• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.903-913
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• 2007

A ring R has weakly stable range one provided that aR+bR=R implies that there exists a $y{\in}R$ such that $a+by{\in}R$ is right or left invertible. We prove, in this paper, that every regular element in an exchange ring having weakly stable range one is the sum of an idempotent and a weak unit. This generalize the corresponding result of one-sided unit-regular ring. Extensions of power comparability and power cancellation are also studied.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.411-422
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• 2002

In this note we are concerned with relationships between one-sided ideals and two-sided ideals, and study the properties of polynomial rings whose maximal one-sided ideals are two-sided, in the viewpoint of the Nullstellensatz on noncommutative rings. Let R be a ring and R[x] be the polynomial ring over R with x the indeterminate. We show that eRe is right quasi-duo for $0{\neq}e^2=e{\in}R$ if R is right quasi-duo; R/J(R) is commutative with J(R) the Jacobson radical of R if R[$\chi$] is right quasi-duo, from which we may characterize polynomial rings whose maximal one-sided ideals are two-sided; if R[x] is right quasi-duo then the Jacobson radical of R[x] is N(R)[x] and so the $K\ddot{o}the's$ conjecture (i.e., the upper nilradical contains every nil left ideal) holds, where N(R) is the set of all nilpotent elements in R. Next we prove that if the polynomial rins R[x], over a reduced ring R with $\mid$X$\mid$ $\geq$ 2, is right quasi-duo, then R is commutative. Several counterexamples are included for the situations that occur naturally in the process of this note.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.653-661
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• 2010

Let R be a ring, and let $\Psi$(R) be the ideal generated by the set {x $\in$R | 1 + sxt $\in$ R is unit-regular for all s, t $\in$ R}. We show that $\Psi$(R) has "radical-like" property. It is proven that $\Psi$(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.

• Journal of Chest Surgery
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• v.14 no.3
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• pp.235-240
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• 1981

A total of 102 patients who had an Open Heart Surgery from April 1976 to July 1981 were reviewed. 55 paeitnts were congenital heart disease and 47 patients were acquired heart disease. Among SS patients of congenital heart disease, 18 T 0 F, 18 V S D, 8 A S D, and each one case of l\ulcorner 0 R V, Truncus arteriosus, Ebstein anomaly, Single ventricle, P D A, P 5, A S D + P 5, E C D, V 5 D + P D A, A - P window, D C R V were noted respectively. In 47 patients of acquired heart disease and one Ebstein patient, 46 prosthetic values were implanted: 17 had M V R, 4 had A V R, 2 had M V R + A V R, and 4 had M V R + T V R and one T V R. The operative mortality was 8.S% in acquired heart disease and 17% in congenital heart disease. The follow up period was between 6 months and 6 years. There were 3 cases of late mortality in acquired heart disease and one case in congenital heart disease.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.87-90
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• 2000

Let R be an integral domain with identity. We show that each associated prime ideal of a principal ideal in R[X] has height one if and only if each associated prime ideal of a principal ideal in R has height one and R is an S-domain.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.471-481
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• 2013

The current VaR Model based on J. P. Morgan's RiskMetrics has problem that actual loss exceeds VaR under unstable economic conditions because the current VaR Model can't re ect future economic conditions. In general, any corporation's stock price is determined by the rm's idiosyncratic factor as well as the common systematic factor that in uences all stocks in the portfolio. In this study, we propose an One-factor VaR Model for stock portfolio which is decomposed into the common systematic factor and the rm's idiosyncratic factor. We expect that the actual loss will not exceed VaR when the One-factor Model is implemented because the common systematic factor considering the future economic conditions is estimated. Also, we can allocate the stock portfolio to minimize the loss.

• Microbiology and Biotechnology Letters
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• v.22 no.4
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• pp.340-346
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• 1994

Six bacterial strains capable to grow on medium containing cholesterol as sole carbon source were isolated from soil, pork fat and cheese. Three of them were tentatively identified as Rhodococcus species, Rhodococcus sp. CD-1, R. sp. CD-2, and R. sp. CD-3. All the isolates showed a varying amount of cholest-4-en-3-one as the degradation product, and three strains of Rhodococcus spp. showed rapid degradation of cholesterol. Radioisotopic studies revealed that cholesterol was degraded to non-sterol hydrophilic compounds via cholest-4-en-3-one, and presumably to C0$_{2}$- These strains showed two distinct patterns in further degradation of cholest-4-en-3-one. By one group, R. sp. CD-1 and R. sp. CD-3, cholest-4-en-3-one was rapidly converted to non-sterol inter- mediates without significant accumulation of sterol derivatives in the culture broth. In contrast, by another group, R. sp. CD-2, the substantial amount of cholest-4-en-3-one was accumulated indica- ting a lower conversion of the compound to the next metabolites.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.289-298
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• 2017

Let R denote a commutative Noetherian (not necessarily local) ring and let I be an ideal of R of dimension one. The main purpose of this note is to show that the category ${\mathfrak{M}}(R,\;I)_{com}$ of I-cominimax R-modules forms an Abelian subcategory of the category of all R-modules. This assertion is a generalization of the main result of Melkersson in [15]. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category ${\mathcal{C}}^1_B(R)$ of all R-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all R-modules.

• Molecules and Cells
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• v.27 no.2
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• pp.205-209
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• 2009

The loci of the 5S and 45S rRNA genes were localized on chromosomes in five species of Capsicum, namely, annuum, chacoense, frutescens, baccatum, and chinense by FISH. The 5S rDNA was localized to the distal region of one chromosome in all species observed. The number of 45S rDNA loci varied among species; one in annuum, two in chacoense and frutescens, and chinense, and four in baccatum, with the exceptions that 'CM334' of annuum had three loci and 'tabasco' of frutescens gad one locus. 'CM334'-derived BAC clones, 384B09 and 365P05, were screened with 5S rDNA as a probe, and BACs 278M03 and 262A23 were screened with 25S rDNA as a probe. Both ends of these BAC clones were sequenced. FISH with these BAC probes on pachytenes from 'CM334' plant showed one 5S rDNA locus and three 45S rDNA loci, consistent with the patterns on the somatic chromosomes. The 5S rDNA probe was also applied on extended DNA fibers to reveal that its coverage measured as long as 0.439 Mb in the pepper genome. FISH techniques applied on somatic and meiotic chromosomes and fibers have been established for chili to provide valuable information about the copy number variation of 45S rDNA and the actual physical size of the 5S rDNA in chili.

• YAKHAK HOEJI
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• v.51 no.1
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• pp.56-62
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• 2007

Twelve epoxy and hydroxydiosgenin derivatives (DI-1${\sim}$DI-12) were synthesized from diosgenin (25(R)-5-spirosten-3${\beta}$-ol). Diosgenin was epoxidized with m-chloroperoxybenzoic acid (mCPBA) to oxidize 25(R)-4${\alpha}$,5${\alpha}$-epoxyspirostane (DI-1). Diosgenin was reacted with DDQ to form 25(R)-1,4,6-spirostatrien-3-one (DI-2), which was treated with 30% H$_2$O$_2$ to give 25(R)-1${\alpha}$,2${\alpha}$-epoxy-4,6-spirostadien-3-one (DI-3) and treated with mCPBA to form 25(R)-6${\alpha}$,7${\alpha}$-epoxy-1,4-spirostadien-3-one (DI-7), respectively. DI-3 was reduced with NaBH$_4$ to afford 25(R) -1${\alpha}$,2 ${\alpha}$-epoxy-4,6-spirostadien-3${\beta}$-ol(DI-4) and reacted with Li metal in absolute ethanol to form 25(R)-2-ethoxy-1,4,6-spirostatrien-3-one (DI-5). DI-7 was reduced with NaBH$_4$ to produce 25(R)-3${\beta}$,7${\alpha}$-dihydroxy-4-spirostene (DI-8) and treated with Li metal in liquid ammonia to produce 25(R)-7${\alpha}$-hydroxy-4-spirosten-3-one (DI-9). DI-2 was reduced with NaBH$_4$ to form 25(R) -4,6-spirestadien-3${\beta}$-ol(DI-10), which was stirred with 30% H$_2$O$_2$ to synthesize 25(R)-4,6-spirostadien-3-one (DI-11) and reacted with mCPBA to give 25(R)-4${\beta}$,5${\beta}$ -epoxy-6-spirosten-3${\beta}$-ol (DI-12), respectively. The antinociceptive effects of synthesiz ed compounds were measured by hot plate method and compound DI-7 signifcantly exhibited antinociceptive effect. DI-2 decreased the serum triglyceride and total cholesterol levels in poloxamer P-407 injected rat.