• Journal for History of Mathematics
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• v.21 no.3
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• pp.53-66
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• 2008

The concepts of ratio and proportion are familiar with students but have difficulties in use. The purpose of this paper is to identify the meanings of the concepts of ratio and proportion through investigating the historical development process of the meanings and representations of them. The early meanings of ratio and proportion were arithmetical meanings, however, geometrical meanings had taken the place of them because of the discovery of incommensurability. After the development of algebraic representation, the meanings of ratio and proportion have been growing into algebraic meanings including arithmetical and geometrical meanings. Through the historical development process of ratio and proportion, it is observable that the meanings of mathematical concepts affect development of symbols, and the development of symbols also affect the meanings of mathematical concepts.

• Journal of the Korea Computer Graphics Society
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• v.2 no.1
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• pp.31-38
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• 1996

Many efforts for finding smooth curves and surfaces satisfying given constraints have been made, and interpolation and approximation theories with the help of computers have played an important role in this endeavour. Most research in curve and surface modeling has been largely dominated by the theory of parametric representations. While they have been successfully used in representing physical objects, parametric surfaces are confronted with some problems when objects are represented and manipulated in geometric modeling systems. In recent year, increasing attention has been paid to implicit algebraic surfaces since they are often more effective than parametric surfaces are. In this paper, we summarize the geometric properties and computational processes of objects represented using implicit algebraic functions and explain of the implementation of design tools which can design curves and surfaces of revolution. These surfaces of revolution are played an importance role in effective areas such as CAD and CAM.

• Journal of Korea Water Resources Association
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• v.39 no.9 s.170
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• pp.737-744
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• 2006

The velocity of the inner region of turbulent flow on a smooth bed has complex profile which can not be described with a simple formula. Though there have been a couple of formulas describing the profile, most of them have very complex forms, i.e., with many terms, with integration form, or with implicit forms. It means that it is hard to use them or it is difficult to estimate their parameters. A new single formula that describes the velocity profile of the inner region of the turbulent flow on a smooth bed was proposed. This formula has a form of the traditional log-law multiplied by a damping function. Introducing only one additional parameter, it can describe the whole inner range nicely. It approximates the law-of-the-wall in the vicinity of the bed and approaches to the log-law in the overlap region. The added parameter, damping factor, can be estimated very easily. It is not sensitive to the Reynolds number change and the velocity profile calculated by the formula does not change much due to the change of the parameter.

• KIPS Transactions on Computer and Communication Systems
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• v.11 no.9
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• pp.289-304
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• 2022

It is necessary to apply process algebra and logic in order to analyze and verify safety requirements for Smart IoT Systems due to distributivity and mobility of the systems over some predefined geo-temporal space. However the analysis and verification cannot be fully intuitive over the space due to the fact that the existing process algebra and logic are very limited to express the distributivity and the mobility. In order to overcome the limitations, the paper presents a new logic, namely for GTS-VL (Geo-Temporal Space-Visual Logic), visualization of the analysis and verification over the space. GTS-VL is the first order logic that deals with relations among the different types of blocks over the space, which is the graph that visualizes the system behaviors specified with the existing dTP-Calculus. A tool, called SAVE, was developed over the ADOxx Meta-Modeling Platform in order to demonstrate the feasibility of the approach, and the advantages and practicality of the approach was shown with the comparative analysis of PBC (Producer-Buffer-Consumer) example between the graphical analysis and verification method over the textual method with SAVE tool.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.131-155
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• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

• Journal of the Korea Society for Simulation
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• v.28 no.2
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• pp.119-129
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• 2019

Although line production systems with finite buffers have been studied over several decades, except for some special cases there are no explicit expressions for system performances such as waiting times(or response time) and blocking probability. Recently, a max-plus algebraic approach for buffer-sharing systems with constant processing times was introduced and it can lead to analytic expressions for (higher) moment and tail probability of stationary waiting. Theoretically this approach can be applied to general processing times, but it cannot give a proper way for computing performance measures. To this end, in this study we developed simulation models using @RISK software and the expressions derived from max-plus algebra, and computed and compared blocking probability, waiting time (or response time) with respect to two blocking policies: communication(BBS: Blocking Before Service) and production(BAS: Blocking After Service). Moreover, an optimization problem which determines the minimum shared-buffer capacity satisfying a predetermined QoS(quality of service) is also considered.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.58
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• pp.81-87
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• 2000

대수정규분포와 와이블분포는 비정규분포를 하는 공정특성에 반영된다. Hahn 과 Shapir(1967)의 수치 예를 통해 이러한 대수정규분포와 와이블분포를 식별하는 검정방법으로 최우비 검정(RML)을 사용하였다. 검정결과 와이블분포를 하는 공정으로 판단되어, 와이블분포 의 모수 추정은 실무에서 그래프와 수식으로도 쉽게 추정할 수 있는 수정적률추정량(MME)를 이용하여 공정 능력을 평가하였다. 공정능력의 평가 측도로 공정능력지수와 불량률(PPM)의 측도와 병행하여 나타내었다. 공정능력 평가의 결과로 와이블분포를 하는 공정을 대수정규분포로 잘못 판단함으로써 발생하는 오류를 2가지 측도로 표현함으로써 올바르게 공정능력을 판단할 수 있도록 종합적인 정보를 제시하였다.

• Journal of KIISE:Computing Practices and Letters
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• v.15 no.8
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• pp.534-546
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• 2009

Query by humming is an effective and intuitive querying mechanism when a user wants to find a song without knowing lyrics. The query by humming system takes a user-hummed melody as input, compares it with melodies in a music database, and returns top-k similar melodies to the input. In this paper, we propose a novel algebra for query by humming, and design and implement a real query by humming system called HummingBase by exploiting the algebra. By analyzing existing similarity search techniques, we derive 10 core operators for the algebra. By using the well-defined algebra, we can easily implement such a system in a extensible and modular way. With two case studies, we show that the proposed algebra can easily represent the query processing processes of existing query-by-humming systems.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.