• 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.

• The Mathematical Education
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• v.58 no.3
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• pp.443-458
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• 2019

Mathematical modeling has been a crucial topic in mathematics education as students' problem solving competency are regarded as a core skill for future society. Despite of the importance of mathematical modeling in school mathematics, there have been very limited studies relating pre-service teachers' knowledge and perceptions on mathematical modeling. In this vein, this study aimed to investigate pe-service mathematics teachers' perceptions on mathematical model, mathematical modeling and educational use of mathematical modeling, and their relationships. The current study utilized a survey consisted of 18 items. The responses of 210 pre-service mathematics teachers to the survey items were quantitatively analyzed using descriptive statistics, analysis of variance, exploratory and confirmatory factor analysis, the structural equation model, and multi group analysis. The results of analysis of variance revealed that pre-service teachers in difference groups (majors, grades, and experiences with mathematical modeling) showed statistically significant differences in mean values. Moreover, according to the results from the structural equation modeling analysis, pre-service mathematics teachers' perceptions on mathematical model and modeling affected their perceptions on educational use of mathematical modeling. In addition, depending on their pre-experiences with mathematical modeling, pre-service teachers represented a different relationship between perceptions on mathematical modeling and educational use of mathematical modeling. Implications for future studies and mathematics classrooms were discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.485-491
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• 2000

We obtain the mathematical model of the hard disk drive actuator system from the system response data of the finite element analysis or experimental results. System response data including the dynamics of the considered system are expressed as the mathematical model. It allows the dynamic analysis of the actuator system without resort to the repetitive finite element modeling work. Even though the dynamic characteristics of the system are affected somewhat by the structural modification and the change of the dynamic properties, we can use the modified size and material properties of the actuator system in the mathematical model to some extent. In this study, we express the mathematical model of the simplified rectangular plate first and then proceed to the actual hard disk drive actuator system.

• Transactions of Materials Processing
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• v.13 no.5
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• pp.461-465
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• 2004

Based on the experimental observation, the mathematical friction model, which is an essential information for analyzing the forming process of sheet metal, is developed considering lubricant viscosity, surface roughness and hardness, punch comer radius, and punch speed. By comparing the punch load found by FEM with a proposed friction model with experimental measurement when the coated and uncoated steel sheets are formed in 2-D geometry in dry and lubricant conditions, the validity and accuracy of the developed friction model are demonstrated.

• The Mathematical Education
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• v.48 no.4
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• pp.365-385
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• 2009

Recently, mathematical modeling has been attractive in that it could be one of many efforts to improve students' thinking and problem solving in mathematics education. Mathematical modeling is a non-linear process that involves elements of both a treated-as-real world and a mathematics world and also requires the application of mathematics to unstructured problem situations in real-life situation. This study provides analysis of literature review about modeling perspectives, case studies about mathematical modeling, and textbooks from the United States and Korea with perspective which mathematical modeling could be potential and meaningful to students even in elementary school. Further, teaching method with mathematical modeling was investigated to see the possibility of application to elementary mathematics classroom.

• Journal of Industrial Technology
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• v.28 no.B
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• pp.193-198
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• 2008

When the existing polder levee was constructed, the river's numerical analysis decided the bank raise by applying the planned flood stage or by using the result from the sectional 1st dimensional numerical analysis. But, it was presented that there is a limitation in the 1st dimensional value analysis when the structure like the polder levee obstructs the special shaped running water flow. Therefore, in order to verify the numerical value applicability when the polder levee is constructed, this report compared each other through the 1st and 2nd dimensional numerical analysis and the mathematical principle model laboratory. In case of the polder levee construction through the numerical analysis and the mathematical principle model laboratory, it was decided that there was no big problem in the 1st dimensional numerical analysis applied design, considering the uncertainty of mathematical principle analysis though the first dimensional numerical analysis was calculated a little bigger than the second. But, after construction, it was found that the water level deviation of the 1st, 2nd occurred biggest at the place where the flow was divided into two. Also, as a result of comparing the 1st, 2nd dimensional numerical analysis with the mathematical principle model laboratory, it was confirmed that the 1st numerical analysis applied design decreased the modal safety largely, as the left side water level was calculated smaller more than 0.5m in case of the 1st dimensional numerical analysis.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

• Communications of Mathematical Education
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• v.34 no.4
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• pp.485-506
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• 2020

The purpose of this study is to analyze of the effect in Mathematics Teachers beliefs on their students beliefs by Latent Class Regression Model (LCRM). For this analysis, the study used the findings and surveys of Kang, Hong (2020) who developed a belief profile by analyzing the mathematical beliefs of 60 high school teachers and 1,850 second-year high school students learning from them through the Latent Class Analysis (LCA). As a result It was observed that 'Nature of Mathematics', 'Mathematic Teaching' and 'Mathematical Ability' of mathematics teachers beliefs influence the mathematical beliefs of students. The teacher's belief of 'Nature of Mathematics' statistically significant effects on students' beliefs in 'School Mathematics', 'Problem Solving', 'Mathematics Learning'. The teacher's belief of 'Teaching Mathematics', 'Mathematical Ability' statistically significant effects on students' beliefs in 'School Mathematics', 'Problem Solving', 'Self-Concept'. The results of this study can give a preview of the phenomenon in which teacher's mathematical beliefs are reproduced into student's mathematical beliefs. In addition, the results of observation of this study can be used to the contents that can achieve the purpose of reorientation for mathematics teachers.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• 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.