• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.653-663
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• 2002

We introduce and investigate the concepts of ($(T_i,T_j)$-fuzzy $\alpha-(r.s)$-semiopen $\alpha-(r.s)$-semiclosed) sets and fuzzy pairwise $\alpha-(r.s)$-semicontinuous mappings in smooth bitopological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.27-30
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• 1998

The purpose of this paper is to investigate solutions U$_+$ and U$^+$ for the fuzzy relation equation R$\circ$U= T in cases of R < T, R $\leq$ T, and R = T, when R is irreflexive, U$_+$ ($\chi$$_i$, $\chi$$_k$)=$\bigwedge$[R($\chi$$_i$, $\chi$$_k$) << T($\chi$$_i$, $\chi$$_k$)], U$^+$ ($\chi$$_i$, $\chi$$_k$)=$\bigwedge$[R($\chi$$_i$, $\chi$$_k$)->T($\chi$$_i$, $\chi$$_k$)].

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.649-657
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• 2013

Let R be a commutative Noetherian ring, I an ideal of R and T be a non-zero I-cofinite R-module with dim(T) ${\leq}$ 1. In this paper, for any finitely generated R-module N with support in V(I), we show that the R-modules $Ext^i_R$(T,N) are finitely generated for all integers $i{\geq}0$. This immediately implies that if I has dimension one (i.e., dim R/I = 1), then $Ext^i_R$($H^j_I$(M), N) is finitely generated for all integers $i$, $j{\geq}0$, and all finitely generated R-modules M and N, with Supp(N) ${\subseteq}$ V(I).

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.531-540
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• 2015

Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{&gt;k}(I,A)$ the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all $t{\leq}r$ the sets $$(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/I^n,A)))_{{\geq}k}\;and\\(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/(a_1^{n_1},{\cdots},a_l^{n_l}),A)))_{{\geq}k}$$ are independent of the choice of $n,n_1,{\cdots},n_l$ for any system of generators ($a_1,{\cdots},a_l$) of I.

• Journal of the Korean Society for information Management
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• v.5 no.1
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• pp.31-52
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• 1988

The information policy in Japan have bccir growing rapldlr 111 recent vttars. \'arioi~s level of govc~riimerital organrzatlons, ir~bt~tution arid agrircics have undt~rtak~~rr iriforrnatiori polrcy 111 order to i r l - crease information flow toward tlie society in Japan. At tlie same trme, computerized library systems also h a w uridergoirc rapid expansion. NACSIS(National Ceriter for- Science Informat~on System) wl~icl~ was cstablisl~ed bv Mirristr> of Etlr~c~arion, Sc~ence arid Culture haw witnessed dramatic adv;rnces i r i promoting for corrstructiori of database so as to provide their 11rf'3r.mat1orr nu nationwide scale. T l r i h articlr inrroduccs tlie actr\rtle> and ~mplcmeritat~o~~ of it format in^^ pol~cy wl~i(~li taktas a place hy goverrirnrlit of Japar~ aid arraly~c,.; thi~ ~ I . O I . P S I of deciiioii maltiiig iri polit~cal procedures. So far as b:ast-A\~ari riatioris art, ~ . n r i v t ~ r ~ ~ , e.;pc,ciall\. Kr,rc.an a~rd Japair !rave ,imilar cultural and liistorical backjir. ourii1, ard could t)t. tliif most a p p r o p r i a t ~ ~ caac stlldh for political ~nq~lerncritat~orr. Thus the topic of this artrclc will be useful to r t ~ a l l ~ t . Ore, trail ur~d c r r o r prorex, iri iiiior.matior~ pnlic\ulcorner.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.695-701
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• 2016

Let I and J be two ideals of a commutative Noetherian ring R and M, N be two non-zero finitely generated R-modules. Let t be a non-negative integer such that $H^i_{I,J}(N)$ is (I, J)-minimax for all i < t. It is shown that the generalized local cohomology module $H^i_{I,J}(M,N)$ is (I, J)-Cofinite minimax for all i < t. Also, we prove that the R-module $Ext^j_R(R/I,H^i_{I,J}(N))$ is finitely generated for all $i{\leq}t$ and j = 0, 1.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.337-345
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• 2022

Let R ⊆ T be an extension of a commutative ring and S ⊆ R a multiplicative subset. We say that (R, T) is an S-accr (a commutative ring R is said to be S-accr if every ascending chain of residuals of the form (I : B) ⊆ (I : B²) ⊆ (I : B³) ⊆ ⋯ is S-stationary, where I is an ideal of R and B is a finitely generated ideal of R) pair if every ring A with R ⊆ A ⊆ T satisfies S-accr. Using this concept, we give an S-version of several different known results.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.311-317
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• 2018

Let (R, m) be a commutative Noetherian local ring and I be an ideal of R. In this paper it is shown that if cd(I, R) = t > 0 and the R-module $Hom_R(R/I,H^t_I(R))$ is finitely generated, then $$t={\sup}\{{\dim}{\widehat{\hat{R}_p}}/Q:p{\in}V(I{\hat{R}}),\;Q{\in}mAss{_{\widehat{\hat{R}_p}}}{\widehat{\hat{R}_p}}\;and\;p{\widehat{\hat{R}_p}}=Rad(I{\wideha{\hat{R}_p}}=Q)\}$$. Moreover, some other results concerning the cohomological dimension of ideals with respect to the rings extension $R{\subset}R[X]$ will be included.

• Proceedings of the PSK Conference
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• 2003.10b
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• pp.201.3-201.3
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• 2003

The ethanol extract from the fruit of Terminalia chebula (Combretaceae) and the hook of Uncaria sinensis (Rubiaceae) exhibited significant inhibitory activity on oxidative stress and the age-dependent shortening of the telomeric DNA length. In the peroxidation model using t-BuOOH, human epidermal keratinocytes-neonatal foreskin (HEK-N/F) cells were treated with the T. chebula and U. sinensis extracts. The results showed a notable enhancing effect on the cell viability of 60.5 ${\pm}$ 3.8 and 65.0 ${\pm}$ 3.0%, respectively, by 50 $\mu\textrm{g}$/ml of the extracts. (omitted)