• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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• pp.407-414
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• 2009

The foundation fieldbus(FF) is one of the fieldbuses most widely used for process control and automation, In order for system designer to optimize medium management, it is imperative to predict transmission delay time of data. In a former research, mathematical modeling to analyze transmission delay of FF token-passing system has been developed based on the assumption that a device node has only one priority data(1Q model), From 1Q model, all of the device nodes, which are connected on the FF system, are defined priority level in advance, and as system operates, data are generated based on given priority level. However, in practice, some non-periodic data can have different priority levels from one device. Therefore, new mathematical model is necessary for the case where different priority levels of data are created under one device node(2Q model). In this research, the mathematical model for 2Q model is developed using the equivalent queue model. Furthermore, the characteristics of transmission delay of 2Q model which is presented in this paper were compared with 1Q model. The validity of the analytical model was verified by using a simulation experiment.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.71-95
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• 2012

Nowadays, the big issues on mathematics education are mathematical modeling, mathematization, and problem solving. So, this paper looks about these issues. First, after 1990's, the researchers interested in mathematical model and mathematical modeling. So, this paper looks about mathematical model and mathematical modeling. Second, it looks about Freudenthal' mathematization after 1970's. And then, it compared with mathematical modeling. Also, it looks about that problem solving focused on mathematics education since 1980's. And it compared with mathematical modeling.

• The Mathematical Education
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• v.40 no.2
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• pp.253-263
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• 2001

Developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recent performance based on assessment has focused on the teaching and learning environment in school, emphasizing student's self construction of their learning and its process. Because of this reason, people related to mathematics education including math teachers are taught to recognize the fact that the degree of students'acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) should be estimated formally in math class. However, due to the lack of an evaluation tool for estimating the degree of their thinking skills, efforts at evaluating student's degree of mathematics thinking skills and strategy acquisition failed. Therefore, in this paper, mathematical thinking was studied, and using the results of study as the fundamental basis, mathematical thinking process model was developed according to three types of mathematical thinking - fundamental thinking skill, developing thinking skill, and advanced thinking strategies. Finally, based on the model, evaluation factors related to essential thinking skills such as analogy, deductive thinking, generalization, creative thinking requested in the situation of solving mathematical problems were developed.

• Education of Primary School Mathematics
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• v.5 no.2
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• pp.71-94
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• 2001

The purposes of this study were to design small group collaborative learning models for developing the creativity and to analyze the effects on applying the models in mathematics teaching and loaming. The meaning of open education in mathematics learning, the relation of creativity and inquiry learning, the relation of small group collaborative learning and creativity, and the relation of assessment and creativity were reviewed. And to investigate the relation small group collaborative learning and creativity, we developed three types of small group collaborative learning model- inquiry model, situation model, tradition model, and then conducted in elementary school and middle school. As a conclusion, this study suggested; (1) Small group collaborative learning can be conducted when the teacher understands the small group collaborative learning practice in the mathematics classroom and have desirable belief about mathematics instruction. (2) Students' mathematical anxiety can be reduced and students' involvement in mathematics learning can be facilitated, when mathematical tasks are provided through inquiry model and situation model. (3) Students' mathematical creativity can be enhanced when the teacher make classroom culture that students' thinking is valued and teacher's authority is reduced. (4) To develop students' mathematical creativity, the interaction between students in small group should be encouraged, and assessment of creativity development should be conduced systematically and continuously.

• Journal of Drive and Control
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• v.15 no.2
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• pp.38-45
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• 2018

In this study, the theory of fluid mechanics and dynamics is used to build a mathematical model for a three-stage flow control valve. The significance of the study is that the mathematical model can easily be used to study the effect of different design parameters on the performance of the valve. The geometry of the valve and the properties of the fluid were used in this study to determine the variation in the performance of the valve when varying the magnetic force on the pilot spool. While a linearization technique is not used to solve the developed model, the solution of the mathematical model is found in the time domain by simulation of the equations using a software package. The results indicate that if the developed mathematical model is solved for the different values of magnetic force, the valve behaves linearly; the valve is thus called the proportional flow control valve.

• Structural Engineering and Mechanics
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• v.20 no.1
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• pp.45-67
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• 2005

This paper presents a new approach to predict the racking load-displacement response of plasterboard clad walls found in Australian light-framed residential structures under monotonic racking load. The method is based on a closed-form mathematical model, described herein as the 'Modularised' Closed-Form Mathematical model or MCFM model. The model considers the non-linear behaviour of the connections between the plasterboard cladding and frame. Furthermore, the model is flexible as it enables incorporation of different nailing patterns for the cladding. Another feature of this model is that the shape of stud deformation is not assumed to be a specific function, but it is computed based on the strain energy approach to take account of the actual load deformation characteristics of particular walls. Verification of the model against the results obtained from a detailed Finite Element (FE) model is also reported. Very good agreement between the closed form solution and that of the FE model was achieved.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.112-112
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• 2001

An Anti-lock Brake System ABS is developed to increase the stability of vehicle and to reduce the stopping distance when braking manoeuvres by measuring the wheel and vehicle speed. An ABS mathematical model which describes the dynamics of vehicle and calculate the stopping distance, is explained in this paper. To proceed this study, a mathematical model is produced with simulink software package. Although the model considered here is relatively simple, it retains the essential dynamics of the system. The results are evaluated at the various driving or road conditions. The results from mathematical model show that ABS reduces the stopping distance at the various road conditions. This mathematical model could be ...

• East Asian mathematical journal
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• v.32 no.1
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• pp.139-152
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• 2016

Inflammatory Bowel Disease(IBD) is chronic, relapsing, immune mediated disorder. The exact cause of IBD is still unknown. The immune system is known to play important role in the dynamics of IBD. We focus on relation between T cells and cytokines in immune system that leads to IBD. In this paper, we propose a mathematical model describing IBD under considering immune mediated disorder by using ordinary differential equations. The existence and stability of the model are established, where an applicable basin of attraction are calculated and examined. Some numerical simulations are presented to verify the proposed results and as changing parameter values given by sensitivity analysis, we show how to change dynamic behaviors of the model.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.45-67
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• 2021

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

• Research in Mathematical Education
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• v.26 no.3
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• pp.167-202
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• 2023

A central problem of mathematics teaching worldwide is probably the insufficient adaptive handling of tasks-especially in computational practice phases and modeling tasks. All students in a classroom must often work on the same tasks. In the process, the high-achieving students are often underchallenged, and the low-achieving ones are overchallenged. This publication uses different modeling of the tennis serve as an example to show a possible solution to the problem and develops and discusses one adaptive task each for middle school, high school, and college using three mathematical models of the tennis serve each time. From model to model within the task, the complexity of the modeling increases, the mathematical or physical demands on the students increase, and the new modeling leads to more realistic results. The proposed models offer the possibility to address heterogeneous learning groups by their arrangement in the surface structure of the so-called parallel adaptive task and to stimulate adaptive mathematics teaching on the instructional topic of mathematical modeling. Models A through C are suitable for middle school instruction, models C through E for high school, and models E through G for college. The models are classified in the specific modeling cycle and its extension by a digital tool model, and individual modeling steps are explained. The advantages of the presented models regarding teaching and learning mathematical modeling are elaborated. In addition, we report our first teaching experiences with the developed parallel adaptive tasks.