Volume-7 , Issue-1 , Feb 2020, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Error Reduction in Koshy’s Formula for Ellipse Perimeter: Correction Factor and Improved Approximation

  K. Idicula Koshy

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.1-8, Feb-2020

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  In an article published in IJESIRD, the author has introduced a new empirical formula for ellipse perimeter. He observed that the definite integral for the ellipse perimeter satisfies the first order partial differential equation known as Lagrange’s equation and, therefore, the perimeter must be a function of two appropriate independent solutions of the partial differential equation. Though the actual formula could not be derived, he developed an empirical formula. The maximum absolute relative error in the perimeter as per the formula is less than 6.0*10-5 across all aspect ratios b/a from 0 to 1. In the present article, the author improves his formula, reducing the relative error further to less than (5.93)*10-6 by means of a Correction Factor. When all aspect ratios are considered together, the Improved Perimeter Formula, compared with other formulae of its category, yields lowest ‘maximum relative error and error fluctuation’. Surprisingly, for ellipses with aspect ratios less than 0.15, the relative error due to the Improved Perimeter Formula is less than that due to S. Ramanujan’s Formula II. Moreover, the formula is simple enough for computation using a standard scientific calculator.

  Key-Words / Index Term
  Ellipse, Major/Minor Radii, Aspect Ratio, Simpson’s Rule, Relative error, Correction Factor

  References
  [1] K. I. Koshy, “Ellipse Perimeter: A new Approximate Formula by a New Approach”, International Journal of Engineering Science Invention Research and Development (IJESIRD), Vol. VI, Issue 1, 2019.
  [2] Erwin Kreyszig, “Advanced Engineering Mathematics”, 8th Ed., Wiley, Ch.17, 2010.
  [3] S. Ramanujan, “Modular Equations and Approximations to π”,Quarterly Journal. of Math.(Oxford) Vol. 45, pp 350-372, 1914.
  [4] Mark B Villarino, “Accuracy of Ramanujan’s Formula for Perimeter of an Ellipse”, Journal of inequalities in Pure and Applied Math. Vol. 1, Issue1, pp 1-10, 2006.

  Citation
  K. Idicula Koshy, "Error Reduction in Koshy’s Formula for Ellipse Perimeter: Correction Factor and Improved Approximation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.1-8, 2020

• Open Access   Article

  Numerical Solutions for unsteady flow past a semi- infinite plate using Alternating –Direction-Implicit (ADI) Technique

  A. Kaushik

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.9-14, Feb-2020

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  A study of an unsteady flow past a semi- infinite plate with oscillations in temperature is presented in this work. The non-linear differential equations governing flow and heat transfer have been solved numerically by using Alternating–Direction-Implicit (ADI) Technique. The numerical values of velocity and temperature are obtained and presented graphically at different times and for different values of Prandtl number and frequency parameter. It is observed that velocity decreases with increase in Prandtl number and frequency parameter.

  Key-Words / Index Term
  Heat transfer, oscillating temperature, Prandtl number

  References
  [1] T. Fujii and H. Imura, “Natural Convection heat transfer from a plate with arbitrary inclination”, International Journal of Heat and Mass Transfer, Vol 15, Issue 4, pp 1873-1886, 1972.
  [2] L. Pera and B. Gebhart, “Natural Convection boundary layer flow over horizontal and slightly inclined surfaces”, International Journal of Heat and Mass Transfer, Vol.16, Issue 6, pp 1131-1147, 1973.
  [3] T. S. Chen, H. C. Tien and B. F. Armaly, “Natural Convection on horizontal, inclined and vertical plates with variable surface temperature or heat flux”, International Journal of Heat and Mass Transfer. Vol. 29, Issue 10, pp 1465-1478, 1986.
  [4] K. Ekambavannan and P. Ganesan, “Finite difference solution of unsteady natural convection boundary layer flow over an inclined plate with variable surface temperature”, Wärme and Stoffübertragung, Vol. 30, Issue 2, pp 63-69, 1994.
  [5] N. Pandya and R. K. Yadav, ” Numerical Simulation of Soret-Dufour and Radiation effects on Unsteady MHD flow of Viscoelastic Dusty fluid over Inclined Porous Plate”, International Journal of Computer Sciences and Engineering, Vol.6,Issue6,pp898-908,2018.
  
  [6] M. D. Kelleher and K. T. Yang, “Heat transfer responses of laminar free convection boundary layers along a vertical heated plate to surface temperature oscillations”, The Journal of Applied Mathematics and Physics. Vol. 19, Issue 1, pp 31-44,1968.
  [7] V. M. Soundalgekar and M. R. Patil , “Stoke’s problem for a vertical infinite plate with variable temperature”, Astrophysics and Space Science. Vol. 59, Issue 2, pp 503-506, 1978.
  [8] V. M. Soundalgekar, “Free convection effects on the flow past an infinite vertical oscillating plate”, Astrophysics and Space Science. Vol. 64, Issue 1, pp 165-171, 1979.
  [9] V. M. Soundalgekar, “Unsteady forced and free convective flow past an infinite vertical porous plate with oscillating wall temperature and constant suction”, Astrophysics and Space Sci,Vol. 66, Issue 1, pp 223- 233, 1979.
  [10] M. A. Hossain, “Simultaneous heat and mass transfer on oscillatory free convection boundary layer flow”, International Journal of Energy Research, Vol. 12 , Issue 2, pp 205-206, 1998.
  [11] M. A. Hossain, S. K. Das and I. Pop, “ Heat transfer response of MHD free convection along a vertical plate to surface temperature oscillations”, International Journal of Nonlinear Mechanics. Vol. 33, Issue 3, pp 541-553,1998.
  [12] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Transient free convection flow past an infinite vertical plate with periodic temperature variation”, Transactions of the ASME, Journal of Heat Transfer. Vol. 121, Issue 4, pp 1091-1094, 1999.
  [13] H. P. Rani and R. Devaraj, “Numerical solution of unsteady flow past a vertical cylinder with temperature oscillations”, Forschung im Ingenieurwesen. Vol. 68, Issue 2, pp 75-78, 2003.
  [14] Nawaf H. Saeid, “Periodic free convection from vertical plate subjected to periodic surface temperature oscillating”, International Journal of thermal science. Vol. 43, Issue 6, pp 569-574, 2004.
  [15] H. M. Duwairi, Rebhi A. Damseh and Bourhan Tashtoush , “Transient mixed convection along a vertical plate embedded in porous media with internal heat generation and oscillating temperature”, Chemical Engineering Communications Vol.194, Issue 11,pp 1516-1530, 2007.
  [16] G. Palani and Kwang-Yong Kim,”Numerical solutions for unsteady flow past a semi-infinite inclined plate with temperature oscillations”, Journal of Mechanical Science and Technology, Vol.23, Issue 6, pp 1710-1717, 2009.
  [17] R. Choudhury and D. Dey, “Free Convective Elastico-Viscous Fluid Flow With Heat And Mass Transfer Past An Inclined Plate In Slip Flow Regime”, Latin American Applied Research, Vol. 42, Issue 4, pp 327-332, 2012 .
  [18] I. J. Uwanta, and Murtala Sani, “Heat and Mass Transfer Flow Past an Infinite Vertical Plate with Variable Thermal Conductivity”, International Journal of Applied Information Systems, Vol. 6, Issue 1, pp 16-24, 2013.
  [19] R. P. Chandra, M. C. Raju, G. S. S. Raju, “Thermal and Solutal Buoyancy Effect on MHD Boundary Layer Flow of a Visco-Elastic Fluid Past a Porous Plate with Varying Suction and Heat Source in the Presence of Thermal Diffusion”, Journal of Applied and Computational Mathematics, Vol. 4, Issue 5, pp 249-255, 2015.
  [20] U. S. Rajput and Gaurav Kumar, “Effect of Heat Absorption on MHD Flow Over a Plate with Variable Wall Temperature”, Journal of Applied Science and Engineering, Vol.20, Issue 3, pp 277-282, 2017.
  [21] Arti Kaushik, “Numerical Study Of an Unsteady 2-D Compressible Inviscid Flow with Heat Transfer with Slip Boundary Conditions Using MacCormack Technique”, International Journal of Scientific Research in Mathematical and Statistical Sciences ,Vol.4, Issue 5, pp 17-26, 2017.

  Citation
  A. Kaushik, "Numerical Solutions for unsteady flow past a semi- infinite plate using Alternating –Direction-Implicit (ADI) Technique," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.9-14, 2020

• Open Access   Article

  Cone b-Metric Spaces and Extension of Fixed Point Theorems of Generalized Contraction Mappings with rational expression

  S. K. Tiwari, R. Kurre

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.15-20, Feb-2020

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  In this paper, we establish and extend some unique fixed point theorems for generalized contraction involving rational expressions in cone b- metric space. Our presented theorems are extended and improve of existing literature for mappings satisfying certain rational inequality.

  Key-Words / Index Term
  Fixed Point, Contraction mappings, Complete cone metric space, Complete cone b-metric space, Rational inequality

  References
  [1] S. Banach, “Sur les operations dans less ensembles abstrait et leur application au equations”, integrals Fundam. Math. 3, 133-181, 1922.
  [2] L. G. Huang and X. Zhang, “Cone metric spaces and fixed point theorems of contractive mappi ngs”, J. Math. Anal. Appl. 332(2), 1468 -1476, 2007.
  [3] S. Rezapour and R. Hamlbarani, “Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl. 345, 719-724, 2008.
  [4] N. Hussain and M. H. Shah,“KKM mappings in cone b-metric spaces”. Comput. Mat. Appl. 62, 1677-1684, 2011.
  [5] L. Shi and S. Xu, “Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces”, Fixed point theory and application, no. 120, 2013.
  [6] H. Huang and S. Xu, “Fixed point theorems of contractive mappings in cone b-metric spaces and applications”, Fixed point theory and Appls. 112:2013, 2013.
  [7] R. George and B. Fisher,“Some generalized results of fixed points in cone b-metric spaces”, Mathematic Moravica, 17(2), 38-50, 2013.
  [8] R. Georg and M. S. Khan,“On presic type extension of Banach contraction principle”, Int. J. Math. Anal. 21, 1019-1024, 2011.
  [9] K. P. R. Rao, Md. Mushtaq Ali and B. Fisher, “On Presic type generalization of Banach contraction principle”, Mat Moravic 15(1), 41-47, 2011.
  [10] R. George, K. P. Reshma and R.Rajagopalan, “generalized fixe poin theorem of presic type in Cone Metric spaces and application to Markow process” Fixed point theory, Article ID2011:85, 2011.
  [11] S. K. Tiwari, Rita Pal and R. P. Dubey “Generalization of fixed point theorems in cone b-metric spaces”, Int. J. of Math. Archive, 5 (5), 115-122, 2014.
  [12] G. S. Saluja, “Some Fixed point theorems of contractive type condition in cone b-metric spaces”, Nonlinear analysis forum 20(8), 241-255, 2015.
  [13] P. Kumar and Z. K. Ansari, “Some common fixed point theorems of contractive mappings in cone b-metric spaces”, Int. J. of Math and its application 5 (4-A1), 1- 8, 2017
  [14] S. K. Tiwari and Rukhamani Kurre, “Generalized fixed point theory of cone b-metric spaces”, 8(4), 139-146, 2017.
  [15] G. S. Saluja, “Fixed point Results for generalized contractions in cone b- metric spaces”, Palestine journal of Mathematics, 6(1), 76-83, 2017.
  [16] P. Kumar, Z. K. Ansari and A. Garg, “Fixed-point theorems for Rational contraction mappings in cone b-metric spaces”, South East Asain Journal of Math. & Math. Sci. 13(1), 111- 124, 2017.
  [17] B. K. Dass and S. Gupta,“An extension of Banach contraction principle by rational expression”, Indian J. Pure Appl. Math., 6, 1455-1458, 1975.
  [18] G. S. Saluja, “Some fixed-point results for contractive type condition in cone b-metric spaces and application”, Int. J. Math. Comb., 1, 1-17, 2018.
  [19] I. A. Bakhtin, “Contraction mapping principle inalmost metric spaces”, Funct. Anal. Gos. Ped. Inst. Unianwsk, 30, 26-37, 1989.
  [20] S. Czerwik, “Contraction mappings in b-metric Universitatis Ostraviensis, 1, 5-11, 1993.
  [21] S. Czerwik,“Nonlinear set-valued contraction mappings in b-metric spaces”. Atti Semin. Mat. Fis. Univ. Modena, 46, 263-276, 1998.
  [22] S. Czerwik, D. Krzyszt and S. L. Singh, “Round- off stability of iteration procedures for operators in b-metric spaces”, J. Natur. Phys. Sci., 11, 87-94, 1997.
  [23] S. Czerwik, D. Krzyszt and S. L. Singh,“Round-off stability of iteration procedures for set valued operators in bmetric spaces”, J. Natur. Phys. Sci., (2001).
  [24] S. Jankovic, Z. Kadelburg and S. Radenovic,“On cone metric spaces: a survey” Nonlinear Anal. 4(7), 2591-2601, (2011).

  Citation
  S. K. Tiwari, R. Kurre, "Cone b-Metric Spaces and Extension of Fixed Point Theorems of Generalized Contraction Mappings with rational expression," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.15-20, 2020

• Open Access   Article

  Regularity and Normality in Bitopological Spaces

  R. Roshmi, M.S. Hossain

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.21-25, Feb-2020

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  Abstract
  In this paper, we define one notion of regular and two notions of normal space in bitopological spaces. We find some relationship from topological spaces and bitopological spaces of such notions. Then, we have shown that such notions given satisfy hereditary, projective and productive properties. Furthermore, we have shown some of their features.

  Key-Words / Index Term
  Topology, Bitopology, Regular property, Normal property, Hereditary property

  References
  [1] J.C.Kelly; “Bitopological Spaces”, Proc. London Math. Soc, Vol 13, No 3,pp 71-89,1962.
  
  [2] H.Tietze;“Beitragezurallgemeinen topology 1”, Math. Ann, Vol 88, pp 290-312, 1923.
  [3] J.M. Aarts and M. Mrsevic; “Pairwise complete regularity as a separation axiom”, J. Australian Mathematical Society, Vol 48, No 2, pp 235-245, 1990.
  [4] Hyung-JooKoh; “Separation axioms in bitopological spaces”, Bull. Korean Math. Soc, Vol 16, pp 11-14, 1979.
  [5] S. Lal; “Pairwise concepts in bitopological spaces” , J. Australian Mathematical Society, Vol 26, No 2, pp 241-250, 1978.
  [6] E.P. Lane; “Bitopological spaces and quasi-uniform spaces”,Proc. Lond. Math. Soc, Vol 17, No 3, pp 241-256, 1967.
  [7] T.M. Nour; “A note on five separation axioms in bitopological spaces”, Indian J. Pure Appl. Math, Vol 26, No 7, pp 669-674,1993.
  [8] M. Arunmaran and K. Kannan; “ Discussion on quotient bi-space and on pairwise regular and normal spaces in bitopologicalspaces”, Advances In Mathematical Sciences,Vol 1, pp 13-15, 2019.
  [9] C.Dorsett; “Unique, foundational properties of completely regular, normal and related properties”, J. Mathematical Sciences: Advances and Applications, Vol 44, pp 111-117, 2017.
  [10] T.H. Jasiml and L.H.Othman;“ On completely normal spaces”,Tikrit J. Pure. Sci, Vol 24, No 5, pp 111-114, 2018.
  [11] J. M. H and L. C. A;“Onbicontinuous functions in strongly pairwise normal spaces”, Global J. Pure and Appl.
  Math., Vol 12, No1, pp 1053-1060, 2016.
  [12] A. Mukharjee; “Some new bitopologicalnotions”,Publications De L’InstitutMathematique, Vol 93, No 107, pp 165-172, 2012.
  [13] M.G.Murdeshwar and mS.A.Naimpally;“Quasi-uniform Topologicalspaces”, MonographNoordhoof Ltd, 1966.
  [14] I.L. Reilly;“Onbitopological separation properties”,Nanta Math, Vol 5, pp 14-25, 1972.
  [15] S. Lipschutz;“General topology. Schaum’s outline series”, McGRAW-HILL Book Company, Newyork, 1965.

  Citation
  R. Roshmi, M.S. Hossain, "Regularity and Normality in Bitopological Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.21-25, 2020

• Open Access   Article

  Poisson Regression Model of the Annual Frequency of Tropical Cyclone Genesis in the Western North Pacific

  T.P. Leahy

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.26-32, Feb-2020

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  Abstract
  This study investigated the annual frequency of tropical cyclone genesis in the western North Pacific (WNP). Joint Typhoon Warning Centre data between 1991-2010 identified 332 tropical cyclones as defined by the Saffir-Simpson hurricane wind scale. The primary interest in this study was to understand the large-scale environmental atmospheric and oceanic factors that influence the annual frequency through a composite analysis. This study found an anomalous sea surface temperature (SST) pattern that reflects an El Niño Modoki-like phase generated a central-western North Pacific SST gradient amplifying anomalous westerly low-level zonal winds. These anomalous low-level westerly zonal winds contribute to tropical circulation generating anomalous anticyclonic vorticity suppressing the probability of genesis occurring. As a result of this insight, a simple Poisson generalised linear model was developed with a single covariate to model the annual frequency of tropical cyclone genesis. The single covariate is the mean of the zonal winds in the south-eastern corner of the WNP. This model produced an in-sample correlation with the observed annual frequency of 0.73 and an out-of-sample correlation of 0.67.

  Key-Words / Index Term
  tropical cyclone, Poisson, genesis, Modoki

  References
  [1] K. Emanuel and D. S. Nolan, ‘Tropical cyclone activity and the global climate system’, presented at the 26th Conference on Hurricanes and Tropical Meteorolgy, 2004, pp. 240–241.
  [2] B. Wang, Y. Yang, Q.-H. Ding, H. Murakami, and F. Huang, ‘Climate control of the global tropical storm days (1965–2008)’, Geophys. Res. Lett., vol. 37, no. 7, 2010.
  [3] L. Bengtsson et al., ‘How may tropical cyclones change in a warmer climate?’, Tellus Dyn. Meteorol. Oceanogr., vol. 59, no. 4, pp. 539–561, 2007.
  [4] T. R. Knutson et al., ‘Tropical cyclones and climate change’, Nat. Geosci., vol. 3, no. 3, p. 157, 2010.
  [5] K. J. Walsh et al., ‘Tropical cyclones and climate change’, Wiley Interdiscip. Rev. Clim. Change, vol. 7, no. 1, pp. 65–89, 2016.
  [6] K. A. Emanuel, ‘Downscaling CMIP5 climate models shows increased tropical cyclone activity over the 21st century’, Proc. Natl. Acad. Sci., vol. 110, no. 30, pp. 12219–12224, 2013.
  [7] K. Emanuel, ‘Effect of upper-ocean evolution on projected trends in tropical cyclone activity’, J. Clim., vol. 28, no. 20, pp. 8165–8170, 2015.
  [8] J. C. Chan, J. Shi, and C. Lam, ‘Seasonal forecasting of tropical cyclone activity over the Western North Pacific and the South China Sea’, Weather Forecast., vol. 13, no. 4, pp. 997–1004, 1998.
  [9] J. CL Chan, J. Shi, and K. S. Liu, ‘Improvements in the seasonal forecasting of tropical cyclone activity over the western North Pacific’, Weather Forecast., vol. 16, no. 4, pp. 491–498, 2001.
  [10] J. C. Chan, ‘Interannual and interdecadal variations of tropical cyclone activity over the western North Pacific’, Meteorol. Atmospheric Phys., vol. 89, no. 1–4, pp. 143–152, 2005.
  [11] R. C. Li and W. Zhou, ‘Changes in western Pacific tropical cyclones associated with the El Niño–Southern Oscillation cycle’, J. Clim., vol. 25, no. 17, pp. 5864–5878, 2012.
  [12] J. Huangfu, W. Chen, M. Jian, and R. Huang, ‘Impact of the cross-tropopause wind shear on tropical cyclone genesis over the Western North Pacific in May’, Clim. Dyn., vol. 52, no. 7–8, pp. 3845–3855, 2019.
  [13] S. J. Camargo and A. H. Sobel, ‘Revisiting the influence of the quasi-biennial oscillation on tropical cyclone activity’, J. Clim., vol. 23, no. 21, pp. 5810–5825, 2010.
  [14] S. J. Camargo and A. H. Sobel, ‘Western North Pacific tropical cyclone intensity and ENSO’, J. Clim., vol. 18, no. 15, pp. 2996–3006, 2005.
  [15] J. C. Chan, ‘Tropical cyclone activity in the western North Pacific in relation to the stratospheric quasi-biennial oscillation’, Mon. Weather Rev., vol. 123, no. 8, pp. 2567–2571, 1995.
  [16] M. K. Tippett, S. J. Camargo, and A. H. Sobel, ‘A Poisson regression index for tropical cyclone genesis and the role of large-scale vorticity in genesis’, J. Clim., vol. 24, no. 9, pp. 2335–2357, 2011.
  [17] C. L. Bruyère, G. J. Holland, and E. Towler, ‘Investigating the use of a genesis potential index for tropical cyclones in the North Atlantic basin’, J. Clim., vol. 25, no. 24, pp. 8611–8626, 2012.
  [18] J.-Y. Yu, L.-P. Hsiao, and P.-G. Chiu, ‘Evaluating the Emanuel-Nolan genesis potential index: Contrast between North Atlantic and western North Pacific’, Terr. Atmospheric Ocean. Sci., vol. 29, no. 2, 2018.
  [19] R. C. Li and W. Zhou, ‘Modulation of western North Pacific tropical cyclone activity by the ISO. Part I: Genesis and intensity’, J. Clim., vol. 26, no. 9, pp. 2904–2918, 2013.
  [20] D. Chen, H. Wang, J. Liu, and G. Li, ‘Why the spring North Pacific Oscillation is a predictor of typhoon activity over the Western North Pacific’, Int. J. Climatol., vol. 35, no. 11, pp. 3353–3361, 2015.
  [21] R. Zhan, Y. Wang, and M. Wen, ‘The SST gradient between the southwestern Pacific and the western Pacific warm pool: A new factor controlling the northwestern Pacific tropical cyclone genesis frequency’, J. Clim., vol. 26, no. 7, pp. 2408–2415, 2013.
  [22] X. Zhang, S. Zhong, Z. Wu, and Y. Li, ‘Seasonal prediction of the typhoon genesis frequency over the Western North Pacific with a Poisson regression model’, Clim. Dyn., vol. 51, no. 11–12, pp. 4585–4600, 2018.
  [23] J.-H. Chu, C. R. Sampson, A. S. Levine, and E. Fukada, ‘The joint typhoon warning center tropical cyclone best-tracks, 1945–2000’, Ref NRLMR7540‐02, vol. 16, 2002.
  [24] D. P. Dee et al., ‘The ERA‐Interim reanalysis: Configuration and performance of the data assimilation system’, Q. J. R. Meteorol. Soc., vol. 137, no. 656, pp. 553–597, 2011.
  [25] W. Gardner, E. P. Mulvey, and E. C. Shaw, ‘Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models’, Psychol. Bull., vol. 118, no. 3, p. 392, 1995.
  [26] D. W. Brown, Statistical process control: theory and practice. Chapman and Hall, 1991.
  [27] K. Ashok, S. K. Behera, S. A. Rao, H. Weng, and T. Yamagata, ‘El Niño Modoki and its possible teleconnection’, J. Geophys. Res. Oceans, vol. 112, no. C11, 2007.
  [28] G. Chen and C.-Y. Tam, ‘Different impacts of two kinds of Pacific Ocean warming on tropical cyclone frequency over the western North Pacific’, Geophys. Res. Lett., vol. 37, no. 1, 2010.
  [29] B. Zhou and X. Cui, ‘Sea surface temperature east of Australia: A predictor of tropical cyclone frequency over the western North Pacific?’, Chin. Sci. Bull., vol. 56, no. 2, pp. 196–201, 2011.

  Citation
  T.P. Leahy, "Poisson Regression Model of the Annual Frequency of Tropical Cyclone Genesis in the Western North Pacific," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.26-32, 2020

• Open Access   Article

  A study on the estimation of the Transmuted Generalized Uniform Distribution

  Issa Cherif Geraldo

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.33-39, Feb-2020

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  Abstract
  In this paper, we consider the maximum likelihood (ML) estimation of the parameters a new probability distribution recently developed and called transmuted generalized uniform distribution (TGUD). Because of the complicated form of its log-likelihood function, this ML estimation can only be done by using numerical optimization algorithms but this problem has not been studied yet. We address this lack through a comprehensive simulation study in R software using some of the best optimization algorithms (Newton, quasi-Newton and Nelder-Mead algorithms). It is found that the Nelder-Mead algorithm is the best of all the selected algorithms.

  Key-Words / Index Term
  Numerical optimization, iterative method, maximum likelihood, parameter estimation, transmuted distribution

  References
  [1] Z. Ahmad, G.G. Hamedani, N.S. Butt, “Recent developments in distribution theory: a brief survey and some new generalized classes of distributions”, Pakistan Journal of Statistics and Operations Research, Vol. 15, Issue 1, pp. 87–110, 2019.
  [2] C. Subramanian, A.A. Rather, “Transmuted generalized uniform distribution”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 5, pp. 25-32, 2018.
  [3] C.-S. Lee, “Estimations in a generalized uniform distribution”, Journal of the Korean Data and Information Science Society, Vol. 11, Issue 2, pp. 319–325, 2000.
  [4] R Core Team, “R: A Language and Environment for Statistical Computing”, R Foundation for Statistical Computing, Austria, 2019.
  [5] I. Griva, S.G. Nash, A. Sofer, “Linear and Nonlinear Optimization”, Society for Industrial and Applied Mathematics, USA, 2009.
  [6] J.E. Dennis Jr, R.B. Schnabel, “Numerical Methods for Unconstrained Optimization and Nonlinear Equations”, Society for Industrial and Applied Mathematics, USA, 1996.
  [7] J. Nocedal, S.J. Wright, “Numerical optimization”, Springer, USA, 2006.
  [8] J.A. Nelder, R. Mead, “A simplex algorithm for function minimization”, Computer Journal, Vol. 7, Issue 4, pp. 308–313, 1965.
  [9] J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, “Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions”, SIAM Journal on Optimization, Vol. 9, Issue 1, pp. 112–147, 1998.
  [10] J.C. Lagarias, B. Poonen, M.H. Wright, “Convergence of the restricted Nelder–Mead algorithm in two dimensions”, SIAM Journal on Optimization, Vol. 22, Issue 2, pp. 501–532, 2012.
  [11] G. Luebeck, R. Meza, “Bhat: General likelihood exploration”, R package version 0.9-10, 2013.
  [12] R. Varadhan, “alabama: Constrained Nonlinear Optimization”, R package version 2015.3-1, 2015.

  Citation
  Issa Cherif Geraldo, "A study on the estimation of the Transmuted Generalized Uniform Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.33-39, 2020

• Open Access   Article

  Anomaly detection for Cyber Security: Time Series Forecasting and Deep Learning

  Giordano Colò

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.40-52, Feb-2020

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  Abstract
  Finding anomalies when dealing with a great amount of data creates issues related to the heterogeneity of different values and to the difficulty of modelling trend data during time. In this paper we combine the classical methods of time series analysis with deep learning techniques, with the aim to improve the forecast when facing time series with long-term dependencies. Starting with forecasting methods and comparing the expected values with the observed ones, we will find anomalies in time series. We apply this model to a bank cybersecurity case to find anomalous behaviour related to branches applications usage.

  Key-Words / Index Term
  Anomaly detection, time series, cybersecurity, deep learning, stochastic processes, LSTM

  References
  [1] Ba, J., Hinton, G. E., Mnih, V., Leibo, J. Z., & Ionescu, C.,
  “Layer normalization”, Advances in neural information processing systems, pp. 4331–4339, 2016.
  [2] Michèle Basseville, Igor V Nikiforov, et al.,
  “Detection of abrupt changes: theory and application”, vol. 104, Prentice Hall Englewood Cliffs, 1993.
  [3] Peter J Brockwell and Richard A Davis,
  “Introduction to time series and forecasting”, Springer, 2016.
  [4] Klaus Greff, Rupesh K Srivastava, Jan Koutník, Bas R Steunebrink, and Jürgen Schmidhuber, “Lstm: A search space odyssey”, IEEE transactions on neural networks and learning systems, no. 10, 2222–2232, 2016.
  [5] Kyle Hundman, Valentino Constantinou, Christopher Laporte, Ian Colwell, and Tom Soderstrom, “Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding”, Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, ACM, pp. 387–395, 2018.
  [6] Daehyung Park, Hokeun Kim, Yuuna Hoshi, Zackory Erickson, Ariel Kapusta, and Charles C Kemp, “A multimodal execution monitor with anomaly classification for robot-assisted feeding”, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, pp. 5406–5413, 2017.
  [7] T Januschowski, J Gasthaus, Y Wang, D Salinas, V Flunkert et al., “Criteria for classifying forecasting methods”, International Journal of Forecasting, 36 (1), 167-177, 2020.
  [8] S Sherstinsky, Alex. (2020). “Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) network”. Physica D: Nonlinear Phenomena, To be published, Vol. 404, 2020.
  [9] Fan, Chenyou et al. “Multi-task spatiotemporal neural networks for structured surface reconstruction”, 2018 IEEE Winter Conference on Applications of Computer Vision (WACV), pp. 1273-1282, 2018.

  Citation
  Giordano Colò, "Anomaly detection for Cyber Security: Time Series Forecasting and Deep Learning," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.40-52, 2020

• Open Access   Article

  Design a Solar Power system for Earth orbiting satellite

  M. Raja, Vijayalaxmi Matolia

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.53-56, Feb-2020

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  Abstract
  A satellite is an object in space that orbits or circles around a bigger object in space. The satellite has four parts – a power system (which could be solar or nuclear), a way to control its attitude, an antenna to transmit and receive information and a payload to collect information such as a camera or a particle detector. The Satellites has used for some applications, such as communicate and interchanges weather forecast, navigation, earth/space perception, and logical examinations. To calculates the efficiency of solar cell using MATLAB Environment.

  Key-Words / Index Term
  LEO, Photovoltaic Cell, Ultraviolet Degradation, DC to AC Convertion

  References
  [1] Mukund R. Patel, “Spacecraft Power Systems”, CRC Press, 2004.
  [2] G. N. Tiwari, Solar Energy, Narosa Publishing House, 2013.
  [3] C. M. Mackenzie, Solar Power Systems for satellites in Near-Earth Orbit.
  [4] Craig S. Clarke, Alejandro Lopez Mazarias, “Power system challenges for small satellite missions”.
  [5] Frohlich, R. C., Contemporary measures of the solar constant: The solar output and its variation, Colorado Associated University Press, Boulder, CO, 1977.
  [6] V Parameswaram, Mateen Khan, M Pathan, “Solar power satellite and microwave transmission from space to Earth for generating Electrical power”.
  [7] M Maqsood and M Nauman Nasir, Wireless electricity (Power) transmission using solar based power satellite technology.
  [8] G. D. Rai, “Solar Energy” Utilisation, Khana Publishers, 2005.

  Citation
  M. Raja, Vijayalaxmi Matolia, "Design a Solar Power system for Earth orbiting satellite," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.53-56, 2020

• Open Access   Article

  Composite-Type Estimator of the Coefficient of Variation under SRSWOR

  Rina Shah, P. A. Patel

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.57-63, Feb-2020

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  Abstract
  In this article we address the problem of estimating the coefficient of variation (cv) of a finite population using two auxiliary variables. Estimation of the cv, a measure of variability, is one of the important parameters and the real use of its estimate would be in determining a sample size for a future study. The regression and composite-type estimators of the coefficient of variation are suggested and their performances are compared with the estimators available in the literature empirical study. Also, a small scale Monte Carlo simulation is carried out to support the findings. Among the estimators considered under study, the suggested estimators have performed very well.

  Key-Words / Index Term
  Auxiliary variable, coefficient of variation, finite population, simulation, SRSWOR

  References
  [1] Das, A. K. and Tripathi, T.P. “Sampling strategies for coefficient of variation using knowledge of the mean using an auxiliary character.” Tech.Rep.Stat.Math.5/81.ISI, Calcutta, 1981 a.
  [2] Das, A. K. and Tripathi, T.P. “A class of estimators for coefficient of variation using knowledge on coefficient of variation of an auxiliary character.” Paper presented at 35th annual conference of Ind. Soc. Agricultural Statistics. Held on New Delhi, India. 1981 b.
  [3] Rajyaguru, A. and Gupta, P. “On the estimation of the coefficient of variation from finite population-II.” Model Assisted Statistics and Application, Vol.36, Issue.2, pp.145-156, 2002.
  [4] Rajyaguru, A. and Gupta, P., “On the estimation of the coefficient of variation from finite population- II.” Model Assisted Statistics and Application, Vol.1, Issue.1, pp. 57-66, 2006.
  [5] Tripathi, T.P. Singh, H.P. and Upadhyay, L.N. A general method of estimation and its application to the estimation of coefficient of variation. Statistics in Transition, Vol.5, Issue.6, pp. 887-909, 2002.
  [6] Patel, P.A. and Shah, Rina, “A Monte Carlo comparison of some suggested estimators of coefficient of variation in finite population.” Journal of Statistics sciences, Vol.1, Issue.2, pp.137- 147, 2009.
  [7] Archana, V and Rao, K. A. “Ratio estimators for the coefficient of variation in a finite population”. Pak.j.stat.oper.res. Vol.VII No.2 pp.265-28, 2011
  [8] Kadilar, C. and Cingi, H. “A new ratio estimator using two auxiliary variables”. Applied Mathematics and Computation.” Vol.162, pp. 901-908, 2005.
  [9] Murthy, M. N., Sampling Theory and Methods, Calcutta: Statistical Publishing Society, 1967

  Citation
  Rina Shah, P. A. Patel, "Composite-Type Estimator of the Coefficient of Variation under SRSWOR," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.57-63, 2020

• Open Access   Article

  Reliability Analysis of Solar Energy Resources using Weibull distribution for a Standalone System in Indian Context

  Surendra H.H., Seshachalam D., Sudhindra K.R.

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.1 , pp.64-68, Feb-2020

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  Abstract
  The reliability of a standalone solar power plant is an important objective to deliver economical and quality power for any customer. The unreliable solar power has major socio-economic impact on utility and its customers. Weibull distribution function is used to analyse the time series solar data obtained from the weather stations. The nonlinear behaviour of solar irradiance has major impact on the performance and reliability of a solar power plant. Statistical data of solar energy resources under Indian conditions are simulated using system advisor model and reliability analytics tool kit for reliability analysis. In this paper, a study assessing the impact of the solar irradiance and losses on power generation is presented.

  Key-Words / Index Term
  Reliability, Weibull, irradiance, probability distribution

  References
  [1] Malek Belouda, Jamel Belhadj, Bruno Sareni, Xavier Roboam, “Battery sizing for a stand-alone passive wind system using statistical techniques”, Eight International Multi-Conference on systems, Signals & Devices, 2011. 10.1109/SSD.2011.5767373
  [2] G. B. Shrestha, L. Goel, “A study on optimal sizing of stand-alone photovoltaic Stations”. IEEE Transactions on Energy Conversion, Vol. 13, No. 4, pp. 373-378, December 1998.
  [3] Bogdan S. Borowy, Ziyad M. Salameh, “Optimum photovoltaic array size for a Wind/PV hybrid system “, IEEE Transactions on Energy Conversion, vol. 9, N. 3, 482-488, September 1994.
  [4] Bogdan S. Borowy, Ziyad M. Salameh, “Methodology for optimally sizing the combination of a battery bank and PV array in a Wind/PV hybrid system”, IEEE Transactions on Energy Conversion, vol. 11, No. 2, pp. 367-375, June 1996.
  [5] Safa Fezai , Jamel Belhadj.”Optimal sizing of a Stand-alone photovoltaic system using statistical approach” International journal of renewable energy research Vol.4, No.2, 2014.
  [6] Hongxing Yang, Wei Zhou, Lin Lu, Zhaohong Fang, “Optimal sizing method for stand-alone hybrid solar– wind system with LPSP technology by using genetic algorithm”, Solar Energy 82, 354–367, 2008.
  [7] Ramos Hernanz, Campayo Martín, Zamora Belver, Larrañaga Lesaka, Zulueta Guerrero, Puelles Pérez, “Modeling of Photovoltaic Module “, International Conference on Renewable Energies and Power Quality , 2010.
  [8] Kinal Kachhiya, Makarand Lokhande, Mukesh Patel, “MATLAB/Simulink model of solar PV module and MPPT algorithm”, National Conference on Recent Trends in Engineering & Technology, May 2011.
  [9] Sree Manju B, Ramaprabha R, Mathur B.L, “Design and Modeling of Standalone Solar Photovoltaic Charging System”, International Journal of Computer applications, vol 18, No.2, March 2011.
  [10] Hung D. Q., Mithulananthan N., K. Y. Lee Determining PV Penetration for Distribution Systems with Time-Varying Load Models. IEEE Transactions on Power Systems; 2014,29(6), p.3048-3057.
  [11] N. Blair, A. P. Dobos, J. Freeman, T. Neises, and M. Wagner, “System advisor model, general description,” NREL, Feb. 2014.
  [12] Jussi Ekstrom, Matti Koivisto, Ilkka Mellin, Robert John Millar, Member, IEEE, and Matti Lehtonen, Member, IEEE “A Statistical Model for Hourly Large-Scale Wind and Photovoltaic Generation in New Locations” IEEE Transactions On Sustainable Energy, vol. 8, no. 4, October 2017
  [13] Peng Li, Roger Dargaville, Feng Liu, Jing Xia, and Yong-Duan Song, Senior Member, IEEE “Data-Based Statistical Property Analyzing and Storage Sizing for Hybrid Renewable Energy Systems” IEEE Transactions On Industrial Electronics, vol. 62, no. 11, november 2015
  [14] Syafawati A.N., I.Daut, S.S. Shema, M. Irwanto, Z. Farhana, N. Razliana, Shatri C. “Potential of wind and solar energy using Weibull and hargreaves method analysis” The 5th International Power Engineering and Optimization Conference (PEOCO2011), Shah Alam, Selangor, Malaysia : 6-7 June 2011.
  [15] Abubakar Abdulkarim, Sobhy M. Abdelkader and D. John Morrow “Statistical Analyses of Wind and Solar Energy Resources for the Development of Hybrid Microgrid” 2nd International Congress on Energy Efficiency and Energy Related Materials, Springer International Publishing Switzerland 2015.
  [16] Billinton R and Allen R.N., Reliability Evaluation of Engineering Systems, Springer New York, Plenum, page 6-18,1983.
  [17] Anwar M Hossain and William J Zimmer “Comparison of estimation methods for weibull parameters: complete and censored samples” Journal of statistical computation and simulation 2003 Vol 73(2) 145-153.
  [18] Shambhabi Chatterjee1, Kamalika Ghosh, Debashish Das “Analyzing various approaches for Measurement of Solar PV Potential through Urban Built Form Geometry modifications” International Journal of Computer Sciences and Engineering. Volume-4, Special Issue-6, Aug 2016

  Citation
  Surendra H.H., Seshachalam D., Sudhindra K.R., "Reliability Analysis of Solar Energy Resources using Weibull distribution for a Standalone System in Indian Context," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.64-68, 2020