iosr-Jm   Volume-2 ~ Issue-4

Abstract : Scan statistic requires a large sample, whereas the real problem in the research typically uses small sample. By using Satscan software, this paper aims to replace the direct estimator (DE) with the estimator obtained from small areas (Hierarchical Bayes). Hierarchical Bayes Small Area Estimation (HB SAE) is more efficient than DE. Besides, it also can broaden the parameters prediction in a large area. In general, HB2 (using spatial nearest neighbor weighted) is better than the other HB, both in the simulation and the real data. In addition, analysis of a small data using HB2 SAE is resulting in better statistical properties, such as less biased and consistent.
Keywords: Direct Estimator (DE), Consistent, Efficient, Prediction, Spatial Hierarchical Bayes Small Area Estimation (HB SAE).

[1] T. Siswantining, A. Saefuddin, A.N. Khairil, N. Nunung and M. Wayan. Some Properties of Spatial Scan Statistic Bernoulli Model : Example Simulation for Small and Large Data Using Satscan. IOSRJRM I, 1(6),2012, 21 – 26.
[2] S. Arima, G.S. Dattaand B.Liseoz. Objective Bayesian Analysis of aMeasurement Error Small Area Model.Bayesian Analysis,7, 2012, 363- 384.
[3] M. Ghosh, and J.N.K. Rao. Small Area Estimation: An Appraisal. Statistical Science.,9, 1994,255-93.
[4] J.N.K. Rao. Small Area Estimation. USA : Wiley-Interscience, 2003.
[5] G.P. Patil and W.L. Myers. Digital Governance and hotspot Geoinformatics of Biodiversity Measurement, Comparison and Management in the Age of Indicators and Information Technology. Center of Statistical Ecology & Environmental Statistics, Pennsylvania State University, 2009.
[6] J. Gehrung and Y. Scholz. The application of simulated NPP data improving the assessment of the spatial distribution of biomass in Europe. Biomass and Bioenergy, 33, 2009,712 – 720.
[7] C.R. Rao. Efficient Estimates and Optimum Inference Procedures in Large Samples. Journal of the Royal Statistical Society. Series B (Methodological), 24, 1962, 46-72.
[8] A. Roy. Empirical and Hierarchical Bayesian Methods With Application To Small Area Estimation. Disertation. Graduate School of The University of Florida, 2007.
[9] R.B.Gramacyand N. G. Polson. Simulation-based Regularized Logistic Regression Bayesian Analysis. Bayesian Analysis, 7, 2012,1-24.
[10] M.E. Gonzalez. Use and Evaluation of Synthetic Estimates. Proceedings of The Social Statistics Sections.American Statistical Association, 1973, 33 – 36.

Abstract:In this paper we introduce and investigate intuitionistic N -closed sets and Intuitionistic almost regular space in a intuitionistic topological spaces.
Key words and Phrases:  int ( A), cl (A), intuitionistic almost regular spaces,intuitionistic N -closed sets., AMS subject classification 2010 :57D05.

[1] Dogan Coker; "A Note On Intutionistic Sets And Intutionistic Points." Tr. J. Of Mathematics 20 (1996), 343-351.
[2] Dogan Coker; "An Introduction to Intutionistic Topological Spaces." Busefal 81, 51-56 (2000).
[3] M.Lellis Thivagar,M.Anbuchelvi,Saeid Jafari; "Note on Intuitionistic Compactness." (Communicated).
[4] T.Noiri; " N -closed sets and some separation axioms." Annales de la Societe Scientifique de Bruexelles, T. 88,II,pp.195-199 (1974).
[5] M.K.Singal and Shashi Prabha Arya; "On Almost regular spaces." Glasnik Mat., 4 (24), 89-99, 1969.
[6] Sadik Bayhan and Dogan Coker; "On Separation Axioms in Intutionistic Topological Spaces." IJMMS (2001) 621-630.

Abstract: S.K. Chaubey and R.H. Ojha [4] introduced a semi-symmetric non-metric connection in almost contact manifold and also studied the connection in Sasakian manifold. The present paper deals with some propertied of semi-symmetric non-metric connection in LP-Sasakian manifold.
Key words: Lorentzian almost paracontact manifold, LP-Sasakian manifold and semi-symmetric non metric connection.

[1] I. Mihai, A. A. Shaikh and U. C. De. , On Lorentzian Para Sasakian manifolds, Korean J. Math. Sciences, 6 (1999) , 1-13.
[2] K. Matsumoto, On Lorentzian Para contact manifolds, Bull. of yamagata Univ., Nat. Sci., 12 (1989), 151- 156.
[3] K. Matsumoto and I. Mihai, On a certain transformation in Lorentzian Para contact manifold , Tensor N.S., 47, (1989) , 189-197.
[4] S. K. Chaubey and H. Ojha, On a semi-symmetric non-metric and quarter-symmetric metric connections, Tensor N.S., 70, No. 2 (2008), 202- 213.
[5] U. C. De , K. Matsumoto and A. A. Shaikh , Lorentzian Para Sasakian manifolds , Rendicontidel Seminario Matematico di Messina, Series II , Supplemento No., 3 (1999), 149-158.

Abstract: The aim of this paper is to introduce the study of ultra - upper and lower- slightly continuous ultra multifunctions.

[1] M.C. Dutta ., Contribution to theory of bitopological spaces, Ph.D Thesis, Pilani, 1971.
[2] J.C.Kelli., Bitopological Spaces, Pro.London Math.Soc,13(1963),71-89.
[3] M.Lellis Thivagar., Generalization of (1,2)α-continuous functions, Pure and Applied Mathematika Sciences 33 (1991),55-63.
[4] G.Navalagi, M.Lellis Thivagar and R.RajaRajeswari., (1, 2)α- Hyperconnected spaces, International Journal of Mathematics and Analysis, Vol.3 (2006), 120 -129.
[5] G.Navalagi, M.Leelis Thivagar and R.RajaRajeswari., On ultra multifunctios in bitopo- logical spaces, International Journal of Mathematics, Coputer Science and Information Technology Vol.1,No.1(2008),69-74.
[6] 6. V.Popa., A note on weakly and almost continuous multifunctions,Univ.u Novom sadu, Zb.Rad.Priorod. - Mat.Fak.Ser.Mat.21, 2(1991), 31-38.
[7] 7. V.Popa and T.Noiri., on upper and lower weakly- - continuous multifunctions,Novi.Sad.J.Math ,Vol.32, No.1 (2002), 7-24.
[8] 8. R.RajaRajeswari,Bitopological concepts of some separation properties, Ph.D Thesis, Madurai Kamaraj University, Madurai, India, 2009
[9] 9. M.S.Sarask, N.Gowrisankar and N.Rajesh., on upper and lower γ- continuous mul-tifunctions, Int.J.contemp.Math.Sciences, Vol.5 (2010), No.6, 281 - 288.

Abstract: We introduce Monoid Artex Spaces or M-Artex Spaces over Monoids. We define SubM-Artex Spaces of an M-Artex Space over a Monoid. We give examples for M-Artex Spaces over Monoids and SubM-Artex Spaces. We define a Cap-Quotient Space and a Cup-Quotient Space and we prove these Quotient Spaces are M-Artex Spaces Over monoids.
Keywords: M-Artex Spaces, Cap- Quotient and Cup-Quotient M-Artex Space

[1] K.Muthukumaran and M.Kamaraj, "Artex Spaces Over Bi-monoids", "Research Journal of Pure Algebra", 2(5),May 2012, Pages 135-140.
[2] K.Muthukumaran and M.Kamaraj, "SubArtex Spaces Of an Artex Space Over a Bi-monoid", "Mathematical Theory and Modeling", An USA Journal of "International Institute for Science, Technology and Education", Vol.2, No.7, 2012, pages 39 – 48.
[3] K.Muthukumaran and M.Kamaraj, "Bounded Artex Spaces Over Bi-monoids and Artex Space Homomorphisms", "Research Journal of Pure Algebra", 2(7), July, 2012, pages 206 – 216.
[4] K.Muthukumaran and M.Kamaraj, "Some Special Artex Spaces Over Bi-monoids", "Mathematical Theory and Modeling", An USA Journal of "International Institute for Science, Technology and Education", Vol.2, No.7, 2012, pages 62 – 73. .
[5] K.Muthukumaran and M.Kamaraj, "Boolean Artex Spaces Over Bi-monoids", "Mathematical Theory and Modeling", An USA Journal of "International Institute for Science, Technology and Education", Vol.2, No.7, 2012, pages 74 – 85..
[6] K.Muthukumaran and M.Kamaraj, "Cap-cosets and Cup-cosets of a subset S in an Artex Space A over a Bi-monoid M"(accepted), "IOSR Journal Of Mathematics", A Journal Of "International Organization of Scientific Research".
[7] J.P.Tremblay and R.Manohar, Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw-Hill Publishing Company Limited, New Delhi, 1997.
[8] John T.Moore, The University of Florida /The University of Western Ontario, Elements of Abstract Algebra, Second Edition, The Macmillan Company, Collier-Macmillan Limited, London,1967.
[9] Garrett Birkhoff & Thomas C.Bartee, Modern Applied Algebra, CBS Publishers & Distributors,1987.
[10] J.Eldon Whitesitt, Boolean Algebra And Its Applications, Addison-Wesley Publishing Company, Inc.,U.S.A., 1961.

Abstract: The set of all L - fuzzy topologies on a fixed set X is a complete lattice denoted by LFT(X,L). In this paper, we determine some classes of automorphisms of this lattice when X is a nonempty set and L is an F- lattice. Mathematics Subject Classification: 54A40
Keywords: fuzzy topological space, lattice automorphism, t- homomorphism, pseudo-complement, F-lattice, order reversing involution.

[1] S.Babusunar, Some Lattice Problems in Fuzzy Set Theory and Fuzzy Topology, Thesis for Ph.D. Degree, Cochin University of Science and Technology, 1989.
[2] Juris Hartmanis, On the Lattice of Topologies, Cand. J . Math.} {\bf 10} (1958), 547-553.
[3] Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. Vol.25, Amer. Math.Soc. Pro vidence, 1967.
[4] H.J. Zimmerman, Fuzzy Set Theory and its Applications, Second Edition. Kluwer Academic Publishers, Boston, 1991.
[5] Liu, Ying-Ming & Mao-Kang, Luo, Fuzzy Topology, Advances in Fuzzy Systems-Applications and Theory, Vol.9, World Scientific Pub. Co. Pvt. Ltd. 1997.

Abstract: In this paper,we specialized parameters and argument, Hypergeometric function FE (1, 1, 1, 1, 2, 2; γ1, γ2, γ3; cosh x, cosh y, cosh z) FG, Fk and FN can be reduced to the hypergeometric function of Bailey's F4(1, 2, γ2, γ3; -coshy, - cosh z) and also discussed their reducible cases into Horn's function. In the journal we consider hypergeometric function of three variables and obtain its interesting reducible case into Bailey's F4 & Horn's function. In the section 2, hypergeometric function of four variables can be reduced to the hypergeometric function of one, two & three variables with some new and interesting particular cases.

[1] APPELL, P. (1880): Surles series hypergeometric de deux variable, et surds equationa diiferentiells linearies aux derives partielles, C.R. Acad. Sci. Paris, 90, 296-298.
[2] ERDELYI, A. (1948) : Transformation of the hypergeometric functions of four variables, Bull soco grece (N.S.) 13, 104-113.
[3] EXTON, H. (1972) : Certain hypergeometric functions of four variables, Bull soco grece (N.S.) 13, 104-113.
[4] HORN, J. (1931) : Hypergeometric Funktionen Zweier Veranderlichen Math. Ann, 105, 381 – 407.
[5] SARAN, S. (1955) : integrals associated with hypergoemetric functions of there variables, Not. Inst. of Sc. of India, Vol. 21, A. No. 2, 83-90.
[6] SARAN, S.(1957): Integral representations of laplace type for certain hypergeometric functions of three variables, Riv. Di. Mathematica, parma 133-143.
[7] WHITTAKER, E.T. AND WATSON, G.N. (1902) : A course of Modern Analysis

Abstract: We study a super unified theory with gauge group SU(11). The subgroup SU(6) has been interpreted as a new type of energy source other than SU(5)[SU(5)  SU(3)  SU(2) U(1)], where SU(3) the strong energy group; SU(2) the weak energy group & U(1) the electro dynamics]. We consider a (4+D)–dimensional Friedmann–Robertson–Walker type universe having complex scale factor R + iRI, where R is the scale factor corresponding to the usual 4–dimensional Universe while RI is that of D–dimensional space. It is then compared with (4+D)–dimensional Kaluza–Klein Cosmology having two scale factors R and a(= iRI). It is shown that the rate of compactification of higher dimension depends on extra dimension 'D'. The Wheeler–DeWitt equation is constructed and general solution is obtained. It is found that for D = 6 (i.e. in 10 dimension), the Wheeler–DeWitt equation is symmetric under the exchange RI  R.

[1] P. J. E. Peebles and B. Ratra, Astrophy. J. Lett . 325. L17 (1988) : and R. G. Vishwakarma, Class. Quant. Grav.
14. 945(1997).
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[3] T. A. Appelquist , A. Chodos and P. G. O. Freund, Mo dern Kaluza –Klein Theories, Front iers in Physics Series, (
Volume 65), 1986 (Ed. Addison Wesely).
[4] Brian Greene, The Elegant Universe, W.W.Nor ton&Company, New York (1999), pp. 357 – 358.
[5] G. Riess et al. Astrophys. J. 560, 49(2001).

Abstract: In this paper, We discuss a fuzzy EOQ model for time-dependent deteriorating items and time-dependent demand with shortages. We consider here an EOQ model in which inventory is depleted not only by demand, but also by deterioration. This paper deals with infinite time horizon fuzzy Economic Order Quantity (EOQ) models for weibull deteriorating items with time dependent exponential demand rate. We have taken deterioration parameter 𝛽0 as a triangular fuzzy number 𝛽0−𝛿1,𝛽0,𝛽0+𝛾2 , where 0 < 𝛿1,𝛿2<𝛽0 are fixed real numbers. The traditional parameters such as unit cost ,ordering cost and holding cost have been kept constant. The approximate optimal solution for the fuzzy profit functions have been obtained and numerical example is provided to illustrate the solution procedure for the developed fuzzy EOQ model. Finally, Sensitivity of the optimal solution to changes in the values of some key parameters is also studied.
Keywords: EOQ Model, Shortages with partially backlogging, Weibull Distribution, exponential Demand rate, Fuzzy Deterioration.

[1] T.M. Whitin. "Theory of Inventory Management". Princeton University Press, New Jersey, USA, 1957.
[2] U. Dave and L.K. Patel. "Policy inventory model for deteriorating items with time proportional demand". Journal of theoperational
Research Society, 32(1), 1981, 137-142.
[3] R.H. Hollier and K.L. Malc. "Inventory replenishment policies for deteriorating itemsin a declining market". International Journal
of production Research, 21(7), 1983, 813-826.
[4] H. Xu and H. Wang. "Optimal inventory policy for perishable items with time proportional demand". IIETransactions, 24(5),
1992, 105-110.
[5] A. Goswami and K.S. Chaudhuri. "An EOQ model for deteriorating items with shortages and a linear trend in demand".
Journal of the operational Research Society, 42(12), 1991,1105-1110.
[6] T.Chakrabarti. "An EOQ model for deteriorating items with a linear trend in demand and shortages in all cycles". International
Journal of Production Economics ,49, 1997,205- 213.
[7] T. Chakrabarti. "An EOQ model for items with Weibull distribution deterioration ,shortages and trended demand: An
extension of Phillip‟s model". International Journal of Computers and Operations Research ,25(7/8), 1998.
[8] H.J. Chang and C.Y. Dye. " An EOQ model for deteriorating items with time-varying demand and partial backlogging". Journal of
the Operational Research Society, 50(11),1999,1176-1182.
[9] J.T. Teng, M.S. Chern and H.L. Yang. "An optimal recursive method for various inventory replenishment model with increasing
demand and shortages". NavalResearch Logistics, 44(10),1997,791-806.
[10] M. Valliathal and R. Uthayakumar. "An EOQ model for perishable items under stock and time-dependent selling rate with shortages". ARPN Journal of Engineering and Applied Sciences,4(8),2009,8-14.