access   Article

  FIXED POINT THEOREMS IN C-FUZZY METRIC SET IN FUZZY METRIC SPACES

  R. Krishnakumar, Nagaral Pandit Sanatammappa

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.343-347, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.343347

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  Abstract
  In this paper the fixed point theorems for commute c-fuzzy metric set satisfying the generalized Lipschitzconditions are obtained, without appealing to continuity formappings in the setting of fuzzy metric spaces over the Banach algebra. Furthermore, we notonly get the existence of the fixed point but also get the uniqueness.These results greatly improve and generalize several well-knowncomparable results in the literature.

  Key-Words / Index Term
  Fixed point, c-fuzzy metric set, Fuzzy metric spaces, commuting, invertible,Lipschitzconditions

  References
  
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  Citation
  R. Krishnakumar, Nagaral Pandit Sanatammappa, "FIXED POINT THEOREMS IN C-FUZZY METRIC SET IN FUZZY METRIC SPACES," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.343-347, 2018

• Open Access   Article

  On Review of Multivariate Frailty Distributions

  S.G. Parekh, S.R. Patel

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.348-351, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.348351

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  Abstract
  This paper deals with the construction of bivariate frailty models and discusses in general multivariate frailty models. Whenever the observations are unmeasurable and not observable then in that case we assume the probability model and generating simulated data analysis of these distribution known as frailty distribution is carried out and compared it with that of real data. The frailty models have been categorised in to three forms such as discrete frailty models, continuous univariate frailty model and multivariate frailty model. In discrete frailty model generally starting from Bernoulli frailty to multinomial frailty model. In continuous multivariate frailty models starting from bivariate frailty models were constructed such as bi-variate gamma frailty model, bi-variate compound Poisson frailty model, bi-variate log-normal frailty model. Further multivariate normal frailty model has been discussed for its properties.

  Key-Words / Index Term
  Frailty distribution, bi-variate frailty models, bi-variate gamma frailty model, bi-variate compound Poisson frailty model, bi-variate log-normal frailty model, Multivariate normal frailty model

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  Citation
  S.G. Parekh, S.R. Patel, "On Review of Multivariate Frailty Distributions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.348-351, 2018