• Korean Journal of Mathematics
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• 제6권2호
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• pp.221-229
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• 1998

Let $k$ be a real abelian field and $k_{\infty}$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension. By using the main conjecture of Iwasawa theory, we have the following: If $p$ does not divide $\prod_{{{\chi}{\in}\hat{\Delta}_k},{\chi}{\neq}1}B_{1,{\chi}{\omega}^{-1}$, then $A_n$ = {0} for all $n{\geq}0$, where ${\Delta}_k=Gal(k/\mathbb{Q})$ and ${\omega}$ is the Teichm$\ddot{u}$ller character for $p$. The converse of this statement does not hold in general. However, we have the following when $k$ is of prime conductor $q$: Let $q$ be an odd prime different from $p$. and let $k$ be a real subfield of $\mathbb{Q}({\zeta}_q)$. If $p{\mid}{\prod}_{{\chi}{\in}\hat{\Delta}_{k,p},{\chi}{\neq}1}B_{1,{\chi}{\omega}}-1$, then $A_n{\neq}\{0\}$ for all $n{\geq}1$, where ${\Delta}_{k,p}$ is the $Gal(k_{(p)}/\mathbb{Q})$ and $k_{(p)}$ is the decomposition field of $k$ for $p$.

• 한국통신학회논문지
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• 제31권3C
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• pp.237-244
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• 2006

본 논문에서는 2차원 결합 가우시안 Q-함수(Two-dimensional joint Gaussian Q-function)를 이용하여 AWGN(Additive White Gaussian Noise) 환경에서 M-PSK(M-ary Phase Shift Keying) 신호의 I/Q 위상 불균형(Phase unbalance) 존재 시 수치 적분이 필요 없는 정확하고 일반화된 closed-form 형태의 비트 오류율(Bit Error Rate) 표현을 유도한다. 새롭게 유도된 표현은 평균 BER 뿐만 아니라 k-번째 비트의 BER에 대하여도 일반화된 식으로 되어 있어 다양한 환경으로의 적용이 용이하여 M-PSK를 적용하는 많은 디지털 통신 시스템에서 복조 시 발생할 수 있는 I/Q 위상 불균형에 의한 시스템 성능 변화에 대하여 정확한 이론적 성능 기준을 제공할 것으로 기대된다.

• 대한수학회보
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• 제39권1호
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• pp.1-8
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• 2002

We characterize the commutative Artinian rings R every proper quotient ring (respectively every proper ideal) in which is invariant with respect to all derivations.

• 충청수학회지
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• 제24권3호
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• pp.595-599
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• 2011

We prove that for any positive integer $g{\geq}3$, there are ${\gg}q^{\frac{l}{2g}}$ real cyclotomic function fields whose conductor has degree ${\leq}l$ and ideal class number is divisible by $\frac{g}{gcd(2,g)}$.

• 대한수학회논문집
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• 제20권3호
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• pp.427-436
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• 2005

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple v-ideals $m=P_0\;{\supset}\;P_1\;{\supset}\;{\cdotS}\;{\supset}\;P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i)\;=\;1\;for\;1\;{\leq}\;i\; {\leq}\;{\lceil}\;{\frac{b+1}{2}}{\rceil}\;and\;O(P_i)\;=2\;for\;{\lceil}\;\frac{b+3}{2}\rceil\;{\leq}\;i\;\leq\;t,\;where\;b=n_v$. We also show that $n_w\;=\;n_v$ when w is the prime divisor associated to a simple v-ideal $Q\;{\supset}\;P$ of order 2 and that w(R) = v(R) as well.

• 호남수학학술지
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• 제26권3호
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• pp.247-256
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• 2004

Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

• 전자공학회논문지
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• 제52권2호
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• pp.119-124
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• 2015

본 논문은 광원 라인폭이 spectral amplitude coding (SAC) OCDMA 시스템에 미치는 영향을 구하였다. q와 m값에 따라 다양한 코드를 구현할 수 있으므로 symmetric balance incomplete block design(BIBD) 코드를 분석에 사용하였다. 그 결과 입력파워가 큰 경우 ($P_{sr}=-10dBm$) 이상적인 BIBD 코드가 비이상적인 BIBD 코드보다 더 좁은 광원 라인폭이 요구되었다. 그러나 입력파워가 작은 경우 ($P_{sr}=-25dBm$)에는 그 반대로 비이상적인 BIBD 코드가 이상적인 BIBD 코드보다 더 좁은 광원 라인폭이 필요했다.

• 한국수학교육학회지시리즈A:수학교육
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• 제12권2호
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• 한국정보처리학회논문지
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• 제7권6호
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• pp.1778-1784
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• 2000

We consider the weighted shortest path updating problem, that is, the problem to reconstruct the weighted shortest paths in response to topology change of the network. This appear proposes a distributed algorithms that reconstructs the weighted shortest paths after several processors and links are added and deleted. its message complexity and ideal-time complexity are O(p$^2$+q+n') and O(p$^2$+q+n') respectively, where n' is the number of processors in the network after the topology change, q is the number of added links, and p is the total number of processors in he biconnected components (of the network before the topology change) including the deleted links or added links.

• 대한수학회보
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• 제55권1호
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• pp.311-317
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• 2018

Let (R, m) be a commutative Noetherian local ring and I be an ideal of R. In this paper it is shown that if cd(I, R) = t > 0 and the R-module $Hom_R(R/I,H^t_I(R))$ is finitely generated, then $$t={\sup}\{{\dim}{\widehat{\hat{R}_p}}/Q:p{\in}V(I{\hat{R}}),\;Q{\in}mAss{_{\widehat{\hat{R}_p}}}{\widehat{\hat{R}_p}}\;and\;p{\widehat{\hat{R}_p}}=Rad(I{\wideha{\hat{R}_p}}=Q)\}$$. Moreover, some other results concerning the cohomological dimension of ideals with respect to the rings extension $R{\subset}R[X]$ will be included.