• 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.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.279-289
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• 2011

Let E be a uniformly convex Banach space with a uniformly Gateaux differentiable norm, C be a nonempty closed convex subset of E and f : $C{\rightarrow}C$ be a fixed bounded continuous strong pseudocontraction with the coefficient ${\alpha}{\in}(0,1)$. Let $\{{\lambda}_t\}_{0<t<1}$ be a net of positive real numbers such that ${\lim}_{t{\rightarrow}0}{\lambda}_t={\infty}$ and S = {$T(s)$ : $0{\leq}s$ < ${\infty}$} be a nonexpansive semigroup on C such that $F(S){\neq}{\emptyset}$, where F(S) denotes the set of fixed points of the semigroup. Then sequence {$x_t$} defined by $x_t=tf(x_t)+(1-t)\frac{1}{{\lambda}_t}{\int_{0}}^{{\lambda}_t}T(s)x{_t}ds$ converges strongly as $t{\rightarrow}0$ to $\bar{x}{\in}F(S)$, which solves the following variational inequality ${\langle}(f-I)\bar{x},\;p-\bar{x}{\rangle}{\leq}0$ for all $p{\in}F(S)$.

• Journal of Microbiology and Biotechnology
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• v.29 no.8
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• pp.1266-1272
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• 2019

A bacterial strain, labeled $UR11^T$, was isolated from green alga Ulva pertusa collected from Jeju Island, Korea. $UR11^T$ was identified as a gram-negative, rod-shaped, motile by gliding and aerobic bacterial strain with yellow colonies on R2A plates. The strain $UR11^T$ grew over at a temperature range of $10^{\circ}C$ to $30^{\circ}C$ (optimally at $25^{\circ}C$), a pH range of 6.0-11 (optimally at pH 7.0) and a Nacl range of 0.5-5% Nacl (w/v). Phylogenetic analysis based on 16S rRNA gene sequences revealed that strain $UR11^T$ was a member of the genus Flavobacterium. Strain $UR11^T$ shared close similarity with F. jejuensis $EC11^T$ (98.0%) F. jumunjinense $HME7102^T$ (96.1%), F. haoranii $LQY-7^T$ (95.3%), F. dongtanense $LW30^T$ (95.1%), and F. ahnfeltiae 10Alg $130^T$(94.9%). The major fatty acids (>5%) were $iso-C_{15:0}$ (33.9%), $iso-C_{15:1}$ G (12.4%), $iso-C_{17:0}$ 3-OH (9.0%), $isoC_{16:0}$ (7.0%) and $iso-C_{15:0}$ 3-OH (6.3%). The major polar lipids were phosphatidylethanolamine, seven unknown aminolipids, two unknown aminopolarlipids and two unknown lipids. DNA-DNA hybridization value was 58% at strain $UR11^T$ with F. jejuensis $EC11^T$. Based on phenotypic, chemotaxonomic and phylogenetic evidence, strain $UR11^T$ represents a novel species of the genus Flavobacterium, for which the name Flavobacterium jocheonensis sp. nov. is proposed. The type strain is Flavobacterium jocheonensis is $UR11^T$ (=KCTC $52377^T$ =JCM $31512^T$).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.791-815
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• 2014

We show amongst other that if $f,g:[a,b]{\rightarrow}\mathbb{C}$ are two functions of bounded variation and such that the Riemann-Stieltjes integral $\int_a^bf(t)dg(t)$ exists, then for any continuous functions $h:[a,b]{\rightarrow}\mathbb{C}$, the Riemann-Stieltjes integral $\int_{a}^{b}h(t)d(f(t)g(t))$ exists and $${\int}_a^bh(t)d(f(t)g(t))={\int}_a^bh(t)f(t)d(g(t))+{\int}_a^bh(t)g(t)d(f(t))$$. Using this identity we then provide sharp upper bounds for the quantity $$\|\int_a^bh(t)d(f(t)g(t))\|$$ and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.245-259
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• 2007

We define and study a concept of $T^f$-space for a map, which is a generalized one of a T-space, in terms of the Gottlieb set for a map. We show that X is a $T_f$-space if and only if $G({\Sigma}B;A,f,X)=[{\Sigma}B,X]$ for any space B. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain a sufficient condition to having a lifting $T^{\bar{f}}$-structure on $E_k$ of a $T^f$-structure on X. Also, we define and study a concept of co-$T^g$-space for a map, which is a dual one of $T^f$-space for a map. We obtain a dual result for a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from ${\iota}:X^{\prime}{\rightarrow}cX^{\prime}$.

• The Korean Journal of Nuclear Medicine Technology
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• v.23 no.1
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• pp.69-74
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• 2019

Purpose $^{18}F$-FDOPA using amino acid is particularly attractive for imaging of brain tumors because of the high uptake in tumor tissue and the low uptake in normal brain tissue. But, on the other hand, $^{18}F$-FDG is highly uptake in both tumor tissue and normal brain tissue. The purpose of study is to evaluate comparison of contrasts in $^{18}F$-FDOPA Brain PET/CT and $^{18}F$-FDG Brain PET/CT and to find out optimal scan time by analysis of variation in SUV with the passage of uptake time. Materials and Methods A region of interest of approximately $350mm^2$ at the center of the tumor and cerebellum in 12 patients ($51.4{\pm}12.8yrs$) who $^{18}F$-FDG Brain PET/CT and $^{18}F$-FDOPA Brain PET/CT were examined more than once each. The $SUV_{max}$ was measured, and the $SUV_{max}$ ratio (T/C ratio) of the tumor cerebellum was calculated. In the analysis of SUV, T/C ratio was calculated for each frame after dividing into 15 frames of 2 minutes each using List mode data in 25 patients ($49.{\pm}10.3yrs$). SPSS 21 was used to compare T/C ratio of $^{18}F$-FDOPA and T/C ratio of $^{18}F$-FDG. Results The T/C ratio of $^{18}F$-FDOPA Brain PET/CT was higher than the T/C ratio of $^{18}F$-FDG Brain, and show a significant difference according to a paired t-test(t=-5.214, p=0.000). As a result of analyzing changes in $SUV_{max}$ and T/C ratio, the peak point of $SUV_{max}$ was $5.6{\pm}2.9$ and appeared in the fourth frame (6 to 8 minutes), and the peak of T/C ratio also appeared in the fourth frame (6 to 8 minutes). Taking this into consideration and comparing the existing 10 to 30 minutes image and 6 to 26 minutes image, the $SUV_{max}$ and T/C ratio increased by 0.2 and 0.1 each, compared to the 10 to 30 minutes image for 6 to 26 minutes image. Conclusion From this study, $^{18}F$-FDOPA Brain PET/CT is effective when reading the image, because the T/C ratio of $^{18}F$-FDOPA Brain PET/CT was higher than T/C ratio of $^{18}F$-FDG Brain PET/CT. In addition, in the case of $^{18}F$-FDOPA Brain PET/CT, there was no difference between the existing 10 to 30 minutes image and 6 to 26 minutes image. Through continuous research, we can find possibility of shortening examination time in $^{18}F$-FDOPA Brain PET/CT. Also, we can help physician to accurate reading using additional scan data.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.4
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• pp.353-359
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• 1999

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.