• 한국인터넷방송통신학회논문지
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• 제12권5호
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• pp.185-189
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• 2012

큰 반소수 n=pq의 소인수 p,q를 직접 찾는 것은 현실적으로 거의 불가능하여 대부분의 소인수분해 알고리즘은 $a^2{\equiv}b^2$(mod n)의 제곱합동을 찾아 p=GCD(a-b,n),q=GCD(a+b,n)의 소인수를 찾는 간접 방법을 적용하고 있다. 제곱합동 a,b을 찾는 다양한 방법이 제안되었지만 100자리 이상인 RSA 수에 대해서는 적용이 쉽지 않다. 본 논문에서는 $xa={\lceil}\sqrt{zn}{\rceil}\;or\;{\lceil}\sqrt{zn}{\rceil}+z+z=1,2,{\cdots}$로 설정하고 $(xa)^2{\equiv}(yb)^2$(mod n)을 찾는 간단한 방법을 제안한다. 제안된 알고리즘은 19 자리 수 까지는 제곱합동을 빠르게 찾는데 성공하였으나 39 자리 수에 대해서는 실패하였다.

• 환경영향평가
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• 제23권5호
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• pp.379-392
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• 2014

이 연구는 국립생물자원에서 선정한 기후변화생물지표 중에서 남한의 설악산에 제한적으로 분포하는 눈잣나무의 기후변화에 의한 잠재 서식지 예측을 위해 시행되었다. 눈잣나무의 잠재서식지 예측을위해 IPCC(AR5)의 대표농도경로(RCP)를 기후변화 시나리오로 사용하였다. 종 분포 모형은 Maxent를 사용하였고, 환경변수는 고도, 연평균기온 등으로 총 8개이다. 남한이 눈잣나무 분포지역은 설악산이 유일한 지역으로 지리적 범위는 위도 $38^{\circ}7^{\prime}8^{{\prime}{\prime}}N{\sim}38^{\circ}7^{\prime}14^{{\prime}{\prime}}N$ 경도 $128^{\circ}28^{\prime}2^{{\prime}{\prime}}E{\sim}128^{\circ}27^{\prime}38^{{\prime}{\prime}}E$ 범위에 국지적으로 분포하며, 고도는 1,586m~1,688m 범위에 분포한다. 종 분포 모형의 모형 정확도는 0.978으로 매우 우수하였고 잠재서식지 예측에 기여도가 높은 환경변수는 고도로 나타났다. LPT를 기준으로 선정된 현재기후의 잠재 서식지는 $7,345km^2$이며 기후변화 시나리오를 적용한 미래의 잠재 서식지 면적은 감소하였고 감소폭은 RCP 4.5보다 RCP 8.5가 많았다. 설악산의 눈잣나무 개체군 분포 지역은 한반도의 남방 한계선으로 예상되며 기후변화에 의해 개체군의 축소 및 소실이 예상되므로 전략적인 유전자원 확보를 위한 대책이 필요하다.

• 대한수학회지
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• 제47권2호
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• pp.311-329
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• 2010

In this paper we will prove that the groups $D_{p+1}$(2) and $D_{p+1}$(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson's conjecture for the groups $D_{p+1}$(2) and $D_{p+1}$(3).

• 대한수학회논문집
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• 제15권1호
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• pp.59-69
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• 2000

For a permutation ${\mu}$ in S$\sub$b/, the limit algebra A${\mu}$ of the stationary system given by ${\mu}$ is isomorphic to a refinement limit algebra if and only if its exponent set E(${\mu}$) is the set {0}. In the current paper, we prove a sufficient condition under which E(${\mu}$)={0} when the order of ${\mu}$ is a power of p, where p is a prime number dividing b.

• 대한수학회보
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• 제51권4호
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• pp.1205-1210
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• 2014

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that $$E/S{\sim_=}G$$ is finite. For a prime p, $\hat{S}=S/S^{\prime}S^p$ may be regarded as an $F_pG$-module via conjugation in E. The aim of this article is to prove that $\hat{S}$ is decomposable into two indecomposable modules for finite elementary abelian p-groups G.

• 대한수학회지
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• 제45권1호
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• pp.137-150
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• 2008

In this paper we will prove that the simple groups $B_p(3)\;and\;G_p(3)$, p an odd prime number, are 2-recognizable by the set of their order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G) = $OC(B_p(3))$ if and only if $G{\cong}B_p(3)\;or\;C_p(3)$.

• East Asian mathematical journal
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• 제19권1호
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• pp.81-89
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• 2003

There are many algorithms for factoring integers. The trial division algorithm is one of the most efficient algorithms for factoring small integers(say less than 10,000,000,000). For a number n to be factored, the runtime of the trial division algorithm depends mainly on the size of a nontrivial factor of n. In this paper, we create a function named factors that can implement the trial division algorithm in ActionScript and using the factors function we construct an interactive Prime Factorization Movie and an interactive GCD Movie.

• 대한수학회보
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• 제54권4호
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.25-43
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• 2005

Let F be a finite field of prime power order q(odd) and the multiplicative order of q modulo $2^{n}\;(n>1)\;be\; {\phi}(2^{n})/2$. If n > 3, then q is odd number(prime or prime power) of the form $8m{\pm}3$. If q = 8m - 3, then the ring $R_{2^n} = F[x]/ < x^{2^n}-1 >$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length $2^{n}$ generated by these idempotents are completely described. If q = 8m + 3 then the expressions for the 2n - 1 primitive idempotents of $R_{2^n}$ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n-1 idempotents are also obtained. The case n = 2,3 is dealt separately.

• 대한지역사회영양학회지
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• 제21권5호
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• pp.451-462
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• 2016

Objectives: This study was designed with the goal of understanding the factors affecting the frequency of skipping meals of prime-aged mothers with children as well as their nutritional status. Methods: Utilizing data from the 2010-2011 Korea National Health and Nutrition Survey, the frequency of skipping meals of mothers aged between 30 to 49 years with children aged between 3 to 11 years during a two day period was statistically analyzed. The number of meals skipped calculated and categorized into skipping no meals, skipping one meal, skipping two meals or more. Results: Compared to subjects who corresponded to mean nutrient adequacy ratio(MAR) of 4 quartile, subjects who corresponded to MAR of 2 quartile had 2.766 (95% CI: 1.552-4.931) probability of being in the 1 meal skippers group, while the probability of being in the more than 2 meals skippers group was 2.743(95% CI: 1.353-5.564). Also, compared to subjects who corresponded to MAR of 4 quartile, subjects who corresponded to MAR of 1 quartile had 3.471 (95% CI: 1.871-6.442) probability of being in the 1 meal skippers group, while the odds ratio for being in the more than 2 meals skippers group was 5.258(95% CI: 2.642-10.466). Conclusions: The results have the advantage of being generalized because the study selected subjects from probability sampling of the female population of Korea. The research results showed that the elements influencing skipping meals of prime-aged mothers with children were mean nutrient adequacy ratio and the number of nutrients, under estimated average requirement intake, and others. Therefore, to encourage dietary behaviors in the right direction, an integrated approach that considers the associated factors must be realized. Future studies are needed to understand how the frequency of skipping meals of mothers affects their children.