• 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).

• 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.

• 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.

• 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.

• 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.

• The Journal of the Acoustical Society of Korea
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• v.11 no.6
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• pp.15-22
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• 1992

i.i.d 신호의고차 모멘트와 스펙트럼의 성질에 대하여 4차까지 고찰하였으며 이의 결과를 이용하 여 2차 Volterra 급수로 표시되고, i.i.d. 입력 신호를 갖는 시불변 비선형 시스테므이 파라메타들을 추정 하는 알고리즘을 시간 영역과 주파수 영역에서 각각 제안하였다. 비록 2차 Volterra 급수가 i.i.d. 입력 신호에 대하여 orthogonal 모델이 아닐지라도 입력 신호의 각종 시간지연에 대한 모멘트나 역행렬의 계 산등이 요구되지 않으며 선형 전달함수와 2차 전달함수를 추정할 수 있는 알고리즘이 존재하는 것을 보 았다.

• Journal of Acupuncture Research
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• v.21 no.1
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• pp.51-58
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• 2004

Objective: The purpose of this study is to report that D.I.T.I. can be used for diagnosis of scoliosis. Methods: We measured the posterior trunk surface of the patients with shoulder pain or low back pain. They were ruled out as scoliosis by D.I.T.I. and compared with X-ray finding of T L-spine Ap views and calculated scoliosis angle. Results: In according to the spinoprocess curve in D.I.T.I. we could rule out as scoliosis. Thermal difference of left and right segmental areas of the patients was showed. Scoliosis angle of the patients ranged from $4^{\circ}$ to $11^{\circ}$ in X-ray finding. Conclusions: The results suggest that D.I.T.I. can explain physiologic and functional abnormalities than X-ray, in diagnosis of scoliosis. But further studies are required to for the diagnosis of scoliosis by analysing D.I.T.I..

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• 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).

• 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.