• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.81-98
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• 2009

This study analyzed the types of quantitative reasoning and the characteristics of representation in order to figure out the characteristics of quantitative reasoning of the sixth graders. Three students who used quantitative reasoning in solving problems were interviewed in depth. Results showed that the three students used two types of quantitative reasoning, that is difference reasoning and multiplicative reasoning. They used qualitatively different quantitative reasoning, which had a great impact on their problem-solving strategy. Students used symbolic, linguistic and visual representations. Particularly, they used visual representations to represent quantities and relations between quantities included in the problem situation, and to deduce a new relation between quantities. This result implies that visual representation plays a prominent role in quantitative reasoning. This paper included several implications on quantitative reasoning and quantitative approach related to early algebra education.

• Journal of KIISE:Databases
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• v.29 no.5
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• pp.347-357
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• 2002

Graphs have provided a powerful methodology to solve a lot of real-world problems, and therefore there have been many proposals on the graph representations and algorithms. But, because most of them considered only memory-based graphs, there are still difficulties to apply them to large-scale problems. To cope with the difficulties, this paper proposes a graph representation and graph algorithms based on the well-developed relational database theory. Graphs are represented in the form of relations which can be visualized as relational tables. Each vertex and edge of a graph is represented as a tuple in the tables. Graph algorithms are also defined in terms of relational algebraic operations such as projection, selection, and join. They can be implemented with the database language such as SQL. We also developed a library of basic graph operations for the management of graphs and the development of graph applications. This database approach provides an efficient methodology to deal with very large- scale graphs, and the graph library supports the development of graph applications. Furthermore, it has many advantages such as the concurrent graph sharing among users by virtue of the capability of database.

• 핵융합뉴스레터
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• s.47
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• pp.4-5
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• 2010

지난 겨울 개봉과 동시에 사상 최고의 박스오피스 수입을 기록했던 영화 <아바타>에는 판도라섬의 자원인 '언옵타늄'이 나온다. 영화 속에서 '언옵타늄'은 초전도체의 특성을 지닌 물체로 지구의 에너지자원 고갈물제를 해결해 줄 수 있는 대체에너지 자원으로 설정돼 있다. 이 영화는 비록 현실이 아닌 가상 세계를 통해 미래 세계의 희망을 표현했지만 대체에너지 개발의 중요성를 잘 보여주고 있다.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.15-32
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• 2003

Since algebra before the 19th century was the study of equations and equations are not differentiated from polynomials because of lack of the equality sign, the algebraic symbolism of polynomials plays very important role for tile history of algebra. We deal with the evolution of literal notations of polynomials in western and eastern worlds, and then compare their history.

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.367-382
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• 2005

In this paper, we deal with various contents relating to the group concept in school mathematics and teaching of algebraic structures indirectly by combining these contents. First, we consider structure of knowledge based on Bruner, and apply these discussions to the teaching of algebraic structure in school algebra. As a result of these analysis, we can verify that the essence of algebraic structure is group concept. So we investigate the previous researches about group concept: Piaget, Freudenthal, Dubinsky. In our school, the contents relating to the group concept have been taught from elementary level indirectly. Tn elementary school, the commutative law and associative law is implicitly taught in the number contexts. And in middle school, various linear equations are taught by the properties of equality which include group concept. But these algebraic contents is not related to the high school. Though we deal with identity and inverse in the binary operations in high school mathematics, we don't relate this algebraic topics with the previous learned contents. In this paper, we discussed algebraic structure focusing to the group concept to obtain a connectivity among school algebra. In conclusion, the group concept can take role in relating these algebraic contents and teaching the algebraic structures in school algebra.

• Journal of KIISE
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• v.43 no.5
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• pp.541-552
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• 2016

This paper introduces the new notions of conjunctive and complement choices in process algebra, which reduce both process and system complexities significantly for distributed mobile real-time system during specification and analysis phases. The complement choice implies that two processes make cohesive choices for their synchronous partners at their own choice operations. The conjunctive choice implies choice dependency among consecutive choice operations in a process. The conjunctive choice reduces process complexity exponentially by the degree of the consecutive choice operations. The complement choice also reduces system complexity exponentially by the degree of the synchronous choice operations. Consequently, the reduction method makes the specification and analysis of the systems much easier since the complexity is reduced significantly. This notion is implemented in a process algebra, called ${\delta}$-Calculus. The efficiency and effectiveness are demonstrated with an example in a tool for the algebra, called SAVE, which is developed on ADOxx platform.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.3
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• pp.697-703
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• 2000

As device dimensions are lastly scaled down, impact ionization(I.I.) events are very important to analyze hot carrier transport in high energy region, and the exact model of impact ionization is demanded on device simulation. We calculate full band model by empirical pseudopotential method and the impact ionization rate is derived from modified Keldysh formula. We calculate impact ionization coefficients by full band Monte Carlo simulator to investigate temperature dependent characteristics of impact ionization for GaAs as a function of field. Resultly impact ionization coefficients are in good agreement with experimental values at look. We how energy is increasing along increasing the field, while energy is decreasing along increasing the temperature since the phonon scattering rates for emission mode are very high at high temperature. The logarithmic fitting function of impact ionization coefficients is described as a second orders function of temperature and field. The residuals of the logarithmic fitting function are mostly within 5%. We Dow, therefore, the logarithm of impact ionization coefficients has quadratic dependence on temperature, and we can save time of calculating the temperature dependent impact ionization coefncients as a function of field.

• The Journal of Society for e-Business Studies
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• v.17 no.4
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• pp.209-219
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• 2012

Objects such as products, product reviews, and user profiles are important in e-commerce domain. Vector is one of the most widely used object representation scheme. Information of e-commerce objects may be modeled by vectors in which the featured values are assigned to various dimensions. E-commerce objects are in general quantitatively large while some are similar or even same in reality. It Plays, therefore, an important role to measure the similarity between objects. In this paper, we survey the state-of-the -art vector similarity measures. Similarity measures are analyzed to feature the algebraic characteristics and relationship of those, and upon which we classify the related measures accordingly. We then present such features that standard vector similarity measures should convey.