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A Graph Theoretical Preprocessing Step for Text Compression
Kaushik K. Phukon,Hemanta K. Baruah 보안공학연구지원센터 2015 International Journal of Multimedia and Ubiquitous Vol.10 No.5
This paper presents CSGM2, a text preprocessing technique for compression purposes. It converts the original text into a word net (graph representation) and can retain the detailed contextual information such as word proximity. Specific directed graph is proposed to model this word net where words are stored in vertices and edges represent word transitions. The word net is fully capable of holding the natural word order in the original text and hence can be used directly for encoding purposes.
ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS
Hazarika, Munmun,Phukon, Ambeswar Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions ${\Phi}_0$, ${\Phi}_1$ and ${\Phi}_2$. Here we explicitly evaluate the Schur's function ${\Phi}_3$. Using this value we find necessary and sufficient conditions under which the Toeplitz operator $T_{\varphi}$ is hyponormal, where ${\varphi}$ is a trigonometric polynomial given by ${\varphi}(z)$ = ${\sum}^N_{n=-N}a_nz_n(N{\geq}4)$ and satisfies the condition $\bar{a}_N\(\array{a_{-1}\\a_{-2}\\a_{-4}\\{\vdots}\\a_{-N}}\)=a_{-N}\;\(\array{\bar{a}_1\\\bar{a}_2\\\bar{a}_4\\{\vdots}\\\bar{a}_N}\)$. Finally we illustrate the easy applicability of the derived results with a few examples.
On hyponormality of Toeplitz operators with polynomial and symmetric type symbols
Munmun Hazarika,Ambeswar Phukon 대한수학회 2011 대한수학회보 Vol.48 No.3
In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions [기호]_0, [기호]_1 and [기호]_2. Here we explicitly evaluate the Schur's function [기호]_3. Using this value we find necessary and sufficient conditions under which the Toeplitz operator T_φ is hyponormal, where φ is a trigonometric polynomial given by φ (z)=[수식] and satisfies the condition [수식]. Finally we illustrate the easy applicability of the derived results with a few examples.