• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1315-1322
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• 2010

Let D be a plane domain whose boundary consists of n components and $C_1$, $C_2$ two boundary components of D. We consider the family $F_1$ of conformal mappings f satisfying f(D) $\subset$ {1 < |w| < ${\mu}(f)$}, $f(C_1)=\{|w|=1\}$, $f(C_2)=\{|w|={\mu}(f)\}$. There are conformal mappings $g_0$, $g_1({\in}F_1)$ onto a radial and a circular slit annulus respectively. We obtain the following theorem, $$\{{\mu}(f)|f\;{\in}\;F_1\}=\{\mu|\mu(g_1)\;{\leq}\;{\mu}\;{\leq}\;{\mu}(g_0)\}$$. And we consider the family $F_n$ of conformal mappings $\tilde{f}$ from D onto a covering surfaces of the Riemann sphere satisfying some conditions. We obtain the following theorems, {$\mu|1$ < ${\mu}\;{\leq}\;{\mu}(g_1)$} ${\subset}\;\{{\mu}(\tilde{f})|\tilde{f}\;{\in}\;F_2\}\;{\subset}\;\{{\mu}(\tilde{f})|\tilde{f}\;{\in}\;F_n\}$ and ${\mu}(\tilde{f})\;{\leq}\;{\mu}(g_0)^n$.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• 한국광학회지
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• 제6권3호
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• pp.214-221
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• 1995

레이저매질의 넓은 압력범위(0.5-3.5 기압)에 대해 70ns[FWHM]의 전자빔 가속기(800kV, 21kA)로 여기할 때 free-running XeF$(C\rightarrowA$ 엑시머 레이저의 출력과 Xe 농도와의 상호관계를 조사하였다. 공진기를 쌍색성의 출력거울로 구성하고, 레이저 출력을 레이저매질 $(Xe/F_2/Ar)$의 총압력과 가스혼합비의 함수로써 최적화 하였다. $F_2$ 0.46%를 고정한 조건에서 레이저 고유효율은 총압력 1, 2, 3기압에서 최대 0.38%, 1.03%, 0.29%로 측정되었다. 이때 레이저의 최대 고유효율은 레이저매질의 총압력이 낮을수록 높은 Xe 농도에서 높게 나타났다. 이같은 상호관계를 $XeF^*(C)$의 형성효율 및 XeF$(C\rightarrowA$ 레이저 추출 효율에 대해 동력학적으로 해석하므로써 Xe 농도의 의존성을 설명하였다. 그 결과로 대기압 XeF$(C\rightarrowA$ 레이저의 효율적인 동작을 제안한다.

• 충청수학회지
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• 제31권1호
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• pp.29-42
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• 2018

In this paper, we investigate the stability of two functional equations f(ax+by + cz) - abf(x + y) - bcf(y + z) - acf(x + z) + bcf(y) - a(a - b - c)f(x) - b(b - a)f(-y) - c(c - a - b)f(z) = 0, f(ax+by + cz) + abf(x - y) + bcf(y - z) + acf(x - z) - a(a + b + c)f(x) - b(a + b + c)f(y) - c(a + b + c)f(z) = 0 by applying the direct method in the sense of Hyers and Ulam.

• 충청수학회지
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• 제21권4호
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• 대한수학회지
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• 제48권1호
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• 대한화학회지
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• 제24권2호
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• pp.108-114
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• 1980

정전기적모델과 결합의 단순한 부가성을 이용하여 아주 극성인 화합물의 표준생성열$({\Delta}H_f\;^{\circ})$를 계산하는 간단한 방법을 제안하였다. 이 ${\Delta}H_f\;^{\circ}$에 대한 할로메탄의 bond 기여도는 각각 ${\Delta}H_f\;^{\circ}(C-F)=-36.44\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-Cl)=-2.57\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-Br)=5.32\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-I)=19.18\;kcal/mole,\;and\;{\Delta}H_f\;^{\circ}(C-H)=-3.61\;kcal/mole$로 얻어졌고 이 갑들과 정전기적 에너지들로부터 계산한 ${\Delta}H_f\;^{\circ}$는 실험치와 잘 일치함을 보였다.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2010년도 제39회 하계학술대회 초록집
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• pp.36-36
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• 2010

Low-pressure fluorocarbon plasmas are widely used in microelectronics fabrication for a variety of surface modification purposes. In particular, fluorocarbon plasmas are used for the etching of dielectrics such as silicon dioxide and silicon nitride. Among the various fluorocarbons, this study focuses on C4F6 molecules (C4F6s) which are composed of hexafluorocyclobutene (c-C4F6), hexafluoro-1, 3-butadiene (1, 3-C4F6), and hexafluoro-2-butyne (2-C4F6). We have investigated the dissociation reactions of C4F6s, resulting in CF2, CF3, C2F3, and C3F3 fragments, by using the wB97X-D functional with various basis sets. In this presentation, the geometrical properties, energetics, and dissociation mechanisms of C4F6s will be suggested.

• BMB Reports
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• 제33권2호
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• pp.188-192
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• 2000

Recombinant protein G has been utilized in the purification of antibodies from various mammalian species based on the interaction of antibodies with protein G. The interaction between immunoglobulin and protein G may not be restricted to the Fc protion of antibodies, as many different $F(ab)_2$ or Fab fragments can also bind to protein G. I found both FAb $F(ab)_2$ of 145-2C11, a hamster anti-mouse $CD3{\varepsilon}$ antibody, bound to the protein G-sepharose. Interestingly, Fab and $F(ab)_2$ of 145-2C11 did not bind to the protein A-sepharose. The binding of Fab and $F(ab)_2$ of 145-2C11 to protein G provided a useful method to remove proteases, chopped fragments of the Fc region, and other contaminating proteins. The remaining intact antibody in the protease reaction mixture can be removed by using a protein A-sepharose, because the Fab and $F(ab)_2$ portions of 145-2C11 did not bind to protein A-sepharose. The specific binding of Fab and $F(ab)_2$ portions of 145-sC11 to a protein G-sepharose (though not to a protein A-sepharose) and binding of intact 145-2C11 to both protein A- and G-sepharose will be useful in developing an effective purification protocol for Fab and $F(ab)_2$ portions of 145-2C11.

• 충청수학회지
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• 제4권1호
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• pp.61-69
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• 1991

By $C^{(1)}$[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by $${\parallel}f{\parallel}=\sup_{x{\in}[0,1]}({\mid}f(x){\mid}+{\mid}f^{\prime}(x){\mid})\text{ for }f{\in}C^{(1)}$$. By A we denote the sub algebra of $C^{(1)}$ defined by $$A=\{f{\in}C^{(1)}:f(0)=f(1)\text{ and }f^{\prime}(0)=f^{\prime}(1)\}$$. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1] onto itself.