• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.745-749
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• 1998

Mathematical morphology (MM) has been introduced as a powerful tool for studying the geometrical properties of images, MM is a good approach to digital image processing , which is based on the shape feature. The MM operators such as dilation, erosion, closing and opening have been applied successfully to image noise reduction. The MM filters can easily filter the noise when the noise factors are known. However it is very difficult to reduce the noise when images are ambiguous, because the boundary between the noise and object is vague. In this paper, we propose a new method to reduce noise from ambiguous images by using Fuzzy Mathematical Morphology (FMM) operators. Performance evaluation via simulations show that the FMM filters efficiently reduce the image noise. Furthermore, the FMM filters show a good performance compared with the conventional filters.

• The Mathematical Education
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• v.42 no.5
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• pp.607-622
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• 2003

The research was aimed at finding the dynamic aspects of the linguistic and social interaction with mathematical concept development using a graphing calculator in collaborative learning. This study was broadly divided into two categories: "Knowledge Construction Statement" for understanding how the verbal interaction works when a graphing calculator is used, and "Teacher's Instructional Role" for the research on the reaction of the students and on the teacher's role as a guide in helping students to construct their knowledge. This research used a case study in a collaborative learning environment. An attempt was made to show clearly how the students interacted with one another in a technology environment using a graphing calculator as a tool. A graphing calculator promoted the students' linguistic interaction and changed the characteristics of the linguistic interaction. Although it didn't show the different aspects completely, some changes of the linguistic traits were perceived.aits were perceived.

• East Asian mathematical journal
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• v.26 no.2
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• pp.233-249
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• 2010

It seems that it is critical to comprehend mathematics as a tool subject in order to understand a number of calculations in the professional subjects in the vocational high schools. This study is designed to determine "how much mathematics is connected to specialized subjects in terms of mathematical content at vocational high schools". To investigate the research questions, this study examined the connections between the mathematical topics included in professional subjects and those of mathematics subjects in the vocational high school. In the end, this study suggest that is should be necessary to make new mathematics textbook which reflects the reality and needs of the present vocational high school students.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.597-612
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• 2007

For finding the optimal strategy in Blackout game which was introduced in the homepage of popular movie "Beautiful mind", we have developed and generalized a mathematical proof and an algorithm with a couple of softwares. It did require only the concept of basis and knowledge of basic linear algebra. Mathematical modeling and analysis were given for the square matrix case in(Lee,2004) and we now generalize it to a generalized $m{\times}n$ Blackout game. New proof and algorithm will be given with a visualization.

• East Asian mathematical journal
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• v.40 no.1
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• pp.119-125
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• 2024

Predicting the number of ICU patients holds significant importance, serving as a critical aspect in efficiently allocating resources, ensuring high-quality care for critically ill individuals, and implementing effective public health strategies to mitigate the impact of diseases. This research focuses on estimating ICU patient numbers through the development of a simple mathematical model. Utilizing data on confirmed COVID-19 cases and deaths, this model becomes a valuable tool for predicting and managing ICU resource requirements during the ongoing pandemic. By incorporating historical data on infected individuals and fatalities from previous weeks, we establish a straightforward equation. We found the substantial impact of the delay in infected individuals, particularly those occurring more than five weeks earlier, on the accuracy of ICU predictions. Proactively preparing for potential surges in severe cases becomes feasible by forecasting the demand for intensive care beds, ultimately improving patient outcomes and preventing excessive strain on medical facilities.

• The Journal of the Korea Contents Association
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• v.8 no.5
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• pp.268-275
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• 2008

Providing appropriate and cooperative work among learners is an essential factor of a successful educational authoring system. Although from the viewpoint of beginning authors, many authoring functions are employed in existing authoring tool, there has been little research to solve authoring difficulties by companion's assist and to keep pace with learning. Therefore, in this paper, we designed and developed a educational authoring tool using mathematical language and cooperative work among learners, verified the validity. The authoring tool proposed has key features to hide authoring handicaps and keep pace with learning and cooperate with each other by using networked and language-based authoring tool.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.59-69
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• 2009

The element reduction of a multiset S is to reduce the number of repetitions of an element in S by a predetermined number. Privacy-preserving element reduction of a multiset is an important tool in private computation over multisets. It can be used by itself or by combination with other private set operations. Recently, an efficient privacy-preserving element reduction method was proposed by Kissner and Song [7]. In this paper, we point out a mathematical flaw in their polynomial representation that is used for the element reduction protocol and provide its correction. Also we modify their over-threshold set-operation protocol, using an element reduction with the corrected representation, which is used to output the elements that appear over the predetermined threshold number of times in the multiset resulting from other privacy-preserving set operations.

• East Asian mathematical journal
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• v.35 no.2
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• pp.115-139
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• 2019

In problem solving education, sentence problems are a tool for comprehensive evaluation of mathematical ability. The sentence problems refer to the problem expressed in sentence form rather than simply a numerical representation of mathematical problems. In order to solve sentence problems with a mixture of mathematical terms and general language, problem-solving ability including the ability to understand the meaning of sentences as well as the mathematical computation ability is required. Therefore, it is important to analyze syntactic elements from the linguistic aspects in sentence problems. The purpose of this study is to investigate the complexity of sentence problems in the length of sentences and the grammatical complexity of the sentences in the depth of the sentences by analyzing the 51 sentence problems presented in the $4^{th}$ grade mathematics textbook(2015 revised curriculum). As a result, it was confirmed that it is necessary to examine the length and depth of the sentence more carefully in the teaching and learning of sentence problems. Especially in elementary mathematics, the sentence problems requires a linguistic understanding of the sentence, and therefore it is necessary to consider syntactic elements in the process of developing and teaching sentence problems in mathematics textbook.

• The Mathematical Education
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• v.56 no.4
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• pp.407-434
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• 2017

The purpose of this study is to develop and verify the TPACK measurement tool for middle and high school mathematics teachers in the Korean context. Also, by clarifying the relationship between subordinate factors of Mathematics teachers' TPACK, an attempt was made to provide suggestions on the designs and directions for the in-service and pre-service teacher education and the programs for improving mathematics teachers' TPACK in the future. In order to achieve this goal, TPACK factors of mathematics teachers were extracted by reviewing literature on PCK, MKT, and TPACK. Then, content validity, basic statistical survey, reliability verification, exploratory factor analysis, confirmatory factor analysis, and structural equation model verification were conducted sequentially. At first, preliminary analysis was carried out on 79 mathematics teachers, and 76 items excluding the items with extreme value and reliability were included in the basic statistical analysis. And secondly, an exploratory factor analysis was conducted on 376 mathematics teachers, and this instrument consisted of 7 subordinate factors(CK, PK, TK, PCK, TCK, TPK, TPACK) and 61 items. Also by conducting confirmatory factor analysis and structural equation model test with 254 mathematics teachers, the measurement tool was confirmed the validity and reliability through statistically significant analysis. Then, the importance of integrated knowledge was confirmed by looking at the relationship between the TPACK factors of in-service mathematics teachers. The integrated knowledge(PCK, TCK, TPK) has played a crucial role in the formation of TPACK rather than the knowledge of CK, PK, and TK alone. Finally, the validity of TCK was confirmed through the structural equation modeling of TPACK. TCK not only directly affected TPACK, but also indirectly through TPK. According to these affirmative results, this measurement tool is claimed to be suitable for measuring the factors of Mathematics teachers' TPACK, and also the structural equation model can be regarded as a suitable model for analyzing the structural relationship of mathematics teachers' TPACK.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.1038-1043
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• 1997

To adapt the neural network proess for the purpose of determination of optimal utting onditions (optimal cutting speed and feed rate), some selection strategies for the machining factors are necessary, which is considered planning cutting process. In this case, factors that have both nonlinearity and strong relationship must be selected. Although tool grade and chemical properties of workpiece material have strong effect to cutting speed, it's not easy to find a analytic relation between them. In this paper, a mathematical method for determining the optimal amount of cutting (depth of cut, feed rate) is presented by tool goemetry and heat generation during cutting process. And various tool grade and workpiece material groups ase classified based on its chemical properties. Thier chemical composition and hardness are used as input pattern for neural network learnig. The result of learning shows the relationship between tool grade and workpiece material and it is proved that it can be used as a sub-system for automatic process planning system.