• 한국수학사학회지
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• 제17권1호
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• pp.33-42
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• 2004

In this paper, we identify the essential ideas of Fundamental Theorem of Arithmetic(FTA). Then, we compare these ideas with several theorems of Euclid's Elements to investigate whether the essential ideas of FTA are contained in Elements or not. From this, we have the following conclusion: Even though Elements doesn't contain FTA explicitly, it contains all of the essential ideas of FTA. Finally, we assert two reasons why Greeks couldn't mention FTA explicitly. First, they oriented geometrically, and so they understood the concept of 'divide' as 'metric'. So they might have difficulty to find the divisor of the given number and the divisor of the divisor continuously. Second, they have limit to use notation in Mathematics. So they couldn't represent the given composite number as multiplication of all of its prime divisors.

• 한국멀티미디어학회논문지
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• 제6권4호
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• pp.610-619
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• 2003

This paper presents a concept of cellular automata and a modular exponentiation algorithm and implementation of a basic EIGamal encryption by using cellular automata. Nowadays most of modular exponentiation algorithms are implemented by a linear feedback shift register(LFSR), but its structure has disadvantage which is difficult to implement an operation scheme when the basis is changed frequently The proposed algorithm based on a cellular automata in this paper can overcome this shortcomings, and can be effectively applied to the modular exponentiation algorithm by using the characteristic of the parallelism and flexibility of cellular automata. We also propose a new fast multiplier algorithm using the normal basis representation. A new multiplier algorithm based on normal basis is quite fast than the conventional algorithms using standard basis. This application is also applicable to construct operational structures such as multiplication, exponentiation and inversion algorithm for EIGamal cryptosystem.

• 대한수학회지
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• 제51권3호
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• pp.509-525
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• 2014

Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권3호
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• pp.243-256
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• 2005

Abacus numerals were developed using the concept of the binary system to form decimal numerals. This would allow addition, subtraction, multiplication, and division to be performed based solely on the knowledge of the 14 forms of the numerals and three simple rules. These numerals were taught to 260 elementary school pupils of 3rd and 4th grade. After 90 minutes of instruction, they, nearly all, were able to understand principles to add, and to subtract, and partly to multiply using Abacus Numerals. Protected Abacus Numerals are proposed against forgery. An International Numeration System is proposed based on the form of Abacus Numerals to facilitate international communication. A new type of abacus is proposed.

• 한국초등수학교육학회지
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• 제15권1호
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• pp.1-18
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• 2011

본 연구는 어림하기를 통한 소수점 찍기 활동이 초등학교 5학년 학생들의 연산과 소수점 오류를 줄이는 데에 어떤 영향을 주는지를 판단해 보고자 하는데 그 목적이 있다. 위의 연구를 위하여 실험 집단에는 소수의 연산에서 어림하기를 통한 소수점 찍기 활동을 실시하였고, 비교 집단에는 전통적인 방법의 소수점 찍기 활동을 각각 실시하였다. 그 결과 두 집단 사이의 문제해결력에서는 유의미한 차이가 없었으나 계산력에서 유의미한 차이를 발견할 수 있었으며 어림을 통한 소수점 찍기 활동이 소수점 오류를 줄이는데 지속적으로 영향을 주는 것으로 나타났다. 이는 어림하여 소수점을 찍는 활동이 소수의 개념적 이해와 소수 자릿값에 대한 이해를 도와주며, 소수의 곱셈, 나눗셈에서 소수점의 위치를 정하는데 도움을 준다는 것을 시사한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제18권1호
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• pp.126-146
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• 2024

Caladium bicolor is one of the most popular plants in Thailand. The original species of Caladium bicolor was found a hundred years ago. Until now, there are more than 500 species through multiplication. The classification of Caladium bicolor can be done by using its color and shape. This study aims to develop a model to classify Caladium bicolor using a transfer learning technique. This work also presents a proof of concept, GUI design, and web application deployment using the user-design-center method. We also evaluated the performance of the following pre-trained models in this work, and the results are as follow: 87.29% for AlexNet, 90.68% for GoogleNet, 93.59% for XceptionNet, 93.22% for MobileNetV2, 89.83% for RestNet18, 88.98% for RestNet50, 97.46% for RestNet101, and 94.92% for InceptionResNetV2. This work was implemented using MATLAB R2023a.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 추계학술대회 논문집 전기물성,응용부문
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• pp.151-159
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• 2003

According to the records, approximately 50 percent of power failure were caused by lightning. Conventional fault preventive measures against lightning include reduction of the footing resistance of the tower, multiplication of overhead ground wires and unbalanced insulation of the double circuit transmission tower. In addition to these, transmission line arresters have been recently appeared as an alternatives. In this paper an unbalanced insulation method with transmission line arrester was assumed as another countermeasure against simultaneous double circuit trip of 154 kV transmission line by lightning strike. The lightning performance of line arrester was compared with conventional insulation concept using different numbers of porcelain and glass insulator. Larger numbers of insulator simply increase flashover current level by lightning but the lightning performance doesn't proportional to it. EMTP simulation and predictive calculation of lightning failure rate were carried out to evaluate the performance.

• 대한수학회지
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• 제55권4호
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• pp.797-808
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• 2018

In [1], the authors generalize the concept of the class group of an integral domain $D(Cl_t(D))$ by introducing the notion of the S-class group of an integral domain where S is a multiplicative subset of D. The S-class group of D, $S-Cl_t(D)$, is the group of fractional t-invertible t-ideals of D under the t-multiplication modulo its subgroup of S-principal t-invertible t-ideals of D. In this paper we study when $S-Cl_t(D){\simeq}S-Cl_t(D_T)$, where T is a multiplicative subset generated by prime elements of D. We show that if D is a Mori domain, T a multiplicative subset generated by prime elements of D and S a multiplicative subset of D, then the natural homomorphism $S-Cl_t(D){\rightarrow}S-Cl_t(D_T)$ is an isomorphism. In particular, we give an S-version of Nagata's Theorem [13]: Let D be a Krull domain, T a multiplicative subset generated by prime elements of D and S another multiplicative subset of D. If $D_T$ is an S-factorial domain, then D is an S-factorial domain.

• 한국통신학회논문지
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• 제11권1호
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• pp.53-63
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• 1986

본 논문은 코드레이트가 R, 에러 정정 능력이 t일때, R>1/t를 만족하는 비이진 코드의 디코더 설계에 관한 연구이다. 에러 트래핑 디코딩 방식으로 설계하기 위해 카버링 단항식 개념을 도입하였으며, 실제 이를 이용하여 (15, 11) Reed-Solomon코드의 디코더를 구현하였다. 이 디코더 시스템은 Galois Field 곱셈 및 나눗셈 회로를 필요로 하지 않으므로 간단히 구성할 수 있었으며, 마이크로 컴퓨터를 이용하여 실험하였다. 본 연구의 결과로서, 이 디코더는 하나의 코드 위드를 디코딩하는데 60클럭이 소요되었으며 2개의 심볼 에러와 8개의 이진 버스트 에러를 정정할 수 있으며, 성능을 채널 에러 확률이 $5{\times}10^-4$~$5{\times}10^-5$정도일 때 가장 효율적임을 알 수 있었다.

• 대한수학교육학회지:학교수학
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• 제2권1호
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• pp.29-51
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• 2000

In this study, we tried to suggest an example of the analysis on the use of mathematical manipulatives. Taking algebra tiles as an example of mathematical manipulatives, we analysed several effects resulted from the use of algebra tiles. The algebra tiles make it possible to do activities that are needed to introduce and explain the distributive law and factoring. The algebra tiles have a several advantages; First of all, This model is simple. Even though they cannot make algebra easy, this model can play an important role in the transition to a new algebra course. This model provides access to symbol manipulation for students who had previously been frozen out of the course because of their weak number sense. This model provides a geometric interpretation of symbol manipulation, thereby enriching students' understanding, This model supports cooperative learning, and help improve discourse in the algebra class by giving students objects to think with and talk about. On the other hand, The disadvantages of this model are as follows; the model reinforces the misconception that -x is negative, and x is positive; the area model of multiplication is not geometrically sound when minus is involved; only the simplest expressions involving minus can be represented; It is ineffective when be used the learning of already known concept. Mathematics teachers must have a correct understanding about these advantages and disadvantages of manipulatives. Therefore, they have to plan classroom work that be maximized the positive effect of manipulatives and minimized the negative effect of manipulatives.