• 대한수학회논문집
• /
• 제12권1호
• /
• pp.157-163
• /
• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.

• 한국진공학회지
• /
• 제1권3호
• /
• pp.346-352
• /
• 1992

반자성 반도체인 MnxCd1-xGa2Se4의 단결정을 조성비 ( $0leq$ $X \leq$ 1) 영역에서 TVTP(time-varying temperature profile)에 의한 화학수송법으로 성장하였다. 성장된 단결정 은 자연면을 갖은 경면으로 성장되었으며, X = 1.0 경우인 단결정의 크기는 12 $\times$ 6 $\times$ 1.5mm3이었다. MnxCd1-xGa2Se4의 결정구조는 defect chalcopyrite 구조이었으며, 조성비 X 가 증가함에 따라 격자상수 a는 선형적으로 감소하고, 격자상수 c는 증가하였다. 또한 distortion factor 2-(c/a)는 감소하였다.

• 대한수학회보
• /
• 제52권1호
• /
• pp.35-43
• /
• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1753-1767
• /
• 2008

Consider the nonparametric regression model $Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}$ ($1\;{\leq}\;i\;{\leq}\;n$), where g($\cdot$) is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors {${\epsilon}_{ni}$, $1\;{\leq}\;i\;{\leq}\;n$} have the same distribution as {$V_i$, $1\;{\leq}\;i\;{\leq}\;n$}, here $V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}$ with ${\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|$ < $\infty$ and {$e_t$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($\cdot$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($n^{-1/4}({\log}\;n)^{3/4}$).

• E2M - 전기 전자와 첨단 소재
• /
• 제6권1호
• /
• pp.63-68
• /
• 1993

CO$_{2}$기체의 운동량변환, 진동여기, 전자여기 및 전리충돌 단면적의 결정은 온도 293[.deg.K], 상대전계의 세기 E/N은 1.0[Td].leq.E/N.leq.200[Td]의 범위에서 볼츠만 방정식을 Backward-Prolongation 방법으로 해석하여 전자 이동속도의 계산값을 산출하고 이것을 M. T. Elford에 의해 실험적으로 측정된 이동속도의 값과 비교하였다. 본 연구에서 운동량변환충돌단면적은 Hake & Phelps의 값을 기초로 하였으며 온도 293[.deg.K], 상대전계의 세기 E/N은 3.0[Td].leq.E/N.leq.50[Td]인 범위 전자에너지분포함수 및 전자특성에너지는 상대전계의 세기 E/N이 1.0[Td].leq.E/N.leq.200[Td]인 범위에서 산출하였다.

• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.1-37
• /
• 2004

We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.

• 대한수학회지
• /
• 제51권6호
• /
• pp.1141-1154
• /
• 2014

A k-hypertournament H on n vertices, where $2{\leq}k{\leq}n$, is a pair H = (V,A), where V is the vertex set of H and A is a set of k-tuples of vertices, called arcs, such that for all subsets $S{\subseteq}V$ with |S| = k, A contains exactly one permutation of S as an arc. Recently, Li et al. showed that any strong k-hypertournament H on n vertices, where $3{\leq}k{\leq}n-2$, is vertex-pancyclic, an extension of Moon's theorem for tournaments. In this paper, we prove the following generalization of another of Moon's theorems: If H is a strong k-hypertournament on n vertices, where $3{\leq}k{\leq}n-2$, and C is a Hamiltonian cycle in H, then C contains at least three pancyclic arcs.

• 충청수학회지
• /
• 제26권1호
• /
• pp.147-159
• /
• 2013

Hamada ([8]) and Maruta ([17]) proved the minimum length $n_3(6,\;d)=g_3(6,\;d)+1$ for some ternary codes. In this paper we consider such minimum length problem for $q{\geq}4$, and we prove that $n_q(6,\;d)=g_q(6,\;d)+1$ for $d=q^5-q^3-q^2-2q+e$, $1{\leq}e{\leq}q$. Combining this result with Theorem A in [4], we have $n_q(6,\;d)=g-q(6,\;d)+1$ for $q^5-q^3-q^2-2q+1{\leq}d{\leq}q^5-q^3-q^2$ with $q{\geq}4$. Note that $n_q(6,\;d)=g_q(6,\;d)$ for $q^5-q^3-q^2+1{\leq}d{\leq}q^5$ by Theorem 1.2.

• 설비공학논문집
• /
• 제22권8호
• /
• pp.523-529
• /
• 2010

We investigate two-dimensional laminar flow around rectangular cylinders placed in a uniform stream. Numerical simulations are performed, using finite volume method, in the ranges of $50{\leq}Re{\leq}150$ and $0.1{\leq}W/H{\leq}1.0$, where Re and W/H are the Reynolds number and the width-to-height ratio, respectively. The immersed boundary method is used to handle the rectangular cylinder in a rectangular grid system. Comparisons with the previous results show good agreement in Strouhal number, drag and lift coefficient. The present study reports the detailed information of flow structure at different width-to-height ratios in the ranges of $50{\leq}Re{\leq}150$.

• 대한수학회보
• /
• 제36권2호
• /
• pp.273-285
• /
• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.