• Bulletin of the Korean Chemical Society
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• v.23 no.12
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• pp.1790-1800
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• 2002

The DNA nucleosides(dA, dC, dG, dT)bound to gold nanoparticles (~13 nm) in aqueous solution has been studied as a probe by the SERS and their coordination structures have been proposed on the basis of them. According to UV-Visible absorption of gold nanoparticles after modifying with DNA nucleosides, the rates of absorption of dA, dC, and dG were much faster than that of dT as monitored by the aggregation kinetics at 700 nm. These data indicated that the nucleosides dA, dC, and dG had a higher affinity for the gold nanoparticles surface than nucleoside dT. As the result of SERS spectra, the binding modes of each of the nucleosides on gold nanoparticles have been assigned. A dA binds to gold nanoparticles via a N(7) nitrogen atom of the imidazole ring, which the C(6)-$NH_2$ group also participates in the coordination process. In the case of dC, it binds to the gold surface via a N(3) nitrogen atom of the pyrimidine ring with a partial contribution from the oxygen of C(2)=O group. A coordination of dG to the gold surfaces is also proposed. Although the dG has the two different nitrogens of a pyrimidine ring and the amino group, the N(1) nitrogen atom of a pyrimidine ring has a higher affinity after the hydrogen migrates to the amino group. Conversely, dT binds via the oxygen of the C(4)=O group of the pyrimidine ring. Accordingly, these data suggest that the nitrogen atom of the imidazole or the pyrimidine ring in the DNA nucleosides will bind more fast to the gold nanoparticles surfaces than the oxygen atom of the carbonyl group.

• Journal for History of Mathematics
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• v.10 no.2
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• pp.24-29
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• 1997

Derivation은 Lie group, Lie ring 그리고 Lie Algebra에서 정의되어 사용되며 발전하였으며 ring에서 일반화 되었다. 역시 prime ring에서 연구되어지는 derivation의 성질들은 prime near-ring에서 일반화 시키려고 하고 있다. 1957년 E. Posner는 prime ring에서 두 개의 derivation의 곱(함수합성)이 derivation이면 이들중 하나의 derivation이 0임을 밝혔다. 본 논문에서는 prime ring에서 derivation이 연구된 역사적인 배경을 소개하고 몇가지 성질을 찾는다. 즉, D. F를 prime ring R의 derivation들이라 할 때 정수 $n{\ge}1$에 대하여 $DF^n$=0이면 D=0이거나 또는 $F^{3n-1}$=0이고, $D^nF$=0이면 $D^{9n-7}$=0 이거나 또는 $F^2$=0 이다.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.489-501
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• 2015

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.

• Bulletin of the Korean Chemical Society
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• v.20 no.6
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• pp.663-666
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• 1999

The 4-methylene-1,3-dioxolane(4-MDO) derivatives with dimethoxyphenyl group on the 2-position of 1,3-dioxolane ring, 2-(x,y-dimethoxyphenyl)-4-MDO derivatives (x,y=2,3(1b), 2,4(2b), 2,5(3b) and 3,4(4b)) were prepared by acelalizationof the corresponding benzaldehyde with 3-chloro-1,2-propanediol, followed by dehydrochlorination. 2-(Dimethoxy)phenyl-4-MDO derivatives underwent polymerization wiht ring opening as will as cyclization reaction to afford a mixture of the ring-opened polymer and 3(2H)-dihydrofuranone derivative with boron trifluoride as a cationic catalyst. Both the methylene group and 1,3-dioxolane ring were participated in the reaction with cationic catalyst. The key intermediate of the polymerization is a benzyl cation generated by ring opening, and the cyclization reaction proceed via proton addition to oxygen atom of 1,3-dioxolane ring.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Bulletin of the Korean Chemical Society
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• v.33 no.8
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• pp.2585-2591
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• 2012

A series of heterocyclic chalcone derivatives bearing heterocycles such as thiophene or furan ring as an isostere of benzene ring were carefully prepared, and the influence of heterocycles on 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activities was systematically investigated. Structure-activity relationships (SAR) analysis showed that the activities of thiophene ring-containing chalcones were higher than those of furan ring-containing chalcones, and the presence of methyl substituent of heterocyclic ring distinctly affected the activities compared with non-substituted heterocycles in an opposite manner, with the 4'-methyl group of thiophene ring increasing activity and the 3'-methyl group of the furan ring decreasing activity. The distinct isosteric effect of heterocycles (i.e., thiophene or furan ring) on radical scavenging activities of heterocyclic chalones was distinctly demonstrated in our work.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1097-1106
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• 2010

Let R be a commutative ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will investigate some ring theoretic properties of R by considering $\Gamma$(R), the zero-divisor graph of R, under the regular action on X by G as follows: (1) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then there is a vertex of $\Gamma$(R) which is adjacent to every other vertex in $\Gamma$(R) if and only if R is a local ring or $R\;{\simeq}\;\mathbb{Z}_2\;{\times}\;F$ where F is a field; (2) If R is a local ring such that X is a union of n distinct orbits under the regular action of G on X, then all ideals of R consist of {{0}, J, $J^2$, $\ldots$, $J^n$, R} where J is the Jacobson radical of R; (3) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then the number of all ideals is finite and is greater than equal to the number of orbits.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.771-778
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• 2005

In this paper we shall give some group properties derived from the characteristic ring-module $_X(M)$, using the fact that $_X(M)_H$ is a conjugate to $_X(M)_{Ha}$ when M is an invertible right R-module. Also we shall prove that_X(M)$ is group-isomorphic to TR and some normal subgroup properties if M is invertible and R is commutative.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.57-64
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• 2006

It is proved that if G is a direct sum of countable abelian $p$-groups and R is a special selected commutative unitary highly-generated ring of prime characteristic $p$, which ring is more general than the weakly perfect one, then the group of all normed units V (RG) modulo G, that is V (RG)=G, is a direct sum of countable groups as well. This strengthens a result due to W. May, published in (Proc. Amer. Math. Soc., 1979), that treats the same question but over a perfect ring.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1033-1039
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• 2011

Let R be a ring with identity 1, I(R) be the set of all idempotents in R and G be the group of all units of R. In this paper, we show that for any semiperfect ring R in which 2 = 1+1 is a unit, I(R) is closed under multiplication if and only if R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication and eGe is contained in the group of units of eRe. In particular, for a left Artinian ring in which 2 is a unit, R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication.