• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.312-315
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• 2008

In this paper, we investigate some characterizations for fuzzy weakly (r, s)-continuous mapping on an intuitionistic fuzzy topological space in ${\check{S}}ostak's$ sense.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.401-408
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• 2019

A ring R is called right (resp., left) nilpotent-duo if N(R)a ⊆ aN(R) (resp., aN(R) ⊆ N(R)a) for every a ∈ R, where N(R) is the set of all nilpotents in R. In this article we provide other proofs of known results and other computations for known examples in relation with right nilpotent-duo property. Furthermore we show that the left nilpotent-duo property does not go up to a kind of matrix ring.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.305-312
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• 2011

In this paper, we denote that R is a near-ring and G an R-group. We initiate the study of the substructures of R and G. Next, we investigate some properties of R-groups, d.g. near-rings and monogenic (R, S)-groups.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.769-772
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• 2022

Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number r₀ such that for r ≥ r₀, every group G of order p^rm has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number r₀ in the case where every group of order p^rm is solvable for all r, and we obtain the value of r₀ for a case where m is a product of two primes.

• Journal of the Korean Chemical Society
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• v.44 no.1
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• pp.30-36
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• 2000

Upon Pd(0)-catalyzed coupling reaction of (2R)-2-(N,N-ditosylimido)-3-butenyl methyl malonate (4) which was selected for the total synthesis of A-factor, (3R)-2-(6-methylheptanoyl)-3-hydroxy methyl-4-buttinolide (1), an unexpected 14-membered cyclic compound, bis(2-methoxycabonyl-(4E)-hexenolide) (15) was obtained. The structure of this compound was conformed by X-ray crystallography. This result implies that this method can be applied the synthesis of various size of symmetrical macrocyclic compounds.

• Bulletin of the Korean Chemical Society
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• v.34 no.5
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• pp.1371-1377
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• 2013

A new synthetic route to N-Cbz-cis-(3R,4R)-3-methylamino-4-methylpiperidine, key intermediate for CP-690,550, was disclosed with L-malic acid as the chiral pool starting material. The title compound was obtained in 16 steps with a total yield of 26% and more than 98% ee.

• Bulletin of the Korean Chemical Society
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• v.8 no.1
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• pp.15-19
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• 1987

Preparation of optically pure (3R, 4R)-4-acetoxy-3-[(1R)-1-hydroxyethyl]azetidin-2-o ne derivatives, which can be employed as starting materials for synthesis of carbapenem and penem antibiotics, was established in high efficiency from 6-amino-penicillanic acid (6-APA). 6-APA was diazotized and brominated to give 6, 6-dibromopenicillanic acid and its methyl ester was metalated with methylmagnesium bromide and condensed with acetaldehyde. The product, methyl 6-bromo-6-(1-hydroxyethyl)penicillanate was reduced with Zn-$NH_4Cl-NH_4OH$-acetone efficiently to give methyl 6-(l-hydroxyethyl)-penicillanate, which was protected either with ${\beta},{\beta},{\beta}$ -trichloroethoxycarbonyl group or with t-butyldimethylsilyl group. The thiazolidine rings of these compounds were cleaved by treatment of mercury(II) acetate in acetic acid and permangante in acetone in sequence to afford the desired optically pure final products.

• Bulletin of the Korean Chemical Society
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• v.18 no.2
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• pp.193-197
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• 1997

Theoretical studies on the base-catalyzed deprotonation of 4-phenacylpyridinium cations, R1-CO-CH2-C5H4N-R2, I (R1=YC6H4 -and R2=CH3), and II (R1=C6H5 and R2=CH2C6H4Y) have been carried out with bases, NH3 and XC6H4NH2 using AM1 MO method. The Brψnsted α values are 0.20 and 0.22 and the βB values are 0.62 and 0.61, respectively for cations I and II. The negative Ⅰ (=α-βB) values obtained are in accord with the experimental results in aqueous solution, although the theoretical gas-phase α values for I are somewhat smaller than the experimental values in water due to neglect of solvation effect. It has been stressed that the Brψnsted α is distorted not only by the lag in the resonance and solvation development in the carbanion, but also by the difference in the distance between the anionic center and substituents in the TS and in the product anion.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.281-284
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• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• Proceedings of the Korean Magnestics Society Conference
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• 2008.12a
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• pp.4.2-4.2
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• 2008