• Journal of the Korean Chemical Society
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• v.43 no.4
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• pp.447-455
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• 1999

Allyl (5R)-(Z)- and (5R)-(E)-6-[(2S)-2,3-isopropylidenedioxypropylidene]Penicillanate(10a and 10b) were prepared from allyl (5R)-dibromopenicillanate(6) via a sequence of reactions involving condensation with 2,3-O-isopropylidene-D-glyceraldehyde, reduction with $Zn-NH_4OAc$, and Mitsunobu elimination. Deprotection of isopropylidene and allyl groups of 10a gave potassium (5R)-(Z)-6-[(2S)-2,3-dihydroxypropylidene]penicillanate(4). However, deprotection of isopropylidene group of 10b afforded ${\alpha},\;{\beta}$-unsaturated-lactone(12). Allyl (5R)-(Z)- and (5R)-(E)-6-[(2S)-2-(t-butyldimethlsilyloxy)propylidene]penicillanate(18a and 18b) were prepared from ally (5R)-dibromopenicillanate(6) via a sequence of reactions involving condensation with (2S)-2-(t-butyldimethylsilyloxy)propanal(15), reduction with $Zn-NH_4OAc$ and Mitsunobu elimination or mesylation-elimination. Deprotection of t-butyldimethylsilyl and allyl groups of 18a and 18b gave potassium (5R)-(Z)- and (5R)-(E)-6-[(2S)-2-hydroxypropylidene]penicillanate(5a and 5b), respectively.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.599-605
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• 2009

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that $u^sH(u)u^t$ = 0 for all u $\in$ L, where s $\geq$ 0, t $\geq$ 0 are fixed integers. Then H(x) = 0 for all x $\in$ R unless char R = 2 and R satisfies $S_4$, the standard identity in four variables.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.542-545
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• 1987

THE ELECTRICAL CHARACTERISTICS Of RAPID THERMAL OXIDES AND NITRIDED OXIDES HAVE BEEN INVESTIGATED. R.T.OXIDE FILMS HAVE BEEN PREPARED BY ONLY R.T. OXIDATION OR R.T.OXIDATION AND SUBSEQUENT R.T.ANNEAL. NITRIDED OXIDE FILMS HAVE BEEN PREPARED BY R.T.OXIDATION AND SUBSEQUENT R.T.NITRIDATION.AND CONVENTIONAL OXIDES ALSO HAVE BEEN PREPARED TO COMPARE WITH R.T.P OXIDES. R.T.ANNEALED OXIDES SHOW EXCELLENT BREAKDOWN FIELD. LEAKAGE CURRENT AND TDDB CHARACTERISTICS. ALSO, CAPACITANCE Of R.T NITRIDED OXIDES ARE SUPERIOR BY 10% TO CONVENTIONAL OXIDES, BUT TDDB CHARACTERISTIC ARE POORER THAN OXIDE FILMS.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.1-10
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• 2011

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.177-184
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• 2012

In this paper, we study the four different types of relations, $\mathcal{P}(X,T)$, $\mathcal{R}(X,T)$, $\mathcal{L}(X,T)$, and $\mathcal{S}(X,T)$ in a transformation (X,T), and obtain some of their properties. In particular, we give a relationship between $\mathcal{R}(X,T)$ and $\mathcal{S}(X,T)$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1127-1133
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• 2014

Let S be a nonempty subset of a ring R. A map $f:R{\rightarrow}R$ is called strong commutativity preserving on S if [f(x), f(y)] = [x, y] for all $x,y{\in}S$, where the symbol [x, y] denotes xy - yx. Bell and Daif proved that if a derivation D of a semiprime ring R is strong commutativity preserving on a nonzero right ideal ${\rho}$ of R, then ${\rho}{\subseteq}Z$, the center of R. Also they proved that if an endomorphism T of a semiprime ring R is strong commutativity preserving on a nonzero two-sided ideal I of R and not identity on the ideal $I{\cup}T^{-1}(I)$, then R contains a nonzero central ideal. This short note shows that the conclusions of Bell and Daif are also true without the additivity of the derivation D and the endomorphism T.

• Korean Chemical Engineering Research
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• v.60 no.1
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• pp.100-115
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• 2022

In this study, integrated hybrid system (IHS) composed of two alternatively-operating UV/photocatalytic reactor (AOPR) process and biofilter processes of a biofilter system having two units (i.e., R_up and R_dn) with an improved design (R reactor) and a conventional biofilter (L reactor) was constructed, and its transient behavior was observed to perform the successful treatment of waste air containing ethanol and hydrogen sulfide (H₂S). At the IHS-operating stages of HA1, HA2 and HA3T of reversed feed direction, the AOPR process showed not only ethanol-removal efficiencies of 55, 50 and 45%, respectively, but also H₂S-removal efficiencies of 70, 60 and 37%, respectively. In particular, a drastic decrease of H₂S-removal efficiency at the stage of HA3T was observed due to a doubling of H₂S-inlet concentration fed to AOPR from 10 ppmv to 20 ppmv at the stage of HA3T. The order of ethanol-breakthroughs and the order of the magnitude of ethanol-removal efficiencies at the sampling ports of each unit of R reactor at the stages of HA1, HB1, HA2, HB2, and the first half of HA3T, were reversed, respectively, at the stages of the second half of HA3T and HB3T. In case of H₂S, R reactor did not show H₂S-breakthrough as prominent as the ethanol-breakthrough, but showed the trend similar to the ethanol-breakthrough.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.11-16
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• 2006

In this article we show that if R is a Noetherian ring with the global dimension at most one, then every S-torsion free R-module T has a divisible envelope of the form $T{\hookrightarrow}S^{-1}T$

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.487-494
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• 2021

In this paper, we study rings with Noetherian spectrum, rings with locally Noetherian spectrum and rings with t-locally Noetherian spectrum in terms of the polynomial ring, the Serre's conjecture ring, the Nagata ring and the t-Nagata ring. In fact, we show that a commutative ring R with identity has Noetherian spectrum if and only if the Serre's conjecture ring R[X]_U has Noetherian spectrum, if and only if the Nagata ring R[X]_N has Noetherian spectrum. We also prove that an integral domain D has locally Noetherian spectrum if and only if the Nagata ring D[X]_N has locally Noetherian spectrum. Finally, we show that an integral domain D has t-locally Noetherian spectrum if and only if the polynomial ring D[X] has t-locally Noetherian spectrum, if and only if the t-Nagata ring $D[X]_{N_v}$ has (t-)locally Noetherian spectrum.