• 대한수학회보
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• 제55권5호
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• pp.1397-1404
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• 2018

For a connected graph G, an r-maximum edge-coloring is an edge-coloring f defined on E(G) such that at every vertex v with $d_G(v){\geq}r$ exactly r incident edges to v receive the maximum color. The r-maximum index $x^{\prime}_r(G)$ is the least number of required colors to have an r-maximum edge coloring of G. In this paper, we show how the r-maximum index is affected by adding an edge or a vertex. As a main result, we show that for each $r{\geq}3$ the r-maximum index function over the graphs admitting an r-maximum edge-coloring is unbounded and the range is the set of natural numbers. In other words, for each $r{\geq}3$ and $k{\geq}1$ there is a family of graphs G(r, k) with $x^{\prime}_r(G(r,k))=k$. Also, we construct a family of graphs not admitting an r-maximum edge-coloring with arbitrary maximum degrees: for any fixed $r{\geq}3$, there is an infinite family of graphs ${\mathcal{F}}_r=\{G_k:k{\geq}r+1\}$, where for each $k{\geq}r+1$ there is no r-maximum edge-coloring of $G_k$ and ${\Delta}(G_k)=k$.

• 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.

• 대한치과기공학회지
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• 제36권4호
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• pp.247-253
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• 2014

Purpose: The aim of this study was to evaluate the effect of colored zirconia with different coloring liquids. Methods: Total 30 specimens were prepared. Specimens were classified into 6 groups: IPS e.max Ceram(P), Uncolored zirconia(C), VITA In-Ceram$^{(R)}$2000 YZ LL1(L), Zirkonzahn coloring liquid(Z), Wieland coloring liquid(W), and Kuwotech coloring liquid(K). Four different types of zirconia coloring liquid, VITA In-Ceram$^{(R)}$ 2000 YZ LL1(VITA Zahnfabrik, Germany), Zirkonzahn coloring liquid(Zirkonzahn, Italy), Wieland coloring liquid(Wieland, Germany), Kuwotech coloring liquid(Kuwotech, Korea) were used to fabricate colored zirconia by using infiltrating method and then completely sintered. The color of the all specimens was measured using the spectrophotometer(CM-2600d, Konica Minolta, Japan) and expressed in terms of the 3-coordinated values(CIE $L^*a^*b^*$). Color differences were calculated using the equation $${\Delta}E^*=[({\Delta}L^*)^2+({\Delta}a^*)^2+({\Delta}b^*)^2]^{1/2}$$. Results: $L^*a^*b^*$ values of the colored zirconia were affected by the coloring liquids. The uncolored zirconia(C) group showed the highest $L^*$ value and zirkonzahn coloring liquid(Z) group showed the lowest $L^*$ value. Zirkonzahn coloring liquid(Z) showed the highest $a^*$ value and VITA In-Ceram 2000 YZ LL1(L) group showed the highest $b^*$ value. Generally, the color difference(${\Delta}E^*$) in all groups showed higher than 3.7 except between IPS e.max Ceram(P) and wieland coloring liquid(W) group. Conclusion: Within the limitations of this study, various coloring liquids influenced the $L^*$, $a^*$, and $b^*$ values of colored zirconia. IPS e.max Ceram(P) and wieland coloring liquid(W) group did not show clinically perceiving color difference.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.909-913
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• 2009

For a family of graphs $\mathcal{H}$ and an integer k, we denote by $R^k(\mathcal{H})$ the corresponding k-Ramsey number, which is defined to be the smallest integer n such that every k-coloring of the edges of $K_n$ contains a monochromatic copy of a graph in $\mathcal{H}$. The local k-Ramsey number $R^k_{loc}(\mathcal{H})$ and the mean k-Ramsey number $R^k_{mean}(\mathcal{H})$ are defined analogously. Let $\mathcal{G}$ be the family of non-bipartite graphs and $T_n$ be the family of all trees on n vertices. In this paper we prove that $R^k_{loc}(\mathcal{G})=R^k_{mean}(\mathcal{G})$, and $R^2(T_n)$ < $R^2_{loc}(T_n)4 = $R^2_{mean}(T_n)$ for all $n\;{\ge}\;3$.

• 한국패션뷰티학회지
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• 제3권1호
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• pp.72-77
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• 2005

The present study was to investigate the effects of different types of conditioner on the morphological changes of hair cuticles after coloring treatment. The virgin hair, aged 22 years served as a subject. Coloring treatment was done with a commercial hair dye agent for 35 minutes as routine procedures at $25^{\circ}C$, 50% R.H. environmental condition. The two different types of conditioner, Essence and LPP were applied to the colored hair 10 times with 2 days interval for 20 days. The hair cuticles were observed by a scanning electron micro scopy before and after coloring and conditioner treatment. The main results were as follows. Coloring treatment damaged the hair cuticles, and both of Essence and LPP had a direct conditioning effect. Also, the damaged hair cuticles were recovered by the repeated application of hair conditioner. Moreover, LPP was more effective in hair curing compared to Essence. These results show that a hair conditioner can be helpful to keep healthy hair and to shorten an interval of coloring.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.379-389
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• 2020

An r-color Rado number N = R(𝓛, r) for a system 𝓛 of equations is the least integer, provided it exists, such that for every r-coloring of the set {1, 2, …, N}, there is a monochromatic solution to 𝓛. In this paper, we study the 2-color Rado number R(𝓔, 2) for 𝓔 : x₁ + x₂ + ⋯ + x_n = y₁ + y₂ = z when n ≥ 4.

• 한국조리학회지
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• 제8권2호
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• pp.153-171
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• 2002

This study had three major purpose: 1) to examine the relationship between coloring factor of Hors d'oeuvre and preference of dishes. 2) to examine the relationship between coloring factor of Hors d'oeuvre and selection of dishes. 3) to examine the relationship between coloring factor of Hors d'oeuvre and customer satisfaction. Questionnaires for the study were distributed 300 subjects in deluxe class hotels in Seoul. Among 300 questionnaires, 280 subjects were collected and utilized for analysis. In HY hotel, 35 subjects of customers, 24 subjects of cooks, and 32 subjects of service personnels were collected. In R hotel, 29 subjects of customers, 32 subjects of cooks, and 32 subjects of service personnels were collected. In H hotel, 29 subjects of customers, 34 subjects of cooks, and 33 subjects of service personnels were collected. Analysis ways used for this study were frequency analysis, factor analysis, reliability analysis, ANOVA, To accomplished the objective 1), ANOVA was utilized. To accomplished the objective 2) and 3), regression analysis was unitized. The findings from this study were as follows. First it was found that selection of dishes was affected by coloring factory of Hors d'oeuvre. Secondly, it was found that customer satisfaction was affected by coloring factor of Hors d'oeuvre. Consequently, development of Hors d'oeuvre by harmonizing of various colorings should be activated to raise level of preference of dishes. Also, in regard to level of satisfaction, harmony of various colorings should be required.

• 한국환경과학회지
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• 제14권12호
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• pp.1195-1201
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• 2005

In order to develop a dye coloring technology on Conchiolin layer in cultured pearls, appropriate dyes were selected, their solubilities in various solvents were studied, and adsorption and desorption experiments were performed. Solubilities of several basic dyes known to suitable for the pearl coloring, i.e., Rhodamine 6G(R6), Rhodamine B(RB) and Methylene Blue(MB), in several solvents (distilled water, methanol, ethanol, and acetone) were investigated. Among these dyes, R6 was chosen as a dye for single component adsorption and desorption experiment due to the relatively good solubility in various solvents tested. Solubilities of dyes were judged to be enough to color the pearls since dye concentrations in pearl coloring are, in general, not so high. The internal surface area of the pearl layer is believed to be directly related to the dye adsorption, the single-point internal surface area of the pearl layer measured at the nitrogen relative pressure of 0.3 was found to be $0.913m^2/g$, and the BET internal surface area, $1.01m^2/g$ The most probable diameters of micropores and macropores were found to be $40{\AA}$and $5000{\AA}$ respectively, from the pore size distribution data. Adsorption isotherm was well fitted to the Langmuir isotherm model, resulting in q=$\frac{1.62C}{1+1.09C^{.}}$

• 정보처리학회논문지B
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• 제11B권2호
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• pp.221-226
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• 2004

개미 집단 시스템(Ant Colony System ACS) 알고리즘은 조합 최적화 문제를 해결하기 위한 새로운 메타 휴리스틱 방법이다. 이것은 그리디 탐색뿐만 아니라 긍정적 피드백에 의한 탐색을 이용한 모집단에 근거한 접근법으로 조합 최적화 문제를 해결하기 위해 제안되었다. 최근까지 인접한 노드($v_i, v_j$)가 같은 색을 갖지 않도록 그래프 G의 노드 V에 색을 배정하는 문제인 그래프 착색 문제의 최적 해를 구하기 위하여 다양한 접근 방식들과 해법들이 제안되고 있다. 본 논문에서는 기존의 그래프 착색 문제의 해법으로 잘 알려진 그리디 알고리즘, 시뮬레이티드어넬링, 타부 탐색 등이 아닌 개미 집단 시스템 알고리즘으로 해법을 구하는 방법인 ANTCOL 알고리즘을 소개하고, ANTCOL을 해결하기 위해 제안된 기존의 생성 함수들(ANT_Random ANT_LF, ANT_SL, ANT_DSATUR, ANT_RLF)과, 본 논문에서 새롭게 제안된 방법으로 RLF에 무작위 기법을 적용한 XRLF를 생성 함수로 사용한 ANT_XRLF 방법과 ANT_XRLF에 재검색을 추가한 방법(ANT_XRLF_R)의 그래프 착색 결과 및 실행 시간을 비교, 분석하여 제안된 방법이 더 빠르게 수렴할 수 있음을 실험을 통해 알 수 있었다.

• 분석과학
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• 제26권1호
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• pp.99-105
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• 2013

염모제품 중 유효성분의 품질검사는 식품의약품안전청의 "의약외품에 관한 기준 및 시험방법"에 따라 제품에 표기된 산화염료들을 박층크로마토그래프법(TLC방법)으로 확인시험을 하도록 되어있다. 그러나 TLC방법은 원료분량이 미량이거나, $R_f$ 값이 비슷한 성분들이 존재하면 확인시험이 어려운 문제점이 있다. 본 연구에서는 미량성분 검출이 용이하며 분석시간이 짧다고 보고된 UPLC를 이용하기 위한 시료 전처리 및 분석조건을 탐색하였다. 유효성분들을 분석할 수 있는 검출한계는 6.7-77.9 ${\mu}g/L$, 정량한계는 22.3-259.7 ${\mu}g/L$ 이었으며, 회수율은 ${\alpha}$-naphthol를 제외하고는 96.2-101.5%로 양호하였다. 유효성분 추출하기 위한 시료 전처리에는 헥산-증류수를 사용하였다. 시료 전처리 시 복잡한 추출과정을 거치지 않고, UPLC방법은 빠르고 정확하게 염모제품에 함유되어 있는 유효성분들을 동시에 분석 할 수 있었다.