• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.241-246
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• 2007

For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• The Journal of Internal Korean Medicine
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• v.14 no.1
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• pp.129-138
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• 1993

This report on the $T{\acute{o}}u\;f{\bar{e}}ng$ and Migraine comes to conclude, through the study of the Oriental- Western medical references, as follow; 1. First, $T{\acute{o}}u\;f{\bar{e}}ng$ and Migraine had some concurrencies that both the two symptoms have appeared severe and recurrent headache and more often to the female. 2 Many of them e.g. Sensory disturbance, Vertigo, Nausea, Vomiting, Tinnitus etc. in the prodrome and main symptom of $T{\acute{o}}u\;f{\bar{e}}ng$ and Migraine were identical, especially the symptom of the $f{\bar{e}}ng\;t{\acute{a}}n\;t{\acute{o}}u\;t{\grave{o}}ng$ was similar to the prodrome of the Migraine. We could find out the semilarity of the symptoms through that Migraine is proximately set in unilateral, and $Pi{\bar{a}}nT{\acute{o}}u\;f{\bar{e}}ng$ is so called alias $B{\grave{a}}n\;bi{\bar{a}}n\;t{\acute{o}}u\;t{\grave{o}}ng$. 3. The pathogeny of $T{\acute{o}}u\;f{\bar{e}}ng$ include the case of ‘$f{\bar{e}}ng\;xi{\acute{e}}\;r{\grave{u}}\;n{\bar{a}}o$’, the patient feeling weak condition, $T{\acute{a}}n,\;T{\acute{a}}nshi,\;T{\acute{a}}nhu{\breve{o}},\;Y{\grave{u}}q{\grave{i}}$, etc. and, ‘$t{\acute{a}}n\;zhu{\grave{o}}\;sh{\grave{a}}ng\;y{\acute{a}}o$’, ‘$G{\bar{a}}n\;y{\acute{a}}ng\;hu{\grave{a}}\;f{\bar{e}}ng$’. There were variable that $F{\bar{e}}ng,\;Xu{\grave{e}},\;F{\bar{e}}ngr{\grave{a}},\;F{\bar{e}}ngx{\bar{u}},\;Xu{\grave{e}}x{\bar{u}},\;Hu{\check{o}}$ in the left, and $t{\acute{a}}n,\;R{\grave{e}},\;t{\acute{a}}nr{\grave{e}},\;Qir{\acute{a}}$ in the right partial pathogeny. It was referred $Sh{\grave{a}}o\;y{\acute{a}}ng\;j{\bar{i}}ng$, $Ju{\acute{e}}\;y{\bar{i}}n\;j{\bar{i}}ng$, $Y{\acute{a}}ng\;m{\acute{i}}ng\;j{\bar{i}}ng$, $T{\grave{a}}i\;y{\acute{a}}ng\;j{\bar{i}}ng$ in connection with the Meridian system. And otherwise the primary cause of Migraine is still unknown to us. Heredity is probably important, but the mode of transmission is uncertain. Recently, the important assumption is the vasomotor change caused by vasoconstrictors like that norepinephrine, epinephrine, and serotonin etc.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• Nuclear Engineering and Technology
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• v.4 no.3
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• pp.214-222
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• 1972

In the optic,11 grade LiF crystal, the electron traps corresponding to the thermoluminescence(abbreviated to TL) glow peak develop as irradiation dose is increased. Originally the electron trap of the crystal has two levels but as the dose reaches to the order of 10$^4$rontgen, it attains five levels as observed in the TL glow curves. The five trap depths are determined from the glow peak temperatures for two different heating rates, $\theta$=6.6$^{\circ}C$/sec and 3.4$^{\circ}C$/sec. The electron trap depths have the following values E$_1$=0.79 eV, E$_2$=0.93 eV, E$_3$=1.02 eV, E$_4$=1.35 eV, E$_{5}$=1.69eV. The special feature of thermoluminescence of optical grade LiF is that the traps, except E$_1$and E$_2$corresponding to 12$0^{\circ}C$ glow peak and 15$0^{\circ}C$ glow peak for $\theta$=6.6$^{\circ}C$/sec, have severe thermal instability, namely E$_3$, E$_4$and E$_{5}$ levels disappear during bleaching process. These defects in the optical grade LiF crystal seem annealed out during the course of TL measurement. The fresh or long time unused LiF(Mg) crystal shows only two glow peaks at 17$0^{\circ}C$ and 23$0^{\circ}C$ for $\theta$=6.6$^{\circ}C$/sec, but upon sensitization with r-ray irradiation, it converts to the six glow peak state. The four electron traps, E$_1$, E$_2$, E$_3$, and E$_{6}$ created by r-ray irradiation and corresponding to the glow peaks at T=10$0^{\circ}C$ 13$0^{\circ}C$, 15$0^{\circ}C$ and 29$0^{\circ}C$ are stable and not easily annealed out thermally, The sensitization essentially required to LiF(Mg) dosimeter is to give the crystal the stable six levels in the electron trap. In optical grade LiF, the plot between logarithm of total TL output versus logarithm of r-ray dose gives more supra-linear feature than that of LiF(Mg). However, if one takes the height of 12$0^{\circ}C$ glow peak(S=6.6$^{\circ}C$/sec), instead of the total TL output, the curve becomes close to that of LiF(Mg).

• 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.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• Biomolecules & Therapeutics
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• v.10 no.4
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• pp.293-302
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• 2002

The classical concept for iron uptake into mammalian cells has been the endocytosis of transferrin( $T_{f}$ )-bound F $e^{3+}$ via the $T_{f}$ - $T_{f}$ receptor cycle. In this case, we could not explain the uptake of F $e^{2＋}$ ion and the export of iron from endosome. Studies on iron transport revealed that other transport system exists in epithelial cells of the intestine. One of non- $T_{f}$ -receptor-mediated transport systems is Nramp2/DMT1/DCT1 which transports M $n^{＋＋}$, $Mg^{＋＋}$, Z $n^{＋＋}$, $Co^{＋＋}$, N $i^{＋＋}$ or C $u^{＋＋}$ ion as well as F $e^{+2}$ ion. DMT1 was cloned from intestines of iron-deficient rats and shown to be a hydrogen ion-coupled iron transporter and a protein regulated by absorbed dietary iron. DMT1 is founded in other cells such as cortical and hippocampal glial cells as well as endothelial cells in duodenum. Two F $e^{3+}$ ion bound to transferrin( $T_{f}$ ) are taken up via the $T_{f}$ - $T_{f}$ receptor cycle in the intestinal epithelial cell. F $e^{3+}$ in endosome was converted to F $e^{2＋}$ ion, and then exported to cytosol via DMT1. F $e^{2＋}$ ion is taken up into cytosol via DMT1. Several other transporters such as FET, FRE, CCC2, AFT1, SMF, FTR, ZER, ZIP, ZnT and CTR have been reported recently and dysfunction of the transporters are related with diseases containing Wilson's disease, Menkes disease and hemochromatosis. Evidences from several studies strongly suggest that DMT1 is the major transporter of iron in the intestine and functions critically in transport of other metal ions.

• Journal of the Korean Home Economics Association
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• v.28 no.4
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• pp.1.1-13
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• 1990

Authors have performed the sensory evaluation tests according to each given items after selecting various lines in order to assess the visual effects by the lines in cloth designing. The evaluations were done by means of ranking tests followed by paired comparison tests. The results obtained were as follows : 1. In the item in than "Shoulder width looks wide", the design C3 showed the best visual effect, and then B1, F8, and A5 comes in order. In "Shoulder width looks narrow", they were A2, F5, F7, and B2 in order. 2. In "Bust looks big", the effect was best in F9, and then B1, F5, C3, and A5 and order. "Bust looks small" item showed A3, C1, and F1 in order. 3. In "Waist looks thick", they were B2, D1, and F7 while in "Waist looks thin", they were B3, F8, and D6 in order. 4. In the item in that "Hip looks big", the best effect was in F9, and then E3, C2, and B4 in order. In "Hip looks small", the best one was C1, and then comes. E1, F6, and F8. 5. In "Upper body looks thick", they were D2, D4, F8, C3 and A5 in order whild in "Upper body looks thin", they were A1, F5, and D7 in order. 6. In the item "Lower body lookds thick", they were F9, C2, E3, B3, and D3 in order. In "Lower body looks thin", the best one was C1, and then D1, E2, F6, and F8 comes in order. 7. In "whole body looks thick", they were F9, F3, D3, and A5, and in "Whole body looks thin", they were F5, A1, C1, and D6 in order. 8. In "Height looks tall", the effects were in order of A4, D6, E1, and F7 while in "Height looks short", they were E3, F9, B4, D2, and D1. 8. In "Height looks tall", the effects were in order of A4, D6, E1, and F7 while in "Height looks short", they were E3, F9, B4, D2, and D1. F9, B4, D2, and D1.