• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.1-14
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• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

• The Korean Journal of Pesticide Science
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• v.12 no.3
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• pp.277-282
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• 2008

To assess the resistance to prochloraz, $EC_{50}$ values of Fusarium isolates obtained from rice seed were investigated through the agar dilution method. $EC_{50}$ value of 36 isolates of Fusarium spp. to prochloraz ranged from 0.020 to $1.78{\mu}g\;mL^{-1}$ with an average of $0.25{\mu}g\;mL^{-1}$. According to the species of Fusarium, the average $EC_{50}$ value was fluctuated; $0.091{\mu}g\;mL^{-1}$ for F. moniliformis, $0.11{\mu}g\;mL^{-1}$ for F. proliferatum and $0.31{\mu}g\;mL^{-1}$ for F. fujikuroi. The resistant baseline was decided at $0.5{\mu}g\;mL^{-1}$ to determine if the isolate was resistant to prochloraz or not. Based on the resistant baseline, the ratio of resistant isolates was 14%. There was no correlation between the resistance to prochloraz and the pathogenicity of Fusarium spp. on rice seedlings. The resistant isolates of F. fujikuroi did not show the cross-resistance to other sterol biosynthesis inhibiting fungicides, triflumizole, hexaconazole, difenoconazole and tebuconazole.

• The Korean Journal of Nuclear Medicine
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• v.28 no.3
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• pp.331-337
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• 1994

In order to develop a $^{18}F$-labelled myocardial perfusion agent(flow tracer) for PET, $^{18}F$-labelled organic ammonium cations were synthesized and evaluated in relation to their biodistribution. Five quaternary organic ammonium compounds were labelled with $^{18}F$ in a side chain with moderate to good yields by direct introduction of $^{18}F$-fluoride. Radiochemical yields have been achieved in 30-40min by the precursors (tosylates) in dimethylsulfoxide 15-60% (decay corrected). The reaction was found to be autocatalyzed. A remote controlled procedure was developed in these synthesis. $^{18}F$-Labelling and HPLC-purification of com-pounds needed about 60 min(Yield; 7-20%). Up to now the two compounds N-4-[$^{18}F$]fluorobutyl-pyridinium cation(1) and N, N dibenzyl-4(2-[$^{18}F$]fluoroethyl)piperidinium cation(2) were investigated in relation to their biodistribution in mice. Compound 1 showed at 1 min post injection the high uptake of 19.22% ID/g organ in the myocardium but a following fast decline to 1.12% ID/g organ after 40min. Uptake of compound 2 was after 1min in the heart 5.90% ID/g organ but after 40min at the relative high value of 4.33% ID/g organ. Heart:blood ratio for compound(1) at 1 min was 8.3, at 40 min 2.6 for compound II 2.0(1min) and 15.0(40 min). As data of compound 2 showed greater heart uptake, slower myocardial release, and higher heart: blood ratios, compound 2 is a good candidate for further evaluation.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.143-148
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• 2001

First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

• Food Science and Biotechnology
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• v.16 no.2
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• pp.285-289
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• 2007

A 3% suspension of heat-stabilized defatted rice bran was treated with papain, followed by inactivating the enzyme by heat, and centrifuged. The supernatant was subjected to ultrafiltration, and fractions with various molecular sizes, F1 (>30 kDa), F2 (10-30 kDa), F3 (5-10 kDa), F4 (3-5 kDa), and F5 (3 kDa<), were freeze-dried, and evaluated for antimutagenicity by Ames test using Salmonella typhimurium TA 100 against phenazine methosulfate. The F3 fraction containing highest antimutagenicity from ultrafiltration was separated into 6 fractions by DEAE-Sephadex A-25 ion-exchange column chromatography (F3-1-F3-6). Each fractions having protein contents were pooled, dialyzed, freeze dried, and evaluated for antimutagenicity. Among the six fractions, the F3-1, F3-2, and F3-6 fractions showed antimutagenicity, which were 80.2, 53.4, and 58.6% at concentration of $100\;{\mu}g/plate$, respectively. These F3-1, F3-2, and F3-6 fractions were subjected to Sephadex G-50 gel filtration column chromatography for further purification. Among the purified fractions, the F3-1-1, F3-2-2, and F3-6-1 fractions showed antimutagenicity of 84.5, 58.6, and 69.8% at concentration of $100\;{\mu}g/plate$, respectively. It is thought that these peptides can find application for nutraceutical and pharmaceutical products.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.41-53
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• 2023

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ and L = {±1, ±2, ±3, … , ±ρ} called the set of labels. Consider a mapping f : V ⟶ L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

• Honam Mathematical Journal
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• v.31 no.3
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• pp.451-462
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• 2009

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.179-190
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• 2007

In this paper, we consider the general variational inequality GVI(F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type method $u_{n+l}=(1-{\alpha}+{\theta}_{n+1})Tu_n+{\alpha}u_n-{\theta}_{n+1g}(Tu_n)-{\lambda}_{n+1}{\mu}F(Tu_n),\;n{\geq}0$. for solving the general variational inequalities. The sequence $\{x_n}\$ is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.