• Journal of the Optical Society of Korea
• /
• 제12권2호
• /
• pp.65-68
• /
• 2008

The miniband structure of a quantum dot lattice based on GaN/AlN nanowire arrays has been investigated using the finite element method and Floquet theorem. The quantum dot modes and the quantum wire modes in the nanowire arrays were graphically verified. The optimum geometries of GaN/AlN quantum wire arrays were investigated by using a correlation between the width of nanowires and the separation of the minibandgap which is to be larger than the thermal energy at room temperature.

• 한국결정성장학회지
• /
• 제13권4호
• /
• pp.172-175
• /
• 2003

We have investigated effects of the lattice mismatch between the LPE films and the substrates. We have grown $La_{2-x}Sr_{x}CuO_{4}$(x=0.1 to 0.15) single crystalline films on single crystalline substrates having different lattice parameter ratio c/a e.g., $La_{2-x}Sr_{x}Cu_{1-y}Zn_{y}O_{4},\;La_{2-x}Ba_{x}CuO_{4},\; LaSrAlO_{4}\;and\;La_{2-x}Sr_{x}Cu_{1-y}Al_{y}O_{4}$ etc., using the IR-LPE technique. The superconducting properties of the grown films were found to vary significantly depending on the lattice mismatch with different substrates.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제13권2호
• /
• pp.1003-1019
• /
• 2019

Threshold ring signature scheme enables any t entities from N ring members to spontaneously generate a publicly verifiable t-out-of-N signature anonymously. The verifier is convinced that the signature is indeed generated by at least t users from the claimed group, but he cannot tell them apart. Threshold ring signatures are significant for ad-hoc groups such as mobile ad-hoc networks. Based on the lattice-based ring signature proposed by Melchor et al. at AFRICRYPT'13, this work presents a lattice-based threshold ring signature scheme, employing the technique of message block sharing proposed by Choi and Kim. Besides, in order to avoid the system parameter setup problems, we proposed a message processing technique called "pad-then-permute", to pre-process the message before blocking the message, thus making the threshold ring signature scheme more flexible. Our threshold ring signature scheme has several advantages: inherits the quantum immunity from the lattice structure; has considerably short signature and almost no signature size increase with the threshold value; provable to be correct, efficient, indistinguishable source hiding, and unforgeable.

• Journal of applied mathematics & informatics
• /
• 제15권1_2호
• /
• pp.503-510
• /
• 2004

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;=\;y_i,\;for\;i\;=\;1,\;2,\;\cdots,\;n$. In this paper the following is proved: Let H be a Hilbert space and L be a commutative subspace lattice on H. Let H and y be vectors in H. Let $M_x\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_ix\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;and\;M_y\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_iy\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}. Then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in ${\overline{M_x}}^{\bot}$, AE = EA for all $E\;{\in}\;L\;and\;A^{*}\;=\;A$. (2) $sup\;\{\frac{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;<\;{\infty},\;{\overline{M_u}}\;{\subset}{\overline{M_x}}$ and < Ex, y >=< Ey, x > for all E in L.

• 한국진공학회지
• /
• 제17권2호
• /
• pp.109-112
• /
• 2008

고집적화된 반도체 소자 기술은 나날이 발전하고 있다. 특히 금속 배선을 위한 박막제조 공정에서 배선 선폭은 감소하고 있으며, 그 길이는 더욱 증가하게 되었다. 이러한 상황에서 금속 배선 물질에 대한 연구가 진행 되었고 그 결과 Cu가 그 대안으로 인식되었다. 하지만 Cu는 저온에서도 Si기판과 반응하므로 인하여 접촉면의 저항이 급격히 증가하여 소자로써의 기능이 불가능하게 되는 단점이 있다. 따라서 이러한 Cu와 Si기판 사이의 반응을 효과적으로 방지할 확산방지막의 개발이 필수 요건이 되었다. 본 연구는 Cu의 확산을 방지하는 W-C-N 확산방지막에 대한 연구로 질소비율과 열처리 온도를 변화하여 실험하였으며, 특히 격자상수 변화를 통하여 W-C-N 확산방지의 특성에 대하여 연구하였다.

• 전기전자학회논문지
• /
• 제6권2호
• /
• pp.136-145
• /
• 2002

정상상태에서 소자 내부의 격자온도 분포를 해석할 수 있는 시뮬레이터를 개발하였다. Slotboom 변수를 사용하여 열흐름 방정식을 이산화하였고, 요소내에서 열전도율의 적분값을 해석적으로 구할 수 있는 방법을 제안하였다. 제안된 방법의 타당성을 검증하기 위해 $N^+P$ 접합 다이오드와 BJT에 대해 모의실험을 수행하였고 DAVINCI와 MEDICI의 결과와 비교하였다. $N^+P$ 접합 다이오드에서 순방향 인가전압이 1.4[V]일 때 격자 온도분포는 DAVINCI의 결과와 2%의 상대오차를 보였으며 BJT에서 컬렉터 전압이 5.0[V]이고 베이스 전압이 0.5[V]일 때 격자 온도분포는 MEDICI의 결과와 3%의 상대오차를 보였다. BANDIS에서 제안된 열전도율의 적분방법을 사용하는 경우 수렴을 위해 평균 3.45회의 행렬 연산이 필요하나 DAVINCI에서는 평균 5.1회의 행렬 연산이 필요하였고 MEDICI는 평균 4.3회 행렬연산이 필요하였다.

• 대한수학회논문집
• /
• 제13권1호
• /
• pp.7-20
• /
• 1998

In this paper, we will investigated certain two types of isomorphisms of $B^{(n)}_{2n}$ which are closely related.

• 대한수학회지
• /
• 제54권4호
• /
• pp.1121-1148
• /
• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• Journal of applied mathematics & informatics
• /
• 제11권1_2호
• /
• pp.431-436
• /
• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;:\;y_i,\;for\;i\;=\;1,\;2,\;{\cdots},\;n$. In this article, we obtained the following : $Let\;x\;=\;\{x_i\}\;and\;y=\{y_\}$ be two vectors in a separable complex Hilbert space H such that $x_i\;\neq\;0$ for all $i\;=\;1,\;2;\cdots$. Let L be a commutative subspace lattice on H. Then the following statements are equivalent. (1) $sup\;\{\frac{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}y\$\mid$}{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}x\$\mid$}\;:\;l\;\in\;\mathbb{N},\;\alpha_{\kappa}\;\in\;\mathbb{C}\;and\;E_{\kappa}\;\in\;L\}\;<\;\infty\;and\;$\mid$y_n\$\mid$x_n$\mid$^{-1}\;=\;1\;for\;all\;n\;=\;1,\;2,\;\cdots$. (2) There exists an operator A in AlgL such that Ax = y, A is a unitary operator and every E in L reduces, A, where AlgL is a tridiagonal algebra.

• 한국결정성장학회지
• /
• 제9권5호
• /
• pp.470-474
• /
• 1999

We have successfully grown <111>-oriented $(La,Sr)(Al,Ta)O_{3}\;(LSAT)$ mixed-perovskite single crystals and <0001>-oriented ${Ca_{8}La_{2}(PO_{4})}_{6}O_2$ (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 are promising as new substrates for the growth of high quality GaN epitaxial layers.