• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권2호
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• pp.179-188
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• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

• East Asian mathematical journal
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• 제21권1호
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• pp.61-64
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• 2005

Let R be a commutative ring with identity, and let $f,\;g_i(i=1,\;\ldots,\;n),\;g_{\alpha}(\alpha{\in}S)$ be elements of R. We show that the following statements are equivalent; (i) $X_f{\subseteq}{\cup}_{\alpha{\in}S}X_{g\alpha}$ only if $X_f{\subseteq}X_{g\alpha}$ for some $\alpha{\in}S$, (ii) $V(f){\subseteq}{\cup}_{\alpha{\in}S}V(g_{\alpha})$ only if $V(f){\subseteq}V(g_{\alpha})$ for some $\alpha{\in}S$, (iii) $V(f){\subseteq}{\cup}^n_{i=1}V(g_i)$ only if $V(f){\subseteq}V(g_i)$ for some i, (iv) Spec(R) is linearly ordered under inclusion.

• Journal of Plant Biology
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• 제29권1호
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• pp.53-65
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• 1986

The montane forests of Ulreung Island, Korea, were investigated by the ZM school method. By comparing the montane forests of this island with those of Korean Peninsula and of Japan, a new order, F a g e t a l i a m u l t i n e r v i s, a new alliance, F a l g i o n m u l t i n e r v i s, a new association, H e p a t i c o-F a g e t u m m u l t i n e r v i s and Rhododendron brachycarpum-Pinus parviflora community were recognized. The H e p a t i c o - F a g e t u m m u l t i n e r v i s was further subdivided into four subassociations; Subass. of Sasa kurilensis, Subass. of Rumohra standishii, Subass. of Rhododendron brachycarpum and Subass. of typicum. Each community was described in terms of floristic, structural and environmental features.

• 한국광물학회지
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• 제15권2호
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• pp.95-103
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• 2002

본 연구는 일라이트-스멕타이트 혼합층광물(I-S)의 구조를 MacEwan 결정자 모델과 기본입자 모델을 통하여 살펴봄으로써, 팽창성(% $S_{XRD}$), MacEwan 결정자두께( $N_{CSD}$), 평균기본입자두께( $N_{F}$ ) 간의 관계를 정량적으로 해석하고자 하였다. 두 모델에 대한 비교를 통하여, % $S_{XRD}$, $N_{CSD}$, $N_{F}$ 는 서로 독립된 변수들이 아니고 I-S 구조 내에서 특정한 기하학적 관계를 가지고 있음을 알 수 있었다. % $S_{XRD}$는 단범위적층효과에 의해 $N_{CSD}$에 영향을 받고, $N_{F}$ 및 스멕타이트 층간개수( $N_{S}$ )와 $N_{s}$ =( $N_{F-}$1)/(100%/% $S_{XRD-}$ $N_{F}$ ) 관계가 성립함을 알 수 있었다. 특히, 이 관계로부터 % $S_{XRD}$와 $N_{F}$ 는 물리적으로 제한된 조건인 1< $N_{F}$ <100%/ % $S_{XRD}$를 만족해야 한다는 결과를 도출할 수 있었다. 본 연구는 이러한 물리적 제한조건을 이용하여, % $S_{XRD}$, $N_{F}$ , $N_{s}$ , 질서도 등을 종합적으로 해석하는데 유용할 것으로 사료되는 다이어그램을 제시하였으며, 금성산화 산암복합체에서 산출되는 I-S에 대한 XRD 자료를 이용하여, 이를 검증하였다. 또한, 자연상 I-S는 % $S_{XRD}$가 감소할수록, $N_{F}$ 는 물리적 상한조건인 $N_{F}$ =100%/% $S_{XRD}$에서 점차 멀어지게 됨을 알 수 있었으며, 이러한 결과는 기본입자가 두꺼워질수록 적층능력이 감소하는 것에서 기인한 것으로 사료된다.다.하는 것에서 기인한 것으로 사료된다.다.

• 대한수학회지
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• 제15권1호
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• 대한수학회보
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• 제61권1호
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.

• 건축사
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• 통권660호
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• pp.106-119
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• 2024

• 산업경영시스템학회지
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• 제20권42호
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• pp.143-149
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• 1997

먼저 Cantor dust 의 성질 및 유사성, 축소인자, 불변집합, $\delta$ - covering, Box counting 차원 등에 대한 정의를 하였다, {f_i}{\;}{{\infty}\atop{i=1}}$ 를 $R^n$ 상에서 개집합 조건을 만족시키는 축소인 자 $C_i$에 대한 유사성 이라하자. F를｛{f_i}{\;}{{\infty}\atop {i=1}}$ 에 대한 $R^n$상의 불변집합, 즉, F = $\bigcup_{i=0}^\infty{\;}f_1(F)$를 만족시키는 집합이라 하자. 이때, $\sum\limits_{n=0}^\infty{\;}C^s_i{\;}=1,{\;}0{\;}<{\;}C_1{\;}<{\;}1$ 일 때, $dim{\;}_H{\;}F{\;}={\;}dim{\;}_B{\;}F{\;}={\;}s$ 임을 보임으로서, 자기동형집합의 후랙탈 차원에 대하여 논의 하고자 한다.

• 대한수학회논문집
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• 제9권3호
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• pp.539-545
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• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.