• 제목/요약/키워드: crossed product

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Department of Mathematics, Dongeui University

  • Yoon, Suk-Bong
    • 대한수학회보
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    • 제38권3호
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    • pp.527-541
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    • 2001
  • We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).

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MORITA EQUIVALENCE FOR NONCOMMUTATIVE TORI

  • Park, Chun-Gil
    • 대한수학회보
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    • 제37권2호
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    • pp.249-254
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    • 2000
  • We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$ which hasa trivial bundle structure. It is well known that stable isomorphism of two separable $C^{*}-algebras$ is equibalent to the existence of eqivalence bimodule between the two stably isomorphic $C^{*}-algebras{\;}A_{\omega}$ and $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$.

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THE TENSOR PRODUCT OF AN ODD SPHERICAL NON-COMMUTATIVE TORUS WITH A CUNTZ ALGEBRA

  • Boo, Deok-Hoon;Park, Chun-Gil
    • 충청수학회지
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    • 제11권1호
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    • pp.151-161
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    • 1998
  • The odd spherical non-commutative tori $\mathbb{S}_{\omega}$ were defined in [2]. Assume that no non-trivial matrix algebra can be factored out of $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_{km}(\mathbb{C})$. It is shown that the tensor product of $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has the trivial bundle structure if and, only if km and 2d - 1 are relatively prime, and that the tensor product of $\mathbb{S}_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when km > 1.

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THE TENSOR PRODUCTS OF SPHERICAL NON-COMMUTATIVE TORI WITH CUNTZ ALGEBRAS

  • Park, Chun-Gil;Boo, Deok-Hoon
    • 충청수학회지
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    • 제10권1호
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    • pp.127-139
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    • 1997
  • The spherical non-commutative $\mathbb{S}_{\omega}$ were defined in [2,3]. Assume that no non-trivial matrix algebra can be factored out of the $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_k(\mathbb{C})$. It is shown that the tensor product of the spherical non-commutative torus $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has a trivial bundle structure if and only if k and 2d - 1 are relatively prime, and that the tensor product of the spherical non-commutative torus $S_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when k > 1.

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Styryl-6-Methoxy-2-Naphthyl Ketone 유도체의 합성 및 특성 분석 (Synthesis, Characterization and Correlation Analysis in Styryl 6-Methoxy-2-Naphthyl Ketones)

  • Thirunarayanan, G.
    • 대한화학회지
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    • 제51권2호
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    • pp.115-124
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    • 2007
  • α, β-불포화 케톤 유도체를 실리카-황산 촉매 하에서 비용매 교차 알돌 응축 반응법을 이용하여 합성하였다. 합성 수율은 90% 이상이었으며, 사용된 촉매는 회수 가능하였다. 합성돤 화합물들의 물리화학적인 특성은 IR, NMR, Mass 등의 분광학적 분석 방법을 이용하여 결정하였다. 케톤 생성물에 미치는 치환기 효과는 측정된 분광 데이터와 Hammet 치환기 상수간의 상관관계로 표현되는 다중 상관계수 방정식에 의하여 잘 설명될 수 있었다.

ON THE STRUCTURE OF NON-COMMUTATIVE TORI

  • Boo, Deok-Hoon;Park, Won-Gil
    • 충청수학회지
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    • 제13권1호
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    • pp.1-11
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    • 2000
  • The non-commutative torus $A_{\omega}=C^*(\mathbb{Z}^n,{\omega})$ may be realized as the $C^*$-algebra of sections of a locally trivial $C^*$-algebra bundle over $\widehat{S_{\omega}}$ with fibres $C^*(\mathbb{Z}^n/S_{\omega},{\omega}_1)$ for some totally skew multiplier ${\omega}_1$ on $\mathbb{Z}^n/S_{\omega}$. It is shown that $A_{\omega}{\otimes}M_l(\mathbb{C})$ has the trivial bundle structure if and only if $\mathbb{Z}^n/S_{\omega}$ is torsion-free.

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A Gas-Phase Investigation of Oxygen-Hydrogen Exchange Reaction of O(3P) + C2H5 → H(2S) + C2H4O

  • Jang, Su-Chan;Park, Min-Jin;Choi, Jong-Ho
    • Bulletin of the Korean Chemical Society
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    • 제35권3호
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    • pp.839-844
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    • 2014
  • The gas-phase radical-radical reaction $O(^3P)$ + $C_2H_5$ (ethyl) ${\rightarrow}$ $H(^2S)$ + $CH_3CHO$(acetaldehyde) was investigated by applying a combination of vacuum-ultraviolet laser-induced fluorescence spectroscopy in a crossed beam configuration and ab initio calculations. The two radical reactants $O(^3P)$ and $C_2H_5$ were respectively produced by photolysis of $NO_2$ and supersonic flash pyrolysis of the synthesized precursor azoethane. Doppler profile analysis of the nascent H-atom products in the Lyman-${\alpha}$ region revealed that the average translational energy of the products and the average fraction of the total available energy released as translational energy were $5.01{\pm}0.72kcalmol^{-1}$ and 6.1%, respectively. The empirical data combined with CBS-QB3 level ab initio theory and statistical calculations demonstrated that the title exchange reaction is a major channel and proceeds via an addition-elimination mechanism through the formation of a short-lived, dynamical addition complex on the doublet potential energy surface. On the basis of systematic comparison with several exchange reactions of hydrocarbon radicals, the observed small kinetic energy release can be explained in terms of the loose transition state with a product-like geometry and a small reverse activation barrier along the reaction coordinate.

CAPS marker에 의한 Arabidopsis의 자외선 B 감수성 유전자 지도작성 (Mapping of UV-B sensitive gene in Arabidopsis by CAPS markers)

  • 박홍덕;김종봉
    • 생명과학회지
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    • 제12권6호
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    • pp.715-720
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    • 2002
  • Arabidopsis thaliana columbia의 종자에 EMS를 처리하여 돌연변이체들을 만들었고 이중 UV-B에 감수성이 높은 돌연변이체를 골랐다. 이 UV-B 감수성 돌연변이체의 원인 유전자를 밝히기 위하여 교배 실험을 한 결과 이는 Mendel 유전법칙을 따르고 단일 유전자의 돌연변이에 의하여 나타나며 열성 유전을 하는 것으로 밝혀져 이 유전자를 uvs라 하였다. 염색체상의 uvs의 위치를 밝히기 위하여 CAPS maker를 이용한 연관분석을 하고자 하였고 이를 위하여 각각 maker의 primer 10종류를 제작하였다. 이를 이용, 각 PCR 산물에 대하여 uvs mutant와는 다른 제한효소 pattern를 갖는 Lansberg와 uvs mutant를 교배시켜서 얻은 것들로부터 DNA를 추출하여 PCR을 수행하였다. 이들과 자외선과의 감수성을 연관시켜 교차율을 계산한 결과 5번 염색체의 LFY3과 가장 가까웁게 연관되어 있었다.

Evaluation of Polyvoltine Hybrids Based on Silk Productivity in Silkworm, Bombyx mori L.

  • Rao, C.G.P.;Chandrashekaraiah;Ramesh, C.;Basha, K.Ibrahim;Seshagiri, S.V.;Nagaraju, H.
    • International Journal of Industrial Entomology and Biomaterials
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    • 제8권2호
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    • pp.181-187
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    • 2004
  • Polyvoltine silkworm breeds/hybrids play an important role in tropical sericulture. In the process of synthesizing more potential polyvoltine hybrids(polyvoltine${\times}$bivoltine) of superior quantity and quality, the Andhra Pradesh State Sericulture Research and Development Institute (APSSRDI) has developed 8 promising polyvoltine breeding lines (SDMG2, APM16, APM15, APM14, APM5, RM2, APM3, APM13). In order to study their hybrid vigour and performance, these breeds were crossed with 4 potential bivoltine testers (SDD1, SDD2, SDD3, APS8), and 32 different hybrid combinations were prepared and evaluated for their mid parent heterosis (MPH) and better parent heterosis (BPH) of silk productivity. Since silk is the ultimate product required for commercial purpose, based on silk productivity and its heterosis, three superior polyvoltine hybrid combinations namely RM2${\times}$APS8 (24.3%), APM3${\times}$APS8 (12.4%) and APM15${\times}$SDD2 (10.8%) were adjudicated as potential heterotic hybrid combinations of superior silk yield and hence recommended for further large scale field trails and commercial exploitation.

Aphrodisiac Evaluation in Sexually Naive Male Mice after Chronic Administration of Eurycoma longifolia Jack

  • Ang, Hooi Hoon;Sim, Meng-Kwoon
    • Natural Product Sciences
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    • 제4권2호
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    • pp.58-61
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    • 1998
  • Eurycoma longifolia Jack was evaluated for aphrodisiac property on sexually naive male mice using the electrical copulation cage. Optimum condition was provided for this study and the male mice were treated with 500 mg/kg of either chloroform, methanol, water or n-butanol fractions from E. longifolia Jack. However, the mice in the yohimbine and control groups received 30 mg/kg and 3 ml/kg of yohimbine and normal saline respectively. The male mice were then conditioned to seek either an estrous female, sexually vigorous male or no mouse, a measurement of right, wrong or no choice respectively. Besides this, hesitation time which was the time spent before the sexually naive male mice crossed the electrical grid (maintained at 0.12 mA) was also determined. Results showed that E. longifolia Jack possesses aphrodisiac property on the sexually naive male mice as shown by the slow and transient reduction in hesitation time and also a similar manner in the increase in the % of sexually naive male mice scoring right choice throughout the investigation period. Hence, this further supports the folkuse of this plant as aphrodisiac.

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