• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.321-327
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• 2007

We say that a triangle ${\Delta}$ tiles the polygon ${\rho}\;if\;{\rho}$ can be decomposed into finitely many non-overlapping triangles similar to ${\Delta}$. Let ${\rho}$ be a parallelogram with angles ${\delta}\;and\;{\pi}-{\delta}\;(0<{\delta}{\leq}{\pi}/2)$ and let ${\Delta}$ be a triangle with angles ${\alpha};{\beta},\;{\gamma}\;({\alpha}{\leq}{\beta}{\leq}{\gamma})$. We prove that if ${\Delta}$ tiles ${\rho}$ then either ${\delta}{\in}\;({\alpha},\;{\beta},\;{\gamma},\;{\pi}-{\gamma},\;{\pi}-2{\gamma})\;or\;dimL_{\rho}=dimL_{{\Delta}}$. We also prove that for every parallelogram P, and for every integer n $(where\;n{\geq}2,\;n{\neq}3)$ there is a triangle ${\Delta}$ so that n similar copies of ${\Delta}\;tile\;{\rho}$.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.357-368
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• 2012

We introduce the concepts of fuzzy ${\delta}$-interior and show that the set of all fuzzy ${\delta}$-open sets is also a fuzzy topology, which is called the fuzzy ${\delta}$-topology. We obtain equivalent forms of fuzzy ${\delta}$-continuity. More-over, the notions of fuzzy ${\delta}$-compactness and fuzzy locally ${\delta}$-compactness are defined and their basic properties under fuzzy ${\delta}$-continuous mappings are investigated.

• Bulletin of the Korean Chemical Society
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• v.16 no.1
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• pp.53-58
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• 1995

Heats of solution of aniline (AN), benzylamine (BA), ethyl-(EBS) and 2-phenylethyl benzenesulfonates (PEB) are calorimetrically measured in acetonitrile-methanol mixtures at 25.0 $^{\circ}C$. The activation parameters, ${\Delta}H^{\neq}$, ${\Delta}S^{\neq}$ and ${\Delta}G^{\neq}$, are determined for the reactions of EBS and PEB with AN and BA using the kinetic data at three temperatures. Calorimetric transfer enthalpies of initial state, ${\delta}H_t^{0{\rightarrow}x})$(IS), and kinetically derived activation enthalpies, ${\delta}\;{\Delta}H^{\neq}$, in the MeCN-MeOH mixtures are combined to determine the transfer enthalpies of transition state, ${\delta}H_t^{0{\rightarrow}x})$(TS); ${\delta}H_t^{0{\rightarrow}x})$(IS) = ${\delta}{\Delta}H^{\neq}\;+\;{\delta}H_t^{0{\rightarrow}x}$(IS) The preferential solvation of anionic charge in the TS predicts a loose TS with a greater degree of bond cleavage for the reactions of PEB than for EBS, and also for the reactions with BA compared to the reactions with AN.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.205-215
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• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.735-742
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• 2010

In this paper, we define and study the concept of $\wedge^s_{\delta}$-closure operator and the associated topology $\tau^{\wedge}^s_{\delta}$ on a topological space (X, $\tau$) in terms of g.$\wedge^s_{\delta}$-sets.

• East Asian mathematical journal
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• v.23 no.2
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• pp.159-174
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• 2007

In this paper, the concepts of pairwise fuzzy $G_{\delta}$-connected spaces and pairwise fuzzy $G_{\delta}$-extremally disconnected spaces are introduced. The concept of pairwise fuzzy $G_{\delta}$-basically disconnected spaces is defined. Characterizations of the above spaces are given besides giving several examples. Interrelations among the spaces introduced are discussed and some relevant counter examples are given.

• Journal of the Korean Professional Engineers Association
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• v.41 no.2
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• pp.40-44
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• 2008

The construction of korea grand canal supplys nation as below:$\Delta$ return to clean and clear river $\Delta$ offer urbanite space for re-charging $\Delta$ offer local resident tourist attractions $\Delta$ alternative for global warming $\Delta$ economic project for development and growth $\Delta$ awake sleeping inland city $\Delta$ strengthen business competitiveness $\Delta$ reduction of logistic cost

• Journal of the Korean Chemical Society
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• v.42 no.2
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• pp.150-155
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• 1998

Kinetic studies on the reaction of isoquinoline with para-substituted benzylbromides were conducted under various pressures (1 ~1000 bar) in acetonitrile. From the rate constants obtained, the activation parameters such as$\DeltaV^{\neq}, \Delta\beta^{\neq}, \DeltaH^{\neq}, \DeltaS^{\neq}, \DeltaG^{\neq}$ and Ea were evaluated. Reaction rate increasing the pressure and temperature. The activation compressibility coefficient and the activation entropy showed negative values. From the substituent effect and the results, it was found that the reaction proceeds through $S_N2$ mechanism, but the structure of transition state was slightly changed with substituents and pressure.

• Microbiology and Biotechnology Letters
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• v.17 no.4
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• pp.273-276
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• 1989

The isolate SPO 3, an oligosporogenous and crystalliferous mutant, which was isolated from Bacillus thuringiensig subsp, israelensis by heat treatment at 42$^{\circ}C$ for 24 hit. The $\delta$-endotoxin of the mutant had a relatively low hemolytic activity on human red blood cells; the $\delta$-endotoxin of the mutant had 25 times less hemolytic activity compared to that of wild strain. The loss of 28 KDa hemolytic protein subunit in $\delta$-endotoxin of the mutant was confirmed by means of double immunodiffusiori, immunoelectrophoresis, and SDS-PAGE.

• Journal of the Korean Chemical Society
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• v.36 no.4
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• pp.517-522
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• 1992

The reaction of ${\beta}$-picoline with substituted benzoyl chlorides has been studied by means of conductometry under various pressures in acetonitrile. From the values of pseudo-first order and second order rate constants, the activation parameters (${\Delta}V{\neq}$, ${\Delta}{\beta}{\neq}$, ${\Delta}H{\neq}$, ${\Delta}S{\neq}$ and ${\Delta}G{\neq}$) and the pressure dependence of Hammett ${\rho}$ value were studied. The activation volume, the activation compressibility coefficient and the activation entropy were all negative. By increasing pressure the rate constant and Hammett ${\rho}$ value were increased, and the reaction mechanism was proceed in bond formation favored.