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• Open Access   Article

  A Non-Parametric Analysis of Some Raga Characteristics

  Nandini Sarma, Pranita Sarmah

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.1-8, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.18

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  Abstract
  A musical composition is highly patterned as it involves repetition either in the form of individual sequences of notes, chords, dynamics, rhythmic beats or tempo etc. Hence it leads to the possibility of treating music mathematically. Though mathematics has been applied to the study of music for centuries, relatively few attempts have been made to answer questions in musicology using statistical methods. The same is also true for Indian Classical music. In North Indian classical music there arises a number of questions concerning raga characteristics that can be subjected to statistical enquiry for their proper verification. Under such circumstances statistical test procedures could be employed for examining various musical propositions corresponding to a raga composition. In this paper some non-parametric techniques such as Wilcoxon Signed rank test, Binomial test and Run test of randomness have been applied for examining such propositions related to characteristics of ragas. The concept of structure function is also utilized for defining a raga and its classification.

  Key-Words / Index Term
  Non-Parametric, Component, Music, Raga, Wilcoxon Signed rank test

  References
  [1] V N Bhatkhande, “Hindustani Sangeet Paddhati”, Kramik PustakMallika, Vol 1-6, Sangeet Karyalaya, Hathras, 1993
  [2] S Chakraborty, S Chauhan, K Krishnapriya , M Kumari , S S Solanki , R K Shukla and Loveleen, “A Statistical Analysis Of A Raga-Based Song”, Georgian Electronic Scientific Journal: Musicology and Cultural Science, No. 2(4), 2009
  [3] S Chakraborty, S Chauhan, K Mahto, S Roy, S S Solanki , S S and Tripathy, “A Statistical Approach to Modeling Indian Classical Music Performance”, Archive of Cornell University e-library, http://arxiv.org/abs/0809.3214, 2008
  [4] S Chakraborty, S Chauhan, K Mahto , R Ranganayakulu, and S S Solanki, “Which notes are Vadi-Samvadi in Raga Rageshree?”, Archive of Cornell University e-library, http://arxiv.org., 2008
  [5] W J Conover, “Practical Non-parametric Statistics”, Wiley India Pvt Ltd, 3rd Edition, 2006.
  [6] J D Gibbons, “Nonparametric Statistical Inference”, McGraw-Hill, 1971.
  [7] W Y Liu and E S Field, “Modeling Music as Markov Chains: Composer Identification”, Music, 254 Final Report Stanford University, https://ccrma.stanford.edu, 2002
  [8] N A Jairazbhoy,”Factors underlying important notes in North Indian music”, Ethnomusicology ,Vol 16, 63-81, 1972
  [9] G S Mansukhani, “Indian Classical Music and Sikh Kirtan”, www.esikhs.com, 1982
  [10] N Sarma and P Sarmah, “Empirical Analysis of Octave Patterns in Some North Indian Classical Ragas: An Application of Markov Chain”, J. Stat. & Appl. ,Vol. 6, No. 3-4, pp. 143-157, 2011
  [11] N Sarma and P Sarmah, “Empirical Analysis of Ascending and Descending Movements of Notes Corresponding to North Indian Classical Ragas: Application of Stochastic Process”, International Journal of Statistics and Analysis, Volume 2, Number 1, pp. 77-87, 2012
  

  Citation
  Nandini Sarma, Pranita Sarmah, "A Non-Parametric Analysis of Some Raga Characteristics," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.1-8, 2018

• Open Access   Article

  A Deterministic Inventory Model for Perishable Items with Lead Time and Price Dependent Demand

  S. Kumar and U.S. Rajput

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.9-17, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.917

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  Abstract
  In the present paper, an attempt has been made to develop a deterministic inventory model for perishable items with lead time and price dependent demand. Shortages are allowed and completely backlogged. The problem of perishability or deterioration plays an important role in the field of inventory control and management. The purpose of our study is to minimize the total variable inventory cost during a given period of time. A numerical example is given to demonstrate the developed model.

  Key-Words / Index Term
  Inventory, Deterioration, Lead Time and Price Dependent Demand

  References
  [1] A. Goswami and K. S. Chaudhuri, “An EOQ model for deteriorating items with linear trend in demand and allowing shortages”, Journal of Operational Research Society, Vol. 42, pp.1105-1110,1991.
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  [4] M. Hargia, “An EOQ model for deteriorating items with time varying demand”, Journal of Operational Research Society, Vol. 47, pp. 205-213, 1996.
  [5] B. C. Giri and K. S. Chaudhuri, “A deterministic inventory model for deteriorating items with stock dependent demand rate and non linear holding cost”, European Journal of Operational Research, Vol.105, pp.464-467,1998.
  [6] H. J. Chang and C. Y. Dye, “An EOQ model for deteriorating items with time varying demand and partial backlogging”, Journal of Operational Research Society, Vol. 50, pp.1176-1182, 1999.
  [7] K. J. Chung, P. Chu and S. P. Lan, “A note on EOQ models for deteriorating items with stock dependent selling rate”, European Journal of Operational Research, Vol.124, pp.550-559, 2000.
  [8] B. Lin, B. Tan and W. C. Lee, “An EOQ model for deteriorating items with time varying demand and shortages”, International Journal of Systems Science, Vol. 31, pp.391-400, 2000.
  [9] S. Papachristos and K. Skouri, “An optimal replenish policy for an inventory model of deteriorating items with time varying demand and exponential type acklogging rate”, Operations Research Letters, Vol. 27, pp.175-184, 2000.
  [10] S. K. Goyal and B. C. Giri, “Recent trends in modeling of deteriorating inventory”, European Journal of Operational Research, Vol. 134, pp.1-16, 2001.
  [11] H. J. Chang and C.Y. Dye, “An inventory model for deteriorating items with permissible delay in payments and allowing shortages”, International Journal of System Science, Vol. 32, pp.345- 352, 2001.
  [12] K. Skouri and S. Papachristos, “A continuous review inventory model for perishable items with time dependent demand and partial backlogging”, Applied Mathematical Modeling, Vol. 26, pp.603-617, 2002.
  [13] K. S. Wu, “An EOQ model for weibull deteriorating items with time varying demand and partial backlogging” International Journal of Systems Science, Vol. 33, pp.323-329, 2002.
  [14] S. P. Wang, “An optimal lot-sizing policy for an inventory model of deteriorating items with time varying demand and shortages”, Journal of Chinese Institute of Industrial Engineering, Vol. 20, pp.449-456, 2003.
  [15] S. K. Goyal and B. C. Giri, “A production inventory model for deteriorating items with time varying demand rate”, European Journal of Operational Research, Vol. 147, pp. 549- 557, 2003.
  [16] W. H. Lee and J. W. Wu, “A note on EOQ model for deteriorating items with exponential distribution deterioration and time dependent demand and shortages” International Journal of Systems Science, Vol.31, pp.677-683, 2004.
  [17] Y. Dye and L. Y. Ouyang, “An EOQ model for perishable items with stock dependent selling rate and time dependent artial backlogging”, European Journal of Operational Research, Vol. 163, pp.776-783, 2005.
  [18] N. H. Shah, “An inventory model for deteriorating items together with time value of money for a finite time horizon under permissible delay in payments”, International Journal of Systems Science, Vol. 37, pp.9-15, 2006.
  [19] K. L. Hou and L. C. Lin, “An EOQ model for deteriorating items with price and stock dependent selling rate under inflation and time value of money” , International Journal ofSystems Science, Vol. 37, pp.1131-1139, 2006.
  [20] C. Y. Dye, “A joint pricing andordering policy for deteriorating
  items with partial backlogging”, Omega-The International Journal Management Science, Vol. 35, pp.184-189, 2007.
  [21] A. Roy, M. Maiti and M. K. Kar, “An inventory model for deteriorating items with stock dependent rate and time discounting over a random planning horizon under fuzzy inflation”, Applied Mathematical Modeling, Vol. 33, pp.744-759, 2009.
  [22] J. Min and Y. W. Zhou, “A perishable inventory model for deteriorating items with stock dependent selling rate, shortages together with capacity constraints”, International Journal of SystemsScience, Vol. 40, pp.33-44, 2009.
  [23] D. K. Jain, B. Das and T. K. Roy, “An inventory model for perishable items with fuzzy type inflation and cash discounting over random planning horizon”, Advances in Operations Research, Vol. 2013, pp.1-15, 2013.
  [23] D. Panda, M. Rong and M. Maiti, “A two warehouse inventory model for deteriorating items with fuzzy type demand rate and lead time”, European Journal of Operations Research, Vol. 22, pp.187-209, 2014.
  [24] A. Roy, “Fuzzy inventory model of deteriorating items with price dependent demand rate”, International Journal of Management Science and Engineering Management, Vol. 10, Issue. 4, pp.237-241, 2015.
  [25] R. R. Chaudhari and V. Sharma, “A model for weibull deteriorating items with price dependent demand rate and inflation”, Indian Journal
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  [26] M. Maragatham and R. Palani, “An inventory model for deteriorating items with lead time, price dependent demand and shortages”, Advances in Computational Science and Technology, Vol. 10, Issue. 6, pp.1839-1847, 2017.
  

  Citation
  S. Kumar and U.S. Rajput, "A Deterministic Inventory Model for Perishable Items with Lead Time and Price Dependent Demand," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.9-17, 2018

• Open Access   Article

  One Raised Product Prime Labeling of Some Star Related Graphs

  B.S. Sunoj, T.K. Mathew Varkey

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.18-23, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.1823

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  Abstract
  One raised product prime labeling of a simple. finite and un direct graph G with p vertices and q edges is the labeling of the vertices of the graph with first p natural numbers, edges with product of the labels of the end vertices plus one. If the greatest common divisor of each vertex of degree greater than one is one then the graph is called one raised product prime graph. Here the greatest common divisor of the labels of the edges incident on a vertex is called greatest common incidence number of that vertex. Here we proved that star, bistar, splitting graph of a star, shadow graph of a star , jelly fish graph and some more star related graphs admit one raised product prime labeling.

  Key-Words / Index Term
  Graph labeling, product, prime labeling, prime graphs, star

  References
  [1] Apostol. Tom M, Introduction to Analytic Number Theory, Narosa, (1998).
  [2] F Harary, Graph Theory, Addison-Wesley,Reading, Mass, (1972
  [3] Joseph A Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics(2015), #DS6, Pages 1 – 389.
  [4] T K Mathew Varkey, Some Graph Theoretic Operations Associated with Graph Labelings, PhD Thesis, University of Kerala 2000.
  [5] Sunoj B S, Mathew Varkey T K, “One Raised Product Prime Labeling of Some Cycle Related Graphs ”, Journal of Harmonized Research in Applied Science, Vol.6-No.2, May 2018, pp 49-54.
  [6] Sunoj B S, Mathew Varkey T K, “One Raised Product Prime Labeling of Some Snake Graphs ”, International Journal of Research in Advent Technology, Vol.6-No.5, May 2018, pp 455-459.
  [7] Sunoj B S, Mathew Varkey T K, “One Raised Product Prime Labeling of Some Path Related Graphs”, Research Guru – Online Journal of Multidisciplinary Subjects, Vol.12-No.1, June 2018, pp 950-959.
  [8] Sunoj B S, Mathew Varkey T K, “Hexagonal Difference Prime Labeling of Some Path Graph”, Mapana J Sci., Vol.16, No.3, June 2017, pp 41-46.
  

  Citation
  B.S. Sunoj, T.K. Mathew Varkey, "One Raised Product Prime Labeling of Some Star Related Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.18-23, 2018

• Open Access   Article

  Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations

  M. Saradha and S. Ruban Raj

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.24-33, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.2433

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  Abstract
  In this paper we study Error analysis of numerical methods for second order hybrid fuzzy fractional differential equations. We solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition by using variational iteration method. We consider a second order differential equation with fractional values and we compared the results with their exact solutions in order to demonstrate the validity and applicability of the method. We further give the definition of the Degree of Sub element hood of hybrid fuzzy fractional differential equations with examples.

  Key-Words / Index Term
  Hybrid fuzzy fractional differential equations, Degree of Sub Element hood, Runge Kutta Fehlberg 6th order Method

  References
  [1] Arshad, S, Lupulescu, V, “Fractional differential equation with the fuzzy initial condition”, Electron. J. Differ. Equ. 34, 1-8 (2011)
  [2] Agarwal, RP, Lakshmikanthama, V, Nieto. JJ, “On the concept of solution for fractional differential equations with uncertainty”, Nonlinear Anal. 72, 2859-2862 (2010)
  [3] Ekhtiar Khodadadi and Ercan Çelik, “The variational iteration method for fuzzyfractional differential equations with uncertainty”, Fixed Point Theory and Applications 2013, 2013:13
  [4] K. Miller and B. Ross, “An introduction to the fractional calculus and fractional differential equations”, Wiley, New York, 1993.
  [5] M. Z. Ahmad and M. K. Hasan, “Numerical methods for fuzzy initial value problems under different types of interpretation: a comparison study,” in Informatics Engineering and Information Science, vol. 252 of Communications in Computer and Information Science, pp. 275–288, Springer, Berlin, Germany, 2011.
  [6] S. Pederson and M. Sambandham, “Numerical solution to hybrid fuzzy systems”, Mathematical and Computer Modelling 45 (2007), 1133–1144.
  [7] S. Ruban Raj, M. Saradha, “Properties of Fuzzy Soft Set”, International Journal for Basic Sciences and Social Sciences (IJBSS), ISSN:2319-2968, 2(1) (2013), pp.112-118.
  [8] S. Ruban Raj, M. Saradha, “Solving Hybrid Fuzzy Fractional Differential Equation By Modified Euler Method”, Annexure II of Anna University-2014 and ICMAA–2014. 550-560.
  [9]. S. Ruban Raj, M. Saradha, “Solving Second Order Hybrid Fuzzy Fractional Differential Equation By Runge Kutta Fourth Order Method”, International Journal of Science and Research, ISSN (Online): 2319-7064, Volume4, Issue 1, January 2015.
  [10] S. Ruban Raj, M. Saradha, “Solving Hybrid Fuzzy Fractional Differential Equation By Runge Kutta Fourth Order Method”, International Journal of Science and Research, ISSN (Online): 2319-7064, Volume4, Issue 2, February 2015.
  

  Citation
  M. Saradha and S. Ruban Raj, "Error Analysis between Runge Kutta Fourth Order Method & Fehlberg 6th Order Method of Hybrid Fuzzy Fractional Differential Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.24-33, 2018

• Open Access   Article

  A Skew Extension of the Multivariate Generalized T Distributions with Applications

  A.M. Fares, V.V. Haragopal

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.34-39, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.3439

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  Abstract
  We propose an asymmetric extension of Arslan multivariate generalization of the Generalized T distributions introduced by McDonald and Newey, the proposed Skew Multivariate Generalized T distribution (MSGT) includes the skew multivariate Normal distribution of Azzalini and Valle as well as the skew multivariate t distribution introduced by Azzalini and Capitanio, besides, MSGT contains many other distributions as a limiting or special cases, a stochastic representation of MSGT random vector has been obtained along with a simulation study, the flexibility added of this distribution makes it a potential candidate in modeling multidimensional data of different tail behaviors for providing an outstanding fit which we have practically illustrated by using this distribution for modeling multivariate data of the American financial market.

  Key-Words / Index Term
  Multivariate; Skew; Generalized T-distribution

  References
  [1] Azzalini A., “A class of distributions which includes the normal ones”, Scandinavian journal of statistics, pp171–178, 1985.
  [2] Azzalini A., Valle A. D., “The multivariate skew-normal distribution”, Biometrika, Vol.83, Issue.4, pp715–726, 1996.
  [3] Azzalini A., Capitanio A., “Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution” , Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol.65, Issue.2, pp367–389, 2003.
  [4] Genton M. G., Loperfido N. M., “Generalized skew-elliptical distributions and their quadratic forms” , Annals of the Institute of Statistical Mathematics, Vol.57, Issue.2, pp389–401, 2005.
  [5] Arslan O., “Family of multivariate generalized t distributions”, Journal of Multivariate Analysis, Vol.89, Issue.2, pp329–337, 2004.
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  [7] Nadarajah S., “On the generalized t (gt) distribution”, Statistics, Vol.42, No.5, 467–473, 2008.
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  [11] Fares A. M., Haragopal, V. V., “The generalized double Lomax distribution with applications”, Statistica, Vol.76, Issue.4, pp341-352, 2016.
  [12] Fang K., Zhang Y., “Generalized multivariate analysis”, Science Press, Springer-Verlag, Beijing, 1990.
  [13] McDonald J. B., Xu Y. J., “A generalization of the beta distribution with applications”, Journal of Econometrics, Vol.66, Issue.1, pp133–152, 1995.
  [14] Wang J., Boyer J., Genton M. G., “A skew-symmetric representation of multivariate distributions”, Statistica Sinica, pp1259–1270, 2004.
  [15] Azzalini A., "R package sn: The skew-normal and skew-t distributions (version 0.4-17)", 2011.
  [16] Gupta A., “Multivariate skew t-distribution”, Statistics: A Journal of Theoretical and Applied Statistics, Vol.37, Issue.4, pp359–363, 2003.
  [17] Luethi D., Breymann W., “ghyp: A package on the generalized hyperbolic distribution and its special cases”, R package version, Vol.1, Issue.5, 2011.
  [18] Mead M., “Generalized inverse gamma distribution and its application in reliability”, Communications in Statistics-Theory and Me hods, Vol.44, Issue.7, pp1426–1435, 2015.
  [19] Ruppert D., “Statistics and data analysis for financial engineering”, Springer, New York, 2011.
  [20] G.V.L.N. Srihari, S.V.S.Girija, A.V. Dattatreya Rao, “On Discrete Wrapped Exponential Distribution- Characteristics”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp57-64, 2018.
  [21] Team R. D. C., et al., “A language and environment for statistical computing”, R foundation for statistical computing, Vienna, Austria, 2011.
  [22] Theodossiou P., “Financial data and the skewed generalized t distribution”, Management Science, Vol.44, Issue.12, pp1650–1661, 1998.
  

  Citation
  A.M. Fares, V.V. Haragopal, "A Skew Extension of the Multivariate Generalized T Distributions with Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.34-39, 2018

• Open Access   Article

  Some Interval Time Series Models for Temperature Data in India

  A. Srinivasulu, B. Sarojamma, P. Ramakrishna Reddy, S. Venkataramana Reddy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.40-47, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.4047

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  Abstract
  The temperature is fluctuated by special climate changes during seasons in India. In this paper, we were taking temperature data from 2000 to 2016. Maximum and minimum temperature values for season wise i.e., Jan-Mar(Spring), Apr-June(Summer), July-Sep(Autumn), Oct-Dec(Winter) has to be taken throughout India. The organization of the work is divided into two parts, first part contains data from 2000 to 2010 as test group and second part contains from 2011 to 2016 as main group. For this maximum and minimum temperature seasonal data we apply nine models. Among the nine, seven are ARIMA models, the 8th one is Adaptive smoothing model and the last one is non linear model. In this paper, two measures of accuracy are used. They are Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The nine models are empirically tested using Maximum and Minimum temperature data of season wise in India.

  Key-Words / Index Term
  Seasonal temperature data, Adaptive smoothing model, ARIMA models, MAE, RMSE

  References
  [1] Grant Foster, Stefan Rahmstorf, “Global Temperature Evolution 1979-2010”, Environ. Res. Lett.6, 044022,2011.
  [2] Grant Foster, Niamh Cahill, Stefan Rahmstorf, , “Global Temperature Evoluation: Recent Trends and Some Pitfalls” , Environmental Research Letters, 12 , 054001,2017.
  [3] Chonggunag Li, Lu Zhang, Tao Xiong , Yukun Bao, Zhongyi Hu, “A Combination Method for Interval Forecasting of Agricultural Commodity Futures Prices”, Knowledge-Based Systems ,77,92-102,2015.
  [4] Markus Glaser, Martin Weber, Thomas Langer, “ True Overconfidence in Interval Estimates: Evidence Based on a New Measure of Miscalibration”, journal of Behavioral Decision Making, 26:405-417,2012.
  [5] Aidan McDermott, Francesca Dominici, Jonathan M. Samet, Scott L.Zeger, “On the Use of Generalized Additive Models in Time Series Studies of Air Pollution and Health”, American Journal of Epidemiology, vol. 156, No. 3,2002.
  [6] Heather A. Walton, H. Ross Anderson, Inga C. Mills, Richard W. Atkinson, “Fine Paricle Componens and Health- a Systematic review and Meta-Analysis of Epidemological Time Series Studies of Daily Mortality and Hospital Admissions”, Journal of Exposure Science and Environmental Epidemiology,25,208-214,2015.
  [7] Alesssandro Baccini, Alexndra Tyukavina, Belinda Arunarwati Margono, Ilona Zhuravleva, Matthew C Hansen Peter Potapov, Scott Goetz, Svetlana Turubanova, “Mapping and Monitoring Deforestation and Forest Degradation in Sumatra (Indonesia) using Land sat time series data sets from 1990 to 2010”, Environ. Res. Lett.7, 034010, 2012.
  [8] http//:www.data.gov.in.
  

  Citation
  A. Srinivasulu, B. Sarojamma, P. Ramakrishna Reddy, S. Venkataramana Reddy, "Some Interval Time Series Models for Temperature Data in India," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.40-47, 2018

• Open Access   Article

  Global Dynamics of an SEIR Epidemic model with saturated incidence under treatment

  M. Badole, S. K. Tiwari, V. Gupta, A. Agrawal

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.48-57, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.4857

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  Abstract
  An SEIR epidemic model with saturated incidence rate under a limited resource for treatment function which is proposed by W. Wang (2006) is investigated in this paper. We have assumed that treatment rate is proportional to the number of infective when it is below the capacity and is a constant when the number of infective is larger than the capacity. The existing threshold conditions of all kinds of the equilibrium points are obtained. The local and global stability of the disease free equilibrium and the endemic equilibrium of the model are discussed. The local asymptotical stability of equilibrium is verified by analyzing the eigen values and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the disease free equilibrium by using, Lyapunov function and endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Finally, numerical simulations are given to illustrate the validity of the proposed results.

  Key-Words / Index Term
  SEIR epidemic model, Treatment, Basic reproduction number, Lyapunov function, Stability analysis.

  References
  [1] A. Agrawal, “Global Analysis of an SEIRS epidemic model with saturated incidence and saturated treatment”, Asian Journal of Mathematics and Computer Research, Vol. 22(2), pp 43-56, 2017.
  [2] D. Xiao, S. Runa, “Global analysis of an epidemic model with non-monotonic incidence rate”.Mathematical Bioscience, Vol. 208: pp419-429, 2007.
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  [10] L. Zhou, M. Fan, “Dynamics of an SIR epidemic model with limited medical resources revisited,” Nonlinear Analysis: Real World Applications, Vol. 13, no. 1, pp. 312–324, 2012.
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  [13] T. K .Kar, Batabyal, Ashim., “Modeling and analysis of an epidemic model with non-monotonic incidence rate under treatment”, Journal of Mathematics Research, Vol. 2(1), pp103-115, 2010.
  [14] V. Capasso, G. Serio, “A generalization of the kermack-mckendrick deterministic epidemic mode”l, Math Bioscience Vol. 42, pp 43–61, 1978.
  [15] W.M. Liu, S.A. Levin, Y. “I was a, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models”, J. Math. Biol. Vol. 23, pp 187–204, 1986.
  [16] W.O Kermark , A.G. Mckendrick ,” Contributions to the mathematical theory of Epidemics-I”, Proceedings of the Royal Society, London A, Vol. 115, pp 700-721, 2007.
  [17] W. Wang, “Backward bifurcation of an epidemic model with treatment”, Mathematical Bioscience, Vol. 201, pp 58-71, 2006.
  [18] W. Wang, S. Ruan ,”Bifurcations in an epidemic model with constant removal rate of invectives”, Journal of Mathematical Analysis and Application Vol. 291, pp 775–793, 2004.
  [19] X. Zhang and X. N. Liu , “Backward bifurcation of an epidemic modelwith saturated treatment function”, Journal of
  [20] Mathematical Analysis and Applications, Vol. 348, no. 1, pp. 433–443, 2008.
  [21] Z. Zhonghua, Yaohong, Suo,” Qualitative analysis of a SIR epidemic model with saturated treatment rate”, Journal of Applied Mathematics and Computing, Vol. 34:pp177–194, 2010.
  

  Citation
  M. Badole, S. K. Tiwari, V. Gupta, A. Agrawal, "Global Dynamics of an SEIR Epidemic model with saturated incidence under treatment," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.48-57, 2018

• Open Access   Article

  A Repetitive Acceptance Sampling Plan for Generalized Inverted Exponential Distribution Based on Truncated Life Test

  Navyodh Singh, Navjeet Singh, Harpreet kaur

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.58-64, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.5864

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  Abstract
  n this paper, we consider the generalized inverted exponential distribution (GIED) as a life model to develop various acceptance sampling schemes for truncated life tests. We develop the repetitive acceptance sampling plan (RASP) by attributes based on truncated life test and determine the design parameters satisfying both the producer’s risk (α) and consumer’s risk (β) simultaneously for the specified quality levels in terms of true median life ratio to the specified life. We are also to minimize average sample number where the constraints are related to the lot acceptance probabilities at the acceptance and limiting quality levels. The performance of the proposed plan is compared with single acceptance sampling plan under the GIED. The proposed sampling plan reduces the average sample number as compare to the single acceptance sampling plan. Tables are obtained for various values of shape parameter and the results are discussed. Also, discussion about the effect of misspecification of shape parameter is explained.

  Key-Words / Index Term
  Consumer’s risk, repetitive acceptance sampling plan, median life, generalized inverted exponential distribution, producer’s risk

  References
  [1] B. Epstein, “Truncated life tests in the exponential case”, The Annals of Mathematical Statistics, 25(3),pp.555-564, 1954.
  [2] N. Balakrishnan, l. Leiva, and J. Lopez, “Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution”, Communications in Statistics-Simulation and Computation. 36, pp.643-656, 2007.
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  [4] R.E. Sherman, “Design and evaluation of repetitive group sampling plan”, Technometrics, 7:1121, 1965.
  [5] S. Balamurali, C.H. Jun, “Repetitive group sampling procedure for variables inspection”, Journal of Applied Statistics, 33(3):327338, 2006.
  [6] A. M. Abouammoh, and A. M. Alshingiti, “Reliability estimation of generalized inverted exponential distribution”, Journal of Statistical Computation and Simulation, 79, pp.1301-1315, 2009.
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  [8] S. Dey,”Inverted exponential distribution as a life distribution model from a Bayesian viewpoint”, Data Science Journal, 6, pp.107-113, 2007.
  [9] Sukhdev Singh and Yogesh Mani Tripathi and Chi-Hyuck Jun,“Sampling plans based on truncated life test for a generalized inverted exponential distribution”, Industrial Engineering Management Systems, 14(2), pp.183-195, 2015.
  [10] H. Krishna and K. Kumar,”Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample”, Journal of Statistical Computation and Simulation, 83, pp.1007-1019, 2013.
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  Citation
  Navyodh Singh, Navjeet Singh, Harpreet kaur , "A Repetitive Acceptance Sampling Plan for Generalized Inverted Exponential Distribution Based on Truncated Life Test," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.58-64, 2018

• Open Access   Article

  Comparison of Exponential Smoothing Models for Forecasting Cassava Production

  O.V. Oni and Y.O. Akanle

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.65-68, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.6568

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  Abstract
  This paper evaluated and compared the performance of a family of smoothing models such as Simple Exponential Smoothing (SES), Holt’s Linear Trend (HLT), Exponential trend (ET) and Holt’s Damped Methods: additive and multiplicative; to forecast the annual Cassava production in Nigeria. The predictive capabilities were compared in terms of Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Percentage Error (MPE) and Mean Absolute Percentage Error (MAPE) based on the validated data set. The Holt’s Exponential Trend with parameter α=0.8556 and β=0.0001 was found to have best described the data having the lowest ranked error statistics in an out of sample performance.

  Key-Words / Index Term
  Cassava, Simple Exponential Smoothing, Holt’s Linear Trend, Exponential Trend, Holt’s Damped Additive and Holt’s Damped Multiplicative

  References
  [1]. World Bank, “Agriculture in Nigeria”. World Bank Published Report, 729: pp 52-68., 2010
  [2]. FAO. “Cassava production” FAOSTAT statistical database retrieve from http://faostat.fao.org, 2013
  [3]. Olayiwola O. O. “Short Term Market Forecast for Cassava Crops in Oyo State, Nigeria” Journal of Agriculture and Food Technology 4 (9) pp 11-18, 2014.
  [4]. B Siregar, I A Butar-Butar, R.F Rahmat, U Andayani & F Fahmi. “Comparison of Exponential Smoothing Methods in Forecasting Palm Oil Real Production”, Journal of Physics: Conference Series 801 012004 doi:10.1088/1742-6596/801/1/012004, 2017.
  [5]. Fried, R.; & George, A.C. “Exponential and Holt-Winters Smoothing”, International Encyclopedia of Statistical Science, Springer Berlin Heidelberg, 2014.
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  [7]. Hyndman, R. J.; Anne B, Koehler J, Keith Ord and Ralph D. Snyder. “Forecasting with exponential smoothing: the state space approach”, Springer-verlg, Berlin Heidelberg, 2008
  [8]. Holt, C. C. “Forecasting trends and seasonal by exponentially weighted averages”, O.N.R. Memorandum 52/1957, Carnegie Institute of Technology, 1957.
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  [10]. Taylor, J. W. "Exponential Smoothing with a Damped Multiplicative Trend”, International Journal of Forecasting, 2003
  
  

  Citation
  O.V. Oni and Y.O. Akanle, "Comparison of Exponential Smoothing Models for Forecasting Cassava Production," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.65-68, 2018

• Open Access   Article

  On Weakly m-semi-I-Open Sets in Minimal Spaces

  R. Mariappan, M. Murugalingam

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.3 , pp.69-72, Jun-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.6972

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  Abstract
  In this paper, we introduce and study the notions of weakly m-semi-I-open sets and weakly m-semi-I-continuity, and their related notions in ideal minimal spaces. Also we investigate the decomposition of weakly m-semi-I-open set. 2000 Mathematics Subject Classification: 54D10

  Key-Words / Index Term
  Ideal minimal space, m-semi-I-open sets, m-semi-I-closed sets, m-semi-I-continuity

  References
  [1] Boonpok C, “Almost and weakly M -continuous functions in m-spaces”, East J. Math Sci, Vol.43, pp.41-58, 2010.
  [2] S. Jafari, N. Rajesh and R. Saranya, “Semiopen sets in Ideal mimimal spaces”, Vasile Alecsandri University of Bacau Faculty of Sciences Scientific Studies and Research Series Mathematics and Informatics, Vol.27, Issue.1, pp.33-48, 2017, .
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  [4] Maki. H, K.C. rao and A. Nagoor, “On generalizing semi-open and preopen sets”, Pure Appl. Math. Sc., Vol.42, pp.13-21, 1993.
  [5] W. K. Min, “m-Semiopen sets and M-Semicontinuous functions on Spaces with minimal structures”, Honam Math. J., Vol.31, Issue.2, pp.239-245, 2009.
  [6] W. K. Min, Kim Y. K, “m-preopen sets and M -precontinuous functions on Spaces with minimal structures”, Advances in Fuzzy Sets and Systems, Vol.4, Issue.3, pp.237-245, 2009.
  [7] W. K. Min, “αm-open sets and αM-continuous functions”, Commun. Korean Math. Soc., Vol.25, Issue.2, pp.251-256, 2010.
  [8] O.B. Ozbakir and E.E. Yildirim, “On some closed sets in ideal minimal spaces”, Acta Math. Hungar., Vol.125, Issue.3, pp.227-235, 2009.
  [9] V. Popa and T.Noiri, “On the definition of some generalized forms of continuity under minimal condition”, Mem. Fac. Sci. Kochi. Uni. Ser. Math., Vol.22, pp.9-19,2001.
  [10] V. Popa and T.Noiri, “On M-continuous functions”, Anal Uni. "Durarea de Jos", Galati,Ser. Mat. Fis. Me. Teor., Vol.18, Issue.23, No.2, pp.31-41, 2000.
  [11] Takashi Noiri and Veleriu Popa, “On Iterate Minimal Structures and m-Iterate Continuous Functions”, Fasciculi Mathematici, Vol.50, pp.109-118, 2013.
  

  Citation
  R. Mariappan, M. Murugalingam, "On Weakly m-semi-I-Open Sets in Minimal Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.3, pp.69-72, 2018