• 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 Chemical Society
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• v.32 no.5
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• pp.436-442
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• 1988

The $^1H-nmr$ lineshapes of $H_2O$ in the solution containing $Al^{3+}$ ion have been measured as a function of temperature and $H^+$-ion concentration. Above [$H^+$] = 0.06, the lineshape were analyzed by the uncoupled two-site exchange model. From the proton exchange rate between hexaaquaaluminium ion and bulk water as a function of H-ion concentration. These kinetic data could be fitted to a following linear rate law; that is; 1/${\tau}$ = k$_1$/12 + $k_2$[$H^+$]/6. The following proton exchange parameters were obtained; $k_1^{298}$ = 38.5s$^{-1}$ ${\{Delta}H_1^{\neq}$ = $42.9kJ mole^{-1}$ ${\{Delta}S_1^{\neq}$ = -48.6J $mole^{-1}K^{-1}$ $k_2^{298}$ = $172s^{-1}mole^{-1}$ ${\{Delta}H_2^{\neq}$ = 27.8kJ $mole^{-1}$ ${\{Delta}S_2^{\neq}$ = -90.3J $mole^{-1}K^{-1}$ These activation parameters are indicating an associative interchange, Ia, mechanism for the acid-hydrolysis of hexaaquaaluminium ion and the proton exchange between the hydration spheres of $Al^{3+}$ and $H^+$.

• Korean Journal of Animal Reproduction
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• v.15 no.1
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• pp.7-13
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• 1991

This study was carried out to investigate the effects of pH of sperm-washing solution, sperm-washing frequency and individual bull on concentration of hydrogen ion in sperm-washed solution and sperm acrosome reaction. The results obtained were as follow. 1. When bovine sperm was washed at 4 times with SHP solution and incubated, the difference of light absorbance between sperm-washing and sperm-washed solution(${\Delta}$Ao-${\Delta}$At) was higher in 2nd sperm-washed solution than that in the other washed solutions. 2. When sperm was thrice washed with SHP solutions of pH 5.99, 6.38, 6.78, 7.10, 7.40, 7.69, 8.15, 8.45, and 8.83, ${\Delta}$Ao-${\Delta}$At was significantly increased at pH7.69 to 8.83, and ${\Delta}$Ao-${\Delta}$At in 1st sperm washed solution was significantly higher than that in 2nd and 3rd sperm washed solution. 3. When sperm of Holstein, KNC and Hereford was thrice washed with SHP solutions of pH 5.99, 6.38, 6.78, 7.10, 7.40, 7.69, 8.15, 8.45, and 8.83, Holstein showed higher ${\Delta}$Ao-${\Delta}$At of sperm Washed solution than KNC and Hereford, and ${\Delta}$Ao-${\Delta}$At in sperm washed solution was significantly increased at 7.69 for Holstein and at 8.15 for KNC and Hereford, respectively. 4. When sperm was thrice with SHP solution of pH 6.8, 7.1 and 7.4, and then incubated in mTALP of pH 7.4 for 15 minutes, in 1st and 2nd sperm washing ${\Delta}$Ao-${\Delta}$At of sperm washed solution was significantly higher at pH 7.1 and 7.4 than at pH 6.8, and the sperm acrosome reaction of pH 6.8, 7.1 and 7.4 was 49.1, 68.8 and 72.9%, respectively. The sperm acrosome reaction of pH 7.1 and 7.4 was higher than that of pH 6.8.

• Journal of the Korean Applied Science and Technology
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• v.22 no.4
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• pp.323-331
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• 2005

Fatty acid compositions of the seed oils of P. schinseng, A. continentalis and A. sessiliflorus, were analyzed by gas chromatography (GC) equipped with a capillary column. A large unusual peak was observed just before the peak corresponding to oleic acid $(cis-9-C_{18:1})$. This unknown fatty acid was isolated by silver ion chromatography and then derivatized into the picolinyl ester. The mass spectrum of the picolinyl ester showed molecular ion at m/z=373 with other diagnostic ions such as m/z=178, 218, 232, 246, 274, 288, 302 and 344. Characteristic absorption peaks at $720\;cm^{-1}$, $1640\;cm^{-1}$ and $3010\;cm^{-1}$ in IR spectrum indicated the presence of cis-configurational double bond in the molecule. The $^1H-NMR$ spectrum of this acid gave two quintets centered at ${\delta}1.638$ (2H, C-3) and ${\delta}1.377$ (2H, C-4), and two multiplets centered at ${\delta}2.022{\sim}2.047$ (2H, C-5) and ${\delta}2.000{\sim}2.022$ (2H, C-8), and multiplet signals of olefinic protons centered at ${\delta}5.3015{\sim}5.3426$ (C-6, J=9.5 Hz) and ${\delta}\;5.3465{\sim}5.3877$ (C-7, J=9.5 Hz). The $^13C-NMR$ spectrum showed 18 carbon resonance signals including an overlapped signal at ${\delta}29.7002$ for C-12 and ${\delta}29.6520$ for C-13 (or they can be reversed), and other highly resolved signals at ${\delta}33.950$, ${\delta}24.558$, ${\delta}26.773$ and ${\delta}27.205$ due to C-2, C-3, C-5 and C-8 of a ${\Delta}^6-octadecenoic$ acid, respectively. From analysis results this unknown fatty acid could be identified as cis-6-octadecenoic acid. The seed oils of P. schinseng and A. sessiliflorus contained petroselinic acid (59.7%, 56.0%), oleic acid (18.3%, 6.1%) and linoleic acid (16.2%, 30.4%) with small amount of palmitic acid (3.0%, 3.1%) while the seed oil of A. continentalis comprised mainly oleic acid (30.2%), petroselinic acid (29.0%), linoleic acid (24.1%) and palmitic acid (13.1%).

• Microbiology and Biotechnology Letters
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• v.21 no.5
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• pp.393-398
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• 1993

One strain of mosquitocidal Bacillus thuringiensis, H9B, was isolated from soil. The biochemical characteristics and flagella antigenicity of the strain H9B is similar to that of B. thuringiensis subsp. darmstadiensis. The delta-endotoxin of the strain H9B coincided with that of B. thuringiensis subsp. darmstadiensis strain 73E10-2 on agarose double immunodiffusion test. The delta-endotoxin of B. thuringiensis subsp. israelensis contains hemolysin fragment (28 kb) on SDS-PAGE when the delta-endotoxin was solubilized in alkali, while that of the strain H9B does not contain 28 kb protein.

• 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.

• 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.

• Economic and Environmental Geology
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• v.27 no.3
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• pp.219-229
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• 1994

The Sangra Pb-Zn deposit is located in the Gampo area. Most Cretaceous sedimentary rocks and Paleogene felsic intrusives in the study area have experienced intense propylitization. Such propylitization and Pb-Zn mineralization in ore veins are involved with the fluid having very low oxygen isotopic composition.Sulfurisotopic equilibrium temperature during the main Pb-Zn mineralization (late stage I) is calculated as $T=275^{\circ}{\sim}295^{\circ}C$. Oxygen and sulfur fugacity in late stage I fluid is estimated as $logfO_2=-34.4{\sim}-29.1$ and $logfS_2=-12.0{\sim}-8.2$ bars. It is inferred that the sulfur isotopic composition oflate stage I fluid was very high such as ${\delta}^{34}S_{{\Sigma}S}=+22.4{\sim}+22.5$‰ and the origin of sulfur was ocean water sulfate. Oxygen and hydrogen isotopic composition of water in ore-forming fluid was gradually increased and more abundantly affected by ocean water from early to late mineralization stage as follows; (late stage I) ${\delta}^{18}O_{H2O}=-7.2{\sim}-1.1$‰, ${\delta}D_{H2O}=-87{\sim}-84$‰, (stage II) ${\delta}^{18}O_{H2O}=-2.4{\sim}-0.8$‰, ${\delta}D_{H2O}=-39{\sim}-21$‰ (stage III) ${\delta}^{18}O_{H2O}=+0.7{\sim}+12.6$‰, ${\delta}D_{H_2O}=-49{\sim}-42$‰. The pH in ore-forming fluid was about 4.7 during late stage I and is thought to have been gradually decreased from late stage I to stage II mineralization.

• Journal of the Korean Chemical Society
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• v.45 no.1
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• pp.7-13
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• 2001

The interaction of benzenesulfonate anion and its derivatives ($C_6H_5SO_3^-, p-$CH_3C_6H_4SO_3^-, and $p-C_2H_5C_6H_4SO_3^-$) with the micellar system of cationic surfactant TTAB(tetradecyltrimethylammonium bromide) was studied by UV/Vis spectrophotometric method. The solubilization constants($K_s$) of benzenesulfonate anions into the micellar phase of this surfactant have been measured with the change of temperature. The effects of additives(n-pentanol and NaBr) on the solubilization of benzenesulfonate anions by this surfactant system have been also measured. There was a great decrease on the values of $K_s$ and CMC simultaneously with these additives so that the measured values of ln$K_s$ were linear relationships with the values of lnCMC. For the thermodynamic study, various thermodynamic parameters(${\Delta}G^0_s$, ${\Delta}H^0_s$ and ${\Delta}S^0_s$) have been calculated and analyzed from the dependence of Ks values on temperature.

• Journal of the Korean Chemical Society
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• v.24 no.2
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• pp.150-154
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• 1980

Kinetic studies of the reaction of benzyl benzenesulfonate with pyridine in acetone were carried out by the electric conductivity method under 1 to 2000 bars and at 20 to $40^{\circ}C$. The rate increases with increasing pressure and temperature. The activation enthalpy $({\Delta}H^{\neq}),\;entropy\;({\Delta}S^{\neq})$ and activation volume $({\Delta}V^{\neq})$ of the reaction are obtained by the above experiment. The isokinetic relationship between $({\Delta}H^{\neq})\;and\;({\Delta}S^{\neq})$ for pressure change in the reaction was shown, and its isokinetic temperature was $342^{\circ}K$. From all of the above results it was found that this reaction precedes on the $S_N2$ reaction mechanism in which the rate of the reaction was determined by $C{\cdots}N$ bond formation at transition state.