• Journal of Biosystems Engineering
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• v.12 no.3
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• pp.17-29
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• 1987

A 10-degree of freedom mathematical model of motion for power tiller-trailer system was developed. This model can predict motion characteristics of power tiller trailer system while travelling over smooth and irregular ground surfaces under various operating conditions. The model provide, the fundamental data needed to improve the stability of power tiller-trailer systems.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.

• Journal of Korean Society for Quality Management
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• v.50 no.1
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• pp.125-138
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• 2022

Purpose: Failure Mode and Effect Analysis (FMEA) is a widely utilized technique to measure product reliability by identifying potential failure modes. Even though FMEA techniques have been studied, the form of Risk Priority Number (RPN) used to evaluate risk priority in FMEA is still questionable because of its shortcomings. In this study, we suggest common RPN(cRPN) to resolve shortcomings of the traditional RPN and show the extensibility of cRPN. Methods: We suggest cRPN which is based on Cobb-Douglas production function, and represent the various application on weighting risk factors, weighted RPN in a mathematical way, and show the possibility of statistical approach. We also conduct numerical study to examine the difference of the traditional RPN and cRPN as well as the potential application from the analysis on marginal effects of each risk factor. Results: cRPN successfully integrates previously suggested approaches especially on the relative importance of risk factors and weighting RPN. Moreover, we analyze the effect of corrective actions in terms of econometric analysis using cRPN. Since cRPN is rely on the reliable mathematical model, there would be numerous applications using cRPN such as smart factory based on A.I. techniques. Conclusion: We propose a reliable mathematical model of RPN based on Cobb-Douglas production function. Our suggested model, cRPN, resolves various shortcomings such as consideration of the relative importance, the effect of combinations among risk factors. In addition, by adopting a reliable mathematical model, quantitative approaches are expected to be applied using cRPN. We find that cRPN can be utilized to the field of industry because it is able to be applied without modifying the entire systems or the conventional actions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.6
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• pp.546-552
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• 2013

A cantilevered piezoelectric energy harvester(PEH) and an auxiliary mass-spring unit can be integrated into a novel two-degrees-of-freedom PEH where its lowest eigenmode is not an in-phase modes but an out-of-phase mode. This typical behavior was shown to enhance output power considerably compared with its stand-alone counterpart. The objective of this study is to newly develop a continuum-based mathematical model suitable for efficient analysis of the mode-sequence reversed PEH. Once such a mathematical model is available, various physical behaviors can be analytically investigated for better designs. After a new mathematical model is developed, its validity is checked by using ANSYS results, in terms of resonant frequency, open-circuit voltage, and output power with a specified external resistance.

• Proceedings of the KSR Conference
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• 2004.06a
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• pp.1233-1239
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• 2004

This study analysis the current level of the Korea High Speed Line by mathematical model of the rail and compensation capacitors. The rail and compensation capacitors are represented by transmission parameters and the analysis is processed by computer simulation.

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.467-471
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• 1998

A mathematical model is developed to predict the fatigue notch factor of butt welds subject to number of parameters such as weld geometry, residual stresses under dynamic combined loading conditions (tensile and bending). Linear elastic fracture mechanics, finite element analysis, dimensional analysis and superposition approaches are used for the modelling. The predicted results are in good agreement with the available experimental data. As a result, scatters of the fatigue data can be significantly reduced by plotting S-N curve as ($S{\cdot}K_f$) vs. N.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.303-310
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• 2017

The model updating problems, which are to find the optimal approximation to the discrete quadratic model obtained by the finite element method, are critically important to the vibration analysis. In this paper, the structured model updating problem is considered, where the coefficient matrices are required to be symmetric and positive semidefinite, represent the interconnectivity of elements in the physical configuration and minimize the dynamics equations, and furthermore, due to the physical feasibility, the physical parameters should be positive. To the best of our knowledge, the model updating problem involving all these constraints has not been proposed in the existed literature. In this paper, based on the semidefinite programming technique, we design a general-purpose numerical algorithm for solving the structured model updating problems with incomplete measured data and present some numerical results to demonstrate the effectiveness of our method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.571-588
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• 2010

We introduce the Landau-de Gennes model in order to understand molecular structures in ferroelectric liquid crystals. We investigate equilibrium configurations of the governing energy functional by means of bifurcation analysis. In particular, we obtain periodic solutions of the functional, which is a signature of a rich variety of applications of ferroelectric materials.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.385-400
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• 2009

The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.3
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• pp.125-130
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• 2017

In this study, the influence of various factors on surface roughness was investigated using the Taguchi experimental method through high-speed machining processing. Feed rate, pitch, tool diameter, and depth of cut are widely applied to high-speed machining conditions for mold production. Each of these factors was implemented and classified into three levels; then, after high speed machining, surface roughness was measured, the S/N ratio was analyzed, and the influence on the surface roughness of control factors was analyzed quantitatively by ANOVA. Using this information, a mathematical model for predicting surface roughness was derived from multiple regression analysis. This mathematical model enables the surface roughness value after high-speed machining to be predicted at the production stage, before machining, for a wide range of machining conditions.