• 대한수학회지
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• 제15권1호
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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 ${\delta}$.

• 한국세라믹학회지
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• 제28권4호
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• pp.269-278
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• 1991

Fine AlN powder was synthesized by carbothermal reduction and nitridation of alumimun hydroxide prepared from Al-isopropoxide. AlN ceramics with Y2O3 and CaO were prepared by hot-pressing under the pressure of 30 MPa at 180$0^{\circ}C$ for 1 h in N2 atmosphere. Grain boundary behavior and purification mechanism of AlN lattice were examined by heat treatment of AlN ceramics at 185$0^{\circ}C$ for 1-6 h in N2 atmosphere. AlN ceramics without sintering additives showed poor sinterability. However, Y2O3-doped and CaO-doped AlN ceramics were fully densified nearly to theoretical density. As the heat treatment time increased, c-axis lattice parameter increased. This is attributed to the removal of Al2O3 in AlN lattice. This purification effect of AlN attice depended upon the quantity of secondary oxide phase in the inintial stage of heat treatment and the heat treatment time.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.153-163
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• 2003

The fuzzification of a positive implicative filter is considered, and some of properties are investigated. The relation among fussy filter, fuzzy n-fold implicative filter, and fuzzy n-fold positive implication filter is discussed.

• 대한수학회보
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• 제55권2호
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• pp.449-467
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• 2018

In this paper we introduce and study the lattice paths for which the horizontal step is allowed at height $h{\geq}0$, $h{\in}{\mathbb{Z}}$. By doing so these paths generalize the heavily studied weighted lattice paths that consist of horizontal steps allowed at height zero only. Six q-series identities of Rogers-Ramanujan type are studied combinatorially using these generalized lattice paths. The results are further extended by using (n + t)-color overpartitions. Finally, we will establish that there are certain equinumerous families of (n + t)-color overpartitions and the generalized lattice paths.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• Journal of the Korean Physical Society
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• 제73권12호
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• pp.1808-1813
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• 2018

I develop a transfer matrix algorithm for computing the geometric quantities of a square lattice polymer with nearest-neighbor interactions. The radius of gyration, the end-to-end distance, and the monomer-to-end distance were computed as functions of the temperature. The computation time scales as ${\lesssim}1.8^N$ with a chain length N, in contrast to the explicit enumeration where the scaling is ${\sim}2.7^N$. Various techniques for reducing memory requirements are implemented.

• 한국결정성장학회:학술대회논문집
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• 한국결정성장학회 1999년도 PROCEEDINGS OF 99 INTERNATIONAL CONFERENCE OF THE KACG AND 6TH KOREA·JAPAN EMG SYMPOSIUM (ELECTRONIC MATERIALS GROWTH SYMPOSIUM), HANYANG UNIVERSITY, SEOUL, 06월 09일 JUNE 1999
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• pp.3-26
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• 1999

We have successfully grown <111>-oriented (La,Sr)(Al,Ta)$O_3$(LSAT) mixed-perovskite single crystals and <0001>-oriented $Ca_8La_2(PO_4)_6O_2$(CLPA) single crystals with the apatite structure by the Czochralski method. The compositional and lattice parameter uniformity of the crystals are discussed in relation to the growth conditions. Since LSAT and CLPA single crystals have excellent lattice matching with GaN, they ar promising as new substrates for the growth of high quality GaN epitaxial layers.

• 한국세라믹학회지
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• 제26권1호
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• pp.13-20
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• 1989

After sintering Si3N4 containing 20wt% of variable composition ratio of Y2O3 and Al2O3 at 1$600^{\circ}C$, the specimens were annealed at 125$0^{\circ}C$ and 135$0^{\circ}C$ for 5, 10, 15 hours in order to crystallize the remanining oxynitride glass phases. The main grain-boundary crystalline phases in the Si3N4-Y2O3-Al2O3 system were melilite and YAG. By annealing 15hrs. at 125$0^{\circ}C$, almost all of the glasses were crystallized. During the growth of melilite, lattice volyume of $\beta$-Si3N4 was increased as Al3+ and O2- ions in the oxynitride glass diffuse into $\beta$-Si3N4 lattice, but during the growth of YAG, lattice volume of $\beta$-Si3N4 was decreased by reverse diffusion of Al3+ and O2- ions. In case of crystallization of glass phase to melilite, thermal expansion of sample was decreased, but in case of crystallization to YAG, inverse phenomen on was observed.

• 한국인터넷방송통신학회논문지
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• 제24권2호
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• pp.105-111
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• 2024

격자 그래프의 최소 선형 배열(MinLA)은 선형 복잡도 O(n)의 근사 알고리즘이 적용되고 있으며, 33×33격자의 최적 MinLA는 31,680으로 알려져 있다. 본 논문은 격자의 정확한 해 MinLA를 복잡도 O(1)으로 구하는 분할배열 알고리즘을 제안하였다. 분할배열 알고리즘은 컨테이너에 박스를 넣는 방법으로 m행을 r₁,r₂,r₃로, n열을 c₁,c₂,c₃로 분할하여 7개 컨테이너를 얻고 규칙을 가지도록 분할한다. 분할된 박스들에 있는 정점들 위치 순서로 번호를 부여하여 MinLA를 구한다. m,n≥11에 대해 C₂,C₄,C₆ 박스 크기를 2씩 증가시키면서 MinLA가 증가할 때까지 반복 수행한다. 이 과정은 m,n≤100에 대해 최대 4회 반복 수행하는 특징이 있다. 제안된 알고리즘은 m=n과 m≠n인 모든 격자에 적용할 수 있다. 분할배열 알고리즘을 2≤n≤100 격자에 적용하였으며, 33×33과 100×100 격자에 대해 기존 알고리즘들보다 월등히 좋은 최적의 결과를 얻었다. 제안된 알고리즘은 간단하면서도 보다 정확한 해를 얻을 수 있어 m,n이 무한히 크더라도 쉽게 해를 얻을 수 있어 VLSI 회로 설계 분야에 응용이 될 수 있을 것이다.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.503-503
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• 1994