Volume-6 , Issue-3 , Jun 2019, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Analysis of splitting of dust particles in the atmosphere using mathematical modeling Techniques

  P. Meenapriya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.1-11, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.111

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  Abstract
  The paper presents the behaviour of splitting of dust particles in the atmosphere filled with couple stress fluid. A two dimensional geometry flow through a horizontal channel has been considered with an applied electric field. By using regular perturbation technique the partial differential equation have been derived and hence solved analytically. The analytical results for the splitting of dust particles using various relevant parameters are depicted as graphs. Thus it is seen that the transport of pollutants depend upon the rate of introduction of the pollutant and other parameters like electric number and couple stress parameter in the atmosphere.

  Key-Words / Index Term
  Couplestressfluid, Electricnumber, Mixturetheory

  References
  [1] W.N. Gill, R. Sankarasubramanian, “Exact analysis of unsteady convective diffusion”, Proc.Roy.Soc.London Series, Vol.A, Issue.4, pp.341, 2012.
  [2] E.R. Jayaratne, T.S. Verma , “Environmental aerosols and their effect on the earth’s local fair weather electric field”, Journal of meteorol. Atmos. Phys., Vol.86, Issue.(3-4) pp. 275-280, 2004.
  [3] P.Meenapriya,Nirmala P.Ratchagar, “Generalized dispersion of atmospheric aerosols on unsteady convective diffusion in couple stress fluid bounded by electrodes”, International Journal of Applied Mathematics and Engineering Sciences, Vol. 5, Issue. 1, pp. 59-72, 2011.
  [4] P.Meenapriya,Nirmala P.Ratchagar,“EHD dispersion of atmospheric aerosols through a vertical channel with temperature distributions”, World Journal of Engineering, Vol. 9, Issue. 4, pp. 293-306, 2012.
  [5] N. Rudraiah, N. Devaraju, “Effects of reaction rate and large size deformable aerosols on dispersion in atmospheric flow regarded as the turbulent fluid saturated porous media”, Journal of Porous Media, Vol.14. Issue.3, pp.187-199, 2011.
  [6] J.J. Schmidt, “Experimental study of electro-Coalescence in a unit reactor (D)”, Master Thesis, Austin, USA; University of Texas, 2000.
  [7] V.K. Stokes,. “couple stress in fluids”, Phys. Fluids,Vol. 9, pp. 1709-1715, 1966.
  [8] G.I. Taylor, “Dispersion of Soluble matter in solvent flowing slowly through a tube”, Proc. Roy. Soc. London, Vol. A, Issue. 219, pp. 186, 1953.
  [9] Wang H. Zeng, M. Loewenberg, “Particle aggregation due to combined gravitational and electrophoretic motion”, Journal of colloid interface sci.Vol. 187, Issue. 1, pp. 213-22, 1997.
  

  Citation
  P. Meenapriya, "Analysis of splitting of dust particles in the atmosphere using mathematical modeling Techniques," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.1-11, 2019

• Open Access   Article

  Classification of The Nigerian States by Reproductive Health Variables for Optimal Reproductive Health Service Delivery

  Umoren M. U and Odom Conleth C.

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.12-21, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.1221

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  Abstract
  In this paper, we make use of cluster analysis to group the states in Nigeria into zones according to their similarity in reproductive health outcomes. Specifically, Ward’s hierarchical clustering method and k-means clustering method were used sequentially to group the thirty-six states of Nigeria and the federal capital territory into zones. Calinski and Harabasz’s variance-ratio criterion was used to determine the optimal number of zones. Three clusters of states with similar reproductive health outcomes within each cluster were found. The cluster solution was validated using Silhouette. The result shows that, for optimal reproductive health service delivery, grouping the states into zones according to their similarity in reproductive health outcomes poses a better alternative to the earlier grouping according to geopolitical zones.

  Key-Words / Index Term
  Cluster Analysis, Ward’s Hierarchical Clustering, k-means Clustering, Variance Ratio Criterion, Reproductive Health Intervention

  References
  [1]. United Nations Children’s Fund [Nigeria] (n.d.). The children, maternal and child health. http://www.unicef.org/nigeria/children_1926.html. Accessed 18 July 2016.
  [2]. The UN Inter-agency Group for Child Mortality Estimation. 2013. Child Mortality Report. United Nations Children’s Fund, 3 UN Plaza, New York, New York, 10017 USA
  [3]. Kana, M. A., Doctor, H. V., Peleteiro, B., Lunet, N., & Barros, H. (2015). Maternal and child health interventions in Nigeria: a systematic review of published studies from 1990 to 2014. BMC public health, 15(1): 1.
  [4]. Lassi, Z. S., Kumar, R., Mansoor, T., Salam, R. A., Das, J. K., & Bhutta, Z. A. (2014). Essential interventions: implementation strategies and proposed packages of care. Reproductive health, 11(1): 1.
  [5]. Cooke, J. G., & Tahir, F. (2013). Maternal health in Nigeria: with leadership, progress is possible. Washington DC, USA: Center for Strategic and International Studies (CSIS).
  [6]. Shittu, O., Ejembi, C., Adaji, S., Abdul, M., Idris, S., Abdulkarim, B., ... & Potts, M. (2010). The current state of reproductive health in rural northern Nigeria in the context of the pursuit of the MDGs: Perspectives from a community-based research training program. African Journal of Reproductive Health, 14(3): 15-18.
  [7]. Wollum, A., Burstein, R., Fullman, N., Dwyer-Lindgren, L., & Gakidou, E. (2015). Benchmarking health system performance across states in Nigeria: a systematic analysis of levels and trends in key maternal and child health interventions and outcomes, 2000–2013. BMC medicine, 13(1): 1.
  [8]. Jones, G., Steketee, R. W., Black, R. E., Bhutta, Z. A., Morris, S. S., & Bellagio Child Survival Study Group. (2003). How many child deaths can we prevent this year?. The lancet, 362(9377): 65-71.
  [9]. Singh, J., Chaturvedi, H. K., & Pandey, A. (2015). Factors Influencing Antenatal Care Services Utilization in Empowered Action Group (EAG) States, India: A Spatial and Multilevel Analysis. Global Journal of Human-Social Science Research, 15(8).
  [10]. Kumar, C., Singh, P. K., & Rai, R. K. (2012). Under-five mortality in high focus states in India: a district level geospatial analysis. PLoS One, 7(5): e37515.
  [11]. Eze, T. C., Sunday, C. O., & Ogbodo, J. C. (2014). Patterns of inequality in human development across Nigeria’s six geopolitical zones. Dev Country Stud, 4(8): 97-101.
  [12]. National Population Commission (NPC) [Nigeria] and ICF International. 2014. Nigeria Demographic and Health Survey 2013. Abuja, Nigeria, and Rockville, Maryland, USA: NPC and ICF International.
  [13]. Rencher, A. C. (2003). Methods of multivariate analysis (Vol. 492). John Wiley & Sons.
  

  Citation
  Umoren M. U and Odom Conleth C., "Classification of The Nigerian States by Reproductive Health Variables for Optimal Reproductive Health Service Delivery," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.12-21, 2019

• Open Access   Article

  Construction of un-equally replicated Pairwise Balanced Block Design using unreduced symmetrical BIBD

  A. Rajarathinam, M.Sindu

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.22-25, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.2225

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  Abstract
  A new method has been proposed for the construction of un-equally replicated Pairwise Balanced Block Design using unreduced Symmetrical Balanced Incomplete Block Design. The constructed method is illustrated with suitable numerical example. Optimality criteria has been derived and the constructed design is found to be universal optimum.

  Key-Words / Index Term
  Block design, Incidence matrix, Pairwise balanced block designs, Concurrent matrix, Symmetric BIBD

  References
  [1] R. C. Bose and S. S. Shrikhand, “On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler”, Transactions of the American Mathematical Society, Vol 95, Issue 2,pp. 191-209,1960.
  [2] E. O. Effanga, J. A. Ugboh, , E. I. Enang, and B. E. A. Eno,” A tool for constructing Pair wise balanced incomplete block design”. Journal of Modern Mathematics and Statistics, vol 3, Issue 4, 69-72, 2009.
  [3] D.K. Ghosh and N.R. Desai,” Optimal Pair wise balanced designs from Triangular PBIB Designs with v=10”, Int.J.Agrcult.Stat.Sci.,vol 10, Issue 2,pp. 297-304,2014.
  [4] A.Das,”An introduction to optimality criteria and some results on optimal block design”, Design Workshop lecture note,ISI,Kolkatta, November 25-29,pp.1-21,2002
  [5] A. Hedayat and J. Stufken ,” A relation between Pair wise balanced and Variance balanced block designs”, Journal of the American Statistical Association, vol 84, Issue 407, pp. 753-755, (1989).
  [6] A. Rajarathinam, S. Mahalakshmi and D.K. Ghosh, “Construction of Pair wise balanced design”, Journal of Modern Applied Statistical Methods.,vo 15, Issue 1, pp. 193-205,2016.
  

  Citation
  A. Rajarathinam, M.Sindu, "Construction of un-equally replicated Pairwise Balanced Block Design using unreduced symmetrical BIBD," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.22-25, 2019

• Open Access   Article

  Multi Criteria Decision Making Approach for Multivariate Stratified Sampling Problem

  M.V.Ismail and A.Razzaq

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.26-30, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.2630

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  Abstract
  In this paper, we consider the multivariate allocation problem with upper limits on the available costs for various characters. This problem is formulated as a multi criteria decision making (MCDM) problem with several convex objective functions and linear constraints. The cutting plane technique is used for linearizing the convex functions and then the optimum allocation is obtained by using MCDM approach. A numerical example is solved to illustrate the procedure.

  Key-Words / Index Term
  Multivariate stratified sampling, optimum allocation, convex objective function, cutting plane technique, MCDM

  References
  [1] J.E. Kelly,”The cutting Plane Method for Solving Convex Programs”, Jour. Soc. Indust. Appl. Math,. Vol.8, pp.703-712, 1960.
  [2] S.P. Ghosh, “A note on stratified random sampling with multiple characters”, Cal. Stat. Assoc. Bull., Vol. 8, pp.81-89, 1958.
  [3] F. Yates, “Sampling methods for censuses and surveys(2nd ed.)”, Charles Griffin and Co. Ltd. London, 1960.
  
  [4] W.G. Cochran, “Sampling Techniques”, John Wiley & Sons, New York, 1977.
  
  
  
  
  [5] A.R. Kokan and S.U. Khan, “Optimum allocation in multivariate surveys-An analytical solution”, Jour. Roy. Stat. Soc. Ser. B, Vol. 29, pp.115-125, 1967.
  [6] H. Aoyama, ” Stratified random sampling with optimum allocation for multivariate populations”, Ann. Inst. Stat. Math., Vol. 14, pp.251-258,1963.
  
  [7] N. Jahan, M.I.M. Khan and M.J.Ahsan, “A generalized compromise allocation”, Journal of the Indian Statistical Association, Vol. 32, pp. 95-101, 1994.
  [8] S. Chatterjee, “Multivariate Stratified Surveys”, Jour. Amer. Stat. Assoc., Vol. 63, pp. 530-534, 1968.
  [9] J.R. Chromy, “Design optimization with multiple objectives”, Proceedings of the Survey Research Section, ASA, pp.194-199, 1987.

  Citation
  M.V.Ismail and A.Razzaq, "Multi Criteria Decision Making Approach for Multivariate Stratified Sampling Problem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.26-30, 2019

• Open Access   Article

  A Mathematical Model to Study the Growth of Dominant Herbivores

  Nabajyoti Bhattacharjee

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.31-34, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.3134

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  Abstract
  The National Parks, Wildlife Reservoir and Sanctuary are declared to save some specific species from extinction in that region. But due to ecological and social disturbances the growth rate of rhinoceros gets affected and consequently their number reduces from the actual number. In this paper, we shall construct a mathematical model to describe the growth rate of a dominant herbivore species like rhinoceros and elephant to study and investigate graphically the effect of both ecological(natural birth and death, intraspecific, interspecific competition) and social(poachers) disturbances in the growth of that species in that region and in a given period of time.

  Key-Words / Index Term
  Mathematical modelling, Difference equation, Population dynamics, Poaching, Competition, Predation

  References
  [1] J. H. Connell, “The influence of interspecific competition and other factors on the distribution of the barnacle Chthamalus stellatus”, JSTOR, Vol. 42, No. 4, 1961.
  [2] L. L. Eberhardt, J. M. Breiwick, “Models for Population Growth Curves”, ISRN Ecology, Vol. 2012, 2011
  [3] D. E. Goldberg, A. M. Barton, “Patterns and Consequences of Interspecific Competition in Natural Communities: A Review of Field Experiments with Plants”, The American Naturalist, 139(4), pp-771-801, 1992
  [4] Report on the regional meeting for India and Nepal IUCN/SSC Asian Rhino Specialist Group, Kaziranga National Park, Assam, India, 2007.
  [5] “Note on Mathematicals in Biology”, University of Kwazulu-Natal, Durban
  [6] Lindeman, RL, “The trophic-dynamic aspect of ecology”, Ecology, 23(1942), pp-399-418, 1942
  [7] P. L. Munday, G. P. Jones, M. J. Caley, “Interspecific Competition and Coexistence in a guild of Coral-Dwelling Fishes”, Ecological Society of America, 82(8), pp-2177-2189, 2001.
  [8] AN Tsoularis, J. Wallace, “Analysis of Logistic Growth Models”, Mathematical Bioscience, 179(1), pp-21-55, 2002.
  [9] AN TsoularisN, J. Wallace, “A Markov chain model of predator-model-mimic interactions”, Journal of Biological Systems, 13(03), 2011.
  [10] V. Volterra, “Variations and flucuations of the number of individuals in animal species living together in animal ecology”, Chapman, R. N.,McGraw-Hill, 1931.

  Citation
  Nabajyoti Bhattacharjee , "A Mathematical Model to Study the Growth of Dominant Herbivores," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.31-34, 2019

• Open Access   Article

  Bianchi Type I Bulk Viscous Fluid String Dust Magnetized Cosmological Model with Λ-Term in Bimetric Theory of Gravitation

  S. S. Charjan, P. R. Dhongle, M. S. Borkar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.35-40, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.3540

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  Abstract
  Bianchi Type I bulk viscous fluid string dust magnetized cosmological model with cosmological constant term have been evaluated by solving Rosen’s field equations. The cosmological constant plays the important role and it affects the physical behavior of the model in the presence as well as in the absence of both the magnetic field and the bulk viscosity. The model is studied for the positive, negative and zero values of cosmological constant. Further in special cases, the physical and geometrical aspects of the model are studied in the absence of magnetic field and in the absence of bulk viscosity.

  Key-Words / Index Term
  Bimetric Theory, Bulk Viscous Fluid, Cosmic String, Magnetic Field, Bianchi Type I

  References
  [1] N. Rosen, “A Theory of Gravitation”, Annals of Phys., Vol. 84, pp. 455-473, 1974.
  [2] N. Rosen, “Topics in Theoretical and Experiential Gravitation Physics”, edited by V. D. Sabtta and J. Weber, Plenum Press, London, pp. 273-294, 1977.
  [3] T. M. Karade, “Spherically Symmetric Space Times in Bimetric Relativity Theory I”, Indian J. Pure-appl. Math., Vol. 11, Issue 9, pp. 1202-1209, 1980.
  [4] S. D. Katore, R. S. Rane, “Magnetized Cosmological Models in Bimetric Theory of Gravitation”, Pramana J. Phys., Vol. 67, Issue 2, pp. 227-237, 2006.
  [5] M. Isrelit, “Spherically Symmetric Fields in Rosen’s Bimetric Theories of Gravitation”, General Relativity and Gravitation, Vol. 13, Issue 7, pp. 681-688, 1981.
  [6] G. S. Khadekar, S. D. Tade, “String Cosmological Models in Five Dimensional Bimetric Theory of Gravitation”, Astrophys. Space Sci., Vol. 310, Issue 1, pp. 47-51, 2007.
  [7] D. R. K. Reddy, N. V. Rao, “On Some Bianchi Type Cosmological Models in Bimetric Theory of Gravitation”, Astrophys. Space Sci., Vol. 257, pp. 293-298, 1998.
  [8] K. D. Krori, T. Choudhuri, C. R. Mahanta, “String in Some Bianchi Type Cosmologies”, General Relativity and Gravitation, Vol. 26, Issue 3, pp. 265-274, 1994.
  [9] M. S. Borkar, P. R. Dhongle, “Bianchi Type I String Dust Model with Magnetic Field in Stationary Space-time”, Int. J. Applied Math., Vol. 23, Issue 6, pp. 977-988, 2010.
  [10] R. Bali, S. Dave, “Bianchi Type – IX String Cosmological Models with Bulk Viscous Fluid in General Relativity”, Astrophys. Space Sci., Vol. 288, pp. 503-509, 2003.
  [11] R. Bali, R. D. Upadhaya, “LRS Bianchi Type I String Dust Magnetized Cosmological Models”, Astrophys. Space Sci., Vol. 283, pp. 97-108, 2003.
  [12] R. Bali, D. Singh, “Bianchi Type – V Bulk Viscous Fluid String Dust Cosmological Model in General Relativity”, Astrophys. Space Sci., Vol. 300, pp. 387-394, 2005.
  [13] R. Bali, Anjali, “Bianchi Type I Bulk Viscous Fluid String Dust Magnetized Cosmological Model in General Relativity”, Pramana- J. of Physics, Vol. 63, Issue 3, pp. 481-490, 2004.
  [14] R. Bali, U. K. Pareek, “Bianchi Type I String Dust Cosmological Model with Magnetic Field in General Relativity”, Astrophys. Space Sci., Vol. 312, pp. 305-310, 2007.
  [15] M. S. Borkar, S. S. Charjan, “Bianchi Type I String Dust Cosmological Model with Magnetic Field in Bimetric Relativity”, Int. J. Applied Math., Vol. 22, Issue 3, pp. 445-456, 2009.
  [16] M. S. Borkar, S. S. Charjan, “The Charged Perfect Fluid Distribution in Bimetric Theory of Relativity”, J. Ind. Acad. Math., Vol. 32, Issue 1, pp. 147-152, 2010.
  [17] M. S. Borkar, S. S. Charjan, “LRS Bianchi Type I String Dust Magnetized Cosmological Models in Bimetric Theory of Relativity”, Tensor N. S., Vol. 71, Issue 2, pp. 155-162, 2010.
  [18] M. S. Borkar, S. S. Charjan, “Bianchi Type I Magnetized Cosmological Model in Bimetric Theory of Gravitation”, An Int. J. AAM, Vol. 5, Issue 10, pp. 1660-1671, 2010.
  [19] M. S. Borkar, S. S. Charjan, “Bianchi Type I Magnetized Cosmological Model with - term in Bimetric Theory of Gravitation”, An Int. J. AAM, Vol. 8, Issue 10, pp. 116- 127, 2013.
  [20] N. P. Gaikwad, M. S. Borkar, S. S. Charjan, “Bianchi Type I Massive String Magnetized Baratropic Perfect Fluid Cosmological Model in Bimetric Theory of Gravitation”, Chin. Phys. Lett., Vol. 28, Issue 8, pp. 089803-1-4, 2011.
  [21] P. S. Letelier, “Clouds of Strings in General Relativity”, Physical review, D 20(6), pp. 1294-1302, 1979.
  [22] P. S. Letelier, “String Cosmology”, Physical review, D 28(10), pp. 2414-2419, 1983.
  [23] J. Stachel, “Thickening the String I, The String Perfect Dust”, Physical Review, D 21(8), pp. 2171-2181, 1980.
  [24] A. Pradhan, M. K. Yadav, A. Rai, “Some Bianchi Type III String Cosmological Models with Bulk Viscosity”, Int. J. Theor. Phys., Vol. 46, Issue 11, pp. 2774-2787, 2007.
  [25] A. Pradhan, M. K. Yadav, S. K. Singh, “Some Magnetized Bulk Viscous String Cosmological Models in General Relativity”, Astrophys. Space Sci., Vol. 311, pp. 423-429, 2007.
  [26] A. Pradhan, “Some Magnetized Bulk Viscous String Cosmological Models in Cylindrically Symmetric Inhomogeneous Universe with Variable - term”, Comm. Theor. Phys., Vol. 51, Issue 2, pp. 367-374, 2009.
  [27] X. X. Wang, “Bianchi Type I String Cosmological Models with Bulk Viscosity and Magnetic Field”, Astrophys. Space Sci., Vol. 293, pp. 433-440, 2004.
  [28] X. X. Wang, “Bianchi Type III String Cosmological Models with Bulk Viscosity and Magnetic Field”, Chin. Phys. Lett., Vol. 23, pp. 1702-1704, 2006.
  [29] M. S. Borkar, S. S. Charjan, “Bianchi Type I Bulk Viscous Fluid String Dust Cosmological Model with Magnetic Field in Bimetric Theory of Gravitation”, An Int. J. AAM , Vol. 5, Issue 1, pp. 96-109, 2010.
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  [31] Y. B. Zel’dovich, “Cosmological Fluctuations near Singularity”, Mon. Not. R. Astron. Soc., Vol. 192, pp. 663 – 667, 1980.

  Citation
  S. S. Charjan, P. R. Dhongle, M. S. Borkar, "Bianchi Type I Bulk Viscous Fluid String Dust Magnetized Cosmological Model with Λ-Term in Bimetric Theory of Gravitation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.35-40, 2019

• Open Access   Article

  Private Dominating Sets and Private Domination Polynomial of Friendship Graphs

  AngelinKavithaRaj S and SenthilMurugan P

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.41-44, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.4144

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  Abstract
  Let G be a simple graph of order n and V denotes vertex set and E denotes edge set of G. A subset S of V is called Private domination set of graph G if it is dominating set and also every u in S there exist an external private neighbour v in other than S in V. And Private Domination Polynomial of G is the polynomial denoted as PD(G,x)) , is the sum of Private dominating sets Pd(G,j), where Pd(G,j) be the cardinality of the family of Private domination set with cardinality j . Let m be any positive integer and Fm be the Friendship graph constructed by joining K1 and m times of K2. In this paper, we investigate the properties of Private domination set and Private Domination Polynomial for family of Friendship graph and a special case called Friendship graph with missing vertex.

  Key-Words / Index Term
  Dominating set, Domination Polynomial, Private Domination set, Private Domination Polynomial, Friendship Graph, Missingvertex

  References
  [1] B.J. Prasad, T. T Chelvan, S. R Chellathurai, “Private Domination number of a graph”, Journal of Discrete Mathematical Sciences and Cryptography, Vol.5, Issue.5 October 2007.
  [2] I.Heinrich, P.Tittmann, “Neighborhood and Domination Polynomial of Graphs”, Graphs and Combinatorics 34(6), pp. 1203-1216 , 2018.
  [3] P.Erdos , A. Renyi, V.T.Sos, “On a problem of graph theory”, Studia Sci.Math,Hungar, pp. 215-235, 1966.
  [4] S. A.K.Raj , S. R.Chellathurai, “Weak dominating sets and Weak Domination Polynomial of Complete Graphs”, Journal of Computer and Mathematical Sciences, Vol.9, Issue.12, pp. 238-248, 2018.
  [5] S.Alkhani , Y.h.Peng, “Introduction to Domination Polynomial of a graph”, Ars Combinatoria- Winnipeg, May 2009.
  [6] S.Akhani, J.I.Brown, S.Jahari, “On the Domination Polynomials of Friendship Graphs”, JSTOR,2016.
  [7] S.S.Kahar, A.J.M.Khalal, R.Hasni, “Dominating sets and Domination Polynomial of Stars”,Australian Journal of Basic & Applied Sciences Vol.8, Issue.6, pp.383-386, January 2014.
  [8] S. Alikhani, S.Jahari, “Domination Polynomial of generalized book graphs,” Journal of Mathematical Extension,Vol 10, pp.35-45, 2016
  [9] S.Alikahani, S.Jahari, “Domination Polynomial of lexicographic product of specific graph”, Journal of Information and Optinization Sciences, Vol.3, Issue.9,5, pp.1019-1028, 2018.
  [10] T.W. Haynes, S.T. Hedetniemi, P.J. Slater,”Fundamental of Domination in Graphs”, 1998.
  [11] K.Kanagalakshmi,S.Shenbagavadivu,”Frequecy Domain Enhancement Filters:A Survey” International Journal of Computer Sciences and Engineering, Vol.7, Issue.2, jan 2019.
  [12] P.Roy, S.Adhikari, J.K.Mandal “A Shortest Path SimilarityMatrix based Spectral Custering ”,International Journal of Computer Sciences and Engineering, Vol.4, Issue.1, 2016.

  Citation
  AngelinKavithaRaj S and SenthilMurugan P , "Private Dominating Sets and Private Domination Polynomial of Friendship Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.41-44, 2019

• Open Access   Article

  Construction of Optimal Pairwise Balanced Block Designs Based on 3n Symmetrical Factorial Design

  M.Sindu, A. Rajarathinam

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.45-48, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.4548

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  Abstract
  A new method for constructing Optimal Pairwise Balanced Block Design using the concept of 3n symmetrical factorial design has been proposed. The constructed method is illustrated with numerical example and the design is found to be universal optimal.

  Key-Words / Index Term
  Block design, Incidence matrix, Balanced Design, Pairwise Balanced Block Designs, Concurrent matrix

  References
  [1] R. C. Bose, & S. S. Shrikhande, “On the falsity of Euler’s conjecture about the non-existence of two orthogonal latin square of order” , Proceedings of the National Academy of Sciences of the United States of America, Vol.45,Issue.5, pp.734-737,1959(a).
  [2] R. C. Bose, & S. S. Shrikhande, “On the composition of balanced incomplete block designs”, Canadian Journal of Mathematics, Vol. 12, pp.177-188,1960(a).
  [3] R. C. Bose, & S. S. Shrikhande, “On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler” , Transactions of the American Mathematical Society, Vol.95, Issue.2, pp.191-209,1960(b).
  [4] D.K. Ghosh, and N.R. Desai,“Optimal Pairwise balanced designs from Triangular PBIB Designs with v=10”, Int.J.Agrcult.Stat.Sci., Vol.10.Issue .2,pp.297-304,2004.
  [5] A.Das,”An introduction to optimality criteria and some results on optimal block design”, Design Workshop lecture note,ISI,Kolkatta, November 25-29,pp.1-21,2002
  [6] A. Rajarathinam, S. Mahalakshmi and D.K. Ghosh “Construction of Pairwise balanced design”, Journal of Modern Applied Statistical Method, Vol.15,Issue. 1, pp.193-205,2016.
  

  Citation
  M.Sindu, A. Rajarathinam, "Construction of Optimal Pairwise Balanced Block Designs Based on 3n Symmetrical Factorial Design," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.45-48, 2019

• Open Access   Article

  Parametric and Nonparametric Regression Modeling for Oil Sectors Stock Prices Time Series Data

  Manikandan B. and Rajarathinam A.

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.49-54, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.4954

  Abstract

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  Citation

  Abstract
  The present investigation is carried out to study the trends in different oil sectors viz., Indian Oil Corporation, Bharat Petroleum and Hindustan Petroleum, stock prices time series data based on parametric and nonparametric regression models. In parametric models different linear models are employed. The statistically most suited parametric models are selected on the basis of highest adjusted R2, significant regression co-efficient and co-efficient of determination (R2), assumptions of normality and independence of residuals. The best fitted model is selected based on the model performance measures such as, Root Mean Square Error, Mean Absolute Error, and Mean Absolute Percentage Error. Nonparametric estimates of underlying growth functions are computed at each and every time points. Relative growth rates are estimated based on the best fitted trend function. In this study none of the parametric models are found suitable to study the trend. Nonparametric regression is found an appropriate tool to study the trends. Decreases in trends with no significant jump have been observed. The mean growth rate is high for Bharat Petroleum Corporation Limited in comparison to that of Hindustan Petroleum Corporation Limited and Indian Oil Corporation.

  Key-Words / Index Term
  Parametric model, Nonparametric, Kernel Smoothers, Band width, Cross–validation

  References
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  Citation
  Manikandan B. and Rajarathinam A., "Parametric and Nonparametric Regression Modeling for Oil Sectors Stock Prices Time Series Data," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.49-54, 2019

• Open Access   Article

  The numerical analysis of the effect of suction, slip and inclination, on the non-Darcy MHD flow of a Casson fluid over a nonlinearly stretching sheet in a porous medium

  Bhim Sen Kala

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.55-78, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.5578

  Abstract

  Full-Text HTML

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  Citation

  Abstract
  In this paper, we have studied the numerical analysis of the effect of suction, slip and inclination, on the non-Darcy MHD flow of a Casson fluid over a nonlinearly stretching sheet in a porous medium. In the mathematical model, using similarity variables, the momentum, energy and concentration equations are transformed to non-dimensional ordinary differential equations. And then these are solved numerically using bvp4c method, a Matlab in- built bvp4c-programm. A discussion for the effects of the parameters involved on the boundary layer regions and the magnitude of the velocity, temperature and concentration and Local skin friction , Local Nusselt Number and Local Sherwood Number have been done graphically and numerically using figures and tables.

  Key-Words / Index Term
  Casson fluid, magnetic parameter, darcy parameter, slip parameters, forchheimrer parameter, power index parameter, inclination parameter, suction parameter

  References
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  Citation
  Bhim Sen Kala, "The numerical analysis of the effect of suction, slip and inclination, on the non-Darcy MHD flow of a Casson fluid over a nonlinearly stretching sheet in a porous medium," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.55-78, 2019