• 대한수학회논문집
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• 제12권2호
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• pp.251-256
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• 1997

We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

• 충청수학회지
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• 제26권1호
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• pp.91-103
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• 2013

Let (D,B) be an admissible pair. Then recall that $B\;{\times}^L_HD^{{\rightarrow}{\pi}_D}_{{\leftarrow}i_D}\;D$ are bialgebra maps satisfying ${\pi}_D{\circ}i_D=I$. We have solved a converse in case D is a Hopf algebra. Let D be a Hopf algebra with antipode $S_D$ and be a left H-comodule algebra and a left H-module coalgebra over a field $k$. Let A be a bialgebra over $k$. Suppose $A^{{\rightarrow}{\pi}}_{{\leftarrow}i}D$ are bialgebra maps satisfying ${\pi}{\circ}i=I_D$. Set ${\Pi}=I_D*(i{\circ}s_D{\circ}{\pi}),B=\Pi(A)$ and $j:B{\rightarrow}A$ be the inclusion. Suppose that ${\Pi}$ is an algebra map. We show that (D,B) is an admissible pair and $B^{\leftarrow{\Pi}}_{\rightarrow{j}}A^{\rightarrow{\pi}}_{\leftarrow{i}}D$ is an admissible mapping system and that the generalized biproduct bialgebra $B{\times}^L_HD$ is isomorphic to A as bialgebras.

• 한국농촌건축학회논문집
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• 제3권2호
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• pp.13-24
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• 2001

Some companies of domestic construction indicate recently that modern life for the aged prefer an advanced technical alliance between O.D.L and I.D.L systems. It means the quality of housing life of the aged has been raised and changed quickly as well as the O.D.L and I.D.L systems since the last year. These preliminary studies suggest that the aged people in the country suffer from insufficient O.D.L and I.D.L systems caused by nation-wide economic poverty compared with the aged people in Seoul. The information from the country has been restricted for several decades therefore some details of the results of the studies are at times difficult to believe and differ depending on the research methods. The purpose of this study is to clarify the quality housing life of the aged, based on the comparative analysis between the O.D.L and I.D.L systems. The quality of housing life of the aged in countryside has been revealed by the clarification of the conditions housing supply, facilities, and therefore housing the cost amount. The conclusions are as follows ; The quickly changing architectural O.D.L elements are presented below in 17 items, while the I.D.L elements are presented in 18 items.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.517-523
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• 2007

Let R/I be an Artinian algebra of codimension 3 with Hilbert function H such that $h_{d-1}>h_d=h_{d+1}$. Ahn and Shin showed that A cannot be level if ${\beta}_{1,d+2}(Gin(I))={\beta}_{2,d+2}(Gin(I))$ where Gin(I) is a generic initial ideal of I. We prove that some certain graded Artinian algebra R/I cannot be level if either ${\beta}_{1,d}(I^{lex})={\beta}_{2,d}(I^{lex})+1\;or\;{\beta}_{1,d+1}(I^{lex})={\beta}_{2,d+1}(I^{lex})\;where\;I^{lex}$ is a lex-segment ideal associated to I.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.15-23
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• 2009

Let D be an integral domain, P be a nonzero prime ideal of D, $\{P_{\alpha}{\mid}{\alpha}{\in}{\mathcal{A}}\}$ be a nonempty set of prime ideals of D, and $\{I_{\beta}{\mid}{\beta}{\in}{\mathcal{B}}\}$ be a nonempty family of ideals of D with ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\neq}(0)$. Consider the following conditions: (i) If $P{\subseteq}{\cup}_{{\alpha}{\in}{\mathcal{A}}}P_{\alpha}$, then $P=P_{\alpha}$ for some ${\alpha}{\in}{\mathcal{A}}$; (ii) If ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\subseteq}P$, then $I_{\beta}{\subseteq}P$ for some ${\beta}{\in}{\mathcal{B}}$. In this paper, we prove that D satisfies $(i){\Leftrightarrow}D$ is a generalized weakly factorial domain of ${\dim}(D)=1{\Rightarrow}D$ satisfies $(ii){\Leftrightarrow}D$ is a weakly Krull domain of dim(D) = 1. We also study the t-operation analogs of (i) and (ii).

• 한국컴퓨터정보학회논문지
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• 제20권2호
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• pp.63-70
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• 2015

최대 지배집합의 수인 도메틱 수 문제 (DNP)는 정확한 해를 다항시간으로 구하는 알고리즘이 존재하지 않아 NP-완전 문제로 알려져 있다. 본 논문은 DNP의 해를 다항시간으로 구하는 알고리즘을 제안하였다. 그래프의 최대 차수 ${\Delta}(G)$ 정점 $v_i$를 $D_i,i=1,2,{\cdots},k$의 지배집합의 원소로 선택하는 방법을 적용하고, $V_{i+1}=V_i{\backslash}D_i$의 축소된 그래프에 대해 $D_{i+1}$을 구하였다. 또한 $V{\backslash}D_i=N_G(D_i)$로 $D_i$가 지배집합으로 되는지 여부를 검증하였다. 제안된 알고리즘을 15개의 다양한 그래프에 적용한 결과 정확한 해를 다항시간 복잡도 O(kn)으로 구하는데 성공하였다. 결국, 제안된 알고리즘은 도메틱 수 문제가 P-문제임을 보였다.

• 대한화장품학회지
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• 제50권2호
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• pp.153-161
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• 2024

비타민 D는 주로 자외선에 의해 피부에서 만들어지는 지용성 비타민이다. 멜라토닌과 함께 대표적인 '크로노바이오틱(chronobiotic)' 물질로써 피부가 낮과 밤을 구분하는데 중요한 역할을 한다. 하지만 비타민 D는 조효소 역할을 하는 비타민이자 여러 종류의 유전자 발현을 조절하는 호르몬적 역할을 하기 때문에 화장품에 직접적으로 사용할 수 없다. 따라서 화장품에 사용할 수 있는 비타민 D 전구체인 프로 비타민 D (7-dehydrocholesterol)의 피부 효능에 대해서 알아보고자 하였다. 그 결과, 프로 비타민 D는 멜라닌 생성 효소인 타이로시네이즈(tyrosinase)의 단백질 발현을 억제하여 멜라닌 생성을 억제할 수 있음을 확인할 수 있었다. 이와 같은 피부톤 케어 효과는 인공 피부에서도 검증되었다. 또한 프로 비타민 D는 피부 염증을 일으키는 TNFa의 발현을 억제하고, 자외선에 의해 비타민 D로 전환되면 항균 펩타이드인 CAMP (LL-37)의 발현을 증가시킨다는 것이 확인되었다. 프로 비타민 D가 멜라닌 생성을 억제하는 것은 멜라닌이 자외선을 흡수하여 프로 비타민 D가 비타민 D로 전환되는 것을 억제하기 때문인 것으로 보인다. 따라서 화장품 제형에 프로 비타민 D를 활용한다면 피부톤을 조절하고 피부 면역을 증진시킴과 동시에 일상 생활 속에서 자외선에 의해 비타민 D 전환되면 다른 피부 효능, 즉 피부 항노화, 장벽 기능 향상 등도 기대할 수 있을 것으로 생각한다.

• East Asian mathematical journal
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• 제33권3호
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• pp.317-322
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• 2017

Let $D{\subseteq}E$ be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D, and let H(D, E) and H(D, I) (resp., h(D, E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this article, we show that H(D, E) is an Archimedean ring if and only if h(D, E) is an Archimedean ring, if and only if ${\bigcap}_{n{\geq}1}d^nE=(0)$ for each nonzero nonunit d in D. We also prove that H(D, I) is an Archimedean ring if and only if h(D, I) is an Archimedean ring, if and only if D is an Archimedean ring.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.335-342
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• 2010

Let D be an integral domain with quotient field K,$\mathcal{I}(D)$ be the set of nonzero ideals of D, and $w$ be the star-operation on D defined by $I_w=\{x{\in}K{\mid}xJ{\subseteq}I$ for some $J{\in}\mathcal{I}(D)$ such that J is finitely generated and $J^{-1}=D\}$. The D is called a Pr$\ddot{u}$fer $v$-multiplication domain if $(II^{-1})_w=D$ for all nonzero finitely generated ideals I of D. In this paper, we show that D is a Pr$\ddot{u}$fer $v$-multiplication domain if and only if $(A{\cap}(B+C))_w=((A{\cap}B)+(A{\cap}C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $(A(B{\cap}C))_w=(AB{\cap}AC)_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $((A+B)(A{\cap}B))_w=(AB)_w$ for all $A,B{\in}\mathcal{I}(D)$, if and only if $((A+B):C)_w=((A:C)+(B:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with C finitely generated, if and only if $((a:b)+(b:a))_w=D$ for all nonzero $a,b{\in}D$, if and only if $(A:(B{\cap}C))_w=((A:B)+(A:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with B, C finitely generated.

• Bulletin of the Korean Chemical Society
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• 제34권4호
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• pp.1232-1236
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• 2013

The Cu cation binding sites of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex have been investigated to explain the $[Cu{\cdot}DNA]$ biological activity caused by the Cu association to DNA. The structure of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex was investigated by electrospray ionization mass spectrometry (ESI-MS). The fragmentation patterns of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex were analyzed by MS/MS spectra. In the MS/MS spectra of $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex, three fragment ions were observed with the loss of d(CpG), {d(CpG) + Cyt}, and {d(CpG) + Cyt + dR}. The Cu cation binds to d(CpG) mainly by substituting the $H^+$ of phosphate group. Simultaneously, the Cu cation prefers to bind to a guanine base rather than a cytosine base. Five possible geometries were considered in the attempt to optimize the $[Cu(I){\cdot}d(CpG){\cdot}d(CpG)-2H]^{-1}$ complex structure. The ab initio calculations were performed at B3LYP/6-31G(d) level.