iosr-Jm   Volume-9 ~ Issue-4

Abstract: This paper is devoted to introduce the notion of fuzzy supra semi ̃ =0, 1, 2 space, fuzzy supra semi Di =0, 1, 2 space, and use the notion of fuzzy quasi coincident in their definitions, study some properties and theorems related to these subjects.

Key words: Fuzzy supra semi open set, fuzzy supra semi D set, fuzzy supra semi ̃ = 0, 1, 2 space, fuzzy supra semi Di =0, 1, 2 space.

[1] Abd EL-Monsef M.E. and Ramadan A. E. "on fuzzy supra topological spaces" J. Pure app. Math., 18(4):322-329(1987).
[2] Chakrabarty, M.K. and Ahsanullal,T.M.G." Fuzzy topology on fuzzy sets And Tolerance Topology" Fuzzy sets and systems 45,103-108(1992).
[3] Ghanim M.H, Tantawy O.A. and SelimFawziaM."Gradation of supra-openness", Fuzzy sets and Systems, 109, 245-250, (2000).
[4] HoqueMd F., and Ali D.M "Supra fuzzy Topological space" Lap Lambert Academic Publishing GmbH and Co. KG, (2012).
[5] Kandil , A. and El-Shafee, M. E., "Regularity Axioms in Fuzzy Topological Spaces and FRi-Proximities", Fuzzy Sets and Systems , 27 , 217-231 , (1988).
[6] Kandil , A. , Saleh, S. and Yakout, M. M. , " Fuzzy Topology On Fuzzy Sets : Regularity And Separation Axioms", American Academic and Scholarly Research Journal , No.2 , Vol. 4 , (2012).
[7] Kider , J. R. "Fuzzy Locally Convex-Algebras"Ph . D. Thesis , School of Applied Sciences , Univ. Technology ,(2004).
[8] Mahmuod, F.S., FathAlla M.A, and AbdEllah S.M," Fuzzy topology on Fuzzy sets: Fuzzy semi continuity And Fuzzy separation axioms", APP M m 153 127-140),(2003).
[9] Mashhour A.S. and GhanimM.H."Fuzzy closure spaces"J.Math.Anal.And Appl.106,pp. 145-170(1985).
[10] P. M. Pu and Y. M. Liu "Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence" Journal of Mathematical Analysis and Applications, vol. 76, no. 2, pp. 571-599(1980).

Abstract: In this paper, we present the space of functions of bounded - variation in the sense of Riesz – Korenblum, denoted by [ ], which is a combinations of the notions of bounded – variation in the sense of Riesz and of bounded – variation in the sense of Korenblum. In the light of this, we prove that the space generated by this class of functions is Banach algebra with respect to a given norm and we give a brief characterization of the composition (Nemystkii) operator on the space [ ].

Key words: Banach algebra norm, Bounded k - Variation, composition (Nemystkii) operator.

[1] B. Korenblum (1975) "An extension of Nevanlinna theory", Acta mathematica, Vol. 135, No. 3-4, pp. 187-219.
[2] C. Rembling, Banach algebras. Academic Press: San Diego, 2010.
[3] D. Cyphert, J. A. Kelingos, (1985) "The decomposition of functions of bounded k-variation into difference of k-decreasing functions", Studia mathematica, Vol. 81, No. 2, pp. 185-195.
[4] D. Waterman (1972) On convergence of Fourier series of functions of Generalized Bounded Variation. Studia Maths. 44: 107-117.
[5] F. Riesz (1953) "Unter suchugen uber systeme intergrierbarer funktionen", mathematische Annalen, Vol. 69, No. 4, pp. 115-118.
[6] H. G. Dales, P. Aiena, J. Eschmeier, K. Laursen & G. A. Willis (2003). "Introduction to Banach algebra, Operators, and Harmonic Analysis", Cambridge University Press: United Kingdom.
[7] J. Banas (2010). Functions of two variables with bounded variation in the sense of Riesz, Journal of Mathematics and Applications, No 32, pp 5-23 (2010).
[8] J. Park "On the Functions of bounded – Variation(I)" Journal of Applied Mathematics and informatics, vol. 23, pp 487-498, 2010.
[9] M. Castillo, S. Rivas, M. Sonaja, I. Zea, (2013) "functions of bounded in the sense of Riesz-Korenblum, Hindawi publishing corporation, Journal of function spaces and applications, Vol. 2013, Article 718507.
[10] M. Adispavic (1986). Concept of Generalized Bounded Variation and the Theory of Fourier series, Internat. J. Math. & Sci. Vol. 9 No. 2 : 223-244.

Paper Type	:	Research Paper
Title	:	KummerDirichlet Distributions of Matrix Variate in the Complex Case
Country	:	India
Authors	:	Ms. Samta Gulia, Prof. (Dr.) Harish Singh
	:	10.9790/5728-0941321

Abstract:The aim of this paper is to investigate matrix variate generalizations of multivariate Kummer-Beta and multivariate Kummer-Gamma families of distributions in the complex case. The multivatiateKummer-Beta and multivariate Kummer-Gamma families of distributions have been proposed and studied recently by Ng and Kotz. These distributions are extensions of Kummer-Beta and Kummer-Gamma distributions. Many known or new results have been made with the help of multivatiateKummer-Beta and multivariate Kummer-Gamma families of distributions.

[1] C. Armero and M. J.Bayarri, A Bayesian analysis of a queneing system with unlimited service, J. Statist. Plann. Inference 58
(1997), no. 2, 241-261. CMP 1 450015.Zbl 880.62025.
[2] M.Gordy, Computationally convenient distributional assumptions for common-value auctions, Comput. Econom. 12 (1998), 61-78.
Zbl 912.90093.
[3] A. K. Gupta and D. K. Nagar, Matrix Variate Distributions, Chapman & Hall/ CRC Monographs and Surveys in Pure and Applied
Mathematics, vol. 104, Chapaman& Hall/CRC, Florida, 2000. MR 2001d:62055. Zbl 935.62064.
[4] W.R. Javier and A.K. Gupta, On generalized matric variate beta disgtributions, Statistics 16 (1985), no. 4, 549-557, MR
86m:62023. Zbl 602.62039.
[5] D.K. Nagar and L. Cardeno, Matrix variateKummer – Gamma distribution, Random Oper. Stochastic Equations 9 (2001), no. 3,
207-218.
[6] D.K. Nagar and A.K. Gupta, Matrix variateKummer-Beta distribution, to appear in J. Austral Math.Sec.
[7] K. W. Ng and S. Kotz, Kumer-Gamma and Kummer-Beta univariate and multivariate distributions, Research report, Department of
Statics, The University of Hong Kong, Hong Kong, 1995.
[8] Arjun K. Gupta: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221,
USA.
[9] Liliamcardeno and Daya K. Nagar: Departmento de Mathematicas, Universidad de Antioquia, Medellin, A. A. 1226, Colombia.

Paper Type	:	Research Paper
Title	:	A Study of Classification and Discriminant Analysis of Infants at Birth in Nigeria
Country	:	Nigeria
Authors	:	Adejumo, A. O., Onyenekwe, C. E
	:	10.9790/5728-0942226

Abstract:In Nigeria there is no recognized scientific method of discriminating and classifying babies statistically into groups of study.
The purpose of this study includes to set up a discriminant function and classification rule that can be used to classify babies into two groups; to estimate the proportion of observations in each of the prior group; and to estimate the probability of correct classification and misclassification respectively. To this effect, a sample of 270 cases (infants) was observed with the following measurements: Age of mother (x1), weight at 36th week (x2), birth weight (x3), Parity (x4), Gestation Period (x5), and sex of the baby (x6). The birth weight was used to do the initial classification. Group 1 termed underweight (< 2.5kg) and Group 2 termed normal weight (≥ 2.5kg). We observed that the Discriminant Function Z= -0.02947228X1- 0.0514773X2- 8.130338X3 + 0.062259X4 + 0.0946538X5 + 0.5888918X6. Also 95.8 % of the original grouped cases were correctly classified. The percentage of misclassification is 4.15%. Conclusively the measure of the predictive ability which is the percentage of correct classification shows that discriminant analysis can be used to predict infants into two classes of weight and can also be used to predict group membership of any subject matter.
Keywords: Dicriminant, Classification, Multivariate, Misclassification, Gestational age, Confusion Matrix

[1] Adimora, G.N, Nigerian Journal of Clinical Practices. Vol 7.2004, pg 33- 36 Official Publication of the Medical and Dental
Consultants Association of Nigeria.
[2] Deswal B. S., Singh J. V., Kumar D.- A Study of Risk Factors for Low Birth Weight, Indian J. Community Med. 24, 2008: 127-
131
[3] Philip, J. Disala, Clinical Gynaecologicon.cology.(4th Edition). Mosby year book Inc. 1995
[4] Geoffrey .V.P Chamberline, Gynaecology by Ten Teachers.(16th Edition). ELBS. 1988.

[5] Daniel B.Rowe, Multivariate Bayesian Statistics. Chapman and Hall/CRC, 2003.
[6] Anderson, T.W . An Introduction toMultivariate Statistical Analysis. New York: Wiley. 1984.
[7] Barnett,V. (ed.), Interpreting Multivariate Data. Wiley. 1981
[8] David,W.Stockburger, Multivariate Statistics: Concepts, Models and Applications. 1998
[9] Nwobi and Nduka . Statistical Notes and Tables for Research, Second Edition. Alphabet Nigeria Publishers. 2003
[10] Nwachukwu V.O, Principles of Statistical Inference. Second Edition. Zelon Enterprises. 2006.