• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1183-1198
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• 2013

We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.6
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• pp.1137-1148
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• 2021

The main obstacle for implementing CSIDH-based cryptography is that it requires generating a kernel of a small prime order to compute the group action using Velu's formula. As this is a quite painstaking process for small torsion points, a new approach called radical isogeny is recently proposed to compute chains of isogenies from a coefficient of an elliptic curve. This paper presents an optimized implementation of radical isogenies and analyzes its ideal use in CSIDH-based cryptography. We tailor the formula for transforming Montgomery curves and Tate normal form and further optimized the radical 2- and 3- isogeny formula and a projective version of radical 5- and 7- isogeny. For CSIDH-512, using radical isogeny of degree up to 7 is 15.3% faster than standard constant-time CSIDH. For CSIDH-4096, using only radical 2-isogeny is the optimal choice.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.729-741
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• 2019

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.601-608
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• 2012

The following statements for an infra-Krull domain $R$ are shown to be equivalent: (1) $R$ is a Krull domain; (2) for any essentially finite $w$-module $M$ over $R$, the torsion submodule $t(M)$ of $M$ is a direct summand of $M$; (3) for any essentially finite $w$-module $M$ over $R$, $t(M){\cap}pM=pt(M)$, for all maximal $w$-ideal $p$ of $R$; (4) $R$ satisfies the $w$-radical formula; (5) the $R$-module $R{\oplus}R$ satisfies the $w$-radical formula.

• Herbal Formula Science
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• v.12 no.1
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• pp.255-262
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• 2004

The inhibitory effect of the aerial parts of Fagopyrum esculentum on the 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical was examined. The n-butanol fraction from the methanol extract of title plant showed stronger inhibitory effect than other fractions on DPPH radical. Two flavonoids were isolated from n-butanol fraction having the potent activity and elucidated as quercetin-3-O-${\alpha}$-L-rhamnoside and quercetin-3-O-rutinoside on the basis of spectral evidence. The $IC_{50}$ values of these compounds on DPPH radical were 6.56 ${\mu}M$ and 8.37 ${\mu}M$, respectively.

• Herbal Formula Science
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• v.13 no.2
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• pp.93-100
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• 2005

In order to find the new hepatoprotective agents preliminary screening of twelve prescriptions which have been used for the treatment of hepatic disease in Oriental traditional medicine has been carried out. Both DPPH free radical scavenging and hepatoprotective effect on tacrine-induced cytotoxicity in Hep G2 cells are performed. Osumokkya-tang which is one of the prescription belongs to interior-warming properties showed the DPPH free radical scavenging effect as well as hepatoprotective activity significantly. It is also suggested that its hepatoprotective effect is derived from Chaenomelis Fructus.

• Herbal Formula Science
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• v.8 no.1
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• pp.241-255
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• 2000

Sihosamultang(SST) has been used for the treatment of puerperal fever, liver disease in traditional medicine. The present study was carried out to evaluate the antioxidant effects of SST extract in vitro. The inhibitory effect of SST extract on lipid peroxidant was examined in the linoleic acid autoxidation system. In this test, SST extract significantly inhibited the time course of the lipid peroxidation. And SST extract showed about 73% scavenging effect on DPPH radical. And this extract inhibited not only the lipid peroxide formation induced by hydroxyl radical derived from $ H_{2}O_{2}-Fe^{2+}$ in the rat liver homogenate, but also the superoxide generation from xanthine-xanthine oxidase system in a dose-dependent manner. In addition, SST extract protected the hepatic cell death induced by tert-butyl hydroperoxide. These data indicated that SST might play a protective role against oxidative injury by free radicals.

• Herbal Formula Science
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• v.12 no.1
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• pp.159-175
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• 2004

The inhibitory effects of 207 oriental medicines and 19 oriental prescriptions on the 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical were examined. The most effective oriental medicines were the fruit of Terminalia chebula, followed in order by the seed of Areca catechu, the heart wood of Caesalpinia sappan, the pericarp of Castanea crenata, the seed of Nelumbo nucifera, Rhus galls, the root of Sanguisorba officinalis, and the bark of Betula platyphylla at the concentration of 10 ${\mu}g$／mL. Of the 19 oriental prescriptions, Buyeonsan and Samsinhwan showed the potent scavenging activities of 88% and 71% on DPPH radical at the concentration of 5 ${\mu}g$／mL, respectively.

• Herbal Formula Science
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• v.9 no.1
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• pp.289-317
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• 2001

The purpose of this study was to reseach the effect of Daesihotang and its component groups on diabetes, free radical and antioxidative defense system in alloxan-induced diabetic rats. The experimental group was divided into three groups: Daesihotang (DS), Soyangyak (DS1), Yangmyungyak (DS2). The results were obtained as follows: The level of glucose, triglyceride, total cholesterol, creatinine in serum were considerablely reduced by Daesihotang. And the level of HDL cholesterol, albumin, total protein in serum were increased by Daesihotang significantly. And the level of BUN has some decreased, but with no significancy. In the study of Daesihotang on free radical scavenging effect in vitro, it has shown that Daesihotang and its components group have significant suppressing effect on peroxidation of linoleic acid on concentration. And in other experiments as scavenging effect of DPPH radical, inhibitory effect of superoxide in xanthine-xanthine oxidase system and inhibitory effect on lipid peroxidation reaction by hydroxy radical in $H_2O_2-Fe^{2+}$ system, Daesihatang have some activity, but with no significancy. In the study of Daesihotang on antioxidative defense system in vivo, the activity of GOT and GPT in serum were significantly increased; and the amounts of lipid peroxide in serum was reduced significantly but in liver no significancy. In hepatic catalase activity, Daesihotang has showed significant effect. In the level of hepatic glutathione, Daesihotang increased the amount of glutathione significantly. And in the activity of glutathione-s-transferase, Daesihotang has decreasing effect but has no significancy. These result suggest that Daesihotang has strong effect on diabetes and it is useful to prevent diabetes, but has less effect on peroxidative damage by free radical.

• Herbal Formula Science
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• v.10 no.2
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• pp.127-141
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• 2002

Objectives: Haeganjeon(HGJ) has been used for the treatment of liver disease in traditional medicine. The present study was carried out to evaluate the antioxidant and protective effects of HGJ extract on oxidative damage of hepatocytes by tert-butyl hydroperoxide(t-BHP). Methods: In the linoleic acid water-alcohol system, the levels of lipid peroxide(LPO) were determined by TBA method. The scavenging effect of HGJ on ${\alpha},{\alpha}-diphenyl-{\beta}-picrylhydrazyl$(DPPH) radical was determined according to the method of Hatano. In the Fenton system(ferrous ion reaction with hydrogen peroxide), the levels of hydroxyl radical induced LPO in rat liver homogenate were determined according to the method of TBA. Inhibitory effect of HGJ on superoxide generation was measured by xanthine-xanthine oxidase system. In order to evaluate antioxidative activity of HGJ in the liver cell, cultured normal rat liver cells(Ac2F) were prepared and incubated with or without HGJ. After 18hr, cells placed in DMEM medium without serum, and then incubated with 1mM tert-butyl hydroperoxide(t-BHP) for 2hrs. Viable cells were detected by MTT assay. Conclusions: In the linoleic acid autoxidation system, HGJ extract significantly inhibited the time course of the lipid peroxidation. These effects were similar to those of BHA HGJ extracts showed about 70% scavenging effect on DPPH radical. And HGJ extract inhibited the lipid peroxide formation in rat liver homogenate induced by hydroxyl radical derived from Fenton system. In addition, HGJ extract protected the cell death induced by t-BHP and significantly increased cell viability in the normal rat liver cell. These result indicated that HGJ extract might playa protective role against oxidative hepatic cell injury by means of free radical scavenger.