• Bulletin of the Korean Chemical Society
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• 제20권5호
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• pp.531-534
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• 1999

Irradiation (300 nm UV light) of dibenzoylmethane and 1,4-naphthoquinone in dichloromethane gave 1,5-dike-tone as the major product, along with β-hydroxyketone as the minor product. Anthraquinone and anthrone also added photochemically to dibenzoylmethane to give 1,5-diketones as the major products. In contrast, tetrahalo-1,4-benzoquinones added to dibenzoylmethane to give two types of 1,5-diketones via oxetane and cyclobutane intermediates. Comparison of the potential energy values of the photoproducts reveals that the 1,5-diketones are more stable than the corresponding oxetanes or cyclobutanes due to the ring-strain of the bicyclic compounds.

• 약학회지
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• 제28권1호
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• pp.1-10
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• 1984

A total synthesis of dehydrojuvabione which has high juvenile hormone activity, is described. The kinetic enloate of mesityl oxide is used as nucleophilic synthon for this synthesis. 1,4-Dioxaspiro [4,5] decan-8-carboxaldehyde was treated with kinetic enolate of mesityl oxide to give 8-(1'-hydroxy-5'-methyl-3'-oxo-4'-hexenyl)-1,4-dioxaspiro [4,5] decane. The latter compound was dehydrated. The resulted dienone was treated with lithium dimethylcuprate. After that, appropriate transformation was performed to give dehydrojuvabione.

• 약학회지
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• 제44권2호
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• pp.128-134
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• 2000

The synthesis of new 6-exomethylene penams with triazole ring was described. The 6,6-dibromopenam 5 was treated with $CH_3$MgBr and carbaldehyde 4 to afford the 6-bromo-6-(1-hydroxy-1-methyl)penicillanate 6, which was reacted with acetic anhydride to give acetoxy compound 7. The deacetobromination of 7 with zinc and acetic acid gave 6-exomethylenpenams, Z-isomer 8 and E-isomer 9, which were oxidized to sulfones 10 and 11 by m-CPBA. The p-methoxybenzyl compounds 6~11 were deprotected by AlCl$_3$ and neutralized to give the sodium salts 12~17.

• 약학회지
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• 제48권5호
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• pp.303-308
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• 2004

The synthesis of new 6-triazole exomethylenepenams was described. The 6,6-dibromopenam 5 was reacted with $CH_3$MgBr and substituted triazole 4 to afford the 6-bromo penicillanate 6, which was treated with acetic anhydride to give acetoxy compound 7. The deacetobromination of acetoxy compound 7 with zinc and acetic acid gave 6-exomethylene penams 8 and 9, which were oxidized to sulfones 10 and 11 by m-CPBA. The p-methoxybenzyl compounds 6-11 were deprotected by AlCl$_3$ and neutralized to give the sodium salts 12-17.

• 대한수학회지
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• 제58권6호
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• pp.1421-1431
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• 2021

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C⁰-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

• 대한수학회논문집
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• 제36권3호
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• pp.413-422
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• 2021

The Study determinant is known as one of replacements for the determinant of matrices with entries in a noncommutative ring. In this paper, we give a generalization of the Study determinant and show its relationship with the Cayley-Dickson process. We also give some properties of a non-associative ring obtained by the Cayley-Dickson process with a not necessarily commutative, but associative ring as the initial ring.

• 대한수학회보
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• 제56권2호
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• pp.333-349
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• 2019

We give explicitly an average value formula under the multiplication-by-2 map for the x-coordinates of the 2-division points D on the Jacobian variety J(C) of a hyperelliptic curve C with genus g if $2D{\equiv}2P-2{\infty}$ (mod Pic(C)) for $P=(x_P,y_P){\in}C$ with $y_P{\neq}0$. Moreover, if g = 2, we give a more explicit formula for D such that $2D{\equiv}P-{\infty}$ (mod Pic(C)).

• Korean Journal of Mathematics
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• 제26권4호
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• pp.601-614
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• 2018

We consider the magnetic $Schr{\ddot{o}}dinger$ operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.

• 호남수학학술지
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• 제41권1호
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• pp.175-183
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• 2019

In this paper, it is investigated Lorentz force equations for $N_1$ and $N_2$-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in ${\mathbb{E}}^3$. Then, we obtain a new characterization for a magnetic field V. Also, we also give examples for each curve.

• 호남수학학술지
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• 제41권2호
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• pp.329-342
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• 2019

In this paper, we give a geometric approach to Killing magnetic flux surfaces in Euclidean 3-space and solve the differential equations which expressed the mentioned surfaces. Furthermore we give some examples and draw their pictures by using the programme Mathematica.