Volume-5 , Issue-6 , Dec 2018, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Square Sum Labeling of a Class of Almost Complete Bipartite Graph

  M. Ganeshan, M.S. Paulraj

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.86-88, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.8688

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  Abstract
  The square sum labeling of a given (p,q) graph G = (V, E) consists of a bijective map f:V→{0,1,2..p-1} and an injective map f^*: E→N defined by f *(e) = [f(u)]2+[f(v)]2 , for every edge e ∈ E, Where e is incident with the vertices u and v. A graph is said to be a square sum if it admits a square sum labeling. In this paper, we have considered that the almost complete bipartite graphs Kn,n +e and have proved that such graphs are square sum for 3 ≤ n ≤10.

  Key-Words / Index Term
  Labeling, Square sum labelling, Almost bipartite graph

  References
  [1] Ajitha V, Studies in Graph Theory-Labeling of Graphs, Ph D thesis(2007), Kannur University, Kannur.
  [2] V. Ajitha, S. Arumugam, and K. A. Germina, On square sum graphs, AKCEJ Graphs and Combinatorics, 6(1), (2009), 1−10.
  [3] A. Blinco, S.I. El-Zanati, and C. Vanden Eynden, On the cyclic decomposition of complete graphs into almost-bipartite graphs, DiscreteMath. 284 (2004), 71–81. [4] R.C. Bunge, S.I. El-Zanati, and C. Vanden Eynden, On γ-labelings of 2-regular almost- bipartite graphs, in preparation.
  [5] J A Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 18(2015), DS#6.
  [6] M. Ganeshan, M.S. Paulraj, Square Sum Labeling of almost Bipartite Graph and Mongolian Tent, International Journal for Research in Engineering Application & Management (IJREAM), ISSN : 2454-9150 Vol-04, Issue- 08, Nov 2018.
  [7] Germina K.A and Reena Sebastian,(2013).Further Results on Square Sum Graph, International Mathematical Forum, Vol. 8, 2013, no. 1, 47 – 57.
  [8] Germina K.A and Reena Sebastian,(2013).On Square sum graphs, Proyecciones Journal of Mathematics(32),107-117.
  [9] J. Shiama, Square sum labeling for some middle and total graphs, International Journal of Computer Applications, 37(4), (January 2012).
  [10] S.A. Shirali, To find four distinct positive integers such that the sum of any two is a square, 18 September 2009. International Journal of Pure and Applied Mathematics, Volume 106 No. 8 2016, 1-6ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on- line version).
  [11] Wallis W.D., Labeling, A Beginner’s Guide to Graph Theory (2007).
  [12] D B West, Introduction to Graph Theory, Prentice-Hall, India, 2001.
  

  Citation
  M. Ganeshan, M.S. Paulraj, "Square Sum Labeling of a Class of Almost Complete Bipartite Graph," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.86-88, 2018

• Open Access   Article

  Some More Results on Stolarsky-3 Mean Labeling of Graphs

  S.Kavitha, S.S. Sandhya, E.Ebin Raja Merly

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.89-93, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.8993

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  Abstract
  In this paper, we contribute some new results for Stolarsky-3 Mean labeling of graphs. We have already proved Stolarsky-3 Mean labeling of some standard Graphs. We use some more standard graphs to derive the results of Stolarsky-3 Mean labeling. We prove Stolarsky-3 Mean labeling of Bistar, Planar Grid, Crown and Square of a Path.

  Key-Words / Index Term
  Graph Labeling, Mean Labeling, Stolarsky-3 Mean Labeling, Bistar, Crown

  References
  [1] J.A. Gallian, “A dynamic survey of graph labeling”, The electronic Journal of Combinatories 17(2017),#DS6.
  [2] F.Harary, 1988, “Graph Theory” Narosa Puplishing House Reading, New Delhi.
  [3] S.Somasundram, and R.Ponraj 2003 “Mean Labeling of Graphs”, National Academy of Science Letters Vol. 26, p.210-213.
  [4] S.Somasundram, R.Ponraj and S.S.Sandhya, “ Harmonic Mean Labeling of Graphs” communicated to Journal of Combinatorial Mathematics and combinational computing.
  [5] S.S.Sandhya, S.Somasundaram and S.Anusa “Some More Results on Root Square Mean Graphs” Journal of Mathematics Research; Vol.7, No.1; 2015.
  [6] S.S.Sandhya, E.Ebin Raja Merly and S.Kavitha “Stolarsky-3 Mean Labeling of Graphs” Journal of Applied Science and Computations; Volume 5, Issue 9, September /2018 PP. 59-66.
  [7] S.S.Sandhya, E.Ebin Raja Merly and S.Kavitha “Stolarsky-3 Mean Labeling of Some Special Graphs” Global Journal of Pure and Applied Mathematics; Volume 14, Number 1(2018)pp.39-47.
  [8] S.S.Sandhya, E.Ebin Raja Merly and S.Kavitha “Some New Results on Super Stolarsky-3 Mean Labeling”International Journal of Mathematics Research; Volume 10, Number 1 (2018), pp. 7-20.
  

  Citation
  S.Kavitha, S.S. Sandhya, E.Ebin Raja Merly, "Some More Results on Stolarsky-3 Mean Labeling of Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.89-93, 2018

• Open Access   Article

  Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function

  Javid Majid, Imtiyaz Majid

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.94-101, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.94101

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  Abstract
  In this paper we will implement the generalized fractional operators induced by Saego-Maeda using the Appell’s F_3 (.) function and set up the image formulas associated with the generalized Miller-Ross function in terms of the generalized Fox- Wright function. We will also employ certain integral transforms on the results obtained from the differentials and the integrals and present some more image formulas.

  Key-Words / Index Term
  Generalized Miller-Ross function, Saego-Maeda fractional operator, Fox Wright function

  References
  [1] D. Baleanu, O. G. Mustafa, “On the Global Existence of Solutions to a Class of Fractional Differential Equations”, Com. Math. Appl, Vol. 59 pp.1835-1841. 2010
  [2] D. Baleanu, P. Agarwal, S. D. Purohit, “Certain fractional integral formulas involving the product of generalized Bessel functions”, Sci. World J. pp.1-9, 2013
  [3] A.A. Kilbas, “Fractional Calculus of the Generalized Wright Function”, Fract. Calc. Appl. Anal, vol.8 No.2 pp.113-126, 2005
  [4] Miller, K. And Ross, B., “An introduction to the Fractional Calculus and Fractional differential Equations”, John Wiley Sons, New York,1993.
  [5] Saigo M., “A Remark on Integral Operators Involving the Gauss Hyper-geometric Functions” Math. Rep. College General Ed. Kyushu Univ., Vol. 11, pp. 135-143, 1978
  [6] G.M. Mittag-Leffler, “Sur la representation analytique de’une branche Uniforme une function monogene”, Acta. Math., 29, pp.101-181. 1905
  [7] T.R. Prabhakar, ”A Singular Integral Equation with a Generalized Mittag-Leffler Function in the Kernel”, Yokohama Math. J., vol 19, pp.7-15, 1971
  [8] D. Kumar, S. D. Purohit, J. Choi, “Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials”, J. Nonlinear Sci. Appl, 9 821, 2016
  [9] J. Ram, D. Kumar, “Generalized fractional integration involving Appell hyper-geometric of the product of two H-functions”, Vijnana Parishad Anusandhan Patrika, Vol. 54,No.3 pp. 33-43, 2011
  [10] J. Zhao, “Positive solutions for a class of q-fractional boundary value problems with p-Laplacian”, J. Nonlinear Sci.Appl., 8 , 442-450.1, 2015
  [11] P. Agarwal, J. Choi, R. B. Paris, Extended Riemann-Liouville fractional derivative operator and its applications. Nonlinear Sci. Appl. Vol. 8 ,pp. 451-466, 2015
  [12] R. K. Saxena, J. Ram, D. Kumar, “Generalized fractional integration of the product of Bessel functions of the First kind”, Proceedings of the 9th Annual Conference, Soc. Spec. Funct. Appl., vol.9 , pp.15-27, 2011
  [13] S. D. Purohit, S. L. Kalla, D. L. Suthar, “Fractional integral operators and the multi index Mittag-Leffler functions”, Sci. Ser. A Math. Sci. ,vol. 21,pp. 87-96, 2011
  [14] S. D. Purohit, D. L. Suthar, S. L. Kalla, “Marichev-Saigo-Maeda fractional integration operators of the Bessel function”, Matematiche (Catania), 67 ,pp. 21-32, 2012
  [15] S. R. Mondal, K. S. Nisar, “Marichev-Saigo-Maeda fractional integration operators involving generalized Bessel function’s”, Math. Probl. Eng., vol. 11 pages.1-9, 2014
  [16] Javid Majid, Imtiyaz, Aarif and Jain, “Certain image formulas associated with the fractional integrals and derivatives of the product of Srivstava polynomials and the K-function”, IJRAR ,Vol. 5,issue 4,pages 32-47,2018
  [17] Shweta Pandey, Sandeep Dixit, ‘Solution of System of Fractional Differential equations using Variational Iteration Method”, International Journal of Computer Sciences and engineering, Vol. 6, Issue 8,pp. 797-802,2018.
  [18] Saigo M., “A Remark on Integral Operators Involving the Gauss Hyper-geometric Functions” Math. Rep. College General Ed. Kyushu Univ., Vol. 11, pp. 135-143, 1978
  [19] Appell, P. and Kampe de Feriet, J., “Functions Hyper-geometriqueset Hyperspheriques Polynomes d`Hermite” . Gauthier-Viliars, Paris. 1926
  [20] Wright E. M., “The asymptotic expansion of the generalized hyper-geometric functions” J. London Math. Soc., Vol. 10, pp. 286-293, 1935
  [21] Rainville E. D., “Special Functions”, the Macmillan Company, New York, 1963
  [22] Farhan, Sharma and Jain, “Generalized Miller-Ross Function and its Integral Representation”, International Journal of Mathematics Trends and Technology- Vol. 16 Number 1, pp. 16-18,2014
  [23] Mathai AM, Saxena RK, Haubold HJ. “The H-Function Theory and Applications” New York, NY: Springer-Verlag 2010
  [24] I.N.Sneddon, “The use of integral transforms”, Tata McGraw- Hill, New Delhi, 1979
  

  Citation
  Javid Majid, Imtiyaz Majid, "Marichev-Saigo Maeda Fractional Operators representations of the Generalized Miller-Ross Function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.94-101, 2018

• Open Access   Article

  Reciprocal Fermat Number in Max- Min Matrices

  N. Elumalai, R. Muthamizh Selvi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.102-108, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.102108

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  Abstract
  Let T be a finite number of multiple set of real numbers taken as increasing order of numbers. The purpose of this article is to study the different properties of MIN matrix and MAX matrix of the set T with minimum and maximum numbers of set of ordered pairs. We are going to do this by interpreting these matrices as Reciprocal fermat max and min matrices and applying the determinant formulae and the inverse formulae for Reciprocal fermat MIN matrices and Reciprocal fermat MAX matrices.

  Key-Words / Index Term
  MIN matrix, MAX matrix, meet matrix, join matrix, Fermat min matrix and Fermat max matrix, Reciprocal Fermat Min Matrix, Reciprocal Fermat Max Matrix

  References
  [1]. Michal Křížek, Praha, Lawrence Somer, A necessary and sufficient condition for the Primality of fermat numbers, Mathematica Bohemica No. 3, 541–549, 2001.
  [2]. H. Neudecker, G. Trenkler, and S. Liu, Problem section, Stat Papers 50, 221–223, 2009.
  [3]. R. Bhatia, Infinitely divisible matrices, Amer. Math. Monthly 113 no. 3, 221–235, 2006.
  [4]. R. Bhatia, Min matrices and mean matrices, Math. Intelligencer 33 no. 2, 22–28, 2011.
  [5]. Crandall, R. E., Mayer, E., Papadopoulos, J.: The twenty-fourth Fermat number is composite, Math. Comp.
  [6]. S. Puntanen, G. P. H. Styan, and J. Isotalo, Matrix Tricks for Linear Statistical Models -Our Personal Top Twenty, 1st ed.,Springer, 2011.
  [7]. R.P. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth and Brooks/Cole, 1986.
  [8]. P. Haukkanen, On meet matrices on posets, Linear Algebra Appl. 249 , 111–123, 1996.
  [9]. E. Altinisik, N. Tuglu, and P. Haukkanen, Determinant and inverse of meet and join matrices, Int. J. Math. Math. Sci. Article ID 37580, 2007.
  [10]. M. Mattila and P. Haukkanen, Determinant and inverse of join matrices on two sets, Linear Algebra Appl. 438, 3891–3904, 2013.
  [11]. Mika mattila and Pentti Haukkanen, Studying the various properties of MIN and MAX matrices-elementary vs. more advanced methods, Spec. Matrices , 4:101-109,2016.
  [12]. Serife Buyukkose, The reciprocal mersenne meet matrices on posets, Int. J. Contemp. Math. Sci., Vol. 4, no. 1, 41-46, 2009.
  [13]. B.S. Shetty, U.V. Kulkarni, Preetee, M. Sonule, ManishaN.Shinde, Fuzzy Hyper-line Segment Neural Network by using Association Rule Mining,JCSE, Vol.6 , Issue.12 , pp.25-31, Dec-2018
  

  Citation
  N. Elumalai, R. Muthamizh Selvi, "Reciprocal Fermat Number in Max- Min Matrices," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.102-108, 2018

• Open Access   Article

  Characterization on Nano Generalized Closed Sets

  M. Bhuvaneswari, N. Nagaveni

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.109-115, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.109115

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  Abstract
  Nano weakly generalized closed set (Nwg-Closed set) is introduced by Nagaveni and Bhuvaneswari in Nano topological space. In this paper we investigated the Nano weakly generalized closed set to know other interesting properties. We have established the various conditions for a nonempty subset of a Nano topological space to be Nwg closed. It is observed that a nonempty subset X of a Nano topological space is Nano weakly generalized closed if its upper approximation is the universal set and the lower approximation is X.

  Key-Words / Index Term
  Nano topological space, Nano closed set, Nano Interior and Nano Closure, Nano weakly generalized closed set

  References
  [1] O. Njastad, “On Some Classes of nearly open sets”, Pacific. J. Math., Vol.15, pp. 961-970, 1965.
  [2] Miguel Caldas , “ A note on some applications of α-open sets”, IJMMS, Vo.2, pp. 125-130, 2013.
  [3] N. Levine, “Generalized closed sets in topology”, Rend. Cire. Math. Palermo., Vol.19, pp.89-96, 1970.
  [4] M. E Abd El-Monsef, S. N. El- Deep and R. A. Mahmoud, “β- open sets and β continuous mapping”, Bll. Fac. Sci. Assiut Univ., Vol.12, pp. 77-90, 1983.
  [5] Ahamad Al-Omari and Mohd.Salmi Md.Noorani, “On generalized b- closed sets”, Bull. Malays. Math. Sci. Soc. Vol.32, Issue.1 , pp. 19-30, 2009.
  [6] D. Andrijevic, “Semi-preopen sets”, Mat. Vesnik, Vol.38, pp. 24-32 , 2014
  [7] Ahmed I and El-maghrabi, “More on γ generalized closed sets in topology”, Journal of Taibah University for Science., Vol.7 , pp. 114-119, 2013.
  [8] N. Nagaveni, “Studies on generalizations of Homeomorphisms in topological spaces”, Ph.D., Thesis, Bharathiar University, Coimbatore-1999.
  [9] P.Rajarajeswari and R.Krishna Moorthy, “On Intuitionistic fuzzy weakly generalized closed set and its application”, International Journal of Computer Applications, Vol. 27, Issue. 11, pp . 9-13, 2011.
  [10] Zdzislaw Pawlak, “Rough sets”, International Journal of computer and information sciences, Vol.11, Issue.5 , pp. 341-356,1982.
  [11] M. Lellis Thivagar and Carmel Richard, “On Nano forms of weakly open sets”, International Journal of Math. Stat. Innovation., Vol.1, pp 31-37, 2013.
  [12] K. Bhuvaneswari and K. Mythili Gnanapriya, " Nano generalized closed sets in Nano Topological Space”, International Journal of Scientific and Research Publication,Vol.4, Issue.5 , pp. 1-3, 2014.
  [13] A. Dhanis Arul Mary and Arockiarani. I, “On Nano gb-closed sets in nano topological spaces”, International Journal of Mathematical Archieve, Vol.6, Issue.2, pp. 54-58, 2015.
  [14] Mohammed M. Khalaf and Kamal N. Nimer, “Nano Ps-open sets and Ps-continuity”, Int. J. of contemp. Math. Sciences, Vol.10, pp. 1-11, 2015.
  [15] R.Thanga Nachiyar , K.Bhuvaneswari, “On Nano generalized α- closed sets and Nano α-generalized closed sets in Nano Topological space”, International Journal of Engineering trends and Technology, Vol.13, pp. 257-260, 2014.
  [16] A. Revathy and G. Ilango, “On nano β-open sets”, Int. J. Eng. Contemp. Math. Sci., Vol.1, Issue.2, pp.1–6, 2016.
  [17] P.L. Powar, Pratibha Dubey, “Decomposition of δ -Continuity and δ*-Continuity”, International Journal of Computer Sciences and Engineering, Vol.5, Issue.9,pp. 89-96, 2017.
  [18] R. S. Suriya and T. Shyla Issac Mary, “Alpha Weakly Semi Closed Sets in Topological Spaces, International Journal of Scientific Research in Mathematical and Statistical Sciences”, Vol.5, Issue.4, pp.233-242, 2018.
  [19] N. Nagaveni and M.Bhuvaneswari, “On Nano weakly generalized closed sets”, International Journal of Pure and Applied Mathematics, Vol.106, Issue. 7, pp.129-137, 2016.
  

  Citation
  M. Bhuvaneswari, N. Nagaveni, "Characterization on Nano Generalized Closed Sets," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.109-115, 2018

• Open Access   Article

  Approximation Techniques for Estimation of Parameters of Rayleigh Lomax Distribution under Different Priors

  S.P. Ahmad, Kawsar Fatima

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.116-122, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.116122

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  Abstract
  In this paper Bayes estimators for the parameter of Rayleigh Lomax (RL) distribution are obtained by using Bayesian approximation techniques like normal and T-K approximations. Moreover different single, double and triple priors have been considered. Also, simulation data sets have been considered to study the efficiency of obtained results using R- software.

  Key-Words / Index Term
  Rayleigh Lomax distribution, priors, normal approximation, T-K approximation

  References
  [1] K. Fatima, S.P. Ahmad (2018). “Bayesian Approximation Techniques of Inverse Rayleigh Distribution.” Research & Reviews: Journal of Statistics, 2018; 7(1): 50–59.
  [2] A.Ahmed,, A.A. Khan, S.P. Ahmad(2007). “Bayesian Analysis of Exponential Distribution in S-PLUS and R-Software’s”. Sri Lankan Journal of Applied Statistics, 8, 95-109.
  [3] S. P. Ahmad , A. Ahmed, A. A. Khan. (2011).“Bayesian Analysis of Gamma Distribution Using S-PLUS and R-Softwares.”Asian Journal of Mathematics and Statistics4, 224-233.
  [4] H. Sultan, S.P. Ahmad( 2015). “Bayesian approximation techniques of Topp-Leone distribution.” International Journal of Statistics and Mathematics, 2(1): 066-070.
  [5] A. Afaq, K. Fatima, S.P. Ahmad. (2017). “Lindley Approximation Technique for the Parameters of Lomax Distribution”. International Journal of Statistics in Medical Research, 6(4): 162-168.
  [6] K. Fatima, S.P. Ahmad and T.A. Chishti (2017). “Posterior Estimates of Exponentiated Minimax Distribution under Different Priors. “Journal of Reliability and Statistical Studies, 10(1), 97-111.
  [7] K. Fatima, U. Jan and S.P. Ahmad (2018). “Statistical Properties of Rayleigh Lomax distribution with applications in Survival Analysis”. Journal of Data Science, 16(3), 531-548.
  [8] L. Tierney, J. Kadane. (1986).“Accurate Approximations for Posterior Moments and Marginal Densities.” Journal of the American Statistical Association, 81, 82-86.
  

  Citation
  S.P. Ahmad, Kawsar Fatima, "Approximation Techniques for Estimation of Parameters of Rayleigh Lomax Distribution under Different Priors," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.116-122, 2018

• Open Access   Article

  A Nonparametric Discriminant Stepwise Algorithm for Classification to Two Populations

  S. Padmanaban, Martin L. William

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.123-129, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.123129

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  Abstract
  This paper provides a nonparametric discriminant stepwise algorithm to discriminate two multivariate populations and an optimal decision rule for classification of a member to either of the two populations. This ‘two-way-stepwise algorithm’ is a combination of the `forward-stepwise` and the ‘backward-stepwise’ approaches recently proposed for the same classification problem by Padmanaban and William (2016a, b). As has been done in the above-referred papers, this paper relaxes the `equal variance-covariance matrices` condition traditionally imposed and develops a discrimination-classification procedure by including variables that contribute to effective discrimination in a ‘forward’ manner one-by-one and excluding variables that do not contribute to effective `discrimination` in a ‘backward’ manner one-by-one. The inclusion of variables in the discriminant is determined on the basis of maximum discriminating ability and exclusion is on the basis of least `discriminating ability` as reflected in `difference` between the distributions of the discriminant in the two populations. A decision-rule for classification or membership-prediction with a view to maximizing correct predictions is provided as done in the forward and backward approaches referred above. The proposed algorithm is applied to develop an optimal discriminant for predicting respiratory tract disease(RD) among newborns of mothers with PPROM in the city of Chennai, India, and its performance is compared with logistic regression.

  Key-Words / Index Term
  Classification, Discriminant, Kolmogorov-Smirnov Statistic

  References
  [1].Baudat, G. and Anouar, F. (2000). Generalized Discriminant Analysis using a Kernel Approach. Neural Computation, 12 (10), 2385-2404
  [2].Bensmail, H. and Celeux, G. (1996). Regularized Gaussian discriminant analysis through eigen value decomposition. J. Amer. Statist. Assoc. 91, 1743-1748
  [3]. Bressan, M. and Vitria, J. (2003). Nonparametric Discriminant Analysis and Nearest Neighbor Classification. Pattern Recognition Letters. 24, 2743-2749
  [4]. Catov, J.M., Bodnar, L.M., Ness, R.B., Barron, S.J. and Roberts, J.M. (2007). Inflammation and Dyslipidemia related risk of Spontaneous Preterm Birth. Am. J. Epidemiol. 166, 1312-1319
  [5]. Chang, W.-C. (1983). On using Principal Components before Separating a Mixture of two Multivariate Normal Distributions. J. Roy. Statist. Soc. Ser C. 32, 267-275
  [6]. Chiang, L.H. and Pell, R.J. (2004). Genetic algorithms combined with discriminant analysis for key variable identification. J. Process Control, 14, 143-155
  [7]. Habbema, J.D.F. and Hermans, J. (1977). Selection of variables in discriminant analysis by F- statistic and error rate. Technometrics. 19, 487-493
  [8]. Hastie, T., Tibshirani, R., and Buja, A. (1994). Flexible Discriminant Analysis by Optimal Scoring. J. Amer. Statist. Assoc. 89, 1255-1270
  [9].Khade, S.A. and Bava, A, K. (2018). Preterm Premature rupture of membranes – maternal and perinatal outcome- International Journal of Reproduction, Contraception, Obstetrics and Gynecology, 7 (11), 4499-4505
  [10].Mudd, L.M., Holzman, C.B., Catov, J.M., Senagore, P.K. and Evans, R.W. (2012). Maternal lipids at mid pregnancy and risk of preterm delivery. Acta Obstet. Gynecol. Scand. 91, 726-735
  [11].Murphy, T.B., Dean, N. and Raftery, A.E. (2010). Variable Selection and updating in Model- Based Discriminant Analysis for High Dimensional Data with Food Authenticity Applications. The Annals of Applied Statistics, Vol.4, No.1, 396-421
  [12].Padmanaban, S and Martin L. William (2016). A nonparametric discriminant variable-selection algorithm for classification to two populations International Journal of Applied Mathematics and Statistical Sciences. 5 (2),87-98
  [13].Padmanaban and William (2016a).A nonparametric discriminant variable-elimination algorithm for classification to two populations. International Journal of Applied Mathematics and Statistical Sciences. 5(6),7-16.
  [14]. Pfeiffer, K.P.(1985). Stepwise Variable Selection and Maximum Likelihood Estimation of Smoothing Factors of Kernel Functions for Nonparametric Discriminant Functions evaluated by Different Criteria. J. Biomed. Informatics. 18, 46-61
  [15]. Raftery, A.E. and Dean, N. (2006). Variable Selection for Model-Based Clustering. J. Amer. Statist. Assoc. 101, 168-178
  

  Citation
  S. Padmanaban, Martin L. William, "A Nonparametric Discriminant Stepwise Algorithm for Classification to Two Populations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.123-129, 2018

• Open Access   Article

  Effects of Viscous Dissipation and Non-Uniform Heat Source/Sink on Casson Fluid Flow Over an Unsteady Inclined Permeable Stretching Surface

  K. Venkateswara Raju, S.R.R. Reddy, P. Bala Anki Reddy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.130-136, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.130136

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  Abstract
  An analysis has been carried out to study the effects of viscous dissipation, non-uniform heat source and sink on casson fluid flow for an unsteady inclined permeable stretching surface. Implementing similarity transformations, the governing equations are transformed to nonlinear ODEs and numerical computations are performed to solve those equations. The influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically and the physical aspects are discussed in detail. Results indicate that temperature dependent heat source/sink plays a vital role on controlling the heat transfer however the surface-dependent heat source/sink also has notable influence on the heat transfer characteristics. Comparisons with previously published work are performed and the results are found to be in excellent agreement.

  Key-Words / Index Term
  Stretching surface; Inclination; Casson fluid flow; Non-uniform heat source/sink; Viscous Dissipation.

  References
  [1] N. Casson, “A flow equation for pigment-oil suspensions of the printing ink type Rheology of Disperse systems, Pergamon Press”, London, UK, 1959.
  [2] Sidra Aman, Ilyas Khan, Zulkhibri Ismail, Mohd Zuki Salleh, Ali Saleh Alshomrani, Metib Said Alghamdi, “Magnetic field effect on Poiseuille flow and heat transfer of carbon nanotubes along a vertical channel filled with Casson fluid”, AIP Advances Vol.7, 015036-1-18, 2017.
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  Citation
  K. Venkateswara Raju, S.R.R. Reddy, P. Bala Anki Reddy, "Effects of Viscous Dissipation and Non-Uniform Heat Source/Sink on Casson Fluid Flow Over an Unsteady Inclined Permeable Stretching Surface," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.130-136, 2018

• Open Access   Article

  Perfect 3-Colorings on 4-Regular Graph of Order 8

  S. Maity, Sk. R. Islam

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.137-142, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.137142

  Abstract

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  Citation

  Abstract
  We study the perfect 3-colorings (also known as the equitable partitions into three parts) on 4-regular graphs of order 8. A perfect n-coloring of a graph is a partition of its vertex set into n parts A1, A2, ..., An such that for all p, q ϵ {1, 2,..., n}, each vertex of Ap is adjacent to apq number of vertices of Aq. The matrix A = (apq) n×n is called quotient matrix or parameter matrix. The concept of a perfect coloring generalizes the concept of completely regular code introduced by P. Delsarte. In particular, we classify all the realizable parameter matrices of perfect 3-colorings on 4-regular graphs of order 8.

  Key-Words / Index Term
  Perfect colorings; equitable partition; regular graph

  References
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  [4] P. Delsarte, “An algebraic approach to the association schemes of coding theory”, Philips Res. Rep. Suppl, Vol. 10, pp. 1-97, 1973.
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  [7] D. G. Fon-Der-Flaass, “Perfect 2-colorings of a hypercube”, Siberian Mathematical Journal, Vol. 4 , pp. 923-930, 2007.
  [8] D. G. Fon-Der-Flaass, “Perfect 2-colorings of 12-dimensional cube that achieve a bound of correlation immunity”, Siberian Mathematical Journal, Vol.4, pp. 292-295, 2007.
  [9] D. G. Fon-Der-Flaass, “A bound on correlation immunity”, Siberian Electronic Mathematical Reports Journal, Vol. 4, pp. 133-135, 2007.
  [10] M Alaeiyan, A Mehrabani, “Perfect 3-colorings of the cubic graphs of order 10”, Electronic Journal of Graph Theory and Applications (EJGTA), Vol. 5, Issue 2, pp. 194-206, 2017.
  [11] M. Alaeiyan, H. Karami, “Perfect 2-colorings of the generalized Petersen graph”, Proceedings.Mathematical Sciences, Vol. 126, pp. 1-6, 2016.
  [12] M. Alaeiyan and A. Abedi, “ Perfect 2-colorings of Johnson graphs J(4, 3), J(4, 3), J(6,3) and Petersen graph”, Ars Combinatoria, (to appear).
  [13] S.V. Avgustinovich, I. Y. Mogilnykh, “ Perfect 2-colorings of Johnson graphs J(6,3) and J(7, 3)”.Lecture Notes in Computer Science, pp. 11-19, 2008.
  [14] S.V. Avgustinovich, I. Y. Mogilnykh, “Perfect colorings of the Johnson graphs J(8,3) and J(8, 4).With two colors”, Journal of Applied and Industrial Mathematics, Vol. 5, pp. 19 - 30, 2011.
  

  Citation
  S. Maity, Sk. R. Islam, "Perfect 3-Colorings on 4-Regular Graph of Order 8," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.137-142, 2018

• Open Access   Article

  Effect of Presence of Outliers in the Estimate of the Parameters of a Johnson SB Distribution

  Tanuja Sriwastava, Sandeep Mishra

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.143-151, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.143151

  Abstract

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  References

  Citation

  Abstract
  An outlier is an observation that deviates in some sense from the rest of the observations. Outliers have strong influence on estimates of the parameters of a model that is being fitted to the data. In this paper, the effect of presence of outlying observation was studied in the estimates of the parameters of a Johnson SB distribution with slippage alternative of location parameters. The largest observation of the data was shifted towards right or the smallest observation was shifted to the left, the estimates of the parameters would be affected. Some examples are also given for highlighting the result.

  Key-Words / Index Term
  Johnson SB distribution, Transformation function, Outlier, Slippage alternative, Maximum likelihood estimation, Least square estimation.

  References
  George, F. and Ramachandran, K. M., (20011). Estimation of parameters of Johnson’s system of distributions. J. of Mordern Applied Statistical Methods,10(2).
  Johnson, N.L. (1949). Systems of frequency curves generated by methods of translation. Biometrica, 58, 547.558.
  Kudus, K.A., Ahmad, M.I. & Lapongan, J. (2011). Nonlinear regression approach to estimating Johnson S_B parameters for diameter data. Canadian Journal of Forest Research.
  Parresol, B.R. (2003). Recovering parameters of Johnson’s S_B distribution. US For. Ser. Res. Paper SRS-31. 9p.
  Slifker, J.F. & Shapiro, S.S. (1980). The Johnson system: selection and parameter estimation. Technometrics, 22, 239-246.
  

  Citation
  Tanuja Sriwastava, Sandeep Mishra, "Effect of Presence of Outliers in the Estimate of the Parameters of a Johnson SB Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.143-151, 2018