• East Asian mathematical journal
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• 제36권3호
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• pp.389-415
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• 2020

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, ξ, η, g) in a complex space form M_n+1(c), c ≠ 0. We denote by R_ξ and R'_X be the structure Jacobi operator with respect to the structure vector ξ and be R'_X = (∇_XR)(·, X)X for any unit vector field X on M, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_ξ𝜙 = 𝜙R_ξ and at the same time R'_ξ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature ${\bar{r}}$ of M holds ${\bar{r}}-2(n-1)c{\leq}0$.

• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.343-353
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• 2006

The two-way balanced one-level rotation design, $r_1^m-r_2^{m-1}$, and the three-way balanced multi-level rotation design, $r_1^m(\iota)-r_1^{m-1}$, were discussed (Park et al., 2001, 2003). Although these rotation designs enjoy balancing properties, they have a restriction of $r_2=c{\cdot}r_1$ (c should be a integer value) which interferes with applying these designs freely to various situations. To overcome this difficulty, we extend the $r_1^m(\iota)-r_1^{m-1}$ design to new one under the most general rotation system. The new multi-level rotation design also satisfies tree-way balancing which is done on interview time, rotation group and recall time. We present the rule and rotation algorithm which guarantee the three-way balancing. In particular, we specify the necessary condition for the extended three-way balanced multi-level rotation sampling design.

• 대한수학회논문집
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• 제9권2호
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• pp.261-264
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• 1994

Throughout this paper, all rings are assumed to be commutative with identity. By a local ring (R, m), we mean a Noetherian ring R which has the unique maximal ideal m. By dim(R) we always mean the Krull dimension of R. Let I be an ideal in a ring R and t an indeterminate over R. Then the Rees algebra R[It] is defined to be(omitted)

• 대한수학회보
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• 제61권1호
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• pp.1-12
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• 2024

In this paper, we introduce the notion of Gorenstein (m, n)-flat modules as an extension of (m, n)-flat left R-modules over a ring R, where m and n are two fixed positive integers. We demonstrate that the class of all Gorenstein (m, n)-flat modules forms a Kaplansky class and establish that (𝓖𝓕_m,n(R),𝓖𝓒_m,n(R)) constitutes a hereditary perfect cotorsion pair (where 𝓖𝓕_m,n(R) denotes the class of Gorenstein (m, n)-flat modules and 𝓖𝓒_m,n(R) refers to the class of Gorenstein (m, n)-cotorsion modules) over slightly (m, n)-coherent rings.

• East Asian mathematical journal
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• 제16권1호
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• pp.111-123
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• 2000

Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[xl-module. Park generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^s]$-module, where S is a submonoid of N(N is the set of all natural numbers). In this paper we show $$Hom_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Hom_R(M,\;N)[[x^S]]$$ and using the above result and this isomorphism, finally we show that $$Ext^i_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Ext^i_R(M,\;N)[[x^S]]$$.

• 대한수학회논문집
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• 제38권1호
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• pp.1-9
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• 2023

An le-module M over a commutative ring R is a complete lattice ordered additive monoid (M, ⩽, +) having the greatest element e together with a module like action of R. This article characterizes the le-modules _RM such that the pseudo-prime spectrum X_M endowed with the Zariski topology is a Noetherian topological space. If the ring R is Noetherian and the pseudo-prime radical of every submodule elements of _RM coincides with its Zariski radical, then X_M is a Noetherian topological space. Also we prove that if R is Noetherian and for every submodule element n of M there is an ideal I of R such that V (n) = V (Ie), then the topological space X_M is spectral.

• 대한수학회보
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• 제51권3호
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• pp.653-657
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• 2014

Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that $$Ext^i{_R}(R/I,H^t{_{I,J}}(M))$$ is finitely generated for i = 0, 1 where t=inf{$i{\in}\mathbb{N}_0:H^2{_{I,J}}(M)$ is not finitely generated}. Also, we prove that $H^i{_{I+J}}(H^t{_{I,J}}(M))$ is Artinian when dim(R/I + J) = 0 and i = 0, 1.

• 대한화장품학회지
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• 제30권1호
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• pp.7-13
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• 2004

3,9-Dihydro-6-oxopterocarpen과 ferulic acid의 에스테르 반응을 통해 페룰산 유도체인 3,9-diferuloyl-6-oxopterocarpen (Tensolin-$F_{(R)}$ )를 합성하여 이를 함유한 주름개선 화장품을 개발하였다. Tensolin-$F_{(R)}$ 는 농도 의존적으로 DPPH와 superoxide radical에 대한 소거효과를 나타냈으며, 각각 0.8 mM에서 78%, 0.053 mM에서 92.9%로 DPPH와 superoxide radical을 소거하여 우수한 항산화 효과를 나타내었다. MMP-1 효소 활성 저해 효과도 0.16 mM에서 74%를 저해하였다. HDF에서 UVA에 의해 발현이 증가되는 MMP-1의 발현 저해 효과는 Tensolin-$F_{(R)}$ 0.8 uM에서 85.5%로 단백질 수준에서 모두 농도 의존적으로 발현 저해효과가 나타났다. Tensolin-$F_{(R)}$ 를 함유한 제품의 피부 주름개선 효과 평가 결과, Tensolin-$F_{(R)}$ 를 함유한 화장품을 약 8주 간 도포한 경우 유의한 주름개선 효과가 있음을 확인 할 수 있었다. 본 연구를 통하여 Tensolin-$F_{(R)}$ 는 항산화 효과와 MMP-1활성 저해 효과 및 UVA에 의한 MMP-1의 발현을 저해하는 효과가 나타났으며 새로운 주름개선 기능성 화장품으로 이용될 수 있을 것이다.

• 대한약학회:학술대회논문집
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• 대한약학회 2003년도 Proceedings of the Convention of the Pharmaceutical Society of Korea Vol.2-2
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• pp.192.2-192.2
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• 2003

Apigenin-7-O-${\beta}$-D-glucoside, chrysoeriol, and luteolin were isolated from the aqueous ethanolic extract of Zostera marina L. leaves as the scavengers of reactive oxygen species (ROS) with the SC$\_$50/ values of 0.18 mM, 0.68 mM, and 0.18 mM against 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 0.04 mM, 0.03 mM, and 0.01 mM against superoxide radicals in the xanthine/xanthine oxidase system, respectively. The luteolin suppressed the expression of matrix metalloproteinase-1 (MMP-1) up to 44% at 4.0 ${\mu}$M. (omitted)

• 대한수학회보
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• 제53권5호
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• pp.1341-1352
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• 2016

Let R be a commutative Noetherian ring, ${\Phi}$ a system of ideals of R and $I{\in}{\Phi}$. In this paper among other things we prove that if M is finitely generated and $t{\in}\mathbb{N}$ such that the R-module $H^i_{\Phi}(M)$ is $FD_{{\leq}1}$ (or weakly Laskerian) for all i < t, then $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all i < t and for any $FD_{{\leq}0}$ (or minimax) submodule N of $H^t_{\Phi}(M)$, the R-modules $Hom_R(R/I,H^t_{\Phi}(M)/N)$ and $Ext^1_R(R/I,H^t_{\Phi}(M)/N)$ are finitely generated. Also it is shown that if cd I = 1 or $dimM/IM{\leq}1$ (e.g., $dim\;R/I{\leq}1$) for all $I{\in}{\Phi}$, then the local cohomology module $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all $i{\geq}0$. These generalize the main results of Aghapournahr and Bahmanpour [2], Bahmanpour and Naghipour [6, 7]. Also we study cominimaxness and weakly cofiniteness of local cohomology modules with respect to a system of ideals.