• 대한수학회보
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• 제51권3호
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• 천문학회지
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• 제15권1호
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• pp.19-36
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• 1982

For ${\sim}240$ nearby stars their age and mass were determined and kinematic parameters determined for 362 stars, applying Woolley's three-dimensional potential. Metallicity and kinematic parameters of these stars were correlated with their age, suggesting the slow collapse ($t{\gtrsim}a$ few billion years) of the Galaxy and the initial rapid enrichment in metal abundance (${\Delta}Z{\approx}1/3Z_1$(present) for ${\sim}4{\times}10^8$ yrs). The late slow enrichment rate is given by $d(Z/Z_{\odot})/dt=5.9{\sim}7.0{\pm}3.4$ per Gyr.

• 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.

• 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.