• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1447-1455
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• 2016

In this note, we mainly discuss the Gorenstein $Pr{\ddot{u}}fer$ domains. It is shown that a domain is a Gorenstein $Pr{\ddot{u}}fer$ domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, $B{\acute{e}}zout$ domain) if and only if it is a Gorenstein $Pr{\ddot{u}}fer$ UFD (resp., Krull domain, GCD domain).

• Research in Mathematical Education
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• v.13 no.3
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• pp.217-233
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• 2009

The purpose of this study is to describe how dynamic geometry systems can be useful in proof activity; teaching sequences based on the use of dynamic geometry systems and to analyze the possible roles of dynamic geometry systems in both teaching and learning of proof. And also dynamic geometry environments can generate powerful interplay between empirical explorations and formal proofs. The point of this study was to show that how using dynamic geometry software can provide an opportunity to link between empirical and deductive reasoning, and how such software can be utilized to gain insight into a deductive argument.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.111-119
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• 1999

This paper discusses jLogic, a mathematical logic education software developed by the author. jLogic is basically a MS-Windows based software that can construct first-order models, formulas and thet their satisfiablity. Logical formulas are easily input by a "keyboard" maintained by jLogic. A special finite model, called the "Toy World" can be visually cinstructed and modified. The user is supposed to answer the following 3 questions about the selected logical expression: 1. Is it a grammatically correct logical formula? 2. Is it a sentence that has a definite truth value? 3. Is th sentence true or false? When the user inputs his answer in the "Inspector window" and then presses the OK button, jLogic instantly tests the validity of the answer and tells the user the result. jLogic is freely downloaded from http://gauss.kyungpook.ac.kr/~jlogic/

• East Asian mathematical journal
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• v.35 no.4
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• pp.387-406
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• 2019

The Korea Foundation for the Advancement of Science and Creativity(KOFAC) developed AlgeoMath, a dynamic geometry software, with support from the Ministry of Education and 17 municipal and provincial education offices. Starting Nov. 7, 2018, AlgeoMath can be used for free by anyone. This study summarizes various discussions on the future direction of math education. The four aspects of the curriculum, textbook, teaching and learning, and assessment were explored on how AlgeoMath could contribute in realizing the future direction of math education. We confirmed that AlgeoMath can faithfully fulfill its role as a tool for changing math education, and we looked at what should be emphasized more and what should be complemented.

• East Asian mathematical journal
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• v.37 no.4
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• pp.499-521
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• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.141-154
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• 2022

Let R be a commutative ring with identity. Denote by w𝒫_w the class of weak w-projective R-modules and by w𝒫_w^⊥ the right orthogonal complement of w𝒫_w. It is shown that (w𝒫_w, w𝒫_w^⊥) is a hereditary and complete cotorsion theory, and so every R-module has a special weak w-projective precover. We also give some necessary and sufficient conditions for weak w-projective modules to be w-projective. Finally it is shown that when we discuss the existence of a weak w-projective cover of a module, it is enough to consider the w-envelope of the module.

• Journal of Biomedical Engineering Research
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• v.30 no.4
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• pp.279-287
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• 2009

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality providing cross-sectional images of a conductivity distribution inside an electrically conducting object. MREIT has rapidly progressed in its theory, algorithm and experimental technique and now reached the stage of in vivo animal and human experiments. Conductivity image reconstructions in MREIT require various steps of carefully implemented numerical computations. To facilitate MREIT research, there is a pressing need for an MREIT software package with an efficient user interface. In this paper, we present an example of such a software, called CoReHA which stands for conductivity reconstructor using harmonic algorithms. It offers various computational tools including preprocessing of MREIT data, identification of boundary geometry, electrode modeling, meshing and implementation of the finite element method. Conductivity image reconstruction methods based on the harmonic $B_z$ algorithm are used to produce cross-sectional conductivity images. After summarizing basics of MREIT theory and experimental method, we describe technical details of each data processing task for conductivity image reconstructions. We pay attention to pitfalls and cautions in their numerical implementations. The presented software will be useful to researchers in the field of MREIT for simulation as well as experimental studies.

• Fisheries and Aquatic Sciences
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• v.14 no.2
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• pp.138-147
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• 2011

Modeling fishing-gear systems is essential to better understand the factors affecting their movement and for devising strategies to control movement. In this study, we present a generalized mathematical modeling methodology to analyze fishing gear and its various components. Fishing gear can be divided into a finite number of elements that are connected with flexible lines. We use an algorithm to develop a numerical method that calculates precisely the shape and movement of the gear. Fishinggear mathematical models have been used to develop software tools that can design and simulate dynamic movement of novel fishing-gear systems. The tool allowed us to predict the shape and motion of the gear based on changes in operation and gear design parameters. Furthermore, the tool accurately calculated the swept volume of towed gear and the surrounding volume of purse-seine gear. We analyzed the fished volume for trawl and purse-seine gear and proposed a new definition of fishing effort, incorporating the concept of fished space. This method may be useful for quantitative fishery research, which requires a good understanding of the selectivity and efficiency of fishing gear used in surveys.

• Journal of The Korean Association of Information Education
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• v.22 no.1
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• pp.159-167
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• 2018

In this study, we have developed an online learning community site using Humhub social network software and promote social constructive learning through the questions and answers in subject specific learning groups. By accumulating learning contents which consist of questions and answers about specific topics, learners can acquire knowledge by searching relevant topics and questions and can create and reconstruct knowledge as well as consuming knowledge by participating in self-regulated learning community. We have developed a mathematical editor feature which enables users to enter mathematical expression such as equations and greek characters. Online learning community sites can be used for inquiry based information education.

• Journal of Communications and Networks
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• v.11 no.3
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• pp.297-305
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• 2009

Multiprotocol label switching (MPLS) networks require dynamic flow admission control to guarantee end-to-end quality of service (QoS) for each Internet protocol (IP) traffic flow. In this paper, we propose to tackle the joint routing and admission control problem for the IP traffic flows in MPLS networks without rerouting already admitted flows. We propose two mathematical programming models for this problem. The first model includes end-to-end delay constraints and the second one, end-to-end packet loss constraints. These end-to-end QoS constraints are imposed not only for the new traffic flow, but also for all already admitted flows in the network. The objective function of both models is to minimize the end-to-end delay for the new flow. Numerical results show that considering end-to-end delay (or packet loss) constraints for all flows has a small impact on the flow blocking rate. Moreover, we reduces significantly the mean end-to-end delay (or the mean packet loss rate) and the proposed approach is able to make its decision within 250 msec.