• Title/Summary/Keyword: finite group

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FIXED POING ALGEBRAS OF UHF-ALGEBRA $S^*$

  • Byun, Chang-Ho;Cho, Sung-Je;Lee, Sa-Ge
    • Bulletin of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.179-183
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    • 1988
  • In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.

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FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS WITH HOMOTOPICALLY TRIVIAL TRANSLATIONS

  • Koo, Daehwan;Park, Eunmi;Shin, Joonkook
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.1
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    • pp.113-132
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    • 2020
  • We show that if a finite group G acts freely with homotopically trivial translations on a 3-dimensional nilmanifold 𝓝p with the first homology ℤ2 ⊕ ℤp, then either G is cyclic or there exist finite nonabelian groups acting freely on 𝓝p which yield orbit manifolds homeomorphic to 𝓝/𝜋3 or 𝓝/𝜋4.

Finite, Fiber-preserving Group Actions on Elliptic 3-manifolds

  • Peet, Benjamin
    • Kyungpook Mathematical Journal
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    • v.62 no.2
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    • pp.363-388
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    • 2022
  • In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. For illustration of our methods a constructive proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert manifolds do not exist for nonzero Euler class, in particular elliptic 3-manifolds. Each type of elliptic 3-manifold is then considered and the possible group actions that fit the given construction. This is shown to be all but a few cases that have been considered elsewhere. Finally, a presentation for the quotient space under such an action is constructed and a specific example is generated.

ON TRANSFER THEOREMS FOR FINITE GROUPS

  • Choi, Eun-Mi
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.917-924
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    • 1996
  • We shall study some transfer theorems of finite groups with respect to a certain commutator subgroup, called "F-commutator" relative to any field F and apply the transfer to the fusion of a group H or to the focal subgroup of H.roup of H.

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THE GROUP OF UNITS IN A LEFT ARTINIAN RING

  • Han, Juncheol
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.99-104
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    • 1994
  • Let R be a left Artinian ring with identity 1 and let G be the group of units of R. It is shown that if G is finite, then R is finite. It is also shown that if 2.1 is a unit in R, then G is abelian if and only if R is commutative.

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Group Key Transfer Protocol Based on Shamir's Secret Sharing (Shamir의 비밀 공유 방식의 그룹 키 전송 프로토콜)

  • Kim, Young-Sik
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.39B no.9
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    • pp.555-560
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    • 2014
  • Recently, there are many researches on sharing group session key for members in a group. Among them, Harn and Lin proposed a scheme based on the Shamir's group session key and Liu, Cheng, Cao, and Jiang improved it to reduce the specific weakness. Especially, these schemes are based on the finite integer ring to protest the insider attack, in which a valid member can derived another member's secret using known information. In this paper, it is shown that the finite integer ring implies the failure of the reconstruction of group session key depending on the adopted parameters. We fix this problem and propose new group session key transfer scheme using the Shamir's secret sharing.

A Group Maintenance Model with Extended Operating Horizon (연장된 운용기간을 활용하는 그룹보전모형)

  • Yoo, Young-Kwan
    • Journal of the Korea Safety Management & Science
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    • v.19 no.3
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    • pp.89-95
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    • 2017
  • This paper presents another maintenance policy for a group of units under finite operating horizon. A group of identical units are subject to random failures. Group maintenances are performed to all units together at specified intervals, and the failed units during operation are remained idle until the next group maintenance set-up. Unlike the traditional assumption of infinite operating horizon, we adopt the assumption of the finite operating horizon which reflect the rapid industrial advance and short life cycle of modern times. The units are under operation until the end of the operating horizon. Further, the operation of units are extended to the first group maintenance time after the end of the horizon. The total cost under the proposed maintenance policy is derived. The optimal group maintenance interval and the expected number of group maintenances during the horizon are found. It is shown that the proposed policy is better than the classical group maintenance policy in terms of total cost over the operating horizon. Numerical examples are presented for illustrations.

Cure simulation in LED silicone lense using dynamic reaction kinetics method (승온 반응속도식을 이용한 LED용 실리콘 렌즈의 경화공정해석)

  • Song, Min-Jae;Hong, Seok-Kwan;Park, Jeong-Yeon;Lee, Jeong-Won;Kim, Heung-Kyu
    • Design & Manufacturing
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    • v.8 no.2
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    • pp.46-49
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    • 2014
  • Silicone is recently used for LED chip lense due to its good thermal stability and optical transmittance. In order to predict residual stress which causes optical briefringence and mechanical warpage of silicone, finite element analysis was conducted for curing process during silicone molding. For analysis of curing process, a dynamic cure kinetics model was derived based on the differential scanning calorimetry(DSC) test and applied to the material properties for finite element analysis. Finite element simulation result showed that the slow cure reduced abrupt reaction heat and it was predicted decrease of the residual stress.

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