• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.5
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• pp.185-189
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• 2012

It is almost impossible to directly find the prime factor, p,q of a large semiprime, n=pq. So Most of the integer factorization algorithms uses a indirect method that find the prime factor of the p=GCD(a-b,n),q=GCD(a+b,n) after getting the congruence of squares of the $a^2{\equiv}b^2$(mod n). Many methods of getting the congruence of squares have proposed, but it is not easy to get with RSA number of greater than a 100-digit number. This paper proposes a fast algorithm to get the congruence of squares. The proposed algorithm succeeded in getting the congruence of squares to a 19-digit number.

• Journal of Environmental Impact Assessment
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• v.23 no.5
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• pp.379-392
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• 2014

This study was performed to predict the future climate envelope of Pinus pumila, a subalpine plant and a Climate-sensitive Biological Indicator Species (CBIS) of Korea. P. pumila is distributed at Mt. seorak in South Korea. Suitable habitat were predicted under two alternative RCPscenarios (IPCC AR5). The SDM used for future prediction was a Maxent model, and the total number of environmental variables for Maxent was 8. It was found that the distribution range of P. pumila in the South Korean was $38^{\circ}7^{\prime}8^{{\prime}{\prime}}N{\sim}38^{\circ}7^{\prime}14^{{\prime}{\prime}}N$ and $128^{\circ}28^{\prime}2^{{\prime}{\prime}}E{\sim}128^{\circ}27^{\prime}38^{{\prime}{\prime}}E$ and 1,586m~1,688m in altitude. The variables that contribute the most to define the climate envelope are altitude. Climate envelope simulation accuracy was evaluated using the ROC's AUC. The P. pumila model's 5-cv AUC was found to be 0.99966. which showed that model accuracy was very high. Under both the RCP4.5 and RCP8.5 scenarios, the climate envelope for P. pumila is predicted to decrease in South Korea. According to the results of the maxent model has been applied in the current climate, suitable habitat is $790.78km^2$. The suitable habitats, are distributed in the region of over 1,400m. Further, in comparison with the suitable habitat of applying RCP4.5 and RCP8.5 suitable habitat current, reduction of area RCP8.5 was greater than RCP4.5. Thus, climate change will affect the distribution of P. pumila. Therefore, governmental measures to conserve this species will be necessary. Additionally, for CBIS vulnerability analysis and studies using sampling techniques to monitor areas based on the outcomes of this study, future study designs should incorporate the use of climatic predictions derived from multiple GCMs, especially GCMs that were not the one used in this study. Furthermore, if environmental variables directly relevant to CBIS distribution other than climate variables, such as the Bioclim parameters, are ever identified, more accurate prediction than in this study will be possible.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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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).

• Communications of the Korean Mathematical Society
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• v.15 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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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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• v.19 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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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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• v.18 no.1_2
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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.

• Korean Journal of Community Nutrition
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• v.21 no.5
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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.