• Elastomers and Composites
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• v.39 no.2
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• pp.153-160
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• 2004

Fullerene oxides were synthesized by fullerene ($C_{70}$) and several amine N-oxides such as 3-picoline N-oxide, pyridine N-oxide hydrate, quinoline N-oxide, and isoquinoline N-oxide under ultrasonic condition at $25{\sim}43^{\circ}C$. The reactivity of fullerene ($C_{70}$) with various amine N-oxides undo, ultrasonic irradiation showed the same in all of the proceeding experiments; 3-picoline N-oxide : pyridine N-oxide hydrate : quinoline N-oxide : isoquinoline N-oxide. The MALDI-TOF MS, UV-vis spectrophotometer and HPLC analysis confirmed that the products of fullerene oxidation are [$C_{70}(O)n$] (n=1).

• Korean Journal of Environmental Agriculture
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• v.41 no.3
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• pp.167-176
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• 2022

BACKGROUND: Nitrogen (N) is an important element for turfgrass (Zoysia matrella) growth; however, standard N application rate for turfgrass is not established yet. This study was conducted to evaluate the effect of N application rates on the growth and quality of turfgrass for establishment of standard N application rate. METHODS AND RESULTS: Treatments were as follows; control (0 N g/m²/month), 1N (1 N g/m²/month), 2N(2 N g/m²/month), 3N (3 N g/m²/month), 4N (4 N g/m²/month), and 5N (5 N g/m²/month). N application improved visual turfgrass quality. Compared with the control, clipping yield of all N treatments increased by 90~194%. The grass shoot weight of 3N, 4N, and 5N treatments increased by 52%, 43%, and 111%, respectively, and the stolon weight of 4N and 5N treatments increased by 412% and 201%, respectively, compared to the control. The N uptake amount and N recovery rate were estimated to be 4.10~6.28 g/m² and 14~58%, respectively. CONCLUSION(S): These results indicate that considering visual quality, clipping yield, N uptake amount, and N recovery, the application rate of 2~3 N g/m²/month was suggested to be suitable for Z. matrella production.

• Nuclear Engineering and Technology
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• v.18 no.2
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• pp.92-96
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• 1986

The $^{93}Nb(n,n\alpha)^{89m}Y$, $^{93}Nb(n,{\alpha})^{90m}Y$ and $^{93}Nb(n,2n)^{92m}Nb$ cross sections at a neutron energy of 14.6 MeV have been measured relative to the $^{27}Al(n,p)^{27}Mg$ and $^{27}Al(n,{\alpha})^{24}Na$ cross sections. A small accelerator utilizing $T(D,n)^4He$ reaction was used as a neutron source and the neutron energy spread is about 0.4MeV at the sample. All induced activities were measured with a 70cc HPGe detector in the same geometry.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• Journal of the Korean Applied Science and Technology
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• v.32 no.1
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• pp.165-169
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• 2015

N-propyl-N,N-dimethylethanolamine was directly ultrasonicated in acidic water for 6 minute to give clear stock solutions. The catalytic hydrolysis of N-propyl-N,N-dimethylethanolamine was studied at $30{\sim}55^{\circ}C$ in the presence of uni-lamellar vesicle and mixture of uni- and multi-lamellar aggregates. The difference of rate between uni- and mixture was observed, where uni-lamellar reaction was more catalytic effect. The phase transition temperature of vesicle was $37{\sim}44^{\circ}C$. The particle size of multi-lamellar than that of uni-lamellar of biological membrane was measured more largely.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.177-193
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• 2010

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type $F_n(x)=\sum\limits_{k=0}^{n}A^n_kG_k(x)$ and $ G_n(x)=\sum\limits_{k=0}^{n}B_k^nF_k(x)$, where 0, 1, 2,$\cdots$. Here $F_n(x)$, $G_n(x)$ denote special polynomial functions, and $A_k^n$, $B_k^n$ denote coefficients found by use of the orthogonal properties of $F_n(x)$ and $G_n(x)$, or by skillful series manipulations. Typically $G_n(x)=x^n$ and $F_n(x)=P_n(x)$, the n-th Legendre polynomial. We give a collection of inverse series pairs of the type $f(n)=\sum\limits_{k=0}^{n}A_k^ng(k)$ if and only if $g(n)=\sum\limits_{k=0}^{n}B_k^nf(k)$, each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.45-54
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• 2013

Let $$S^{\pm}_{(n,k)}\;:=\{(a,b,x,y){\in}\mathbb{N}^4:ax+by=n,x{\equiv}{\pm}y\;(mod\;k)\}$$. From the formula $\sum_{(a,b,x,y){\in}S^{\pm}_{(n,k)}}\;ab=4\sum_{^{m{\in}\mathbb{N}}_{m<n/k}}\;{\sigma}_1(m){\sigma}_1(n-km)+\frac{1}{6}{\sigma}_3(n)-\frac{1}{6}{\sigma}_1(n)-{\sigma}_3(\frac{n}{k})+n{\sigma}_1(\frac{n}{k})$, we find the Diophantine solutions for modulo $2^{m^{\prime}}$ and $3^{m^{\prime}}$, where $m^{\prime}{\in}\mathbb{N}$.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.513-528
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• 1997

A sort sequence $S_n$ is a sequence of all unordered pairs of indices in $I_n\;=\;{1,\;2,v...,\;n}$. With a sort sequence Sn we assicuate a sorting algorithm ($AS_n$) to sort input set $X\;=\;{x_1,\;x_2,\;...,\;x_n}$ as follows. An execution of the algorithm performs pairwise comparisons of elements in the input set X as defined by the sort sequence $S_n$, except that the comparisons whose outcomes can be inferred from the outcomes of the previous comparisons are not performed. Let $X(S_n)$ denote the acverage number of comparisons required by the algorithm $AS_n$ assuming all input orderings are equally likely. Let $X^{\ast}(n)\;and\;X^{\circ}(n)$ denote the minimum and maximum value respectively of $X(S_n)$ over all sort sequences $S_n$. Exact determination of $X^{\ast}(n),\;X^{\circ}(n)$ and associated extremal sort sequenes seems difficult. Here, we obtain bounds on $X^{\ast}(n)\;and\;X^{\circ}(n)$.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.