• 대한수학회지
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• 제39권1호
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• pp.127-135
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m. Then we say that I is an equimultiple good ideal in A, if I contains a reduction Q = ( $a_1$, $a_2$,ㆍㆍㆍ, $a_{s}$ ) generated by s elements in A and G(I) =(equation omitted)$_{n 0}$ $I^{n}$ / $I^{n＋1}$ of I is a Gorenstein ring with a(G(I)) = 1 - s, where s = h $t_{A}$ I and a(G(I)) denotes the a-invariant of G(I). Let $X_{A}$$^{s}$ denote the set of equimultiple good ideals I in A with h $t_{A}$ I = s, R(I) = A [It] be the Rees algebra of I, and $K_{R(I)}$ denote the canonical module of R(I). Let a I such that $I^{n＋l}$ = a $I^{n}$ for some n$\geq$0 and $\mu$$_{A}$(I)$\geq$2, where $\mu$$_{A}$(I) denotes the number of elements in a minimal system of generators of I. Assume that A/I is a Cohen-Macaulay ring. We show that the following conditions are equivalent. (1) $K_{R(I)}$(equation omitted)R(I)＋as graded R(I)-modules. (2) $I^2$ = aI and aA : I$\in$ $X^1$$_{A}$._{A}$./.

• Archives of Pharmacal Research
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• 제22권5호
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• pp.491-495
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• 1999

In order to examine the effects of N-substituted alkyl group on the anticonvulsant activities of N-Cbz-$\alpha$-aminoglutarimides as novel anticonvulsants with broad spectrum, a series of (R) or (S) N-Cbz-$\alpha$-amino-N-alkylglutarimides (1 and 2) were prepared from the corresponding (R) or (S) N-Cbz-glutamic acid and evaluated for the anticonvulsant activities in the maximal electroshock seizure (MES) test and pentylenetetrazol induced seizure(PTZ) test, including the neurotoxicity. The most potent compound in the MES test was (S) N-Cbz-$\alpha$-amino-N-methylglutarimide($ED_{50}$=36.3 mg/kg, PI=1.7). This compound was also most potent in the PTZ test ($ED_{50}$=12.5 mg/kg, PI=5.0). The order of anticonvulsant activities against the MES test as evaluated form $ED_{50}$ values for (R) series was N-methyl > N-H > N-ethyl > N-allyl ; for the (S) series N-methyl > N-H > N-ethyl > N-alkyl > N-isobutyl compound. Against the PTZ tests, the order of anticonvulsant activities showed similar pattern ; for the (R) series, N-methyl > N-H > N-ethyl > N-allyl ; for the (S) series N-methyl > N-H > N-ethyl > N-allyl > N-isobutyl compound. From the above results, N-substituted alkyl groups were though to play an important role for the anticonvulsant activities of N-Cbz-$\alpha$-amino-N-alkylgutarimides.

• 대한수학회지
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• 제53권6호
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• pp.1225-1236
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• 2016

Let R be a commutative ring with $1{\neq}0$ and n a positive integer. In this article, we introduce the n-Krull dimension of R, denoted $dim_n\;R$, which is the supremum of the lengths of chains of n-absorbing ideals of R. We study the n-Krull dimension in several classes of commutative rings. For example, the n-Krull dimension of an Artinian ring is finite for every positive integer n. In particular, if R is an Artinian ring with k maximal ideals and l(R) is the length of a composition series for R, then $dim_n\;R=l(R)-k$ for some positive integer n. It is proved that a Noetherian domain R is a Dedekind domain if and only if $dim_n\;R=n$ for every positive integer n if and only if $dim_2\;R=2$. It is shown that Krull's (Generalized) Principal Ideal Theorem does not hold in general when prime ideals are replaced by n-absorbing ideals for some n > 1.

• 환경생물
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• 제30권3호
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• pp.157-163
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• 2012

Oxidative stress has been reported to be one of causes of neuritis. This study examined antioxidative activities of methanol extracts of six amphibian species known to be medicinal animals (Rana catesbeiana, R. coreana, R. rugosa, R. dybowskii, R. nigromaculata, and Hyla japonica) and investigated their effects of inhibiting nitric oxide (NO) production and cytotoxicity on the murine macrophage RAW264.7 cells. As inflammation is closely associated with reactive oxygen species, assays on 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical scavenging activity, xanthine oxidase inhibitory activity, superoxide anion radical scavenging activity and NO scavenging activity of the extracts of the six species were performed to investigate their antioxidative activity. The results obtained were as follows; All extracts showed antioxidative activity, and the activity of R. dybowskii was the highest in comparison among those. Anti-inflammatory effects of the extracts were also examined, the five extracts except that of R. rugosa did not show cytotoxicity for RAW264.7 cells at the maximal concentration ($1,000{\mu}g\;mL^{-1}$). Selectivity index, meaning NO scavenging activity compared to cytotoxicity, showed the highest level in the extract of R. dybowskii. These results will be very useful basic data for future studies on prevention and treatment of human diseases to understand the biological roles of amphibian extracts throughout the antioxidative or anti-inflammatory pathways.

• 대한수학회논문집
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• 제39권1호
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• pp.93-104
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• 2024

Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a² ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

• Annals of Clinical Neurophysiology
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• 제5권2호
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• pp.197-201
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• 2003

Background: The aim of this study is to present the basic reference data of kinematic gait analysis of normal Korean adults with 3 dimensional electrogoniometer, $Domotion^{(R)}$. Method: The basic kinematic gait parameters of hip, knee and ankle joints on the sagittal plane were obtained from 10 healthy adults with 5 repetition for each. Three-dimensional gait analysis was performed with $Domotion^{(R)}$ electrogoniometer in 10 meters long flat floor. Each data collected was processed with IBM PC equipped with gait analysis program. Results: Mean maximal hip flexion was $23.05^{\circ}{\pm}4.62^{\circ}$and mean maximal hip extension was $6.46^{\circ}{\pm}1.30^{\circ}$. Knee flexion was observed with two peak values. The first peak knee flexion was $6.50^{\circ}{\pm}2.07^{\circ}$ at 20.4% of gait cycle and the second peak flexion was $50.34^{\circ}{\pm}2.23^{\circ}$ at 75.8% of gait cycle. Mean maximum ankle dorsiflexion was $5.57^{\circ}{\pm}1.19^{\circ}$ at 44% of gait cycle and mean maximum ankle plantar flexion was $15.51^{\circ}{\pm}1.73^{\circ}$ at 68.5% of gait cycle. Conclusion: We concluded three dimensional gait analysis with electrogoniometer $Domotion^{(R)}$ offers a valid and reliable kinematic data and the application of this tools for clinical gait evaluation will be helpful in management of pathological gait.

• 대한수학회지
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• 제46권3호
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• pp.577-588
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• 2009

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1 < p < $\infty$, the $L^p$-boundedness of such operators are obtained provided their kernels belong to the spaces $L(log+L)^{k+1}(S^{n-1})$. The results of the corresponding maximal operators are also established.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.117-125
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• 2004

Let T be an integral domain, M a nonzero maximal ideal of T, K = T/M, $\psi$: T \longrightarrow K the canonical map, D a proper subring of K, and R = $\psi^{-1}$(D) the pullback domain. Assume that for each $x \; \in T$, there is a $u \; \in T$ such that u is a unit in T and $ux \; \in R$, . In this paper, we show that R is a weakly Krull domain (resp., GWFD, AWFD, WFD) if and only if htM = 1, D is a field, and T is a weakly Krull domain (resp., GWFD, AWFD, WFD).

• 대한수학회지
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• 제42권5호
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• pp.933-948
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• 2005

Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for every submodule N of M there exists an ideal I of R such that N = 1M. Let M be a non-zero multiplication R-module. Then we prove the following: (1) there exists a bijection: N(M)$\bigcap$V(ann$\_{R}$(M))$\rightarrow$Spec$\_{R}$(M) and in particular, there exists a bijection: N(M)$\bigcap$Max(R)$\rightarrow$Max$\_{R}$(M), (2) N(M) $\bigcap$ V(ann$\_{R}$(M)) = Supp(M) $\bigcap$ V(ann$\_{R}$(M)), and (3) for every ideal I of R, The ideal $\theta$(M) = $\sum$$\_{m(Rm :R M) of R has proved useful in studying multiplication modules. We generalize this ideal to prove the following result: Let R be a commutative ring with identity, P $\in$ Spec(R), and M a non-zero R-module satisfying (1) M is a finitely generated multiplication module, (2) PM is a multiplication module, and (3) P$^{n}$M$\neq$P$^{n+1}$ for every positive integer n, then $\bigcap$$^{$\_{n=1}$(P$^{n}$ + ann$\_{R}$(M)) $\in$ V(ann$\_{R}$(M)) = Supp(M) $\subseteq$ N(M).

• Korean Journal of Mathematics
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• 제6권2호
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• pp.243-257
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• 1998

The purpose of this paper is to give some characterizations of $n$-dimensional CR-submanifolds with ($n-1$) CR-dimension immersed in a complex projective space $CP^{\frac{n+2}{2}}$, in terms of the Riemannian curvature tensor R.