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.