• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.353-364
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• 2008

The purpose of this paper is to investigate the finite extension of weighted word L-delta groups. The paper revealed that a finite extension of a weighted word L-delta group is a weighted word L-delta group, and an abelian group, in addition, is a weighted word L-delta group and simultaneously a word L-delta group.

• Journal of Technologic Dentistry
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• v.23 no.1
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• pp.85-93
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• 2001

The purpose of this study was to evaluate the effects of commercial home-tooth bleaching agents on the color of tooth. Twenty five sound extracted teeth were randomly divided into five groups. The color differences between before and after treatment with five types of tooth bleaching agents (7.5% hydrogen peroxide Nite White $Excel^{(R)}$, 10% carbamide peroxide Nite White $Excel^{(R)}$, 16% carbamide peroxide Nite White $Excel^{(R)}$, 10% carbamide peroxide Insta-BriteTM, 20% carbamide peroxide Insta-$Brite^{TM}$) were evaluated. The results were as follows: 1. By 2 week home tooth bleaching agent applications, the values ($L^*$) of bovine teeth increased as high as 4.38 $\sim$ 8.80 when comparing to those of the samples before treatment, and the color difference (${\Delta}E^*$) showed as high as 10.16 $\sim$ 15.04. 2. 16% carbamide peroxide Nite White Excel induced significantly greater ${\Delta}L^*$ than other test edgroups except for 7.5% hydrogen peroxide Day White Excel, and significantly greater ${\Delta}E^*$ than other tested groups by 2 week bleaching agent treatments (p<0.01). 3. 16% carbamide peroxide Nite White Excel(${\Delta}L^*$=8.80, ${\Delta}E^*$=15.04) induced significantly greater ${\Delta}L^*$ and ${\Delta}E^*$ than 10% carbamide peroxide Nite White Excel(${\Delta}L^*$=5.01, ${\Delta}E^*$=10.16)(p<0.01), but significant difference between 10% carbamide peroxide Insta-Brite(${\Delta}L^*$=4.38, ${\Delta}E^*$=10.51) and 20% carbamide peroxide Insta-Brite(${\Delta}L^*$=5.63, ${\Delta}E^*$=11.23) was not shown in ${\Delta}L^*$ and ${\Delta}E^*$(p>0.01). 4. 16% carbamide peroxide Nite White Excel(${\Delta}L^*$=8.80, ${\Delta}E^*$=15.04) which were applied in night time induced significantly greater ${\Delta}L^*$ and ${\Delta}E^*$ than 7.5% hydrogen peroxide Day White Excel(${\Delta}L^*$=8.47, ${\Delta}E^*$=12.75) which were applied in day time. Conclusions: These results demonstrate that all the commercial home-tooth bleaching agents have appreciable bleaching effect on teeth, and the effects of home-tooth bleaching agents which are used during night time are affected by content of carbamide peroxide. Especially the whitening effect of home tooth bleaching agents that are used through night time is greater than that of short time-applying tooth bleaching agent.

• Membrane Journal
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• v.11 no.4
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• pp.143-151
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• 2001

We have fabricated mixed-ionic conducting membranes, L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ and L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ by the solid state method. Ceramic membranes consisted of perovskite-type structures and exhibited high relative density, >95%. Especially, dense L $a_{0.6}$S $r_{0.4}$Co $O_{3-}$$\delta$/ layer was coated on the L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes by using screen printing technique in order to improve oxygen ion flux. We measured oxygen ion flux on uncoated L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/, uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/, and coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. The L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ membranes showed the highest flux, 0.26 mL/min.$\textrm{cm}^2$ at 90$0^{\circ}C$, after steady state had been reached. The oxygen flux of coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes showed higher value, 0.19 mL/min.$\textrm{cm}^2$ at 95$0^{\circ}C$. This flux was as much as 2 or 3 times higher than those of uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. 3-$\delta$/ membranes.X> 3-$\delta$/ membranes.membranes.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.269-280
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• 2006

Recently $L_{\delta}$-groups were introduced in the study of geometric group theory. Three levels of $L_{\delta}$-groups are difined and discussed. It is shown that each of these levels of $L_{\delta}$-groups is closed under taking a direct product.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1303-1314
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• 2013

An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors. A graph G is said to be injectively $k$-choosable if any list $L(v)$ of size at least $k$ for every vertex $v$ allows an injective coloring ${\phi}(v)$ such that ${\phi}(v){\in}L(v)$ for every $v{\in}V(G)$. The least $k$ for which G is injectively $k$-choosable is the injective choosability number of G, denoted by ${\chi}^l_i(G)$. In this paper, we obtain new sufficient conditions to be ${\chi}^l_i(G)={\Delta}(G)$. Maximum average degree, mad(G), is defined by mad(G) = max{2e(H)/n(H) : H is a subgraph of G}. We prove that if mad(G) < $\frac{8k-3}{3k}$, then ${\chi}^l_i(G)={\Delta}(G)$ where $k={\Delta}(G)$ and ${\Delta}(G){\geq}6$. In addition, when ${\Delta}(G)=5$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{17}{7}$, and when ${\Delta}(G)=4$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{7}{3}$. These results generalize some of previous results in [1, 4].

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.39-57
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• 1978

It is given in the Lecture Note [1] of Berger, Gauduchon and Mazet that, if ${\pi}$n: (${\tilde{M}}$, ${\tilde{g}}$)${\rightarrow}$(${\tilde{M}}$, ${\tilde{g}}$) is a Riemannian submersion with totally geodesic fibers, ${\Delta}$ and ${\tilde{\Delta}}$ are Laplace operators on (${\tilde{M}}$, ${\tilde{g}}$) and (M, g) respectively and f is an eigenfunction of ${\Delta}$, then its lift $f^L$ is also an eigenfunction of ${\tilde{\Delta}}$ with the common eigenvalue. But such a simple relation does not hold for an eigenform of the Laplace-Beltrami operator ${\Delta}=d{\delta}+{\delta}d$. If ${\omega}$ is an eigenform of ${\Delta}$ and ${\omega}^L$ is the horizontal lift of ${\omega}$, ${\omega}^L$ is not in genera an eigenform of the Laplace-Beltrami operator ${\tilde{\Delta}}$ of (${\tilde{M}}$, ${\tilde{g}}$). The present author has obtained a set of formulas which gives the relation between ${\tilde{\Delta}}{\omega}^L$ and ${\Delta}{\omega}$ in another paper [7]. In the present paper a Sasakian submersion is treated. A Sasakian manifold (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$) considered in this paper is such a one which admits a Riemannian submersion where the base manifold is a Kaehler manifold (M, g, J) and the fibers are geodesics generated by the unit Killing vector field ${\tilde{\xi}}$. Then the submersion is called a Sasakian submersion. If ${\omega}$ is a eigenform of ${\Delta}$ on (M, g, J) and its lift ${\omega}^L$ is an eigenform of ${\tilde{\Delta}}$ on (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$), then ${\omega}$ is called an eigenform of the first kind. We define a relative eigenform of ${\tilde{\Delta}}$. If the lift ${\omega}^L$ of an eigenform ${\omega}$ of ${\Delta}$ is a relative eigenform of ${\tilde{\Delta}}$ we call ${\omega}$ an eigenform of the second kind. Such objects are studied.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.6
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• pp.59-66
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• 1995

The hot electron induced effective channel length modulation (${\Delta}L_{H}$) and HEIP characteristics in PMOSFET's after bidirectional stress are presented. Trapped electron charges in gate oxide and lateral field are calculated from the gate current model, and ${\Delta}L_{H}$(${\Delta}L_{HD},\;{\Delta}L_{HS}$) is calculated using trapped electron charges and lateral field. It has been found that ${\Delta}I_{d}$and ${\Delta}L_{H}$ are more affected by the stress order (Forward-Reverse of Reverse or Reverse-Forward) than the stress direction, and they vary logarithmically with the stress time. In contrast, ${\Delta}V_{t}$ and ${\Delta}V_{pt}$ are more affected by the stress direction thatn the stress order. The correlation between ${\Delta}V_{pt}$ and the stress time can be explanined as the following polynomial functin: ${\Delta}V_{pt}$=AT$^{n}$. It has also been shown that PMOSFET degradation is related with the gate current and the effects of ${\Delta}V_{pt}$ is the most significant.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.63-71
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• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• Journal of the Korean Chemical Society
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• v.33 no.5
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• pp.516-521
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• 1989

Reaction between the $N_2O_2-type$ tetradentate ligand, ethylenediamine-N,N'-di-S-${\alpha}$-isobutylacetic acid (SS-emiba) and $RhCl_3{\cdot}3H_2O$ has yielded ${\Delta}-s-cis-\;and\;{\wedge}-uns-cis-[Rh(SS-eniba)Cl_2]-$. ${\Delta}-s-cis-[Rh(SS-eniba)Cl_2]^-$ has been utilized to react with S-methyl-L-cystcine(Smc) to give ${\Delta}-s-cis-[Rh(SS-eniba(Smc)]^+$. The oxidation of ${\Delta}-s-cis-[Rh(SS-eniba(Smc)]^+$ using $H_2O_2$ has produced ${\Delta}-s-cis-[Rh(SS-eniba)(Smc-o)]^+$, in which the coordinated sulfur has been converted into the sulfoxide group. In a separate series of experiments the S-methyl-L-cysteine is oxidized by $H_2O_2$ to give S-methyl-L-cysteine sulfoxide, which is then coordinated to ${\Delta}-s-cis-[Rh(SS-eniba)Cl2]^-$ to make the standard complet of ${\Delta}-s-cis-[Rh(SS-eniba)(Sme-o)]+$ for comparison with the complex obtained from the oxidation of ${\Delta}-s-cis-[Rh(SS-eniba)(Smc)]^+\;by\;H_2O_2.$

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.8
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• pp.72-79
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• 1994

In this paper semi empirical models are presented for the hot electron induced threshold voltage shift(${\Delta}V_{t}$) and effective channel shortening length (${\Delta}L_{H}$) in degraded PMOSFET. Trapped electron charges in gate oxide are calculated from the well known gate current model and ΔLS1HT is calculated by using trapped electron charges. (${\Delta}L_{H}$) is a function of gate stress voltage such as threshold voltage shift and degradation of drain current. From the correlation between (${\Delta}L_{H}$) has a logarithmic function of stress time. From the measured results, (${\Delta}V_{t}$) and (${\Delta}L_{H}$) are function of initial gate current and device channel length.