• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.293-299
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• 2005

Let ${\cal{L}}$ be a commutative subspace lattice on a Hilbert space ${\cal{H}}$ and X and Y be operators on ${\cal{H}}$. Let $${\cal{M}}_X=\{{\sum}{\limits_{i=1}^n}E_{i}Xf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}$$ and $${\cal{M}}_Y=\{{\sum}{\limits_{i=1}^n}E_{i}Yf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}.$$ Then the following are equivalent. (i) There is an operator A in $Alg{\cal{L}}$ such that AX = Y, Ag = 0 for all g in ${\overline{{\cal{M}}_X}}^{\bot},A^*A=AA^*$ and every E in ${\cal{L}}$ reduces A. (ii) ${\sup}\;\{K(E, f)\;:\;n\;{\in}\;{\mathbb{N}},f_i\;{\in}\;{\cal{H}}\;and\;E_i\;{\in}\;{\cal{L}}\}\;<\;\infty,\;{\overline{{\cal{M}}_Y}}\;{\subset}\;{\overline{{\cal{M}}_X}}$and there is an operator T acting on ${\cal{H}}$ such that ${\langle}EX\;f,Tg{\rangle}={\langle}EY\;f,Xg{\rangle}$ and ${\langle}ET\;f,Tg{\rangle}={\langle}EY\;f,Yg{\rangle}$ for all f, g in ${\cal{H}}$ and E in ${\cal{L}}$, where $K(E,\;f)\;=\;{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Y\;f_{i}{\parallel}/{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Xf_{i}{\parallel}$.

• 한국분말재료학회지
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• 제26권5호
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• pp.395-404
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• 2019

Aluminum nitride (AlN) has excellent electrical insulation property, high thermal conductivity, and a low thermal expansion coefficient; therefore, it is widely used as a heat sink, heat-conductive filler, and heat dissipation substrate. However, it is well known that the AlN-based materials have disadvantages such as low sinterability and poor mechanical properties. In this study, the effects of addition of various amounts (1-6 wt.%) of sintering additives $Y_2O_3$ and $Sm_2O_3$ on the thermal and mechanical properties of AlN samples pressureless sintered at $1850^{\circ}C$ in an $N_2$ atmosphere for a holding time of 2 h are examined. All AlN samples exhibit relative densities of more than 97%. It showed that the higher thermal conductivity as the $Y_2O_3$ content increased than the $Sm_2O_3$ additive, whereas all AlN samples exhibited higher mechanical properties as $Sm_2O_3$ content increased. The formation of secondary phases by reaction of $Y_2O_3$, $Sm_2O_3$ with oxygen from AlN lattice influenced the thermal and mechanical properties of AlN samples due to the reaction of the oxygen contents in AlN lattice.

• 대한전자공학회논문지SD
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• 제47권12호
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• pp.39-47
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• 2010

본 논문에서는 하드웨어 효율이 100%가 되는 2차원 이산 웨이블렛 변환 필터 구조를 제안한다. 전체 구조는 두 채널 QMF PR Lattice 필터로 구성된 1차원 DWT 필터 4개로 구성되었다. 1 레벨부터 J 레벨까지 순차적으로 수행함으로써 메모리 사용을 최소화 하면서도 하드웨어 효율이 100%가 되도록 설계하였으며 필터 입력 데이터를 구성해주는 DFC구조와 DCU구조를 제안하였다. 인접한 4개의 데이터를 동시에 입력 받아 처리함으로써 동시에 행방향과 열방향 DWT를 수행하므로 $N{\times}N$ 이미지를 처리하는데 $N^2(1-2^{-2J})/3$ 사이클이 소요되며 이 때 필요한 저장공간은 약 2MN-3N이다. 기존의 2D DWT 구조와 비교해 보았을 때 하드웨어 효율과 동작 속도가 향상되었으며 두 개의 1D DWT를 직렬로 연결하므로 임계경로를 감소시키기 위해서 최대 4 단까지 파이프라인을 적용하여 임계경로를 향상시킬 수 있다. 제안된 구조는 VerilogHDL로 모델링되고 동부아남 $0.18{\mu}m$ 표준셀로 합성되어 검증되었다.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.227-237
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• 2007

We define weak distributive $n$-semilattices and $n$-lattices, using variants of the absorption law and those of the distributive law. From a weak distributive $n$-semilattice, we construct direct system of subalgebras which are weak distributive $n$-lattices and show that its direct limit is a reflection of the category $wDn$-SLatt of the weak distributive $n$-semilattices.

• 대한수학회지
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• 제32권3호
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• pp.573-582
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• 1995

J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.

• 한국자기공명학회논문지
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• 제20권1호
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• pp.1-6
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• 2016

The proton NMR line widths and spin-lattice relaxation rates, $T_1^{-1}$, of ferroelectric $LiH_3(SeO_3)_2$, $Li_2SO_4{\cdot}H_2O$, and $LiN_2H_5SO_4$ single crystals were measured as a function of temperature. The line width measurements reveal rigid lattice behavior of all the crystals at low temperatures and line narrowing due to molecular motion at higher temperatures. The temperature dependences of the proton $T_1^{-1}$ for these crystals exhibit maxima, which are attributed to the effects of molecular motion by the Bloembergen - Purcell - Pound theory. The activation energies for the molecular motions of $^1H$ in these crystals were obtained. From these analysis, $^1H$ in $LiH_3(SeO_3)_2$ undergoes molecular motion more easily than $^1H$ in $LiN_2H_5SO_4$ and $Li_2SO_4{\cdot}H_2O$ crystals.

• 한국재료학회지
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• 제9권7호
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• pp.688-694
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• 1999

Ti-6Al-4V 합금을 타겟트로 사용하여 유리 기판위에 dc reactive magnetron sputtering법으로 $N_2$/(Ar+N_2)$ 비, 기전력 및 시간등의 여러 가지 증착 조건에서 Ti-6Al-4V-N 필름을 증착하였고, 각각의 증착 조건에 따른 결정구조 및 우선방위 거동은 X-선 회절장치를 사용하여 조사하였다. Ti-6Al-4V-N 필름은 본질적으로 fcc 결정구조의 $\delta$-TiN에 Al과 V이 결함으로서 고용된 변형된 형태의 $\delta$-TiN구조이고, TiN의 격자상수(4.240 )보다 작은 값을 나타내었는데, 이는 Ti(1.47 )에 비하여 상대적으로 원자반경이 작은 Al(1.43 )과 V (1.32 )이 Ti의 격자위치에 치환된 결과이다. 그리고 Ti-6Al-4V-N 필름은 $_N2$가스 분압이 감소됨에 따라 (111) 우선방위 성장거동을 하였을 뿐만아니라 증착시간의 증가에 따라 뚜렷한 (111) 우선방위 성장거동을 나타내었다. 그리고 증착속도 및 결정입도의 거동 또한 여러 가지 증착 조건에 크게 의존한다

• 한국표면공학회지
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• 제20권3호
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• pp.106-117
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• 1987

The microhardness and the structural characteristics of the chemically vapor deposited TiN film on the 430 stainless steel substrate have been investigated with various deposition parameters such as the deposition time, the total flow rate, the flow rate ratio $(H_2/N_2)$, and the deposition temperature. The most important factor to affect the microhardness of the TiN film in this study was the denseness of the structure in connection with the degree of the lattice strain. The relationship between the lattice parameter changes and the grain size variation under all deposition conditions generally followed the grain boundary relaxation model. The (111) preferred orientation prevailed in the early stage of the deposition conditions, however, the (200) preferred orientation was developed in the later stage. The surface morphology at optimum conditions displayed a dense diamond shaped structure and the microhardness of the films was high (1700-2400Hv) regardless of the type of the substrates used.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.551-572
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• 2005

Recently, there are some empirical Bayes procedures using NA samples. We point out a key equality which may not hold for NA samples. Thus, the results of those empirical Bayes procedures based on NA samples are dubious

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.513-524
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• 2005

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. Let L be a subspace lattice on H. We obtained a necessary and sufficient condition for the existence of an interpolating operator A which is in AlgL.