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• Open Access   Article

  Approximation of D.I.Y. Water Rocket Dynamics Including Air Drag

  L. Fischer, T. Günther, L. Herzig, T. Jarzina, F. Klinker, S. Knipper, F.G. Schürmann, M. Wollek

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.1-13, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.113

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  Abstract
  If you want to get accurate predictions for the motion of water and air propelled D.I.Y rockets, neglecting air resistance is not an option. But the theoretical analysis including air drag leads to a system of differential equations which can only be solved numerically. We propose an approximation which simply works by the estimation of a definite integral, and which is even feasible for undergraduate physics courses. The results only slightly deviate from the reference data (received by the Runge-Kutta method). The motion is divided into several flight phases that are discussed separately and the resulting equations are solved by analytic and numeric methods. The different results from the flight phases are collected and are compared to data that has been achieved by well explained and documented experiments. Furthermore, we theoretically estimate the rockets drag coefficient. The result is confirmed by a wind tunnel experiment.

  Key-Words / Index Term
  Rocket equation, Thrust, Dynamics, Drag coefficient

  References
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  [6] T. A. Campbell, M. Okutsu, “Model Rocket Projectfor Aerospace Engineering Course: Trajectory Simulation and Propellant Analysis”, arXiv:1708.01970 [physics.ed-ph], 2017.
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  Citation
  L. Fischer, T. Günther, L. Herzig, T. Jarzina, F. Klinker, S. Knipper, F.G. Schürmann, M. Wollek, "Approximation of D.I.Y. Water Rocket Dynamics Including Air Drag," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.1-13, 2019

• Open Access   Article

  Probability Projection of Total Fertility Rate for Assesing the Replacement Level of Fertility of Selected State Using MCMC Technique under Bayesian Modeling

  Abhishek Singh Chauhan, Subhi Srivastava, Anurag Verma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.14-21, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.1421

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  The present paper explains Bayesian methodological approach for projection of Total fertility rate (TFR) for seven states of India taken as (Uttar Pradesh, Bihar, Assam, Madhya Pradesh, Gujarat, Rajasthan, Haryana). The projection has been done by using Gompertz model and the parameters of the model have been estimated using MCMC (Monte Carlo Markove Chain) Technique in Bayesian procedure. Previous year SRS (Sample Registration System) data for TFR is used since 1981 to 2016 for each state. Non-informative prior distribution for estimating parameter in Bayesian approach was used and the entire analysis was done by using WinBUGS (Bayesian Inference using Gibbs Sampling for Windows) software. As a result of our study the projection model shows that Uttar Pradesh will reach to its replacement level in year 2028, Bihar in 2036, Assam in 2018, Gujarat in 2016, Rajasthan in 2025, whereas Haryana has already reached to its replacement level.

  Key-Words / Index Term
  Gompertz Curve, Bayesian Methodology, Total Fertility Rate, Non-informative prior, WinBUGS

  References
  [1] Census of India. Population Projections for India and States 2001–2026.
  [2] Spiegel halter DJ, Thomas A, Best NG, Gilks W, Lunn D. BUGS: Bayesian inference using Gibbs sampling. Version 0.5, (version ii) http://www. mrc-bsu. cam. ac. uk/bugs. 1996 Aug;19.
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  [7] Rahul GP, Singh OP. using WinBUGS to study logistic growth model with an application to population projection of Uttar Pradesh and Uttaranchal. Indian J. Prev. Soc. Med. 2010;41(1&):2.
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  [10] Alkema L, Raftery AE, Gerland P, Clark SJ, Pelletier F, Buettner T, Heilig GK. Probabilistic projections of the total fertility rate for all countries. Demography. 2011 Aug 1; 48(3):815-39.
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  Citation
  Abhishek Singh Chauhan, Subhi Srivastava, Anurag Verma, "Probability Projection of Total Fertility Rate for Assesing the Replacement Level of Fertility of Selected State Using MCMC Technique under Bayesian Modeling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.14-21, 2019

• Open Access   Article

  On Lattice Fuzzy Sub Ordered Gamma – Nearrings

  D. Bharathi, K. Balakoteswararao, S. Ragamayi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.22-27, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.2227

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  Abstract
  In this paper, we introduce and study the concept of L – Fuzzy sub Ordered Г - Near ring, where L is a complete lattice satisfying infinite meet distributive law. Also, we illustrate the homomorphism of an lattice fuzzy sub Ordered Г -Near ring and prove some interesting results on it.

  Key-Words / Index Term
  L – Fuzzy set, L – Fuzzy sub Gamma – Near ring, L – Fuzzy sub Ordered Gamma – Near ring, Normal L – Fuzzy sub Ordered Gamma – Near ring

  References
  [1] Bh. Satyanarayana Contributions to Near – Ring Theory, Doctroral Thesis, Nagarjuna University, 1984
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  [10] Rajesh Kumar; “Fuzzy Algebra”, University Press, University of Delhi, Delhi – 110007.
  [11] S.Ragamayi*, J. Madhusudana Rao,T. Eswarlal and Y. Bhargavi,
  “ Vague Bi-ideal of a Gamma Near Ring ”, published in Asian Journal of Mathematics and Computer Research, Vol.21, No.3,116-126 ,ISSN: 2395-4205 (P),2017.
  [12] S.Ragamayi,” Normal Vague ideal of a Gamma Near Ring” ,
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  [13] S.Ragamayi, J. Madhusudana Rao,T. Eswarlal and Y. Bhargavi,
  ”Some Results on L- Fuzzy Sub Gamma Near Rings” Journal of Global Research in Mathematical Archives,Page No.63-69, ISSN: 23205822, Vol. 4, No.11, Nov 2017.
  [14] S.Ragamayi, J. Madhusudana Rao,T. Eswarlal and Y. Bhargavi ,
  “Vague Ideals of a Gamma Near Ring”,Journal of Global Research in Mathematical Archives,Page No.70-75,ISSN: 23205822, Vol. 4, No.11, Nov 2017.
  [15] S.Ragamayi*,J. Madhusudana Rao T. Eswarlal and Y. Bhargavi,
  ” Vague Magnified Translation of a Gamma Near Ring ”,
  International Journal of Current Research, PP:59714-59717,ISSN: 0975833X, Vol. 9, No.10, OCT 2017.
  [16] S.Ragamayi,J. Madhusudana Rao T. Eswarlal and Y. Bhargavi, “L-Fuzzy ideals in Γ-Near rings”, published in (IJPAM) International Journal of Pure and Applied Mathematics in Volume 118 No. 2 2018, 291-307.
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  [18] S.Ragamayi, Y.Bhargavi,”Some Results on Homomorphismof Vague Ideal of a Gamma-Near Ring”,International Journal Of Scientific and technology Research, Vol.8,Issue.11, Nov 2019,PP: 3809-3812, ISSN: 2277-8616.
  [19] S.Ragamayi, Y.Bhargavi,” A Study of Vague Gamma-Near rings”,International Journal Of Scientific and technology Research, Vol.8,Issue.11, Nov 2019,PP: 3820-3823, ISSN: 2277-8616.
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  Citation
  D. Bharathi, K. Balakoteswararao, S. Ragamayi, "On Lattice Fuzzy Sub Ordered Gamma – Nearrings," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.22-27, 2019

• Open Access   Article

  Heat Transport in Rayleigh-Benard Convection under Rotation Speed Modulation

  S.H. Manjula

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.28-35, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.2835

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  The purpose of this article is to analyse, theoretically, the effect of modulated rotation speed on rotating Rayleigh-Benard convection in a fluid layer. Rayleigh-B`enard momentum equation with Coriolis term has been used to describe the flow. The system is considered rotating about it own axis with non-uniform rotation speed. In particular, we assume that the rotation speed is varying sinusoidally with time. A non-linear stability analysis has been performed to find the effect of modulation on heat transport. Nusselt number is obtained in terms of amplitude of convection, and depicted graphically with respect to time, showing the effect of various parameters of the system on heat transport. It is found that the effect of rotation speed modulation is to stabilize or destabilize the system depending on the frequency of modulation.

  Key-Words / Index Term
  Rotation speed modulation, Rayleigh-B`enard convection, Coriolis force, Taylor number, Nonlinear stability

  References
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  [49]B.S. Bhadauria, P. Kiran, “Weak nonlinear analysis of magneto–convection under magnetic field modulation”, Physica Scripta, 89, 095209, 2014.
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  Citation
  S.H. Manjula, "Heat Transport in Rayleigh-Benard Convection under Rotation Speed Modulation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.28-35, 2019

• Open Access   Article

  A Mixed Integer Linear Programming Approach for Two Stage Supply Chain Network Coordination of Agricultural Products Considering Uncertainty

  M. K. Islam, M. F. Uddin, M. M. Alam, G. M. O. Faruque

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.36-45, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.3645

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  Abstract
  In this paper, presents two stage supply chain network (SCN) coordination of agricultural products considering uncertainty. Most of the agricultural products are in general cost expensive with high risk in probability due to its fluctuating prices. We developed mixed integer linear programming (MILP) model and to analyze the situation of insufficient production capacity for the producer as the reason for shortages. In this paper, we investigated supply chain network (SCN) are two distinct freelance supply organizations. SCN management has the difficulties for the disconnected and freelance economic people. Further, fast technological changes and high fight build SCN a lot of complicated. The problem of locating distribution centers (DCs) is one among the foremost necessary problems in design of SCN. This study, we have to optimize the profit before and after coordination and also to analyze the sensitivity under demand uncertainty. We consider the facilities are coordinated by mutually sharing information with each other between producer and wholesaler. The formulated MILP model is solved by using a mathematical programming language (AMPL) and results obtained by appropriate solver MINOS.

  Key-Words / Index Term
  Mixed integer linear programming, Coordination, Optimization, Agricultural products, Uncertainty

  References
  [1] M. Brandenburg, et al., “Quantitative models for sustainable supply chain management: Developments and directions”, European Journal of Operational Research, Vol. 233, pp. 299–312, 2014.
  [2] H.M. Bidhandi, et al., “Integrated supply chain planning under uncertainty using an improved stochastic approach”, Applied Mathematical Modeling, Vol. 35, pp. 2618–2630, 2011.
  [3] S. Nickel, et al., “A multi-stage stochastic supply network design problem with financial decisions and risk management”, Omega, Vol. 40, pp. 511–524, 2012.
  [4] A. Azaron, et al., “A multi-objective stochastic programming approach for supply chain design considering risk”, International Journal of Production Economics, Vol. 116, pp.129–138, 2008.
  [5] A. Baghalian, et al., “Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case”, European Journal of Operational Research, Vol. 227, pp.199–215, 2013.
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  [9] A. Rong, et al., “An optimization approaches for managing fresh food quality throughout the supply chain”, International Journal of Production Economics, Vol. 131, pp.421–429, 2011.
  [10] M.M. Aung, et al., “Traceability in a food supply chain: Safety and quality perspectives”, Food Control, Vol. 39, pp. 172–184, 2014.
  [11] V. Vorst, et al., “Simulation modeling for food supply chain redesign; integrated decision making on product quality, sustainability and logistics”, International Journal of Production Research, Vol. 47, pp. 6611–6631, 2009.
  [12] M. Shukla, et al., “Agro-fresh produce supply chain management: a state-of the-art literature review”, International Journal of Operations & Production Management, Vol. 33, pp. 114–158, 2013.
  [13] S.K. Goyal,, “An integrated inventory model for a Single supplier-single customer problem”, International Journal of Production Research, Vol. 15( 1), pp. 107-111, 1976.
  [14] M.S. Sajadieh, et al., “Optimizing shipment, ordering and pricing policies in a two stage supply chain with price sensitive demand”, Transportation Research Part E, Vol. 45, pp. 564- 571, 2009.
  [15] Z. Drezner, et al., “Facility Location: Applications and Theory”, Springer Verlag, Berlin, 2002.
  [16] B. Hung, et al., “Bilevel programming approach to optimizing a logistic distribution network with balancing requirements, Transportation Research Record”, Journal of the Transportation Research Board, Vol. 1894, pp. 188-197, 2004.
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  Citation
  M. K. Islam, M. F. Uddin, M. M. Alam, G. M. O. Faruque, "A Mixed Integer Linear Programming Approach for Two Stage Supply Chain Network Coordination of Agricultural Products Considering Uncertainty," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.36-45, 2019

• Open Access   Article

  Appraisal of the Sum of the Polygonal Numbers of Even Order from Stella Octangula Number and Pronic Number Using the Division Algorithm

  S. Vidhya, G. Janaki

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.46-48, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.4648

  Abstract

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  Abstract
  We Present the sum of the Polygonal numbers of even order are derived from Stella Octangula number and Pronic number using division algorithm.

  Key-Words / Index Term
  Polygonal numbers, The division algorithm, Stella Octangula number and Pronic number

  References
  [1] R.D.Carmichael, “History of Theory of numbers and Diophantine Analysis”, Dover Publication, Newyork, 1959.
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  [4] Ivan Niven, Herbert, S.Zuckerman and Hugh L.Montgomery, “An Introduction to the theory of Numbers”, John Wiley and Sons Inc, New York 2004.
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  [6] M.A.Gopalan and V.Pandichelvi, “Two remarkable functions on divisibility”, Acta Ciencia Indica, XXXIV M (3), 1161, 2008.
  [7] G.Janaki and S.Vidhya, “A novel approach of determining Stella Octangula number and Pronic number using initial value theorem in Z-transform”, International Journal of Statistics and Applied Mathematics, Vol. 2, Issue.6, pp.261-263, 2017.
  [8] S.Vidhya and G.Janaki, “Special Dio 3-tuples for Pronic Number - I”, International Journal for Research in Applied Science & Engineering Technology, Vol.5, Issue.XI, pp.159-162, 2017.
  [9] V.Pandichelvi and P.Sivagamasundari, “Evaluation of some centered polygonal numbers by using the division algorithm”, Journal of Mathematics and Informatics, vol.10, Special issue, pp.83-88, 2017.
  [10] C.Saranya and G.Janaki, “Tracing of Polygonal number from Pyramidal numbers and pentatope number using Division Algorithm”, Aryabhatta Journal of Mathematics and Informatics, Vol.10, N0.2, pp.373-376, 2018.
  [11] Vidhya S and Janaki G, “An integral solution of negative Pell’s equation involving two digit sphenic numbers”, International Journal of Computer Sciences and Engineering, Vol.6, Issue.7, pp.444-445, 2018.

  Citation
  S. Vidhya, G. Janaki, "Appraisal of the Sum of the Polygonal Numbers of Even Order from Stella Octangula Number and Pronic Number Using the Division Algorithm," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.46-48, 2019

• Open Access   Article

  Selection of Mixed Sampling Scheme with Conditional Repetitive Group Sampling Plan As Attribute Plan Indexed Through (MAPD, MAAOQ) and (MAPD, AOQL)

  R. Kiruthika, N. Kuppuswamy, S. Praveen

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.49-54, Dec-2019

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  Abstract
  This paper presents the process by which the Mixed Sampling scheme constructed and selected use MAPD as a value standard and MAAOQ as a performance metric with CRGS as an attribute plan using weighted Poisson distribution as a distribution on the base of a repetitive group sample plan. Maximum allowable percent defective is the quality level that corresponds to the point of inflection of the OC curve. Average Outgoing Quality Limit is the maximum AOQ over all possible levels of incoming quality. The MAAOQ is defined as the average outgoing quality (AOQ) at MAPD. The principal advantage of mixed sampling schemes over the pure attribute sampling scheme is a decrease in sample size for a related quantity of protection. The indexed plans are constructed and compared (MAPD, MAAOQ) and (MAPD, AOQL) for the natural selection of the plans and tables are provided.

  Key-Words / Index Term
  Maximum allowable percentage defective, maximum allowable average outgoing quality level, Average outgoing quality level, Operating Characteristic

  References
  [1] P.L. Mayer, “A note on sum of Poisson probabilities and an application’, ‘Industrial Quality Control”, Vol.19, No.5, pp.12-15, 1967.
  [2] V.Soundararajan, “Maximum allowable percent defective (MAPD) single sampling inspection by attribute plan”, Journal of Quality Technology, Vol.7, No.4, pp.173-182, 1975.
  [3] E.G. Schilling, “A General Method for Determining the Operating Characteristics of Mixed Variables-Attributes sampling plans Single side specifications, S.D.known”, Ph.D., Dissertation- Rutgers- The State University, New Brunswick, New Jersy, 1967.
  [4] S. Devaarul, “Certain Studies Relating to Mixed Sampling Plans and Reliability-based Sampling Plans”, Ph.D., Dissertation, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India, 2003.
  [5] R.E. Sherman, “Design and evaluation of a repetitive group sampling plan”, Technometrics, Vol.7, No.1, pp.11-21,1965.
  [6] K. Subramani, “Studies on Designing Attribute Acceptance Sampling Plans with Emphasis on Chain Sampling plans”, Ph.D Thesis, Bharathiar University, Coimbatore, Tamil Nadu, India, 1991.
  [7] V. Soundararajan and M.M. Ramasamy, “Designing repetitive group sampling plan indexed by AQL and LQL”, IAPQR Transaction, Vol.9, No.1, pp.9-14, 1984.
  [8] V. Soundararajan and M.M. Ramasamy, “Procedures and tables for construction and selection of repetitive group sampling plan”, The QR journal, Vol.13, No.13, pp.14-21, 1986.
  [9] R. Sampath Kumar, R .Kiruthika “Comparison of mixed sampling plan indexed through MAPD and LQL with single sampling plan as attribute plan using weighted Poisson distribution”, Journal of statistics science, Vol.3, No.2, pp. 165-173, 2011.
  [10] R. Radhakrishnan et al., “Selection of mixed sampling plan with TNT- (n1, n2; 0) plan as attribute plan indexed through MAPD and MAAOQ”, International Journal of Statistics and system, Vol.5, No.4, pp.477-484.
  [11] R. Sampath Kumar, “Construction and Selection of Mixed Variables - Attributes Sampling Plans” - Ph.D., Dissertation, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India, 2007.
  [12] C. Radhakrishna Rao, “A natural example of a weighted binomial distribution”, The American Statistician, Vol.31, No.1, 1977.
  [13] S. Sudeswari “Designing of Sampling Plan using Weighted Poisson distribution”. M.Phil., Dissertation, Department of Statistics, PSG College of Arts and Science, Coimbatore, 2002.
  [14] L. Mohana Priya, “Construction and Selection of Acceptance Sampling Plans based on Weighted Poisson Distribution”, Ph.D., Dissertation, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India, 2008.
  [15] R. Radhakrishnan and L. Mohana Priya, “Selection of single sampling plan using conditional weighted Poisson distribution”, International Journal of Statistics and Systems, Vol.3, No.1, pp. 91-98, 2008.
  [16] R. Radhakrishnan and L. Mohana Priya, “Comparison of CRGS plans using Poisson and weighted Poisson distribution”, Probstat Forum, Vol.1, No.1, pp.50-61, 2008.
  [17] R. Sampath Kumar, R .Kiruthika “Comparison of mixed sampling plan indexed through MAPD and LQL with single sampling plan as attribute plan using weighted Poisson distribution”, Journal of statistics science, Vol.3, No.2, pp. 165-173, 2011.

  Citation
  R. Kiruthika, N. Kuppuswamy, S. Praveen, "Selection of Mixed Sampling Scheme with Conditional Repetitive Group Sampling Plan As Attribute Plan Indexed Through (MAPD, MAAOQ) and (MAPD, AOQL)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.49-54, 2019

• Open Access   Article

  Union of Fuzzy Semi- “N” Groups and Anti- Fuzzy Semi- “N” Groups (for N = 1,2,….n)

  N. Deepica

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.55-61, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.5561

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  Abstract
  In this paper, The definitions of Fuzzy semi group, fuzzy semi-bigroup and so on Fuzzy semi-“n” groups and The definitions of Anti- Fuzzy semi group, Anti- fuzzy semi bigroup and soon Anti-Fuzzy semi-“n” groups are invented. Moreover, some properties and theorems based on these have been invented.

  Key-Words / Index Term
  Fuzzy semi group , fuzzy semi-bigroup and Fuzzy semi-“n” groups, Anti- Fuzzy semi group, Anti-fuzzy semi-bigroup and Anti- Fuzzy semi-“n” groups

  References
  [1]. Dr. S.Chandrasekaran, N. Deepica “Relation between Fuzzy subgroups and Anti- Fuzzy subgroups“ , IJIRST –International Journal for Innovative Research in Science & Technology| Volume 5 , Issue 9 , pp.1-5, February 2019 .
  [2]. Dr. S. Chandrasekaran, N.Deepica “Union of Fuzzy Sub-Quadradicgroups , Fuzzy Sub - Pendantgroups and Fuzzy Sub- N groups” - International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET),Volume 6, Issue 1, page number : 303-311, January-February 2019.
  [3]. Dr. S.Chandrasekaran, N. Deepica “Algebraic Structure of Union of Fuzzy(Anti-Fuzzy)Normal Subgroups, Fuzzy(Anti-Fuzzy) Normal Sub – Bigroups And Soon Fuzzy (Anti-Fuzzy) Normal Sub – N groups “- International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Volume 6 , Issue 1, page number: 312-322, January-February 2019.
  [4]. Dr.S.Chandrasekaran, N. Deepica, " Connectedness and Compactness of Fuzzy (Anti - Fuzzy) Subgroups and Fuzzy (Anti - Fuzzy) Normal Sub groups", International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Volume 6 , Issue 1, page number : 392-401, January-February 2019.
  [5]. Dr.S. Chandrasekaran ,N. Deepica “Union of Anti - Fuzzy Sub - Quadradic groups , Anti - Fuzzy Sub - Pendant groups and Anti- Fuzzy Sub - N groups” , - International Research Journal of Pure Algebra - / IRJPA- 9(3), March-2019.,Page number : 1-11.
  [6]. N.Duraimanickam, N.Deepica –
  “Algebraic structure of union of fuzzy subgroups and fuzzy sub –bigroups” – National Conference on Emerging Trends in Mathematics - 2017 On 28th July 2017 - Organized by PG and Research Department of Mathematics, A. V. V. M. Sri Pushpam College (Autonomous), Poondi , Thanjavur (Dt.), Tamilnadu. - International journal of current Research and Modern education – Special issues , July – 2017 , ISSN: 2455-5428. Page Number : 95-99.
  [7]. N. Duraimanickam, N. Deepica–“Algebraic structure of union of fuzzy sub - trigroups and fuzzy sub –N groups”–International Journal of Advanced Research Publications, Volume 1, Issue 5, November 2017, Page Number : 374-378
  [8]. N. Duraimanickam, N. Deepica –Algebraic structure of union of Anti-fuzzy subgroups and Anti-fuzzy
  sub –bigroups and Anti- fuzzy
  Sub-trigroups”– In the Proceeding of the 2017 National Conference on Emerging Trends in Mathematical Techniques(NCETMT2017), Organized by PG Department of Mathematics, Sengamala Thayaar Educational Trust Women’s College Mannargudi , Tiruvarur (Dt.), Tamilnadu , India . Page Number : 56 - 64 .
  [9]. S.Arumugam,A.Thangapandi Isaac.-ModernAlgebra-SciTech Publications (India) Pvt. Ltd.(2003) .
  [10]. R. Muthuraj, M. Rajinikannan , M.S. Muthuraman – A Study on Anti- Fuzzy Sub –bigroup – International Journal of Computer Applications Volume 2 –No.1,May 2010 (0975- 8887) .
  [11]. S. Nanda, N.R .Das. - Fuzzy Mathematical concepts. - Narosa Publishing House Pvt. Ltd. (2010).
  [12]. G . Nirmala, S. Suganthi - Fuzzy Sub - Trigroup – Trilevel Properties.- International Journal of Scientific and Research Publications,Volume 2, Issue 6, June 2012.
  [13]. G . Nirmala, S. Suganthi - - Fuzzy Sub-Trigroup – Characteristics.-International Journal of Scientific and Research, Volume: 2, Issue: 11, November 2013.
  [14]. W.B .Vasanthakandasamy - Smarandache Fuzzy Algebra.

  Citation
  N. Deepica, "Union of Fuzzy Semi- “N” Groups and Anti- Fuzzy Semi- “N” Groups (for N = 1,2,….n)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.55-61, 2019

• Open Access   Article

  The Beta Transmuted Gumbel Distribution: Theory and Application

  Ahmed Hurairah

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.62-73, Dec-2019

  Abstract

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  Abstract
  In this paper a composite generalizer of the Gumbel distribution is proposed and studied. The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Gumbel distribution. Several mathematical properties including moments, moment generating function, mean deviation, quantiles, and order statistics are discussed. The maximum likelihood method is used for estimating the new model parameters, and the finite sample performance of the estimators is assessed by simulation. Finally, the usefulness of the new distribution in analyzing positive data is illustrated.

  Key-Words / Index Term
  Transmuted family, Moments, beta Gumbel distribution, mean deviation, maximum likelihood estimation

  References
  [1] E.J. Gumbel, “Statistics of Extremes”, Columbia University Press, New York, 1958.
  [2] S. Kotz, and S. Nadarajah, “Extreme value Distributions: Theory and Applications”, Imperial College Press, London, 2000.
  [3] S. Nadarajah, “The exponentiated Gumbel distribution with climate application”, Environmetrics, Vol.17, pp. 13-23, 2006.
  [4] K. Persson and J. Rydén, “Exponentiated Gumbel distribution for estimation of return levels of significant wave height”, Journal of Environmental Statistics, Vol.1 (3), pp 1-12, 2010.
  [5] K. Cooray, “Generalized Gumbel distribution”, Journal of Applied Statistics, Vol.37 (1), pp. 171-179,2010.
  [6] N. Eugene,C. Lee, F. Famoye, “Beta-normal Distribution and its Applications”, Communications in Statistics – Theory and Methods, Vol.31, pp. 497–512, 2002.
  [7] S. Nadarajah, S. Kotz, “The beta Gumbel distribution, Mathematical Problems in Engineering”, Hindawi Publishing Corporation, Vol1, pp. 323-332, 2004.
  [8] Jamil Ownuk, “The Beta Exponentiated Gumbel Distribution”, Journal of The Iranian Statistical Society, Vol.14 (2), pp 1-14, 2015.
  [9] T. Andrade, H. Rodrigues, M. Bourguignon, and G.Cordeiro, “The exponentiated generalized Gumbel distribution”, Revista Colombiana de Estadística, Vol.38(1), pp 123-143, 2015.
  [10] M. C. Jones, “Family of Distributions Arising from Distribution of Order Statistics”, Test, Vol.13, pp. 1–43, 2004.
  [11] G. R. Aryal, and C. P. Tsokos, “On the transmuted extreme value distribution with application, Nonlinear Analysis: Theory, Methods and Application”, Vol.71, pp. 1401-1407, 2009.
  [12] D. Deka, B. Das, and B. K. Baruah, “Transmuted Exponentiated Gumbel Distribution (TEGD) and its Application to Water Quality Data”, Pakistan Journal of Statistics and Operation Research, Vol.13(1), pp. 115-126, 2017.
  [13] M. Bourguignon, I. Ghosh, and G. M. Cordeiro, “General results for the transmuted family of distributions and new models”, Journal of Probability and Statistics, Vol. 2016, pp. 1-12, 2015.
  [14] G. M. Cordeiro, and S. Nadarajah, “Closed form Expressions for Moments of a Class of Beta Generalized Distributions”, Brazilian Journal of Probability and Statistics, Vol.25, pp. 14–33, 2011.
  [15] L. M. Zea, R. B. Silva, M.Bourguignon, A. M. Santos, and G. M. Cordeiro, “The beta exponentiated Pareto distribution with application to bladder cancer susceptibility”, International Journal of Statistics and Probability, Vol.1, pp. 8-19, 2012.
  [16] I. S. Gradshteyn, and I. M. Ryzhik, “Table of Integrals", Series, and Products”, Academic Press, New York, 2000.
  [17] M. E. Ghitany, B. Atieh and S. Nadarajah, “Lindley distribution and its application, Mathematics and Computers in Simulation”, Vol.78, pp. 493–506, 20008.

  Citation
  Ahmed Hurairah, "The Beta Transmuted Gumbel Distribution: Theory and Application," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.62-73, 2019

• Open Access   Article

  Metric Dimension of Zero-Divisor Graph for the Ring Zn

  Mithun Basak, Laxman Saha, Kalishankar Tiwary

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.74-78, Dec-2019

  Abstract

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  Abstract
  Metric Dimension of a simple connected graph is the minimum number of vertices those are used to identify each vertex of the graph uniquely using distance code. In this paper, we determine metric dimension of zero-divisor graph associated with the ring Zn.

  Key-Words / Index Term
  Ring, Metric Dimension, Zero divisors, Zero-divisor Graph

  References
  [1]Akbari, S., Mohammadian, A. On the zero-divisor graph of finite rings. J. Algebra. 314(1), 168–184, 2007
  [2] Anderson, D. F., Frazier, A., Lauve, A., Livingston, P. S. The Zero-Divisor Graph of a
  Commutative Ring, II, Lecture Notes in Pure and Applied Mathematics. 220, 61–72, 2001
  [3] Anderson, D. F., Levy, R., Shapiro, J. Zero-divisor graphs, von Neumann regular rings, and Boolean algebras. J. Pure Appl. Algebra. 180, 221–241, 2003
  [4] Anderson, D. F., Livingston, P. S. The zero-divisor graph of a commutative ring. J.Algebra. 217 , 434–447, 1999
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  [6] Atiyah, M. F., MacDonald, I. G. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1969
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  [10] Corbas, B., Williams, G. D. Rings of order p5 II. Local rings. J. Algebra. 231(2), 691–704, 2000
  [11] Garey, M. R., Johnson, D. S. Computers and Intractability. A Guide to the Theory of NP-Completeness. New York: Freeman 1979.
  [12] Harary, F., Melter, R. A. On the metric dimension of a graph. Ars Combin. 2, 191–195, 1976
  [13] Khuller, S., Raghavachari, B. and Rosenfeld, A. Landmarks in graphs, Discrete Appl.Math., 70, 217–229, 1996
  [14] Mulay, S. B. Cycles and symmetries of zero-divisors. Commun. Algebra. 30(7), 3533–3558.
  [15] Pirzada, S., Raja, R., Redmond, S. P. Locating sets and numbers of graphs associated to commutative rings. J. Algebra Appl. 13(7), 1450047 18 pp, 2014
  [16] Raja, R., Pirzada, S., Redmond, S. P. On Locating numbers and codes of zero-divisor graphs associated with commutative rings. J. Algebra Appl. 15(1), 1650014 22pp, 2016
  [17] Redmond, S. P. The zero-divisor graph of a noncommutative ring. Int. J. Commutative Rings. 1(4) , 203–211, 2002
  [18] Redmond, S. P. An ideal-based zero-divisor graph of a commutative ring. Commun. Algebra. 31, 4425–4443, 2003
  [19] Sebo, A., Tannier, E. On metric generators of graphs. Math. Oper. Res. 29, 383–393, 2004
  [20] Slater, P. Leaves of trees. Proc. 6th Southeastern Conf. on Combinatorics, Graph Theory and Computing, 14, 549–559, 1975

  Citation
  Mithun Basak, Laxman Saha, Kalishankar Tiwary, "Metric Dimension of Zero-Divisor Graph for the Ring Zn," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.74-78, 2019