• 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.9 no.3
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• pp.539-545
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• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.07b
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• pp.1010-1014
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• 2004

High quality GaN layer and $In_xGa_{1-x}N$ alloy were obtained on (0001)sapphire substrate using ammonia$(NH_3)$ and dimethylhydrazine$(DMH_y)$ as a nitrogen source by gas source molecular hem epitaxy(GSMBE) respectively. As a result, RHEED is used to investigate the relaxation processes which take place during the growth of GaN and $In_xGa_{1-x}N$. The full Width at half maximum of the x-ray diffraction(FWHM) rocking curve measured from Plane of GaN has exhibitted as narrow as 8 arcmin. Photoluminescence measurement of GaN and $In_xGa_{1-x}N$ were investigated at room temperature, where the intensity of the band edge emission is much stronger than that of deep level emission. In content of $In_xGa_{1-x}N$ epitaxial layer according to growth condition was investigated.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1301-1316
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• 2017

It is well known that every $x{\in}(0,1]$ can be expanded to an infinite $L{\ddot{u}}roth$ series with the form of $$x={\frac{1}{d_1(x)}}+{\cdots}+{\frac{1}{d_1(x)(d_1(x)-1){\cdots}d_{n-1}(x)(d_{n-1}(x)-1)d_n(x)}}+{{\cdots}}$$, where $d_n(x){\geq}2$ for all $n{\geq}1$. In this paper, the set of points with some restrictions on the digits in $L{\ddot{u}}roth$ series expansions are considered. Namely, the Hausdorff dimension of following the set $$F_{\phi}=\{x{\in}(0,1]\;:\;d_n(x){\geq}{\phi}(n),\;i.o.n}$$ is determined, where ${\phi}$ is an integer-valued function defined on ${\mathbb{N}}$, and ${\phi}(n){\rightarrow}{\infty}$ as $n{\rightarrow}{\infty}$.

• Korean Journal of Materials Research
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• v.12 no.1
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• pp.54-57
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• 2002

We have grown undoped $In_ xGa_{1-x}N,\; In_xGa_{1-x}N:Si\;and\;In_{0.1}Ga_{0.9}N:Zn$ thin films by MOCVD at temperature between 880 and $710^{\circ}C which endows various In composition in the epilayer from 0.07 to 0.22 as examined using X-ray diffraction, optical absorption(OA), photocurrent (PC) and photoluminescence (PL). The In molar fraction estimated from PL results is higher than that from the OA, PC, and X-ray data for $X{\le}0.22$, which may be caused by phase separation. However, the In molar fraction estimated by X-ray diffraction, OA, PC and PL for $In_xGa_{1-x}N:Si$ does not show discrepancy. With the appropriate Zn doping in undoped $In_{0.1}Ga_{0.9}N$, the emission peak is shifted from 3.15 eV which originates from the band edge emission peak to 2.65 eV which resulted from the conduction band to acceptor transition due to a deep acceptor level.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.5
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• pp.877-886
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• 2019

The energy band gaps and optical constants of zincblende $In_yGa_{1-y}As_{1-x}N_x$ on the variation of temperature and composition are determined by using band anticrossing method. The energy band gaps are decreasing continuously in $In_yGa_{1-y}As_{1-x}N_x$ ($0{\leq}x{\leq}0.05$, $0{\leq}y{\leq}1.0$, 300K) and the bowing parameter is calculated as 0.522eV. The calculation results of energy band gaps are consistent with those of other studies. A refractive index n and a high-frequency dielectric constant ${\varepsilon}$ are calculated by a proposed modeling equation using the results of energy band gaps.

• Journal of the Korean Ceramic Society
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• v.32 no.7
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• pp.809-816
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• 1995

Ti1-xAlxN films were successfully deposited on high speed steel and silicon wafer by plasma-assisted chemical vapor deposition using a TiCl4/AlCl3/N2/Ar/H2 gas mixture. Plasma process enabled N2 gas to nitride AlCl3, which is not possible in sense of thermodynamics. XPS analyses revealed that the deposited layer contained Al-N bond as well as Ti-N bond. Ti1-xAlxN films were polycrystalline and had single phase, B1-NaCl structure of TiN. Interplanar distance, d200, of (200) crystal plane of Ti1-xAlxN was, however, decreased with Al content, x. Al incorporation into TiN caused the grain size to be finer and changed strong (200) preferred orientation of TiN to random oriented microstructure. Those microstructural changes with Al addition resulted in the increase of micro-hardness of Ti1-xAlxN film up to 2800Kg/$\textrm{mm}^2$ compared with 1400Kg/$\textrm{mm}^2$ of TiN.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.12
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• pp.1165-1174
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• 2016

The energy band gaps and the bowing parameters of zincblende InAs1-xN are determined by using an empirical pseudopotential method(EPM) within the improved virtual crystal approximation(VCA), which includes the disorder effect. The direct-band-gap bowing parameter calculated by using the EPM is 4.1eV for InAs1-xNx ($0{\leq}x{\leq}0.05$). The dependences of the band gaps of N-dilute InAs1-xNx on the temperature and composition are calculated by modifying the band anti-crossing(BAC) model. The calculation results are consistent with experimental values, and the coupling parameter CMN of InAs1-xNx is found to be equal to 1.8 by fitting the EPM data.

• Journal of the Korean institute of surface engineering
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• v.45 no.1
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• pp.20-24
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• 2012

Multilayer passivation film on OLED with organic/inorganic hybrid structure as to diminish the thermal stress and expansion was researched to protect device from the direct damage of $O_2$ and $H_2O$ and improve life time characteristics. Red OLED doped with 1 vol.% Rubrene in $Alq_3$ was used as a basic device. The films consist of ITO(150 nm)/ELM200_HIL(50 nm)/ELM002_HTL(30 nm)/$Alq_3$: 1 vol.% Rubrene(30 nm)/$Alq_3$(30 nm) and LiF(0.7 nm)/Al(100 nm) which were formed in that order. Using LiF/$SiN_x$ as a buffer layer was determined because it significantly improved life time characteristics without suffering damage in the process of forming passivation film. Multilayer passivation film on buffer layer didn't produce much change in current efficiency, while the half life time at 1,000 $cd/m^2$ of OLED/LiF/$SiN_x$/E1/$SiN_x$ was 710 hours which showed about 1.5 times longer than OLED/LiF/$SiN_x$/E1 with 498 hours. futhermore, OLED/LiF/$SiN_x$/E1/$SiN_x$/E1/$SiN_x$ with 1301 hours showed about twice than OLED/LiF/$SiN_x$/E1/$SiN_x$ which demonstrated that superior characteristics of life time was obtained in multilayer passivation film. Through the above result, it was suggested using LiF/$SiN_x$ as a buffer layer could reduce the damage from the difference of thermal expansion coefficient in OLED with protective films, and epoxy layer in multilayer passivation film could function like a buffer between $SiN_x$ inorganic layers with relatively large thermal stress.