• Title/Summary/Keyword: process algebra

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The algebraic completion of the rational numbers based on ATD (ATD에 근거한 유리수의 대수학적 completion에 관한 연구)

  • Kim, Boo-Yoon;Chung, Gyeong-Mee
    • The Mathematical Education
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    • v.50 no.2
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    • pp.135-148
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    • 2011
  • We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

The application of fuzzy spatial overlay method to the site selection using GSIS (GSIS를 이용한 입지선정에 있어 퍼지공간중첩기법의 적용에 관한 연구)

  • 임승현;조기성
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.17 no.2
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    • pp.177-187
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    • 1999
  • Up to date, in many application fields of GSIS, we usually have used vector-based spatial overlay or grid-based spatial algebra for extraction and analysis of spatial data. But, because these methods are based on traditional crisp set, concept which is used these methods. shows that many kinds of spatial data are partitioned with sharp boundary. That is not agree with spatial distribution pattern of data in the real world. Therefore, it has a error that a region or object is restricted within only one attribution (One-Entity-one-value). In this study, for improving previous methods that deal with spatial data based on crisp set, we are suggested to apply into spatial overlay process the concept of fuzzy set which is good for expressing the boundary vagueness or ambiguity of spatial data. two methods be given. First method is a fuzzy interval partition by fuzzy subsets in case of spatially continuous data, and second method is fuzzy boundary set applied on categorical data. with a case study to get a land suitability map for the development site selection of new town, we compared results between Boolean analysis method and fuzzy spatial overlay method. And as a result, we could find out that suitability map using fuzzy spatial overlay method provide more reasonable information about development site of new town, and is more adequate type in the aspect of presentation.

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Development of Mathematics 3D-Printing Tools with Sage - For College Education - (Sage를 활용한 수학 3D 프린팅 웹 도구 개발 - 대학 수학교육을 중심으로 -)

  • Lee, Jae-Yoon;Lim, Yeong-Jun;Park, Kyung-Eun;Lee, Sang-Gu
    • Communications of Mathematical Education
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    • v.28 no.3
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    • pp.353-366
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    • 2014
  • Recently, the widespread usage of 3D-Printing has grown rapidly in popularity and development of a high level technology for 3D-Printing has become more necessary. Given these circumstances, effectively using mathematical knowledge is required. So, we have developed free web tools for 3D-Printing with Sage, for mathematical 3D modeling and have utilized them in college education, and everybody may access and utilize online anywhere at any time. In this paper, we introduce the development of our innovative 3D-Printing environment based on Calculus, Linear Algebra, which form the basis for mathematical modeling, and various 3D objects representing mathematical concept. By this process, our tools show the potential of solving real world problems using what students learn in university mathematics courses.

Massive Parallel Processing Algorithm for Semiconductor Process Simulation (반도체 공정 시뮬레이션을 위한 초고속 병렬 연산 알고리즘)

  • 이제희;반용찬;원태영
    • Journal of the Korean Institute of Telematics and Electronics D
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    • v.36D no.3
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    • pp.48-58
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    • 1999
  • In this paper, a new parallel computation method, which fully utilize the parallel processors both in mesh generation and FEM calculation for 2D/3D process simulation, is presented. High performance parallel FEM and parallel linear algebra solving technique was showed that excessive computational requirement of memory size and CPU time for the three-dimensional simulation could be treated successively. Our parallelized numerical solver successfully interpreted the transient enhanced diffusion (TED) phenomena of dopant diffusion and irregular shape of R-LOCOS within 15 minutes. Monte Carlo technique requires excessive computational requirement of CPU time. Therefore high performance parallel solving technique were employed to our cascade sputter simulation. The simulation results of Our sputter simulator allowed the calculation time of 520 sec and speedup of 25 using 30 processors. We found the optimized number of ion injection of our MC sputter simulation is 30,000.

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Formalization of Object-Oriented Dynamic Modeling Technique (객체지향 동적 모델링 기법의 정형화)

  • Kim, Jin-Soo;Kim, Jeong-A;Lee, Gyeong-Hwan
    • The Transactions of the Korea Information Processing Society
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    • v.4 no.4
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    • pp.1013-1024
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    • 1997
  • In the traditional object modeling methodologies, the object model can be said as formal since it has been based on rich semantic model. But almost of all methodolgies lack in formality the dyamic model and modeling process. Dynamic model cannot represent exctly the timing constraints and the interaction among the objects, which are very important features in real-time and multimedia system. In this paper, we formalize the synamic moedl and modeling proxess based on object behavior and state. This model defines the object state space using the concepts in algebra stucture and defines the object behavior func-tion. Also this model can formalize object kifecycle and conurrency among the objects usint the temporal logiction. Also this model can frlmaize object lifecycle and conurrency among the objects using the tempral logic and behavior founction. We apply firing rules to behacior function for modeling the dependency of interaction among the objescts.

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A Historical Analysis on Trigonometric Functions (삼각함수 개념의 역사적 분석)

  • Yoo, Jae Geun
    • Journal of Educational Research in Mathematics
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    • v.24 no.4
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    • pp.607-622
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    • 2014
  • The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

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A Comparative Analysis on Research Trends of Secondary Mathematics Education between Korea and Overseas (국내외 수학교육 연구 동향 비교 분석)

  • Park, Seon-Yeong;Kim, Won-Kyung
    • The Mathematical Education
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    • v.50 no.3
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    • pp.285-308
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    • 2011
  • The objective of this study is to review how researches on mathematics education are being conducted currently in Korea and overseas and to examine the current state of domestic researches on mathematics education from a broader view. Although many efforts have been made to understand trends in researches on mathematics education, there have been few in depth studies on research trends in overseas or for comparison between domestic and overseas trends. Thus, this study classified and analyzed 181 domestic articles between 2005 and 2009 in the journals and and 201 overseas articles in the journals and according to year, research area, research contents, school level, research method, and key words using the PME classification system with some modification. Through these analysis, we examined research trends on secondary mathematics education in Korea and overseas. The research findings are as follows. First, 'teaching learning process' was a spotlight area both at home and overseas, and 'realistic mathematics' and 'social cultural subjects' were not covered much either at home or overseas. 'Mathematical communication' occupied a very small portion in Korea but was a highly interesting area in overseas research. Second, research contents of interest were different between Korea and overseas. Research on general area was the mainstream. But geometry and statistics were mainly studied in Korea and algebra and analysis in overseas. Third, research related to middle school was twice more than that related to high school in Korea, But, research related to middle school was the same as high school in overseas. Fourth, qualitative research was the absolute majority both at home and overseas, and philosophical didactical analysis was used only in Korea. Fifth, the order of key words were problem solving - teacher - curriculum - creativity - textbook in Korea, but teacher - teaching - semiotic - affective factor - proo f- problem solving - technology in overseas.

A Study on the Constructions of Fire Events Probabilistic Safety Assessment Model for Nuclear Power Plants (원자력발전소의 화재사건 확률론적안전성평가 모델 구축에 관한 연구)

  • Kang, Dae Il;Kim, Kilyoo
    • Journal of the Korean Society of Safety
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    • v.31 no.5
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    • pp.187-194
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    • 2016
  • A single fire event within a fire area can cause multiple initiating events considered in internal events probabilistic safety assessment (PSA). For an example, a fire event in turbine building fire area can cause a loss of the main feed-water and loss of off-site power initiating events. This fire initiating event could result in special plant responses beyond the scope of the internal events PSA model. One approach to address a fire initiating event is to develop a specific fire event tree. However, the development of a specific fire event tree is difficult since the number of fire event trees may be several hundreds or more. Thus, internal fire events PSA model has been generally constructed by modifications of the pre-developed internal events PSA model. New accident sequence logics not covered in the internal events PSA model are separately developed to incorporate them into the fire PSA model. Recently, many fire PSA models have fire induced initiating event fault trees not shown in an internal event PSA model. Up to now, there has been no analytical comparative study on the constructions of fire events PSA model using internal events PSA model with and without fault trees of initiating events. In this study, the changing process of internal events PSA model to fire events PSA model is analytically presented and discussed.

Incremental Techniques for Timing Analysis Considering Timing and Circuit Structure Changes (지연시간과 회로 구조 변화를 고려한 증가적 타이밍 분석)

  • O, Jang-Uk;Han, Chang-Ho
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.8
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    • pp.2204-2212
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    • 1999
  • In this paper, we present techniques which perform incremental timing analysis using Timed Boolean Algebra that solves the false path problem and extracts the timing information in combinational circuits. Our algorithm sets histories of internal inputs that are substituted for internal output and extracts maximal delays through checking sensitizability of primary outputs. Once finding the sum of primitive delay terms, then it applies modified delay with referencing histories of primary output and it can extract maximal delays of primary outputs fast and efficiently. When the structure of circuit is changed, there is no need to compute the whole circuit again. We can process partial timing analysis of computing on the gates that are need to compute again. These incremental timing analysis methods are considered both delay changes and structure of circuit, and can reduce the costs of a trial error in the circuit design.

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An analysis of algebraic thinking of fourth-grade elementary school students (초등학교 4학년 학생들의 대수적 사고 분석)

  • Choi, Ji-Young;Pang, Jeong-Suk
    • Communications of Mathematical Education
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    • v.22 no.2
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    • pp.137-164
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    • 2008
  • Given the importance of early experience in algebraic thinking, we designed six consecutive lessons in which $4^{th}$ graders were encouraged to recognize patterns in the process of finding the relationships between two quantities and to represent a given problem with various mathematical models. The results showed that students were able to recognize patterns through concrete activities with manipulative materials and employ various mathematical models to represent a given problem situation. While students were able to represent a problem situation with algebraic expressions, they had difficulties in using the equal sign and letters for the unknown value while they attempted to generalize a pattern. This paper concludes with some implications on how to connect algebraic thinking with students' arithmetic or informal thinking in a meaningful way, and how to approach algebra at the elementary school level.

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