• Honam Mathematical Journal
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• v.32 no.4
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• pp.625-632
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• 2010

The notions of commutative pre-logics and terminal sections are introduced. Characterizations of a commutative prelogic are provided. Properties of deductive systems in pre-logics which are upper semilattices are considered.

• Research in Mathematical Education
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• v.12 no.1
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• pp.27-37
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• 2008

A test as a form of diagnostic of algorithm and logic abilities is considered. Such test for measuring abilities and achievements of talented children has been designed and used at the Kharkiv Regional Olympiad in Informatics. Quality of the test and its items is analyzed. Correlation between the test results of children and their success in creating mathematical models, designing of complicated algorithms and translating these algorithms into computer programs is discussed.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.121.5-121
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• 2001

For the last decade, remarkable progress in the coating weight uniformity of hot dip galvanized product has been made to overcome the tightening quality constraints and produce cost-effective galvanized products. This progress results from research and development works for more efficient air knife, more accurate model of coating process, more precise measurement of coating weight and more efficient control logics. The activities for an efficient mathematical model to predict coating weight and several control logics which has been implemented on the No.1 CGL, No. 2 CGL, and PGL at KwangYang Steel Works are reviewed in this article.

• Proceedings of the KSR Conference
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• 2008.11b
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• pp.1220-1226
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• 2008

A route control in railway is one of the very important system to operate a train. An efficient train route control assures to increase train operation performance with a same railway system. The erroneous route control can accompany serious accidents which occur train collision or derailment which provokes death. A Route control carries out exactly lest the accident should take place. An interlocking table is widely used for the exact route control. The table has the problem of its exactness proving because it has been established by experts. In this paper, We tried to formalize a route control using mathematical logic. A route consists of symbolized tracks, signals, switch and crossing. It represents as a set, respectively. We proposed route setting control logic, converted the elements to set logics and construct route logics with the set logics of the elements. Finally we proposed a model which presents a prototype routes and we proved the proposed logics using the proposed method.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.535-546
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• 2011

Using $\mathcal{N}$-structures, the notion of an $\mathcal{N}$-ideal in a prelogic is introduced. Characterizations of an $\mathcal{N}$-ideal are discussed. Conditions for an $\mathcal{N}$-structure to be an $\mathcal{N}$-ideal are provided.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.61-71
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• 2011

The notion of a complicated pre-logic is introduced and investigated some properties of it. A special set in a pre-logic is established and some related its properties are discussed. Also more extended special sets in a pre-logic are introduced and some relations with deductive systems are obtained.

• Research in Mathematical Education
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• v.12 no.2
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• pp.143-149
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• 2008

Before the 14th century, China had been thought as one of the countries with the most developed mathematics all along. But after the 16th century, Chinese mathematics increasingly walked up to the eclipse. The main reasons include the following points. First, the development of neoteric mathematics was closely associated with the social industrialization, but the lags in feudal China seriously blocked the development of the capitalistic seed, and China was still in the agricultural society then and couldn't step into the industrial society, which impeded the development of mathematics concerned with the industry and commerce. Second. the increasingly carrion feudalization was one of the essential reasons to block the development of Chinese neoteric mathematics. Finally, seeing about the developing logics of Chinese neoteric mathematics, we can find it was a scattered and experiential mathematical knowledge without strict and rational self-organizing structure system, which had the limitations existing in its interior mechanism.

• The Mathematical Education
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• v.37 no.1
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• pp.55-72
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• 1998

We prove many statements in middle and high school mathematics, so it is necessary to have some method for understanding the modes of proof. But it is hard to discuss about the modes of proof without knowing logics. Venn-diagrams can be used in a great variety of situations, and it is useful to the students unfamiliar with logical procedure. Since knowing a mode of proof that could be used may still not guarantee success of proof, it is also necessary to illustrate many cases of proof strategies. To achieve the above reguirements, (1)Even though intuition, the modes of proof used in middle school mathematics should be understood by using venn-diagrams and the students can use the right proof in the right statement. (2)We must illustrate many kinds of proof so that the students can get the proof stratigies from these illustrations. (3)If possible, logic should be treated in middle school mathematics for students to understand the system of proof correctly.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.29-34
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• 2010

The QR method is one of the most common methods for calculating the eigenvalues of a square matrix, however its understanding would require complicated and sophisticated mathematical logics. In this article, we present a simple way to understand QR method only with a minimal mathematical knowledge. A deflation technique is introduced, and its combination with the power iteration leads to extracting all the eigenvectors. The orthogonal iteration is then shown to be compatible with the combination of deflation and power iteration. The connection of QR method to orthogonal iteration is then briefly reviewed. Our presentation is unique and easy to understand among many accounts for the QR method by introducing the orthogonal iteration in terms of deflation and power iteration.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.25-40
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• 2010

We first seek a principle of cognitive development processes by reviewing and summarizing Piaget's cognitive development theory, constructivism and Dubinsky's APOS theory, and also the epistemology on logics of 墨子 and 荀子. We investigate Chapter 8 方程 on the theory of systems of linear equations, of the Nine Chapters, one of the oldest ancient Asian mathematical books, from the viewpoint of our principle of cognitive development processes. We conclude the educational value of the chapter and the value of the research on Asian ancient mathematical works and heritages.