• Journal of the Korea Society of Computer and Information
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• v.17 no.4
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• pp.139-145
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• 2012

Generally, Quicksort selects the pivot from leftmost, rightmost, middle, or random location in the array. This paper suggests Quicksort using middle range pivot $P_0$ and continually divides into 2. This method searches the minimum value $L$ and maximum value $H$ in the length n of list $A$. Then compute the initial pivot key $P_0=(H+L)/2$ and swaps $a[i]{\geq}P_0$,$a[j]<P_0$ until $i$=$j$ or $i$>$j$. After the swap, the length of list $A_0$ separates in two lists $a[1]{\leq}A_1{\leq}a[j]$ and $a[i]{\leq}A_2{\leq}a[n]$ and the pivot values are selected by $P_1=P_0/2$, $P_2=P_0+P_1$. This process repeated until the length of partial list is two. At the length of list is two and $a$[1]>$a$[2], swaps as $a[1]{\leftrightarrow}a[2]$. This method is simpler pivot key process than Quicksort and improved the worst-case computational complexity $O(n^2)$ to $O(n{\log}n)$.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.4
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• pp.813-818
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• 2015

In this paper, WiMedia Distributed-MAC protocol is adopted for development of a seamless N-screen wireless service. Furthermore, to provide the OSMU (One Source Multi Use) N-screen service through P2P streaming in the seamless D-MAC protocol, a new Multicast-free DRP Availability IE is proposed and analyzed. In this Multicast-free DRP Availability IE, indicating Multicast DRP Owner and Receiver is required. The ACK frame transmissions are not required for Multicast transmissions in P2P N-screen services. Using this property, the Multicast-free DRP Availability IE scheme is proposed to expand the number of time slots available for unicast and multicast DRP reservations. Simulation results show that our Multicast scheme enhances performances in vewpoints of DRP reservation conflict and throughput.

• Journal of the Korean Chemical Society
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• v.16 no.3
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• pp.149-156
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• 1972

The responsive characteristics of hydrogen-responsive glass electrode in various buffer solutions of methanol, N,N-dimethylformamide and acetonitrile were examined. The potentials were attained more rapidly with an electrode stored in the same solvent medium than that stored in water before use. However, the time to be required for a stable potential increased with the basicity of buffer solution, and it was not provide a constant potential in the strong basic solution of these solvent. Even in acidic solution, the potential was varied according to the past usage of the electrode.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.195-200
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• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.573-580
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• 2006

In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Bulletin of the Korean Chemical Society
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• v.7 no.3
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• pp.201-204
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• 1986

Reduction of N-arylpyridinium compounds by $NaBH_4$ gave mixtures of the corresponding 1,2-dihydropyridine(major) and 1,4-dihydropyridine(minor), whereas similar reduction by $Na_2S_2O_4$ produced 1,4-dihydropyridines regioselectively. The proportion of 1,4-isomer in the product by $NaBH_4$ reduction appeared to increase with the electron-donating ability of N-aryl groups. When the N-aryl group is p-methylphenyl, p-ethylphenyl or p-methoxyphenyl, the 1,2-dihydropyridines in ethanol-water (4:1) solutions isomerized to the corresponding 1,4-dihydropyridines. N-(p-methylphenyl)-1,2-dihydropyridine and N-(p-ethylphenyl)-1,2-dihydropyridine in solid state also isomerized to the corresponding 1,4-dihydropyridines. The different behaviors of reduction among N-arylpyridiniums and isomerization of the reduction products depending on the substituent in N-aryl group were explained in terms of difference in the electronic effects of the substituents.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.322.2-322.2
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• 2014

Lighting emitting diodes of n-ZnO/MQW/p-GaN structure are fabricated and investigated. To realize this LED structure, n-ZnO/MQW/p-GaN are grown by MOCVD. At several bias voltages, blue-green light is emitted from the ZnO mesa edge. However, the emission is restricted near the mesa edge. It is seen that the hole current does not spread well. It is because conductivity of p-GaN is extremely small. The break down voltage of the device is small compared to conventional InGaN/GaN LEDs. It is seen that ZnO columnar grain boundaries act as leakage current paths and non-radiative recombination center.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1133-1143
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• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.