• 한국수학교육학회지시리즈D:수학교육연구
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• 제1권2호
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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.

• 한국해양공학회지
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• 제37권3호
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• pp.81-88
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• 2023

Maneuverability is a crucial factor for the safety and success of submarine missions. This paper introduces a mathematical model that considers the large drift and angle of attack motions of submarines. Various computational fluid dynamics (CFD) simulations were performed to adapt Karasuno's fishery vessel maneuvering mathematical model to submarines. The study also presents the procedure for obtaining the physics-based hydrodynamic coefficients proposed by Karasuno through CFD calculations. Based on these coefficients, the reconstructed forces and moments were compared with those obtained from CFD and to the hydrodynamic derivatives expressed by a Taylor expansion. The study also discusses the mathematical maneuvering model that accounts for the large drift angles and angles of attack of submarines. The comparison results showed that the proposed maneuvering mathematical model based on modified Karasno's model could cover a large range of motions, including horizontal motion and vertical motions. In particular, the results show that the physics-based mathematical maneuvering model can represent the forces and moments acting on the submarine hull during large drift and angle of attack motions. The proposed mathematical model based on the Karasuno model could obtain more accurate results than the Taylor third-order approximation-based mathematical model in estimating the hydrodynamic forces acting on submarines during large drift and angle of attack motions.

• Geosystem Engineering
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• 제21권6호
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• pp.335-343
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• 2018

Alkali-surfactant polymer flooding has become an important technique to improve oil recovery following the development of oil fields while the function of emulsification in enhanced oil recovery is rarely considered in the existing mathematical model for numerical simulation. In this paper, the mechanism of improving the recovery of the emulsification was analyzed in ASP flooding, and a relatively perfect mathematical model with deep filtration-theory was established, in which oil-water volume equation, saturation equation, viscosity equation, and permeability reduction equation are included. The new model is used to simulate the actual block of an oil field; the simulated results of the new model and an old model without considering the emulsification are compared with the actual well history. It is found that new model which is easy to be realized in numerical simulation has a high precision fitting, and the effect of adding oil and decreasing water is obvious. The sensitivity of emulsification was analyzed, and the results show that the water reducing funnel becomes wider and the rate of water cut decreases rapidly with the increase of emulsifying capacity, and then the rate of recovery slows down. The effect of increasing oil and decreasing water is better, and the degree of recovery increases. The emulsification of the ASP flooding is maintained at a moderate level, which corresponds to ${\Phi}=0.2$ in the new model, and the emulsification is applied to realize the general mathematical quantitative description, so as to better guide the oilfield development.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제34권4호
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• pp.587-603
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• 2020

본 연구는 수학교육에서 중요한 수단이자 교육적 도구인 수학체험교구를 체계적으로 개발하기 위한 기초연구이다. 최근 활동이론(action theory)에 근거한 수학교육이 강조되면서 다양한 수학체험교구가 개발되고 교육현장에서 다양한 비교과활동을 통해 활용되고 있지만, 실제 수학수업에서 개념을 설명하기 위한 도구로 수학체험교구가 개발되어 활용되는 사례는 부족한 실정이다. 특히, 수학과 교육과정에 부합되고, 수학적 근거가 명확한 체험교구는 체계적으로 개발되지 못하고 있다. 이에 본 연구에서는 수학체험교구를 개발하기 위한 체계적인 방법으로 체험교구 개발 모형을 제안한다. 또한 제안한 개발 모형에 따라 최대공약수 체험교구를 개발하였다. 본 연구를 통해 제안된 모형과 실제 구현된 체험교구를 통해 다양한 수학체험교구의 개발이 실제적으로 실행되고, 수학적 기초에 근거한 수학체험교구가 다양하게 개발될 것으로 기대된다.

• 한국수학사학회지
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• 제18권2호
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• pp.75-94
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• 2005

이 연구는 창의적 생산력 계발을 위한 교육 프로그램에서 수학영재 학생들이 생산한 창의적 산출물을 평가할 수 있는 준거를 개발하고자 하였다 수학사를 통해 수학자들이 이룩한 산출물을 토대로 창의적 산출물 생산 모델을 제안하였는데, 이 모델은 수학적 지식, 수학적 사고, 수학적 탐구 기술의 세 가지 요소와 창의적 산출물 전체에 대한 평가요소로 구성되어 있으며, 학생들의 산출물은 모델의 각 요소에 초점을 둔 것에 대응시킬 수 있었다. 수학에서의 창의적 산출물에 대한 평가 준거는 창의적 산출물 생산 모델의 요소에 근거하여 개발하였으며, 이 준거에 의한 평가는 타당성과 신뢰성을 가진 것으로 판단되었다.

• East Asian mathematical journal
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• 제38권3호
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• pp.357-363
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• 2022

Immunological imbalance eventually results in the development of various diseases. A typical example is an imbalance of cytokines with immunomodulatory abilities. In this paper, we propose a two-variable delay model to anti-pro-inflammatory cytokine therapy for autoimmune diseases, which are caused by an imbalance between the pro and anti-inflammatory cytokines. The interaction between pro- and anti-inflammatory cytokines were modeled mathematically to investigate the relevance of cytokines in disease processes. The delay time was estimated to maintain the stability of a biologically important steady state. In particular, the effects of delay with anti-pro-inflammatory cytokines therapy in autoinflammatory diseases were studied.

• 대한수학교육학회지:학교수학
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• 제15권4호
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• pp.785-799
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• 2013

본 연구는 수학적 모델링 수업이 수학 영재 학생들에게 문제해결의 기회를 제공하고 수학적 모델링 활동을 통해 다양한 수학적 사고력을 발전시킬 수 있다는 가정 하에 중학교 3학년 수학 영재 학생들을 위한 수학적 모델링 교수 학습 자료를 개발하였다. 개발된 교수 학습 자료를 적용하여 사례연구를 통해 수학적 모델링의 단계별 활동과정을 살펴보고 각 단계에서 어떠한 수학적 사고능력이 나타나는지 분석하였다. 수학적 모델링 과정에서 다양한 수학적 사고능력이 나타났는데 문제를 이해하는 실세계 탐구과정에서는 정보의 조직화 능력이, 상황모델을 개발하는 과정에서는 직관적 통찰능력, 공간화/시각화 능력, 수학적 추론 능력, 반성적 사고 능력이 나타났다. 수학모델 개발과정에서는 수학적 추상화 능력, 공간화/시각화 능력, 수학적 추론 능력, 반성적 사고가 나타났으며 모델적용 과정에서는 일반화 및 적용 능력과 반성적 사고가 나타났다. 모델링 수업이 진행됨에 따라 반성적 사고능력이 더 많이 나타나는 것을 확인할 수 있었다.

• 한국소음진동공학회논문집
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• 제20권7호
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• pp.637-643
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• 2010

The paper is about the development of 6-DOF active vibration isolation systems using VCM. Firstly, formulate the vertical 3-DOF mathematical model under eccentric load, and compare the model with the case in which the center of mass is located at the centroid. And then, complete the 6-DOF mathematical model by formulating the horizontal 3-DOF mathematical model. Find main parameters by comparing the result of the frequency response test with simulation result on the model. Finally, achieve the performance of vibration isolation by applying loop shaping approach & feedforward controller.

• 한국수학교육학회지시리즈A:수학교육
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• 제34권1호
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• pp.17-63
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• 1995

The exploration of Mathematics-learningmodel on the basis of Cognitive development The purpose of this paper is to sequenctialize Mathematics-learning contents, and to explore teaching-learning model for mathematics, with on the basis of the theory of cognitive development and the period of condservation formation for children. The Specific topics are as follows: (1) Systemizing those theories of cognitive development which are related to Mathematics - learning for children. (2) Organizing a sequence of Mathematics - learning, on the basis of experimental research for the period of conservation formation for children. (3) Comparing the effects of 4 types of teaching - learning model, on the basis of inference activity and operational learning principle. $\circled1$ Induction-operation(IO) $\circled2$ Induction-explanation(IE) $\circled3$ Deduction-operation(DO) $\circled4$ Deduction-explanation(DE) The results of the subjects are as follows: (1) Cognitive development theory and Mathe-matics education. $\circled1$ Congnitive development can be achieved by constant space and Mathematics know-ledge is obtained by the interaction of experience and reason. $\circled2$ The stages of congnitive development for children form a hierarchical system, its function has a continuity and acts orderly. Therefore we need to apply cognitive development for children to teach mathematics systematically and orderly. (2) Sequence of mathematical concepts. $\circled1$ The learning effect of mathematical concepts occurs when this coincides with the period of conservation formation for children. $\circled2$ Mathematics Curriculum of Elementary Schools in Korea matches with the experimental research about the period of Piaget's conservation formation. (3) Exploration of a teaching-learning model for mathematics. $\circled1$ Mathematics learning is to be centered on learning by experience such as observation, operation, experiment and actual measurement. $\circled2$ Mathematical learning has better results in from inductional inference rather than deductional inference, and from operational inference rather than explanatory inference.

• Current Optics and Photonics
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• 제6권1호
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• pp.69-78
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• 2022

A high-resolution camera is a precise optical system. Its vibrations during transportation and launch, together with changes in temperature and gravity field in orbit, lead to different degrees of defocus of the camera. Thermal refocusing is one of the solutions to the problems related to in-orbit defocusing, but there are few relevant thermal refocusing mathematical models for systematic analysis and research. Therefore, to further research thermal refocusing systems by using the development of a high-resolution micro-nano satellite (CX6-02) super-resolution camera as an example, we established a thermal refocusing mathematical model based on the thermal elasticity theory on the basis of the secondary mirror position. The detailed design of the thermal refocusing system was carried out under the guidance of the mathematical model. Through optical-mechanical-thermal integration analysis and Zernike polynomial calculation, we found that the data error obtained was about 1%, and deformation in the secondary mirror surface conformed to the optical index, indicating the accuracy and reliability of the thermal refocusing mathematical model. In the final ground test, the thermal vacuum experimental verification data and in-orbit imaging results showed that the thermal refocusing system is consistent with the experimental data, and the performance is stable, which provides theoretical and technical support for the future development of a thermal refocusing space camera.