• Journal of the Korean Mathematical Society
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• v.48 no.1
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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.

• Journal of the Korea Society of Computer and Information
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• v.17 no.11
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• pp.189-196
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• 2012

This paper proposes Swap algorithm for solving Dynamic Economic Dispatch (DED) problem. The proposed algorithm initially balances total load demand $P_d$ with total generation ${\Sigma}P_i$ by deactivating a generator with the highest unit generation cost $C_i^{max}/P_i^{max}$. It then swaps generation level $P_i=P_i{\pm}{\Delta}$, (${\Delta}$=1.0, 0.1, 0.01, 0.001) for $P_i=P_i-{\Delta}$, $P_j=P_j+{\Delta}$ provided that $_{max}[F(P_i)-F(P_i-{\Delta})]$ > $_{min}[F(P_j+{\Delta})-F(P_j)]$, $i{\neq}j$. This new algorithm is applied and tested to the experimental data of Dynamic Economic Dispatch problem, demonstrating a considerable reduction in the prevalent heuristic algorithm's optimal generation cost and in the maximization of economic profit.

• Journal of Pharmaceutical Investigation
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• v.15 no.2
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• pp.73-82
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• 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.

• Fire Science and Engineering
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• v.16 no.3
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• pp.32-38
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• 2002

The synthesis of $CF_3$I and $C_2F_5I from $CF_3Br$ was studied for the reuse of $CF_3Br$ which is abolished to save the ozone layer of the earth. Reaction experiments were carried out in experimental scale synthesis equipment with catalysts, such as CuI, Kl, $K_2$$CO_3$, KF metal salt/active carbon and alumina support at $400~600^{\circ}C$. Main products of reaction were $CF_3i$ and $C_2F_5I$ with small amounts of $C_2F_5I$, $CF_4$, $CF_2Br_2$ by-products. 7.5wt% KI and $K_2CO_3$over activated carbon catalysts show the highest yield of $CF_3$I and 7.5wt% CuI over alumina catalysts show the highest yield of $C_2F_5i$. And optimal reaction temperature was about $500^{\circ}C$.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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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.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.395-407
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.273-286
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• 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
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• v.11 no.2
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• pp.9-14
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• 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.

• Korean Architects
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• s.660
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• pp.106-119
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• 2024

• The Korean Journal of Physiology and Pharmacology
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• v.1 no.6
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• pp.731-739
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• 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.