iosr-Jm   Volume-4 ~ Issue-1

Abstract :Sugar as a luxurious product now becomes an essential one. Sugarcane is the leading cash crop in India used for sugar extraction. Sugarcane was cultivated on 4 million hectares of land shows increasing trend of production over last 10 years, in India. Sugar production scenario for Pre-WTO and Post-WTO period in India, is studied. The effect of eight predictors on sugar production in Pre-WTO (1985-86 to 1994-95) and Post-WTO period (1995-96 to 2008-09) is analyzed. Matrix plot exhibits the scatterness in predictor and response variables. Principal component analysis (PCA) is used to reduce the dimensionality of the data. Multiple regression models, for sugar production on combined score of selected predictors, are obtained. The significance of auto-correlation in residuals of sugar production in India using multiple regressions is tested by Durbin-Watson test. The analysis reveals that in Pre-WTO, Post-WTO and overall period sugar production in India increases as a combined effect of four selected predictors. Durbin-Watson test indicates that autocorrelation in residuals is insignificant in these periods. The calculations of uncrushed sugarcane in Pre- WTO period is of the order of 50 percent which reduces to 40 percent in Post-WTO period.
Keywords -Autocorrelation, eigen values, matrix plot, principal component, residual.

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Abstract :B. Alspach, C.C. Chen and Kevin Mc Avaney [1] have discussed the Hamiltonian laceability of the Brick product C(2n, m, r) for even cycles. In [2], the authors have shown that the (m,r)-Brick Product C(2n+1, 1, 2) is Hamiltonian-t-laceable for 1 ≤ t ≤ diamC2n+1. In this paper we explore the Hamiltonian-t-laceability of the (m,r)-Brick Product C(2n+1,1,r) for r=3 and 4.
Keywords: Brick product, Connected graph, Hamiltonian-t-laceable graph. 2000 Mathematics subject classification: 05C45, 05C99

[1] Brain Alspach et al., On a class of Hamiltonian laceable 3-regular graphs, Journal of Discrete Mathematics 151(1996), 19-38.
[2] Leena N. shenoy and R.Murali, Laceability on a class of Regular Graphs, International Journal of computational Science and
Mathematics, volume 2, Number 3 (2010), 397-406.

Abstract :The aim of this paper is to introduce R-closed maps, R-open maps, R-homeomorphisms, R*- homeomorphisms, strongly R-continuous, perfectly R-continuous and study their properties. Using these new types of maps, several characterizations and properties have been obtained.
Keyword: R-closed maps, R-open maps, R-homeomorphism, R*-homeomorphism, strongly Rclosed maps, perfectly R-closed maps.

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Abstract :We study the line element proposed by the quantum vacuum KantowshiSachs universe without cosmological constant. We consider the scale factor b(=iRI) of the metric to be imaginary and the other a ( = R) is real, of the KantowskiSachs quantum state space time. It is seen, that in the Einstein‟s space time, the numerical volume of the matter universe once been squeez ed in a zero volume, we may assume then the matter universe transferred into another phase by the phase transition system with the help of latent energy group SU(6) [SU(11)  SU(5)  SU(6)  U(1)] 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 suppose that the original phase transition takes place before the GUT phase transition i.e. in the stage of SUT (Super Unified Theory) phase transition. According to the classical theory it may be assumed an imaginary scale factor, that means, the universe is then belongs to the pseudo-tachyon-field. It may be compared with the internal space "a‟ of the extra dimension "D‟ expressed by the KaluzaKlein cosmological universe.

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