• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.283-308
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• 2018

'Divisor and multiple' is the topic included both in the elementary and in the secondary mathematics curriculum, but there has been lack of research on it. It has been reported that students have a difficulty in understanding the meaning of the greatest common divisor (GCD) and the least common multiple (LCM), while they can find out GCD and LCM. Against the lack of research on how to overcome this difficulty, this study designed teaching methods with a model for visualization to emphasize the meanings of divisor and multiple in finding out GCD and LCM, and implemented the methods in one fourth grade classroom. A questionnaire was developed to explore students' solution methods and interviews with focused students were implemented. In addition, fourth-grade students' thinking was compared and contrasted with fifth-grade students who studied divisor and multiple with the current textbook. The results of this study showed that the teaching methods with a specific model for visualization had a positive impact on students' conceptual understanding of the process to find out GCD and LCM. As such, this study provides instructional implications on how to foster the meanings of finding out GCD and LCM at the elementary school.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.449-457
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• 2017

In this paper we study several generalizations of greatest common divisor of GCD domain with always the greatest common divisor.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.201-218
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• 2012

In this study, the following topics were investigated targeting elementary school students: Schema formed through precise notion of cognitive and the connection of the concepts when studying common divisor, common multiple, and the lowest common multiple, configuration ability and problem solving of the students when learning using a modified schema, how the schema of the student to advance to a higher level, and how the deformation of the schema is carried out student's configuration of concept and problem solving ability. As a result, it was found out that cognition about precise concept, schema and the modified schema are important factors when a primary concept was developed into a secondary concept, and play important roles when the connection and the formation of the modified schema created by cognition about the precise primary concept rather than by the formation of the secondary concept (formation of the secondary schema) created by the connection between the primary concept.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.575-587
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• 2015

The development in data collection techniques results in high dimensional data sets, where discrimination is an important and commonly encountered problem that are crucial to resolve when high dimensional data is heterogeneous (non-common variance covariance structure for classes). An example of this is to classify microbial habitat preferences based on codon/bi-codon usage. Habitat preference is important to study for evolutionary genetic relationships and may help industry produce specific enzymes. Most classification procedures assume homogeneity (common variance covariance structure for all classes), which is not guaranteed in most high dimensional data sets. We have introduced regularized elimination in partial least square coupled with QDA (rePLS-QDA) for the parsimonious variable selection and classification of high dimensional heterogeneous data sets based on recently introduced regularized elimination for variable selection in partial least square (rePLS) and heterogeneous classification procedure quadratic discriminant analysis (QDA). A comparison of proposed and existing methods is conducted over the simulated data set; in addition, the proposed procedure is implemented to classify microbial habitat preferences by their codon/bi-codon usage. Five bacterial habitats (Aquatic, Host Associated, Multiple, Specialized and Terrestrial) are modeled. The classification accuracy of each habitat is satisfactory and ranges from 89.1% to 100% on test data. Interesting codon/bi-codons usage, their mutual interactions influential for respective habitat preference are identified. The proposed method also produced results that concurred with known biological characteristics that will help researchers better understand divergence of species.

• Journal of Elementary Mathematics Education in Korea
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• v.7 no.1
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• pp.45-64
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• 2003

This study analyzes divisor and multiple in elementary school mathematics textbooks published according to the first to the 7th curriculum, in a view point of the didactic transposition theory. In the first and second textbooks, the divisor and the multiple are taught in the chapter whose subject is on the calculations of the fractions. In the third and fourth textbooks, divisor and multiple became an independent chapter but instructed with the concept of set theory. In the fifth, the sixth, and the seventh textbooks, not only divisor multiple was educated as an independent chapter but also began to be instructed without any conjunction with set theory or a fractions. Especially, in the seventh textbook, the understanding through activities of students itself are strongly emphasized. The analysis on the each curriculum periods shows that the divisor and the multiple and the reduction of a fractions to the lowest terms and to a common denominator are treated at the same period. Learning activity elements are increase steadily as the textbooks and the mathematical systems are revised. The following conclusion can be deduced based on the textbook analysis and discussion for each curriculum periods. First, loaming instruction method also developed systematically with time. Second, teaching method of the divisor and multiple has been sophisticated during the 1st to 7th curriculum textbooks. And the variation of the teaching sequences of the divisor and multiple is identified. Third, we must present concrete models in real life and construct textbooks for students to abstract the concepts by themselves. Fourth, it is necessary to develop some didactics for students' contextualization and personalization of the greatest common divisor and least common multiple. Fifth, the 7th curriculum textbooks emphasize inquiries in real life which teaming activities by the student himself or herself.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.181-195
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• 1999

This research is produced as a applet of learning materials, and is made with the internet languages HTML, Java, and NamoWebeditor. It contains "Greatest Common Divisor and Least Common Multiple", "Parallel translation of function of second order", "Pythagoras Theorem", which is the current middle school mathmatics textbook for third graders. The keynote of this research is that the students can study individually through logging into the internet on their own computers; the program is made using graphics and animation on order to develop the learners′ interest in mathematics. I hope that this research can supplement our currently insufficient internet educational data.

• The Mathematical Education
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• v.49 no.4
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• pp.489-500
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• 2010

This study makes clear justification of contents of set in secondary school through the scientific consideration and contents consideration of curriculum about two points - lattice and ring - of set deal with 'number and operation'. In this process, we make clear the greatest common divisor, the least common multiple and operation of set, especially the meaning of symmetric difference, we suggest direction about constitution of contents of set in secondary school. This study helps to raise the specificity on the elements of textbook and presents the first step about the range of teaching in a construct of curriculum.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.3
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• pp.1-10
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• 2006

In this paper we deal with a cell planning issue arisen in a CDMA based multicast network. In a CDMA based wireless network, a terminal can significantly reduce the bit error rate via the cohesion of data streams from multiple base stations. In this case, multiple base stations have to be operated according to a common time line. The cells whose base stations are operated as such are called soft-combined cells. Therefore, a terminal can take advantage of error rate reduction, if the terminal is in a soft-combined cell and at least one neighboring cell is also soft-combined. However, as soft-combining operation gives heavy burden to the network controller, the limited number of cells can be soft-combined. Our problem us to find a limited number of soft-combined cells such that the benefit of the soft-combining operation is maximized.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.847-852
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• 2007

This paper investigates the characteristics of cogging torque and magnetic force of a brushless DC (BLDC) motor due to imperfect magnetization of permanent magnet (PM) numerically and experimentally which results in the magnetically induced vibration. A predicted magnetization pattern of the PM of the BLDC motor, which is derived from the measured surface magnetic flux density along the PM, is applied to the finite element analysis in order to calculate the cogging torque and the unbalanced magnetic force. This research also develops the experimental setup to measure the unbalanced magnetic force as well as the cogging torque. It shows numerically and experimentally that the imperfect magnetization of permanent magnet generates the driving frequencies of cogging torque with integer multiple of slot number in addition to the least common multiple of pole and slot. It also shows that the driving frequencies of unbalanced magnetic force are integer multiple of slot number ${\pm}1$ due to imperfect magnetization of PM even in the rotationally symmetric design.