• 대한수학회지
• /
• 제48권1호
• /
• pp.105-115
• /
• 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.

• 한국컴퓨터정보학회논문지
• /
• 제17권11호
• /
• pp.189-196
• /
• 2012

본 논문은 동적 경제급전의 최적화 문제를 풀기 위해 교환 알고리즘을 제안하였다. 제안된 알고리즘은 첫 번째로, 발전단가 $C_i^{max}/P_i^{max}$가 비싼 발전기는 가동을 중지시키는 개념을 도입하여 총 요구량 $P_d$와 총 발전량 ${\Sigma}P_i$의 균형을 맞추었다. 다음으로 발전량을 $P_i=P_i{\pm}{\Delta}$, (${\Delta}$=1.0, 0.1, 0.01, 0.001)에 대해 $_{max}[F(P_i)-F(P_i-{\Delta})]$ > $_{min}[F(P_j+{\Delta})-F(P_j)]$, $i{\neq}j$이면 $P_i=P_i-{\Delta}$, $P_j=P_j+{\Delta}$로 발전량을 교환하는 방법을 적용하였다. 동적 경제급전 문제의 시험사례에 제안된 알고리즘을 적용한 결과 기존의 휴리스틱 알고리즘 최적화 발전비용을 크기 감소시켜 경제적인 이익을 극대화 시켰다.

• Journal of Pharmaceutical Investigation
• /
• 제15권2호
• /
• pp.73-82
• /
• 1985

Each parching Anemarrhenae Rhizoma with 25% ethanol and normal saline has been used for anti-inflammatory, expectorant, antipyretic, sedative and diuretic, and so on. In order to investigate the differences of referential efficacy about each fractionated part of the aqueous extracts, pharmacological studies were carried out. The results of studies were summerized as follows : 1. By the administration of 25% ethanol treated preparation (F-I-1), the increase in urinary volume and $Na^+$ extraction was significantly recognized. 2. The excretion of electrolyte $Na^+$ by saline solution treated preparation (F-II-1) was significantly recognised in normal rats. 3. The increase of urinary volume and urinary $Na^+$ and $Cl^-$ excretion by F-I-1 and n-butanol insoluble parts of F-I-1 (F-I-3) was significantly recognized in $HgCl_2-induced$ acute renal failure of rats. 4. The increase of plasma $Na^+$ by F-I-1 and urea nitrogen by F-I-1 and F-I-3 in acute renal failure of rats was significantly recognized. 5. The increase of urinary volume by F-I-1 and F-I-3 was recognised in mice.

• 한국화재소방학회논문지
• /
• 제16권3호
• /
• pp.32-38
• /
• 2002

지구의 오존층 보호를 위해 폐기되는 $CF_3Br$재활용을 위해 $CF_3Br$을 원료로 $CF_3I$와 $C_2F_5I$의 합성연구를 수행하였다. 실험실규모의 $CF_3$I와 $C_3F_5I$의 합성실험장치에서 CuI, Kl, $K_2CO_3$, KF등의 금속염을 활성탄과 알루미나에 담지시킨 촉매를 사용하여 $400~600^{\circ}C$에서 반응을 실시하였다. 반응실험 결과 주생성물은 $CF_3I$와 $C_2F_5I$ 이며 미량의 $C_2F_6$, $CF_4$, $CF_2Br_2$등도 생성되었다. $CF_3I$합성촉매로는 활성탄에 7.5wt% KI와 $K_2CO_3$를 담지시킨 것이 가장 우수한 성능을 나타내었으며 $C_2F_5I 의 합성촉매로는 알루미나에 7.5wt% Cul를 담지시킨 것이 가장 우수하였다. 또한 최적 반응온도는 $500^{\circ}C$ 부근이었다.

• 대한수학회보
• /
• 제61권1호
• /
• pp.117-133
• /
• 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.

• Korean Journal of Mathematics
• /
• 제18권4호
• /
• pp.395-407
• /
• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• 충청수학회지
• /
• 제24권2호
• /
• pp.273-286
• /
• 2011

Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equations $${cf\left({\displaystyle\sum_{i=1}^n\;xi}\right)+{\displaystyle\sum_{i=2}^nf}{\left(\displaystyle\sum_{i=1}^n\;x_i-(n+c-1)x_j\right)}\\ {=(n+c-1)\;\left(f(x_1)+c{\displaystyle\sum_{i=2}^n\;f(x_i)}+{\displaystyle\sum_{i in fuzzy Banach spaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제11권2호
• /
• pp.9-14
• /
• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• 건축사
• /
• 통권660호
• /
• pp.106-119
• /
• 2024

• The Korean Journal of Physiology and Pharmacology
• /
• 제1권6호
• /
• pp.731-739
• /
• 1997

The aim of present study is to investigate the effects of cGMP on hyperpolarization activated inward current ($I_f$), pacemaker current of the heart, in rabbit sino-atrial node cells using the whole-cell patch clamp technique. When sodium nitroprusside (SNP, $80{\mu}M$), which is known to activate guanylyl cyclase, was added, $I_f$ amplitude was increased and its activation was accelerated. However, when $I_f$ was prestimulated by isopreterenol (ISO, $1{\mu}M$), SNP reversed the effect of ISO. In the absence of ISO, SNP shifted activation curve rightward. On the contrary in the presence of ISO, SNP shifted activation curve in opposite direction. $8Br-cGMP(100\;{\mu}M)$, more potent PKG activator and worse PDE activator than cGMP, also increased basal $I_f$ but did not reverse stimulatory effect of ISO. It was probable that PKG activation seemed to be involved in SNP-induced basal $I_f$ increase. The fact that SNP inhibited ISO-stimulated $I_f$ suggested cGMP antagonize cAMP action via the activation of PDE. This possibility was supported by experiment using 3-isobutyl-1-methylxanthine (IBMX), non-specific PDE inhibitor. SNP did not affect $I_f$ when $I_f$ was stimulated by $20{\mu}M$ IBMX. Therefore, cGMP reversed the stimulatory effect of cAMP via cAMP breakdown by activating cGMP-stimulated PDE. These results suggest that PKG and PDE are involved in the modulation of $I_f$ by cGMP: PKG may facilitate $I_f$ and cGMP-stimulated PDE can counteract the stimulatory action of cAMP.