• 한국결정성장학회지
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• 제22권1호
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• pp.29-35
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• 2012

Special attention in the role of convection in vapor crystal growth has been paid since some single crystals under high gravity acceleration of $10g_0$ appear considerably larger than those under normal gravity acceleration ($1g_0$). With increasing the gravity acceleration from $1g_0$ up to $10g_0$, the total molar flux for ${\Delta}T$ = 30 K increases by a factor of 4, while for ${\Delta}T$ = 90, by a factor of 3. The maximum molar fluxes for three different gravity levels of $1g_0$, $4g_0$ and $10g_0$, appear approximately in the neighborhood of y = 0.5 cm, and the molar fluxes show asymmetrical patterns, which indicate the occurrence of either one single or more than one convective cell. As the gravitational level is enhanced form $1g_0$ up to $10g_0$, the intensity of convection is increased significantly through the maximum molar fluxes for ${\Delta}T$ = 30 K and 90 K. At $10g_0$, the maximum total molar flux is nearly invariant for for ${\Delta}T$ = 30 K and 90 K. The total molar flux increases with increasing the gravity acceleration, for $1g_0{\leq}g_y{\leq}10g_0$, and decreases with increasing the partial pressure of component B, a noble gas called as Kr (Krypton), $P_B$. The ${{\mid}U{\mid}}_{max}$ is directly proportional to the gravity acceleration for 20 Torr $P_B{\leq}300$ Torr. As the partial pressure of $P_B$ (Torr) decreases from 300 Torr to 20 Torr, the slopes of the ${{\mid}U{\mid}}_{max}s$ versus the gravity accelerations increase from 0.29 sec to 0.54 sec, i.e. by a factor of 2. The total molar flux of $Hg_2Cl_2$ is first order exponentially decayed with increasing the partial pressure of component B, $P_B$ (Torr) from 20 Torr up to 300 Torr.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.669-676
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• 2013

Let $a$ and $b$ be two even integers with $2{\leq}a<b$, and let k be a nonnegative integer. Let G be a graph of order $n$ with $n{\geq}\frac{(a+b-1)(a+b-2)+bk-2}{b}$. A graph G is called an ($a,b,k$)-critical graph if after deleting any $k$ vertices of G the remaining graph of G has an [$a,b$]-factor. In this paper, it is proved that G is an ($a,b,k$)-critical graph if $${\mid}N_G(X){\mid}&gt;\frac{(a-1)n+{\mid}X{\mid}+bk-2}{a+b-1}$$ for every non-empty independent subset X of V (G), and $${\delta}(G)>\frac{(a-1)n+a+b+bk-3}{a+b-1}$$. Furthermore, it is shown that the result in this paper is best possible in some sense.

• 한국결정성장학회지
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• 제19권3호
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• pp.107-115
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• 2009

Particular interest in the role of convection in vapor crystal growth has arisen since some single crystals under high gravity acceleration of $10g_0$ appear considerably larger than those under normal gravity acceleration ($1g_0$). For both ${\Delta}T=60\;K$ and 90 K, the mass flux increases by a factor of 3 with increasing the gravity acceleration from $1g_0$ up to $10g_0$. On the other hand, for ${\Delta}T=30\;K$, the flux is increased by a factor of 1.36 for the range of $1g_0{\leq}g{\leq}10g_0$. The maximum growth rates for $1g_0$, $4g_0$, $10g_0$ appear approximately in the neighborhood of y = 0.5, and the growth rates shows asymmetrical patterns, which indicate the occurrence of either one single or more than one convective cell. The maximum growth rate for $10g_0$ is nearly greater than that for $1g_0$ by a factor of 2.0 at $P_B=20\;Torr$. For three different gravity levels of $1g_0$, $4g_0$ and $10g_0$, the maximum growth rates are greater than the minimum rates by a factor of nearly 3.0, based on $P_B=20\;Torr$. The mass flux increases with increasing the gravity acceleration, for $1g_0{\leq}g_y{\leq}10g_0$, and decreases with increasing the partial pressure of component B, xenon (Xe), $P_B$. The $|U|_{max}$ is directly proportional to the gravity acceleration for $20\;Torr{\leq}P_B{\leq}300\;Torr$. As the partial pressure of $P_B$ (Torr) decreases from 300 Torr to 20 Torr, the slopes of the $|U|_{max}s$ versus the gravity accelerations increase from 0.1 sec to 0.17 sec. The mass flux of $Hg_2Cl_2$ is exponentially decayed with increasing the partial pressure of component B, $P_B$ (Torr) from 20 Torr up to 300 Torr.