• 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 earth science society
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• v.37 no.7
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• pp.389-397
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• 2016

In order to investigate the light curve difference in visual and infrared wavelength of ${\delta}$ Scuti variable Bo Lyn, observations were performed using BOAO 1.8m reflecting telescope and an infrared detector, KASINICS, with J, H, and Ks filters. Infrared light curves of total 7 nights were obtained between March and April in 2011, and those were compared to the V-filter light curve to examine the differences in period, time of maximum light, amplitude, and shape. From the periodic analysis of infrared light curve, a single frequency of $f_1=10.712cycle/day$, $P=0.09335{\pm}0.00002days$ was obtained, and there was no difference in the period along different wavelengths. In the infrared light curve, a frequency of $2f_1$ was detected. This frequency well explains the asymmetric shape of light curve, one of the characteristics of high-amplitude ${\delta}$ Scuti variables. We compared the locations of the measured infrared maxima and the predicted maxima of V-filter, finding that the times of maxima were delayed about 0.3 phase at infrared wavelengths. Amplitude ratios were adopted to be ${\Delta}J/{\Delta}V=0.328$, ${\Delta}H/{\Delta}V=0.216$, and ${\Delta}Ks/{\Delta}V=0.211$, with the range of variation being smaller at longer wavelengths. It seems that the differences in the times of maxima and amplitude occurred because the changes in brightness of a pulsating variable star are mainly caused by the change in temperature.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1996.05a
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• pp.209-216
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• 1996

The shape variation of billet was investigated by numerical method and spray forming work with variation of average substrate withdrawal velocity$\bar{V}$, withdrawal velocity change interval $\Delta$t and velocity deviation from average velocity $V_{dev}$. The shape and diameter with large$\bar{V}$, $\Delta$t, $V_{dev}$ vary seriously. When $\bar{V}$, $\Delta$t, $V_{dev}$ are smaller, the shape of billet is more simillar to that of the billet with constant withdrawal velocity. The average diameter of billet is determined by only $\bar{V}$, independent of $\Delta$t, $V_{dev}$. With $\bar{V}$, : 0.2 mm/sec $\Delta$t: 200 sec and $V_{dev}$. : 0.2mm/sec billet of constant diameter 230mm$\times$ height 1000mm were manufactured.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.153-161
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• 2015

In this work, we consider an elliptic system $$\left{\array {-{\Delta}u=au+bv+{\delta}_1u+-{\delta}_2u^-+f_1(x,u,v) && in\;{\Omega},\\-{\Delta}v=bu+cv+{\eta}_1v^+-{\eta}_2v^-+f_2(x,u,v) && in\;{\Omega},\\{\hfill{70}}u=v=0{\hfill{90}}on\;{\partial}{\Omega},}$$, where ${\Omega}{\subset}R^N$ be a bounded domain with smooth boundary. We prove that the system has at least two nontrivial solutions by applying linking theorem.

• 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.

• Journal of the Korean Chemical Society
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• v.25 no.3
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• pp.152-159
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• 1981

The rates of solvolysis for p-nitrobenzyl chloride have been measured by the electric conductivity method in aqueous ethanol from 0.0 to 0. 5 mole fraction of ethanol under various pressures up to 1200bar at 50 and $60{\circ}C$. The activation parameters, ${\Delta}V_\0^{\neq},\ {\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$ are evaluated from the rate constants. The results indicated that ${\Delta}V_\0^{\neq}$ exhibits an extremum behaviors near 0.3 mole fraction of ethanol and ${\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$ near 0.1 mole fraction of ethanol. This behaviors are discussed in terms of solvent structure variation and the pressure dependences of ${\Delta}H^{\neq},\ {\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$ are also discussed individually. The signs of the pressure dependence of ${\Delta}H^{\neq}$${\Delta}S^{\neq}$ are shown to be consistent with those required by the Maxwell relationships for classical thermodynamic systems.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.357-366
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• 2007

Let G(V, E) be a simple graph, and let f be an integer function on V with $1{\leq}f(v){\leq}d(v)$ to each vertex $v{\in}V$. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex $v{\in}V$ at least f(v) times. The f-edge cover chromatic index of G, denoted by ${\chi}'_{fc}(G)$, is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to ${\delta}_f\;or\;{\delta}_f-1,\;where\;{\delta}_f{=}^{min}_{v{\in}V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. Let G be a connected and not complete graph with ${\chi}'_{fc}(G)={\delta}_f-1$, if for each $u,\;v{\in}V\;and\;e=uv{\nin}E$, we have ${\chi}'_{fc}(G+e)>{\chi}'_{fc}(G)$, then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each $u,\;v{\in}V\;and\;e=uv{\nin}E$ there exists $w{\in}\{u,v\}\;with\;d(w)\leq{\delta}_f(f(w)+1)-2$ such that w is adjacent to at least $d(w)-{\delta}_f+1$ vertices which are all ${\delta}_f-vertex$ in G.

• Bulletin of the Korean Chemical Society
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• v.5 no.3
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• pp.112-117
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• 1984

The association constants (K) of 3,5,N-trimethyl pyridinium iodide in 95 volume percent ethanol-water mixed solvent were determined by a modified UV and conductance method at $25^{\circ},\;30{\circ},\;40{\circ}\;and\;50{\circ}C$ over the pressure range 1 to 2000 bars. The association process is enhanced with increasing pressure and decreasing temperature. From K values, we obtained the total partial molar volume change (${\Delta}V$) and some thermodynamic parameters. The electrostriction volume (${\Delta}V_{el}$) and intrinsic volume (${\Delta}V_{in}$) were also evaluated. The values of ${\Delta}V,\;{\Delta}V_{el},\;{\Delta}V_{in}$ are negative, negative and positive, respectively, and the absolute values of all these three decrease with increasing pressure and temperature. The ion-pair size (a) were varied 3 to 6 ${\AA}$, with pressure and temperature. The solvation number (n) decreased from 2 to 0.5 with increasing temperature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• Journal of Microbiology and Biotechnology
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• v.12 no.1
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• pp.149-152
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• 2002

The effect of pressure on the catalytic properties of glutamate racemase from Aquifex pyrophilus, an extremophilic bacterium, was investigated. The activation volume for the overall reaction $({\Delta}V^{\neq})$ and catalysis $({{Delta}V_{cat}}^{\neq})$ was -96.97 ml/mol and 4.97 ml/mol, respectively, while the reaction volume for the substrate binding (${\Delta}V_{K_m^-1}$) was -101.94 ml/mol. The large negative ${\Delta}V^{\neq}$ for the overall reaction indicated that the pressurization of glutamate racemase resulted in enhanced catalytic efficiencies. In addition, this value was also due to the large negative ${Delta}V_{K_m^-1}$ for the substrate binding. The negative value of ${Delta}V_{K_m^-1}$ implied that the conformational changes in the enzyme molecule occurred during the substrate binding process, thereby increasing the degree of hydration. The small value of ${{Delta}V_{cat}}^{\neq}$suggested that the pressure did not affect the glutamate racemase catalysis after the substrate binding.