• Research in Mathematical Education
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• v.13 no.1
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• pp.49-61
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• 2009

In this paper some attempts have been made: (a) To identify all the elementary minor concepts of the Highest Common Factor (H.C.F.) and the Lowest Common Multiple (L.C.M.), and (b) To find the sequential order of these elementary concepts. Total 385 elementary minor concepts have been identified and sequenced.

• 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 Advanced Information Technology and Convergence
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• v.9 no.2
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• pp.1-14
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• 2019

This paper considers a multiple-input multiple-output (MIMO) power line communication (PLC) network where interference alignment (IA) technique is used to mitigate the interference that arises in multi-user networks. IA as a precoding technique requires perfect channel state information (CSI) to achieve maximum multiplexing gain. Due to the common-mode reception at the receiver ports, we assume imperfect CSI for the IA precoding design. Here, the CSI is quantized and sent via feedback to the transmit ports. For different levels of CSI quantization, we evaluate the performance of various IA algorithms via Monte Carlo simulations. Simulation results reveal the superior performance of the proposed scheme due to common-mode reception in IA MIMO PLC networks. It is shown that for a quantization level of 5 bits, the CM reception improves the sum-rate by up to 70%.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1527-1538
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• 2014

The purpose of this paper is to address the multiple split common fixed point problem. We present two different methods to approximate a solution of the problem. One is cyclic iteration method; the other is simultaneous iteration method. Under appropriate assumptions on the operators and iterative parameters, we prove both the proposed algorithms converge to the solution of the multiple split common fixed point problem. Our results generalize and improve some known results in the literatures.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.05a
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• pp.675-676
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• 2013

This paper presents a design method for multiple-output combinational digital logic systems using time domain based on multiplexing and common multi-terminal extension decision diagrams. The common multi-terminal extension decision diagrams represents extension valued multiple-output functions, while time domain based on multiplexing systems transmit several signals on a single lines. The proposed method can reduce the 1)hardware, 2)logic levels and 3)pins. In the logic system design, we use two types of decision diagrams, that is the common binary decision diagrams and common multi-terminal extension decision diagrams.

• Journal of Korean Institute of Industrial Engineers
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• v.43 no.2
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• pp.127-134
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• 2017

For product or process design and development, it is common to optimize multiple responses (characteristics) based on experimental data. To determine optimal conditions, we need to design the experiment, estimate a proper model for each response, and optimize the multiple responses simultaneously. There are several techniques and many research results on optimizing multiple responses simultaneously, when the experimental data are available. However, the experimental design issue for optimizing multiple responses has not been discussed yet. This paper proposes some idea on how to plan screening design when requirements for multiple performance characteristics are to be met in developing new products. A screening design procedure is developed for securing the requirements of multiple responses. Initial design factors are classified into three categories; specific, non-conflicting common, and conflicting common. After screening experiments, follow-up design region search method is suggested with respect to the most unsatisfied or important response, or overall desirability. A case study on a synthesis of melamine formaldehyde resin is presented to illustrate the procedure and to show the validity of the approach.

• 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.

• The Korean Journal of Applied Statistics
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• v.27 no.7
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• pp.1097-1114
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• 2014

Multiple-life policies pay a benefit on the first death or the last death among the group of lives. In practice, the future lifetime random variable of policy holders has been considered to be independent, but it is more rational to take into account the correlations among the policy holders. In this paper, the Gaussian copula is applied to re ect the correlations among policy holders and then to diversify the common shock of the multiple life policies which follows an exponential distribution. Five case studies demonstrate its usefulness of using copula in calculating the premiums of the multiple-life policies including the common shock.

• 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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.6
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• pp.1288-1293
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• 2005

This paper presents a design method for multiple-output combinational digital logic systems using time domain based on multiplexing(TDBM) and common multi-terminal extension decision diagrams(CMTEDD). The CMIEDDs represents extension valued multiple-output functions, while TDBM systems transmit several signals on a single lines. The proposed method can reduce the 1)hardware, 2)logic levels and 3)pins. In the logic system design, we use two types of decision diagrams(DDs), that is the common binary decision diagrams(CBDDs) and CMTEDDs. Also, we propose an algorithms to derive common multiple-terminal binary decision diagrams(CMTBDD) from CBDDs, and CMTEDDs from CMTBDDs. The CMTEDDs over CBDDs is more compactness in terms of number of non-terminal nodes, where the nodes for output selection variables are not included in the non-terminal nodes. In the logic design, each non-terminal nodes of an CBDDs and an CMTEDDs is realized by a multiplexer(MUX). In addition, we compare the proposed TDBM realization with the conventional one.