iosr-Jm   Volume-8 ~ Issue-1

Abstract: An elliptic curve E defined over a finite field K, E(K) is the set of solutions to the general Weierstrass polynomial E: y2 + a1xy + a3y = x3 + a2x2 + a4x + a6 where the coefficients a1, a2, a3, a4, a6 є K. There exist a well defined addition of points on each curve such that the points form an abelian group under the addition operation. This group is either cyclic or isomorphic to the product of two cyclic groups. These set of solutions that form the group lie in the closure of the field K over which the curve is defined. If we allow the set to lie only in a particular extension of K, the addition operation is well defined there too. Therefore we can associate a group to every extension K' of the field K denoted by E(K'). Will the structure of the group defined over the base field K, be affected if the same group is made to lie in the extension K' of K?

Key words: Cyclic group, Elliptic Curve, Field Extension, Finite Field, Sylow Theorem

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Abstract: In automatic text categorization procedure, quantifiable features' information is extracted from a text and on the basis of the information the text is sorted as a category. This information consists of values of set of one or more measurements, where the measurements can be considered as frequencies or function of frequencies of linguistic elements. In the process of text classification and genre discrimination, the role of the systematic study of word length and the analyses of word-length statistics of different texts has been established by researchers for various languages. In the present paper an attempt has been made to test the contribution of quantitative word length features in classification of written texts of Hindi Language by extracting quantitative measures with the help of word length profiles and frequencies.

Keywords: Categorization, Feature, Text, Word-length.

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