• Title/Summary/Keyword: wreath product

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PRODUCTS OF T-FUZZY FINITE STATE MACHINES

  • Kim, Jae-Gyeom;Cho, Sung-Jin
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1998.06a
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    • pp.80-82
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    • 1998
  • we introduce the concept of coverings, direct products, cascade products and wreath products of T-fuzzy finite state machines and investigate their algebraic structures.

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Products of TL-Finite State Machines

  • Cho, Sung-Jin
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.2
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    • pp.173-177
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    • 2001
  • We introduce cascade products, wreath products, sums and joins of TL-finite state machines and investigate their algebraic structures. Also we study the relations with other products of TL-finite state machines.

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ON THE GALOIS GROUP OF ITERATE POLYNOMIALS

  • Choi, Eun-Mi
    • The Pure and Applied Mathematics
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    • v.16 no.3
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    • pp.283-296
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    • 2009
  • Let f(x) = $x^n\;+\;a$ be a binomial polynomial in Z[x] and $f_m(x)$ be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of $f_m(x)$ is isomorphic to a wreath product group $[C_n]^m$ where $C_n$ is a cyclic group of order n.

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SUMS AND JOINS OF FUZZY FINITE STATE MACHINES

  • CHO, SUNG-JIN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.2
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    • pp.53-61
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    • 2001
  • We introduce sums and joins of fuzzy finite state machines and investigate their algebraic structures.

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FULL NON-RIGID GROUP OF 2,3,5,6-TETRAMETHYLEPYRAZINE AS WREATH PRODUCT AND ITS SYMMETRY

  • Arezoomand, Majid;Taeri, Bijan
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.915-931
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    • 2009
  • The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of 2,3,5,6-Tetramethylpyrazine The f-NRG of this molecule is seen to be isomorphic to the group $\mathbb{Z}_3{\wr}(\mathbb{Z}_2{\times}\mathbb{Z}_2)$, where $\mathbb{Z}_n$ is the cyclic group of order n, of order 324 which has 45 conjugacy classes. We determine the some properties and relations between characters of the group. Also, we examine the symmetry group of this molecule and show that its symmetry group is $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

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DECOMPOSITIONS OF GENERALIZED TRANSFORMATION SEMIGROUPS

  • Cho, Sung-Jin;Kim, Jae-Gyeom
    • Journal of applied mathematics & informatics
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    • v.6 no.1
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    • pp.227-238
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    • 1999
  • We introduce several decompositons of generalized trans-formation semigroups and investigate some of their algebraic struc-tures.

COMPOSITION OF POLYNOMIALS OVER A FIELD

  • Choi, EunMi
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.497-506
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    • 2009
  • This work studies about the composition polynomial f(g(x)) that preserves certain properties of f(x) and g(x). We shall investigate necessary and sufficient conditions of f(x) and g(x) to be f(g(x)) is separable, solvable by radical or split completely. And we find relationship of Galois groups of f(g(x)), f(x) and of g(x).

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Note on Cellular Structure of Edge Colored Partition Algebras

  • Kennedy, A. Joseph;Muniasamy, G.
    • Kyungpook Mathematical Journal
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    • v.56 no.3
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    • pp.669-682
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    • 2016
  • In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.