• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.175-202
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• 2016

Ultrasound imaging is a widely used tool for visualizing human body's internal organs and quantifying clinical parameters. Due to its advantages such as safety, non-invasiveness, portability, low cost and real-time 2D/3D imaging, diagnostic ultrasound industry has steadily grown. Since the technology advancements such as digital beam-forming, Doppler ultrasound, real-time 3D imaging and automated diagnosis techniques, there are still a lot of demands for image quality improvement, faster and accurate imaging, 3D color Doppler imaging and advanced functional imaging modes. In order to satisfy those demands, mathematics should be used properly and effectively in ultrasound imaging. Mathematics has been used commonly as mathematical modelling, numerical solutions and visualization, combined with science and engineering. In this article, we describe a brief history of ultrasound imaging, its basic principle, its applications in obstetrics/gynecology, cardiology and radiology, domestic-industrial products, contributions of mathematics and challenging issues in ultrasound imaging.

• Korean Journal of Construction Engineering and Management
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• 제7권1호
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• pp.73-79
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• 2006

Even though graphical simulation is very useful for construction planning, the application of graphical simulation has a limitation in dealing with objects without fixed form like earthmoving process. In this case, the mathematical/statistical simulation about the productivity of the whole processes based on the numerical data of working time, waiting time and working capacity of using equipment becomes effective. The mathematical/statistical simulation is not fully utilized in the field of construction due to the difficulties of creating process models and securing trust the numerically expressed results of simulation. In this research, the output of discrete-event simulation programs which are the most common mathematical/statistical simulation tool for construction processes were analyzed for the purpose of earthmoving process visualization. The purpose of this research is to develop a graphical simulation system that can help the construction planner select most suitable equipment and construction methods through the visualize the numerical simulation results of the working time, the queuing time as well as the amount resources etc.

• Journal of the Korea Computer Graphics Society
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• 제21권5호
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• pp.1-10
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• 2015

This study proposes a method of developing authoring tool that can easily and intuitively generate diverse digital leaves that compose virtual landscape. The main system of the proposed authoring tool consists of deformation method for the contour of leaf blade based on image warping, procedural modeling of leaf vein and visualization method based on mathematical model that expresses the color and brightness of leaves. First, the proposed authoring tool receives leaf input image and searches for contour information on the leaf blades. It then designs leaf blade deformation method that can generate diverse shapes of leaf blades in an intuitive structure using feature-based image warping. Based on the computed leaf blade contour, the system implements the generalized procedural modeling method suitable for the authoring tool that generates natural vein patterns appropriate for the leaf blade shape. Finally, the system applies visualization function that can express color and brightness of leaves and their changes over time using a mathematical model based on convolution sums of divisor functions. This paper provides texture support function so that the digital leaves that were generated using the proposed authoring tool can be used in a variety of three-dimensional digital contents field.

• Journal for History of Mathematics
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• 제28권4호
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• pp.167-179
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• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• Journal of Gifted/Talented Education
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• 제8권2호
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• pp.69-89
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• 1998

The purpose of this study is to develop a test which can be used in identification of the gifted students in the area of mathematics. This study was carried out for two years from 1996. Mathematical giftedness is, in this study, regarded as a result of interaction of mathematical thinking ability, mathematical creativity, mathematical task committment, background knowledge. This study presumed that mathematical thinking ability is composed of seven thinking abilities: intuitive insights, ability for information organization, ability for visualization, ability for mathematical abstraction, inferential thinking ability(both inductive and deductive thinking abilities), generalization and application ability, and reflective thinking. This study also presupposed that mathematical creativity is composed of 3 characteristics: fluency, flexibility, originality. The test for mathematical creative problem solving ability was developed for primary, middle, and high school students. The test is composed of two parts: the first part is concentrated more on divergent thinking, while the second part is more on convergent thinking. The major targets of the test were the students whose achievement level in mathematics belong to top 15~20% in each school. The goodness of the test was examined in the aspects of reliability, validity, difficulty, and discrimination power. Cronbach $\alpha$ was in the range of .60~.75, suggesting that the test is fairly reliable. The validity of the test was examined through the correlation among the test results for mathematical creative problem solving ability, I. Q., and academic achievement scores in mathematics and through the correlation between the scores in the first part and the scores in the second part of the test for mathematical creative problem solving ability. The test was found to be very difficult for the subjects. However, the discrimination power of the test was at the acceptable level.

• Journal of Gifted/Talented Education
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• 제21권4호
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• pp.847-860
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• 2011

In this study, the instrument of mathematical thinking ability tests were considered, and the differences between gifted and regular high school students in the ability were investigated by the test. The instrument consists of 9 items, and verified its quality due to reliability. Participants were 353 regular and 252 gifted high school students from tenth grade. As a result, not only organizing ability of information but also ability of space perception and visualization and intuitive insight ability could be the characteristics of the mathematical giftedness.

• Journal of The Korean Association of Information Education
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• 제14권3호
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• pp.311-318
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• 2010

In this paper, we proposed the integrated education program of informatics and math for solving problem using EPL. We applied a integrated math curriculum with EPL and analyzed mathematical thinking and attitude to the 3rd and 5th students. We used mathematical thinking test, mathematical attitude test and interview through student review. We also analyzed data of observers who are elementary school teachers. The results of test are as follows; First, we found effective points of meta-cognition and visualization of thought in solving the mathematical problem using Scratch. Second, mathematical thinking and attitude showed the result that 3rd grade students are more increased than 5th grade students in pre and post t-test of the mathematical. Consequently, we expect that the integrated education program of informatics and math using EPL can be applied to solve problem in math effectively.

• Proceedings of the IEEK Conference
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• 대한전자공학회 2002년도 하계종합학술대회 논문집(3)
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• pp.223-226
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• 2002

If one can easily modify the existing motion data to a new motion in making an animation movie, he can save a lot of time for graphic design. To implement this kind of system, we propose a PC-based system composed of low cost commercial animation tool (3D Studio Max) for visualization of the animation and motion editing module that handles optimization process during the motion transform. Researchers studying advanced motion transform techniques only have to focus on the mathematical manipulation of the motion data

• 한국가시화정보학회:학술대회논문집
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• 한국가시화정보학회 2004년도 Proceedings of 2004 Korea-Japan Joint Seminar on Particle Image Velocimetry
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• pp.25-32
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• 2004

The new algorithm for higher performance of dynamic PIV has been proposed. Present study considered mathematical basis of PIV analysis for multiple-time-step images and it enables us to analyze the high time-resolution PIV, which is obtained by dynamic PIV system. Conventional single pair image PIV analysis gives us the velocity field data in each time step but it sometimes contains unnecessary information of target flow. Present technique utilize multi-time step correlation information, and it is analyzed.

• Journal of the Korean School Mathematics Society
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• 제6권2호
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• pp.71-85
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• 2003

In this paper we study the usefulness of Maple in school calculus education. The use of computer and calculator is debated in many aspect in mathematics education. By the computer visualization of mathematical image and proper use of computer we can teach inductively and intuitively the mathematical concept and give rise to the students' interest. Maple is very popular in college but is not in middle school because of language. Maple application which is made by Maplet is very useful multimedia teaching-learning tools. We introduce the use of Maplet and some application of the calculus course which we made.