• Journal of applied mathematics & informatics
• /
• 제27권1_2호
• /
• pp.89-96
• /
• 2009

In this article, we show a generalization of Clement's theorem on the pair of primes. For any integers n and k, integers n and n + 2k are a pair of primes if and only if 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) whenever (n, (2k)!) = (n + 2k, (2k)!) = 1. Especially, n or n + 2k is a composite number, a pair (n, n + 2k), for which 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) is called a pair of pseudoprimes for any positive integer k. We have pairs of pseudorimes (n, n + 2k) with $n{\leq}5{\times}10^4$ for each positive integer $k(4{\leq}k{\leq}10)$.

• 한국정보시스템학회지:정보시스템연구
• /
• 제8권2호
• /
• pp.69-90
• /
• 1999

The purpose of this paper is to study the current status of Y2K settlement in korean business firms. To accomplish the purpose of this paper effectively, first of all, theoretical background of Y2K was reviewed briefly. Second, research hypotheses and methodology were discussed with the following topics: (1) research hypotheses (2) operational definitions of variables (3) survey population (4) data collection method (5) data analysis method. Third, current status and problems of Y2K problems were investigated in detail with the following areas: (1) characteristics of samples (2) comparisons of Y2K settlement by business area (3) comparisons of Y2K settlement by firm sizes (4) comparisons of Y2K settlement by degree of information systems (5) effective ways of settling Y2K problems Finally, this paper was summarized and future research directions were suggested briefly.

• 한국정보과학회논문지:시스템및이론
• /
• 제29권12호
• /
• pp.665-679
• /
• 2002

그래프 G의 고장지름이란 임의의 연결도-1 개 이하의 정점들에 고장이 났을 경우, 모든 두 정점사이의 최단경로 길이의 최대 값을 말한다. 본 논문에서는 $k{\geq}3$인 재귀원형군 $G(2{\leq}m,2{\leq}k)$의 고장 지름을 분석한다. $ dia_{m.k}$를$ G(2^m,2^k)$의 지름이라 하자. $G(2{\leq}m,2{\leq}k/)$일 때, $G(2{\leq}m,2{\leq}k)$의 고장지름은 $2^m-2이고$, m=k+1일 때, 고장지름은 $2^k-1$임을 보인다. 그리고 m>k+1인 재귀원형군 $G(2{\leq}m,2{\leq}k)$에서, m=1 (mod 2k)이면 고장지름은 $dia_{m.k+1}$과 같고, $m{\neq}1$ (mod 2k)이면 고장지름은 $dia_{m.k+2}$ 이하임을 보인다.

• 호남수학학술지
• /
• 제32권2호
• /
• pp.255-260
• /
• 2010

Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. We show the following : Let Alg$\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let x = $(x_i)$ and y = $(y_i)$ be vectors in H. Then the following are equivalent: (1) There exists a compact operator A = $(a_{ij})$ in Alg$\mathcal{L}$ such that Ax = y. (2) There is a sequence ${{\alpha}_n}$ in $\mathbb{C}$ such that ${{\alpha}_n}$ converges to zero and for all k ${\in}$ $\mathbb{N}$, $y_1 = {\alpha}_1x_1 + {\alpha}_2x_2$ $y_{2k} = {\alpha}_{4k-1}x_{2k}$ $y_{2k+1}={\alpha}_{4k}x_{2k}+{\alpha}_{4k+1}x_{2k+1}+{\alpha}_{4k+2}+x_{2k+2}$.

• 대한수학회지
• /
• 제47권2호
• /
• pp.263-275
• /
• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• 호남수학학술지
• /
• 제41권4호
• /
• pp.813-821
• /
• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k)f(y) + (k² - k)f(-y) - 2f(ky) = 0.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제11권2호
• /
• pp.167-173
• /
• 2004

Given vectors x and y in a separable Hilbert space $\cal H$, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate Hilbert-Schmidt interpolation problems for vectors in a tridiagonal algebra. We show the following: Let $\cal L$ be a subspace lattice acting on a separable complex Hilbert space $\cal H$ and let x = ($x_{i}$) and y = ($y_{i}$) be vectors in $\cal H$. Then the following are equivalent; (1) There exists a Hilbert-Schmidt operator A = ($a_{ij}$ in Alg$\cal L$ such that Ax = y. (2) There is a bounded sequence {$a_n$ in C such that ${\sum^{\infty}}_{n=1}\mid\alpha_n\mid^2 < \infty$ and $y_1 = \alpha_1x_1 + \alpha_2x_2$ ... $y_{2k} =\alpha_{4k-1}x_{2k}$ $y_{2k=1} = \alpha_{4kx2k} + \alpha_{4k+1}x_{2k+1} + \alpha_{4k+1}x_{2k+2}$ for K $\epsilon$ N.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권4호
• /
• pp.401-406
• /
• 2008

Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX=Y. In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following: Let ${\pounds}$ be a subspace lattice acting on a separable complex Hilbert space H and let X=$(x_{ij})$ and Y=$(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator $A=(a_{ij})$ in Alg${\pounds}$ such that AX=Y. (2) There is a bounded sequence $\{{\alpha}_n\}$ in $\mathbb{C}$ such that ${\sum}_{n=1}^{\infty}|{\alpha}_n|^2<{\infty}$ and $$y1_i={\alpha}_1x_{1i}+{\alpha}_2x_{2i}$$ $$y2k_i={\alpha}_{4k-1}x_2k_i$$ $$y{2k+1}_i={\alpha}_{4k}x_{2k}_i+{\alpha}_{4k+1}x_{2k+1}_i+{\alpha}_{4k+2}x_{2k+2}_i\;for\;all\;i,\;k\;\mathbb{N}$$.

• 정보처리학회논문지A
• /
• 제14A권6호
• /
• pp.327-332
• /
• 2007

본 논문에서는 $2^{2n-k}{\times}2^k$ 토러스 연결망과 상호연결망 HFN(n,n)과 HCN(n,n) 사이의 임베딩을 분석한다. 먼저, $2^{2n-k}{\times}2^k$ 토러스를 HFN(n,n)에 연장율 3과 밀집율 4로 임베딩 가능함을 보이며, 평균연장율이 2 이하임을 증명한다. 그리고 $2^{2n-k}{\times}2^k$ 토러스를 HCN(n,n)에 연장율 3으로 임베딩 가능함을 보이며, 평균 연장율이 2 이하임을 증명한다. 또한 HFN(n,n)과 HCN(n,n)이 $2^{2n-k}{\times}2^k$ 토러스에 임베딩하는 연장율이 O(n)임을 보인다. 이러한 결과는 토러스에서 개발된 여러 가지 알고리즘을 HCN(n,n)과 HFN(n,n)에서 효율적으로 이용할 수 있음을 의미한다.

• 호남수학학술지
• /
• 제42권3호
• /
• pp.449-460
• /
• 2020

In this paper, we investigate the stability of the additive-cubic functional equations f(x+ky)+f(x-ky)-k² f(x+y)-k² f(x-y)+(k²-1)f(x) - (k²-1)f(-x) = 0, f(x+ky)-f(ky-x)-k² f(x+y)+k² f(y-x)+2(k²-1)f(x)= 0, f(kx+y)+f(kx-y)-kf(x+y)-kf(x-y)-2f(kx)+2kf(x)= 0 by using the fixed point theory in the sense of L. Cădariu and V. Radu.