• 한국산업정보학회논문지
• /
• 제12권2호
• /
• pp.68-78
• /
• 2007

D-클래스는 주어진 동치관계(equivalence relation)에 있는 $n{\times}n$ 불리언 행렬의 집합으로 정의된다. D-클래스 계산은 $n{\times}n$ 불리언 행렬의 전체 집합을 대상으로 이 집합에서 조합할 수 있는 모든 세 불리언 행렬 사이의 곱셈을 요구한다. 그러나 불리언 행렬에 대한 대부분의 연구는 단지 두 개의 불리언 행렬에 대한 효율적인 곱셈에 집중되었으며 모든 불리언 행렬 사이의 곱셈에 대한 연구는 최근에야 소수가 보이고 있다. 본 논문은 모든 세 개의 불리언 행렬 곱셈과 모든 D-클래스를 보다 효율적으로 계산할 수 있는 이론을 제시하고 이를 적용한 알고리즘과 실행결과에 대하여 논한다.

• 대한수학회논문집
• /
• 제10권2호
• /
• pp.349-355
• /
• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• 대한기계학회논문집
• /
• 제2권3호
• /
• pp.53-61
• /
• 1978

This study has been concentrated on the relations between the crack growth rate and the stress intensity factor, the fatigue limit and finally on the condition of the crack propagation along the laminated cross section of the laminated steel under the repeated plane bending through tests. The following results are obtained. 1. The fatigue limit of the laminated steel is higher than the single steel 2. The realtion between the fatigue crack growth rate, dL/dN and Stress intensity factor are ; dL/dN = 2.14 * 10$^{-11}$ $K^{2.95}$ for SUP 9 dL/dN = 1.70 * 10$^{-11}$ $K^{2.95}$ for SMS dL/dN = 9.77 * 10$^{-11}$ $K^{2.95}$ for SPMS dL/dN = 3.57 * 10$^{-8}$ $K^{1.53}$ for SPMM dL/dN = 5.5O * 10$^{-8}$ $K^{1.53}$ for MLD 3. The crack propagation of the laminated steel also tends to be completed through 3 steps; The first step proceeds swiftly, in a second slowly for a long time and last very rapidly for a short moments.

• Archives of Pharmacal Research
• /
• 제20권3호
• /
• pp.259-263
• /
• 1997

In the preparation of acyclic thymidine nucleoside analogues, $K_2CO_3$(or NaH) treated thymine in DMSO was alkylated with .omega.-chloroalkyl nitrite (Cl-(CH_2)n-CN; n=1, 2, 3, 4) to provide an isomeric mixture of 1-(${\omega}$-cyanoalkyl)thymine (2a-d) and 1,3-bis(${\omega}$-cyanoalkyl)thymine in approximately 5:1 ratios. Reduction of the cyano function 2a-d with $NaBH_{4}/CoCl_{2}$ center dot$ 6H_{2}O$gave the corresponding 1-(${\omega}$aminoalkyl)thymine (3a-d). The newly formed primary amino function in 3a-d was directly reacted with 2-chloroethylisocyanate to afford the 1-[.omega.($N^{I}$-2-chloroethylureido) alkyl]thymine (4a-d) in good yields. Nitrosation of 1-[5-($ N^{I}-2$-chloroethylureido)pentyl] thymine (4d) with glacial acetic acid and dry $NaNO_{2}$-powder in anhydrous $CH_{2}Cl_{2}$gave two types of regioisomeric nitrosoureas, 1-[5-($N^{I}$--chloroethyl-$N^{I}$--nitrosoureido)pentylithymine (5d) and 1-[5-($N^{I}-2$-chloroethyl-N-nitrosoureido)pentyllthymine in approximately 5 :1 ratios. The in vitro cytotoxicity of the synthesized compounds (2a-d, 3a-d, 4a-d and 5a-d) against three cell lines (K-562, P-388 and FM-3A) are measured as $IC^{50}$ values. Compounds 3b and 4c showed moderate activities against all three cell lines, and all other compounds were found to be not active.

• Korean Journal of Mathematics
• /
• 제19권4호
• /
• pp.343-349
• /
• 2011

Let D be an integral domain, $D^w$ be the $w$-integral closure of D, X be an indeterminate over D, and $N_v=\{f{\in}D[X]{\mid}c(f)_v=D\}$. In this paper, we introduce the concept of $t$-locally APVD. We show that D is a $t$-locally APVD and a UMT-domain if and only if D is a $t$-locally APVD and $D^w$ is a $PvMD$, if and only if D[X] is a $t$-locally APVD, if and only if $D[X]_{N_v}$ is a locally APVD.

• Bulletin of the Korean Chemical Society
• /
• 제33권3호
• /
• pp.975-979
• /
• 2012

Structure and Dynamics of dilute two-dimensional (2D) ring polymer solutions are investigated by using discontinuous molecular dynamics simulations. A ring polymer and solvent molecules are modeled as a tangent-hard disc chain and hard discs, respectively. Some of solvent molecules are confined inside the 2D ring polymer unlike in 2D linear polymer solutions or three-dimensional polymer solutions. The structure and the dynamics of the 2D ring polymers change significantly with the number ($N_{in}$) of such solvent molecules inside the 2D ring polymers. The mean-squared radius of gyration ($R^2$) increases with $N_{in}$ and scales as $R{\sim}N^{\nu}$ with the scaling exponent $\nu$ that depends on $N_{in}$. When $N_{in}$ is large enough, ${\nu}{\approx}1$, which is consistent with experiments. Meanwhile, for a small $N_{in}{\approx}0.66$ and the 2D ring polymers show unexpected structure. The diffusion coefficient (D) and the rotational relaxation time ($\tau_{rot}$) are also sensitive to $N_{in}$: D decreases and $\tau$ increases sharply with $N_{in}$. D of 2D ring polymers shows a strong size-dependency, i.e., D ~ ln(L), where L is the simulation cell dimension. But the rotational diffusion and its relaxation time ($\tau_{rot}$) are not-size dependent. More interestingly, the scaling behavior of $\tau_{rot}$ also changes with $N_{in}$; for a large $N_{in}$ $\tau_{rot}{\sim}N^{2.46}$ but for a small $N_{in}$ $\tau_{rot}{\sim}N^{1.43}$.

• 한국초전도ㆍ저온공학회논문지
• /
• 제18권2호
• /
• pp.5-7
• /
• 2016

We present an experimental investigation of the superconducting transition temperatures, $T_c$, of superconductor/ferromagnet bilayers with varying the thickness of ferromagnetic layer. FeN was used for the ferromagnetic (F) layer, and NbN and Nb were used for the superconducting (S) layer. The results were obtained using three different-thickness series of the S layer of the S/F bilayers: NbN/FeN with NbN thickness, $d_{NbN}{\approx}9.3nm$ and $d_{NbN}{\approx}10nm$, and Nb/FeN with Nb thickness $d_{Nb}{\approx}15nm$. $T_c$ drops sharply with increasing thickness of the ferromagnetic layer, $d_{FeN}$, before maximal suppression of superconductivity at $d_{FeN}{\approx}6.3nm$ for $d_{NbN}{\approx}10nm$ and at $d_{FeN}{\approx}2.5nm$ for $d_{Nb}{\approx}15nm$, respectively. After shallow minimum of $T_c$, a weak $T_c$ oscillation was observed in NbN/FeN bilayers, but it was hardly observable in Nb/FeN bilayers.

• 대한수학회지
• /
• 제56권5호
• /
• pp.1333-1354
• /
• 2019

In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.

• 대한수학회보
• /
• 제48권6호
• /
• pp.1137-1146
• /
• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• 대한수학회지
• /
• 제32권1호
• /
• pp.141-149
• /
• 1995

Let N denote the set of positive integers. Fix $d_1, d_2 \in N with d = d_1 + d_2$. Let X and Y be real random variables and let ${X_i : i \in N^d_1} and {Y_j : j \in N^d_2}$ be independent families of independent identically distributed random variables with $L(X) = L(X_i) and L(Y) = L(Y_j)$, where $L(\cdot)$ denote the law of $\cdot$.