• Title/Summary/Keyword: D.D.I.

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SYSTEMS OF DERIVATIONS ON BANACH ALGEBRAS

  • Lee, Eun-Hwi
    • Communications of the Korean Mathematical Society
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    • v.12 no.2
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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).

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BIPRODUCT BIALGEBRAS WITH A PROJECTION ONTO A HOPF ALGEBRA

  • Park, Junseok
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.1
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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.

Quickly Changing Architectural O.D.L and I.D.L for the Aged (노인들을 위하여 급변하는 건축적 O.D.L과 I.D.L)

  • Bahk, Sang Hee;Kim, Heung Gon
    • Journal of the Korean Institute of Rural Architecture
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    • v.3 no.2
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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.

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NON-EXISTENCE OF SOME ARTINIAN LEVEL O-SEQUENCES OF CODIMENSION 3

  • Shin, Dong-Soo
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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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.

COVERING AND INTERSECTION CONDITIONS FOR PRIME IDEALS

  • Chang, Gyu Whan;Hwang, Chul Ju
    • Korean Journal of Mathematics
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    • v.17 no.1
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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).

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Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem (도메틱 수 문제에 관한 최대차수 정점 지배집합 알고리즘)

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.2
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    • pp.63-70
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    • 2015
  • In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.

COMPOSITE HURWITZ RINGS AS ARCHIMEDEAN RINGS

  • Lim, Jung Wook
    • East Asian mathematical journal
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    • v.33 no.3
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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.

ON CHARACTERIZATIONS OF PRÜFER v-MULTIPLICATION DOMAINS

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.18 no.4
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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.

Structural Analysis of Cu Binding Site in [Cu(I)·d(CpG)·d(CpG)-2H]-1 Complex

  • Im, Yu-Jin;Jung, Sang-Mi;Kang, Ye-Song;Kim, Ho-Tae
    • Bulletin of the Korean Chemical Society
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    • v.34 no.4
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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.

Comparison of Autorefraction and Refraction with iTrace for Elementary School Children (초등학생의 자동안굴절계와 iTrace로 측정한 굴절검사 값의 비교)

  • Kim, Hyojin;Lee, Koon-Ja;Kim, Sam-Yi;Kim, Se-Rom
    • Journal of Korean Ophthalmic Optics Society
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    • v.15 no.1
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    • pp.99-104
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    • 2010
  • Purpose: Difference of refraction result from the method of autorefraction and iTrace were investigaged for the children of elementary school in Asan City. In iTrace method. exclusion of accommodation without cycloplegia was used. Methods: Manifest refractive stale of 42 eyes of 12~13 years old were measured using autorefractor and iTrace. Refractions of far (more than 5 m) and ncar (30 cm) vision were measured using iTrace. All data showed that the spherical equivalent were classified as being in the group 1 (-0.50D < ~ < +1.00D) and 2 (below -0.50D) according 10 refractive errors. Results: Mean spherical equivalent using autorefractor and iTrace (far and near vision) were -1.08D, -0.29D and -2.34D, respectively (p<0.01). Compared with the far vision using iTrace, autorefraction was measured the myopia with -0.50D ~ -1.00D in 52.4% of total eyes. Autorefraction also statistical significant were measured a more myopia than the far vision using iTrace in group I and 2. Conclusions: The difference of refractive errors between autorefraction and iTrace, objective refraction were measured with far vision of more than 5 m were -0.79D. Autoreftaction showed statistically decreased refraction errors than iTrace with far vision.