• Title/Summary/Keyword: group ring

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Theoretical Studies on Phenyl Group Rearrangement of Protonated Ketones

  • 김창곤;이진각;박형연;이익춘
    • Bulletin of the Korean Chemical Society
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    • v.18 no.6
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    • pp.657-662
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    • 1997
  • Gas-phase phenyl group migration within the protonated ketones has been studied MO theoretically using the AM1 method. The initial state structure shows relatively strong resonance delocalization of positive charge into the nonmigrating (Y) ring, while the ring migration (Z-ring) is nearly complete in the transition state. These results are reflected in the large $p^+_Z$ (<0) and $p^+_$Y (>0) values and in the predominant contribution of resonance (r) over inductive (field, f) effect, r/f ranging from 1.3 ($p^+_r$) to 1.5 ($p^+_z$). The cross-interaction constant $p_{YZ}$ is vanishingly small ($p_{YZ}$=0.03) which is in contrast to the larger magnitudes for benzilic ($p_{YZ}$=-0.48) and azibenzil ($p_{YZ}$=-0.53) rearrangement processes. The relationship found between the extent of resonance contribution in the initial state and the magnitude of $p_{YZ}$ provides strong support for the proportionality between the magnitude of $p_{YZ}$ and the change in the intensity of interaction, ${\Delta}I^{\cdot}_{YZ}$, in the activation process.

FUZZY IDEALS AND FUZZY SUBRINGS UNDER TRIANGULAR NORMS

  • Chon, Inheung
    • Korean Journal of Mathematics
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    • v.10 no.2
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    • pp.149-155
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    • 2002
  • We develop some basic properties of $t$-fuzzy ideals in a monoid or a group and find the sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy subring and the necessary and sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy ideal.

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On regular groups over their endomorphism rings

  • Chung, Jae-Myung
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.311-314
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    • 1996
  • Let G be an abelian group of finite rink and E be the endomorphism ring of G. Then G is a left E-module by defining $f\cdota = f(a)$ for $f \in E$ and $a \in G$. In this case a condition for an E-module G to be regular is given.

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Commuting involutions in a left artinian ring

  • Han, Juncheol
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.221-226
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    • 1992
  • The involutions in a left Artinian ring A with identity are investigated. Those left Artinian rings A for which 2 is a unit in A and the set of involutions in A forms a finite abelian group are characterized by the number of involutions in A.

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Semiempirical MO Calculation of Hetero Atom Three-Membered Ring Compounds(II)${\cdot}$N-Nitroso-azirine and-diaziridine

  • Ki Woon Hwang
    • Bulletin of the Korean Chemical Society
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    • v.12 no.3
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    • pp.328-331
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    • 1991
  • Fully optimized MNDO molecular orbital calculations are performed for N-nitroso-azirine (Ⅰ) and-diaziridine (Ⅱ). The ground state geometries show the nonplanar configuration around the imino nitrogen. The nitroso group rotational energy barriers and the ring inversion energy barriers are also discussed.

Design of Band Pass Ring Filter for Ultra Wideband (UWB용 대역통과 링 필터의 설계)

  • Park, Dong-Kook;Seo, Yong-Keun
    • Journal of Advanced Marine Engineering and Technology
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    • v.33 no.1
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    • pp.138-143
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    • 2009
  • In this paper, a novel ultra-wide band filter which is operating at frequency bands from 3.1 GHz to 10.6 GHz is suggested. It is modified from the conventional ring filter and consisted of a ring with two parallel open-stub with length of ${\lambda}/8$. It improves the sharpness of the conventional ring filter and is compact. The measured results show that the fabricated filter has a insertion loss of 2.1 dB and the measured group delay of the filter is less than 463 ps through UWB frequency bands.

Fairness Measures for Data Communication Networks (데이터 통신망을 위한 공평성 성능 확보 방안)

  • Ju, Un-Gi;Lee, Hyeong-Seop
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2004.05a
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    • pp.135-138
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    • 2004
  • This paper considers a ring loading problem on RPR(Resilient Packet Ring), where RPR is recommended by IEEE802.17 Resilient Packet Ring working group for data optimized networks without the requirements of provisioning circuits. RPR is well suitable for metropolitan area network with two counter-rotating rings that multiple stations share the bandwidth, where the data and its corresponding control traffic is transmitted to the two opposite directional ring, respectively. One of the major concerns on RPR is to provide fairness among traffic requirements. The paper discusses several fairness measures and analysis ring loading problems for the fairness.

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The Wallach Rearrangement The Behaviour of Monosubstituted Azoxybenzenes in Strongly Acidic Solution (强酸溶液中에서의 Azoxybenzene 系化合物들의 轉移反應. Wallach 轉移反應)

  • Hahn, Chi-Sun
    • Journal of the Korean Chemical Society
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    • v.6 no.2
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    • pp.162-170
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    • 1962
  • The rearrangement reaction of azoxybenzenes into hydroxyazobenzenes in strongly acidic solution has been studied by an U. V. spectrophotometric method and by isolation of the rearranged compound. In all cases under investigation, it appeared that the oxygen atom in the azoxy group migrated to the unsubstituted ring, depending neither on the substituent already present in the other ring, nor on the distance between the oxygen atom and the eligible position; whereas, the position in the open ring, ortho or para, to which the oxygen migrates depends on the substituent already present in the other ring. In all compounds besides ${\alpha}$-and ${\beta}$-4-methyl azoxybenzene, the oxygen atom migrates to the para position. In the case of ${\alpha}$ and ${\beta}$-4-methylazoxybenzene, the oxygen atom migrates to the ortho position of the unsubstituted ring.

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RINGS WITH A FINITE NUMBER OF ORBITS UNDER THE REGULAR ACTION

  • Han, Juncheol;Park, Sangwon
    • Journal of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.655-663
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    • 2014
  • Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring $M_n(D)$, $n{\geq}2$, if a, b are singular matrices of the same rank, then ${\mid}o_{\ell}(a){\mid}={\mid}o_{\ell}(b){\mid}$, where $o_{\ell}(a)$ and $o_{\ell}(b)$ are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that $X(R){\neq}{\emptyset}$, $$R{{\sim_=}}{\oplus}^m_{i=1}M_n_i(D_i)$$, with $D_i$ infinite division rings of the same cardinalities or R is isomorphic to the ring of $2{\times}2$ matrices over a finite field if and only if ${\mid}o_{\ell}(x){\mid}={\mid}o_{\ell}(y){\mid}$ for all $x,y{\in}X(R)$.