• 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 ${\delta}$.

• Journal of the Korean Ceramic Society
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• v.28 no.4
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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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• v.13 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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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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• v.20 no.2
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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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• v.73 no.12
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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.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1999.06a
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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.

• Journal of the Korean Ceramic Society
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• v.26 no.1
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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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.2
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• pp.105-111
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• 2024

This paper deals with the minimum linear arrangement(MinLA) of a lattice graph, to which an approximate algorithm of linear complexity O(n) remains as a viable solution, deriving the optimal MinLA of 31,680 for 33×33 lattice. This paper proposes a partitioning arrangement algorithm of complexity O(1) that delivers exact solution to the minimum linear arrangement. The proposed partitioning arrangement algorithm could be seen as loading boxes into a container. It firstly partitions m rows into r₁,r₂,r₃ and n columns into c₁,c₂,c₃, only to obtain 7 containers. Containers are partitioning with a rule. It finally assigns numbers to vertices in each of the partitioned boxes location-wise so as to obtain the MinLA. Given m,n≥11, the size of boxes C₂,C₄,C₆ is increased by 2 until an increase in the MinLA is detected. This process repeats itself 4 times at maximum given m,n≤100. When tested to lattice in the range of 2≤n≤100, the proposed algorithm has proved its universal applicability to lattices of both m=n and m≠n. It has also obtained optimal results for 33×33 and 100×100 lattices superior to those obtained by existing algorithms. The minimum linear arrangement algorithm proposed in this paper, with its simplicity and outstanding performance, could therefore be also applied to the field of Very Large Scale Integration circuit where m,n are infinitely large.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.503-503
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• 1994