• Title, Summary, Keyword: Mathematical model

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Estimation of Maneuvering Mathematical Model by System Identification Techniques (시스템 검증에 의한 조종수학 모형의 평가)

  • Lee, Ho-Young;Shin, Hyun-Kyoung
    • Journal of Ocean Engineering and Technology
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    • v.13 no.4
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    • pp.118-123
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    • 1999
  • The mathematical model used in the simulation of ship's maneuvering contains the hydrodynamic coefficients, which are usually evaluated based on PMM model tests in the towing tank and used to predict ship's maneuvering performance when applied to the proto-type ship. The proper mathematical model has to be developed to predict ship's maneuvering motions with hydrodynamic coefficients very well. The mathematical model for PMM model tests is analyzed with identification program and the hydrodynamic coefficients and maneuvering motions by system identification we compared with those obtained directly from PMM model tests and sea trial. The mathematical model for PMM model tests was established and the magnitudes of ship's maneuvering coefficients were determined. When the identified values of coefficients were used to simulate the maneuvers, a very good agreement was obtained between the numerically simulated motion responses and those obtained from PMM model tests.

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An applied method of mathematical model in the product design process (수학적 Model의 제품 디자인 과정에의 응용방법)

  • 이수봉
    • Archives of design research
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    • v.20
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    • pp.61-72
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    • 1997
  • This study aims to promote understanding level for mathematical model, to improve methods and necessity of application in the process of product design and also to promote approaching and applying methods as a guideline for beginners. For the procedure and method of study first, it was emphasized by linking method and necessity of scientific analysis and a quality of product design and design process. Next, the corresponding relations between mathematical model and design probelem was desciebed, the mathematical model was examinated appeying process of product design. Lastly, approaching and applying methods for beginners was presented based on the discribed studied contents. As the result of the study, some points are by a result or problem : frist, the point that mathematical model is useful to grasp the design problems which various elements are complicately involved quantitatively and structurally, and its necessity can be especially utilized as a tool to justify and convince the convince the conclusion of the designer himself to the persons concerned. Second, the point that in order to apply mathematical model to the design process skillfully, first of all, the substance of all mathematical models which can be applid, and it is not easy to command in perfect method without using computer. Third, the point that since there are many kindsof mathematical models used is mathematical modeland the models which can be applidied to solve design problems differ in accordance with the design types and design process, its applying method can be presented as one kind of standardization or concretely. Fourth the point that in case of approaching mathematical model for the first time, it can start to select model corresponding with design type by stage of design process bassed on understanding for some mathematical knowledge and computer program.

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A Study of Modeling Applied Mathematical Problems in the High School Textbook -Focused on the High School Mathematics Textbookin the First Year- (모델링을 활용한 문제의 연구 - 일반수학을 중심으로 -)

  • 김동현
    • Journal of the Korean School Mathematics Society
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    • v.1 no.1
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    • pp.131-138
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    • 1998
  • The aims of mathematical education are to improve uniformity and rigidity, and to apply to an information age which our society demands. One of the educational aims in the 6th educational curriculum emphasizes on the expansion of mathematical thought and utility, But, The change of contents in the text appears little. This means that mathematical teachers must actively develop the new types of problems. That the interests and concerns about mathematics lose the popularity and students recognize mathematics burdensome is the problems of not only teaching method, unrealistically given problems but abstractiveness and conceptions. Mathematical Modeling is classified exact model, almost exact theory based model and impressive model in accordance with the realistic situation and its equivalent degree of mathematical modeling. Mathematical Modeling is divided into normative model and descriptive model according to contributed roles of mathematics. The Modeling Applied Problems in the present text are exact model and stereotyped problems. That the expansion of mathematical thought in mathematics teaching fell into insignificance appears well in the result of evaluating students. For example, regardless of easy or hard problems, students tend to dislike the new types of mathematical problems which students can solve with simple thought and calculation. The ratings of the right answer tend to remarkably go down. If mathematical teachers entirely treat present situation, and social and scientific situation, students can expand the systematic thought and use the knowledge which is taught in the class. Through these abilities of solving problems, students can cultivate their general thought and systematic thought. So it is absolutely necessary for students to learn the Modeling Applied Problems.

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Analysis of the Equality Sign as a Mathematical Concept (수학적 개념으로서의 등호 분석)

  • 도종훈;최영기
    • The Mathematical Education
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    • v.42 no.5
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    • pp.697-706
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    • 2003
  • In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

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A participatory action research on the developing and applying mathematical situation based problem solving instruction model (상황중심의 문제해결모형을 적용한 수학 수업의 실행연구)

  • Kim, Nam-Gyun;Park, Young-Eun
    • Communications of Mathematical Education
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    • v.23 no.2
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    • pp.429-459
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    • 2009
  • The purpose of this study was to help the students deepen their mathematical understanding and practitioner improve her mathematics lessons. The teacher-researcher developed mathematical situation based problem solving instruction model which was modified from PBL(Problem Based Learning instruction model). Three lessons were performed in the cycle of reflection, plan, and action. As a result of performance, reflective knowledges were noted as followed points; students' mathematical understanding, mathematical situation based problem solving instruction model, improvement of mathematics teachers.

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Study on Establishing Investment Mathematical Models for Each Application ESS Optimal Capacity in Nationwide Perspective (국가적 관점에서 각 용도별 ESS 적정용량 산정을 위한 투자수리모델 수립에 관한 연구)

  • Kim, Jung-Hoon;Youn, Seok-Min
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.6
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    • pp.979-986
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    • 2016
  • At present, electric power industry around the world are being gradually changed to a new paradigm, such as electrical energy storage system, the wireless power transmission. Demand for ESS, the core technology of the new paradigm, has been growing worldwide. However, it is essential to estimate the optimal capacity of ESS facilities for frequency regulation because the benefit would be saturated in accordance with the investment moment and the increase of total invested capacity of ESS facilities. Hence, in this paper, the annual optimal mathematical investment model is proposed to estimate the optimal capacity and to establish investment plan of ESS facility for frequency regulation. The optimal mathematical investment model is newly established for each season, because the construction period is short and the operation effect for the load by seasons is different unlike previous the mathematical investment model. Additionally, the marginal operating cost is found by new mathematical operation model considering no-load cost and start-up cost as step functions improving the previous mathematical operation model. ESS optimal capacity is established by use value in use iterative methods. In this case, ESS facilities cost is used in terms of the value of the beginning of the year.

Mathematical Modeling for Calculating the Vertical Air Temperature Distribution in an Atrium Space (아트리움 공간의 수직공기온도분포 계산을 위한 수학모형의 작성)

  • 박종수;안병욱
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.15 no.6
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    • pp.533-542
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    • 2003
  • This study aims to propose a simplified mathematical model for calculating vertical air temperature distribution in a four-sided atrium. In the first stage of the mathematical modeling, the computer model combined zonal model and solar radiation model using Monte Carlo method and Ray tracing technique went through a computer simulation with architectural variables applied to a four-sided atrium in summer. In the next stage, Curve Expert, a computer program that gets the most suitable solution ac-cording to the least squares method, is used to analyze the results of the computer simulation and to derive the mathematical model. The accuracy of the mathematical model was evaluated through a comparison of calculation results from a mathematical model and computer simulation. In this validation step using the least square method, the R2 value of the Zones 1, 2 and 3 showed higher than 0.945. Zone 4 has an R2 value of 0.911, lower than the previous three zones. However the relative error was below 0.5%, which is considered very small.

Development of a Teaching/Learning Model for the Mathematical Enculturation of Elementary and Secondary School Students

  • Kim, Soo-Hwan;Lee, Bu-Young;Park, Bae-Hun
    • Research in Mathematical Education
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    • v.1 no.2
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    • pp.107-116
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    • 1997
  • The purpose of this study is to develop a teaching/learning model for the mathematical enculturation of elementary and secondary school students. It is clear that the development of teaching and learning in the classroom is essential for the realization of global innovations in mathematics education. Research questions for this purpose are as follow: (1) What can be learned from literatures reviews of the socio-cultural perspective on mathematics education, and of ethnomathematics as a mathematics intrinsic to cultural activities? (2) What is the direction of teaching and learning from the perspective of mathematical enculturation? (3) What is the teaching /learning model for mathematical enculturation? (4) What is the instructional exemplification based on the developed model? This study promotes the establishment of mathematics education theory from the review of literatures on the socio-cultural perspective, the development of a teaching/learning model, and the instructional exemplification based on the developed model.

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Analysis on Types and Roles of Reasoning used in the Mathematical Modeling Process (수학적 모델링 과정에 포함된 추론의 유형 및 역할 분석)

  • 김선희;김기연
    • School Mathematics
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    • v.6 no.3
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    • pp.283-299
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    • 2004
  • It is a very important objective of mathematical education to lead students to apply mathematics to the problem situations and to solve the problems. Assuming that mathematical modeling is appropriate for such mathematical education objectives, we must emphasize mathematical modeling learning. In this research, we focused what mathematical concepts are learned and what reasoning are applied and used through mathematical modeling. In the process of mathematical modeling, the students used several types of reasoning; deduction, induction and abduction. Although we cannot generalize a fact by a single case study, deduction has been used to confirm whether their model is correct to the real situation and to find solutions by leading mathematical conclusion and induction to experimentally verify whether their model is correct. And abduction has been used to abstract a mathematical model from a real model, to provide interpretation to existing a practical ground for mathematical results, and elicit new mathematical model by modifying a present model.

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