• 한국컴퓨터정보학회논문지
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• 제20권3호
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• pp.69-74
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• 2015

본 논문은 램지 수에 대해 해결하지 못한 $43{\leq}R(5,5){\leq}49$와 $102{\leq}R(6,6){\leq}165$의 문제를 해결하였다. $k_n$ 완전 그래프의 램지 수 R(s,t)는 임의의 정점 ${\upsilon}$의 n-1개 부속 간선수가 (n-1)/2=R과 (n-1)/2=B의 2가지 색으로 정확히 양분된다. 따라서 임의의 정점 ${\upsilon}$로부터 거리 개념을 적용하여 {$K_L,{\upsilon}$}의 (n-1)/2=R, ${\upsilon},K_R$의 (n-1)/2=B색이 되도록 $K_n=K_L+{\upsilon}+K_R$ 분할 그래프를 형성하였다. 이로부터 $K_L$이 $K_{s-1)$의 R색을 형성하면 $K_s$를 얻을 수 있다. $K_R$이 $K_{t-1}$의 B색을 형성하면 $K_t$를 얻는다. $K_L$과 $K_R$의 최대 거리는 짝수와 모든 정점의 부속 간선 수는 동일하다는 필요충분조건을 만족시키는 $R(s,t)=K_n$을 구하였다. 결국, R(5,5)=43과 R(6,6)=91을 증명하였다.

• 대한수학회보
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• 제34권1호
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• pp.9-17
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• 1997

Define $\bar{g}{\upsilon, \omega) = -\upsilon_1\omega_1 + \cdots + \upsilon_n\omega_n$ for $\upsilon, \omega in R^n$. $R^n$ together with this metric is called the Lorentzian n-space, denoted by $L^n$, and $R^n$ together with the Euclidean metric is called the Euclidean n-space, denoted by $E^n$. A Lorentzian surface in $L^n$ means an orientable connected 2-dimensional Lorentzian submanifold of $L^n$ equipped with the induced Lorentzian metrix g from $\bar{g}$.

• 대한수학회보
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• 제56권5호
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• 대한수학회보
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• 제52권2호
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• pp.531-540
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• 2015

Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{&gt;k}(I,A)$ the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all $t{\leq}r$ the sets $$(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/I^n,A)))_{{\geq}k}\;and\\(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/(a_1^{n_1},{\cdots},a_l^{n_l}),A)))_{{\geq}k}$$ are independent of the choice of $n,n_1,{\cdots},n_l$ for any system of generators ($a_1,{\cdots},a_l$) of I.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.855-868
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• 2021

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≤ 1, then for 𝜌R ≥ k² and 𝜌 ≤ R, Aziz and Zargar [4] proved that $${\max_{{\mid}z{\mid}=1}}{\mid}p^{\prime}(z){\mid}{\geq}n{\frac{(R+k)^{n-1}}{({\rho}+k)^n}}\{{\max_{{\mid}z{\mid}=1}}{\mid}p(z){\mid}+{\min_{{\mid}z{\mid}=k}}{\mid}p(z){\mid}\}$$. We prove a generalized L^r extension of the above result for a more general class of polynomials $p(z)=a_nz^n+\sum\limits_{{\nu}={\mu}}^{n}a_n-_{\nu}z^{n-\nu}$, $1{\leq}{\mu}{\leq}n$. We also obtain another L^r analogue of a result for the above general class of polynomials proved by Chanam and Dewan [6].

• 정보보호학회논문지
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• 제11권5호
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• pp.63-74
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• 2001

본 논문에서는 공개 키 암호시스템에서의 필수적인 연산인 모듈라 멱승을 처리하기 위한 멱승기의 회로 구조를 제안한다. 제안한 멱승기는 Montgomery 알고리듬을 사용한 곱셈기를 채택하였으며 멱승의 사전·사후 계산 과정을 쉽게 처리할 수 있도록 MUX를 이용한 것이 특징이다. 논문에서 n비트의 모듀라 멱승을 가정하여 L-R 이진 방식과 R-L이진 방식에 기초한 두 가지 형태의 설계 구조를 제안하였다. 구현에 사용된 곱셈기가 m번 클럭의 캐리 처리과정을 포함하여 (n+m)번의 클럭만에, R-L 방식 멱승기는 (n+4)(n+m)번의 클럭 시간에 멱승을 처리할 수 있다.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.143-154
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• 2003

A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group T(l, m, n) = 〈$\chi$, y, z│$\chi$$\^$l/ = y$\^$m/ = z$^n$ = $\chi$yz = 1〉. In [19], the question of finding all triples (l, m, n) such that non-abelian finite simple group are (l, m, n)-generated was posed. In this paper we partially answer this question for the sporadic group Ru. In fact, we prove that if p, q and r are prime divisors of │Ru│, where p < q < r and$.$(p, q) $\neq$ (2, 3), then Ru is (p, q, r)-generated.

• 한국인터넷방송통신학회논문지
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• 제14권5호
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• pp.87-93
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• 2014

n/m=qm+r에서 에서 m=7인 단순한 경우에도 주어진 수 n이 m의 배수 판정법은 간단하지가 않다. 만약, m이 두 자리 수 이상이 되면 더욱 복잡해진다. 일반적인 배수 판정법으로 둔켈스 (Dunkels)법이 있지만 n이 컴퓨터로 처리하지 못하는 매우 큰 자리수인 경우 이 방법도 처리할 수 없다. 본 논문은 n과 m의 자리수와 무관하게 n(modm)=0 여부로 n이 m의 배수인지 여부를 검증하는 간단하면서도 정확한 방법을 제안한다. 제안된 방법은 $n=n_1n_2n_3{\cdots}n_k$, $m=m_1m_2{\cdots}m_l$에 대해 $r_1=n_1n_2{\cdots}n_l(mod m)$으로 설정하고, $r_i=r_{i-1}{\times}10+n_i(mod m)$, $i=2,3,{\cdots},k-1+1$로 n의 자리수를 1자리씩 감소시키는 방법을 적용하였다. 제안된 방법을 다양한 n,m 데이터에 적용한 결과 쉽고, 빠르며 정확한 몫과 나머지 값을 구할 수 있음을 보였다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• 대한수학회보
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• 제20권1호
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• pp.45-49
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• 1983

If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.