• Communications of Mathematical Education
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• v.23 no.2
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• pp.297-312
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• 2009

We study the process of horizontal and vertical mathematization on the polyhedron problems through the history of mathematics, computer experiments, problem posing, and justifications. In particular, we explore the Hamilton cycle problem, coloring problem, and folding net construction on the Archimedean and Catalan polyhedrons. In this paper, we present our mathematical results on the polyhedron problems, and we also present some unsolved problems that we found. We found that the history of mathematics and mathematical experiments are very useful in such R&E exploration as polyhedron problem posing and solving project.

• Honam Mathematical Journal
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• v.5 no.1
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• pp.227-237
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• 1983

• School Mathematics
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• v.7 no.1
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• pp.55-75
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• 2005

Mathematical symbolizing is an important part of mathematics learning. But many students have difficulties m symbolizing mathematical ideas formally. If students had experiences inventing their own mathematical symbols and developing them to conventional ones natural way, i.e. learning mathematical symbols via expressive approaches, they could understand and use formal mathematical symbols meaningfully. These experiences are especially valuable for students who meet mathematical symbols for the first time. Hence, there are needs to investigate how early elementary school students can and should experience meaningful mathematical symbolizing. The purpose of this study was to analyze students' mathematical symbolizing processes and characteristics of theses. We carried out teaching experiments that promoted meaningful mathematical symbolizing among eight first graders. And then we analyzed students' symbolizing processes and characteristics of expressive approaches to mathematical symbols in early elementary students. As a result, we could places mathematical symbolizing processes developed in the teaching experiments under five categories. And we extracted and discussed several characteristics of early elementary students' meaningful mathematical symbolizing processes.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.87-103
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• 2004

A practical estimation method for groundwater contaminant concentration is introduced. Using geostatistical techniques and symmetry, experimental variograms show significant improved correlation compared with those from conventional techniques. Numrical experiments are performed using a field data set.

• East Asian mathematical journal
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• v.14 no.2
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• pp.399-410
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• 1998

In [3], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated-linear systems. In this work, we present computational experiments of W-cycle multigrid method. Computational experiments show that the convergence is uniform as the parameter, $\nu$, goes to 1/2.

• Journal of Biosystems Engineering
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• v.42 no.2
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• pp.86-97
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• 2017

Purpose: This study aims to evaluate the applicability of a tractor-baler system equipped with a newly developed round baler by conducting stability analyses via static-state mathematical simulations and verification experiments for the tractor equipped with a loader. Methods: The centers of gravity of the tractor and baler were calculated to analyze the transverse overturning of the system. This overturning of the system was analyzed by applying mathematical equations presented in previous research and comparing the results with those obtained by the newly developed mathematical simulation. For the case of the tractor equipped with a loader, mathematical simulation results and experimental values from verification experiments were compared and verified. Results: The center of gravity of the system became lower after the baler was attached to the tractor and the angle of transverse overturning of the system steadily increased or decreased as the deflection angle increased or decreased between $0^{\circ}$ and $180^{\circ}$ on the same gradient. In the results of the simulations performed by applying mathematical equations from previous research, right transverse overturning occurred when the tilt angle was at least $19.5^{\circ}$ and the range of deflection angles was from $82^{\circ}$ to $262^{\circ}$ in counter clockwise. Additionally, left transverse overturning also occurred at tilt angles of at least $19.5^{\circ}$ and the range of deflection angles was from $259^{\circ}$ to $79^{\circ}$ in counter clockwise. Under the $0^{\circ}$ deflection angle condition, in simulations of the tractor equipped with a loader, transverse overturning occurred at $17.9^{\circ}$, which is a 2.3% change from the results of the verification experiment ($17.5^{\circ}$). The simulations applied the center of gravity and the correlations between the tilt angles, formed by individual wheel ground contact points excluding wheel radius and hinge point height, which cannot be easily measured, for the convenient use of mathematical equations. The results indicated that both left and right transverse overturning occurred at $19.5^{\circ}$. Conclusions: The transverse overturning stability evaluation of the system, conducted via mathematical equation modeling, was stable enough to replace the mathematical equations proposed by previous researchers. The verification experiments and their results indicated that the system is workable at $12^{\circ}$, which is the tolerance limit for agricultural machines on the sloped lands in South Korea, and $15^{\circ}$, which is the tolerance limit for agricultural machines on the sloped grasslands of hay in Japan.

• Transactions of Materials Processing
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• v.11 no.5
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• pp.394-404
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• 2002

The drawbead model for a three-dimensional a finite element analysis of sheet metal forming processes is developed. The mathematical models of the basic drawbeads like circular drawbead, stepped drawbead, and squared drawbaed are first derived using the bending theory, belt-pulley equation, and Coulomb friction law. Next, the experiments for finding the drawing characteristics of the drawbead are performed. Based on mathematical models and drawing test results, expert models of basic drawbeads are then developed employing a linear multiple regression method. For the expert models of combined drawbeads such as the double circular drawbead, double stepped drawbead, circular-and-stepped drawbead, etc., those of the basic drawbeads are summed. Finally, in order to verify the expert models developed, the drawing characteristics calculated by the expert models of the double circular drawbead and circular-and-stepped drawbead are compared with those obtained from the experiments. The predictions by expert models agree well with the measurements by experiments.

• East Asian mathematical journal
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• v.37 no.3
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• pp.333-354
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• 2021

A support vector machine (SVM) is a state-of-the-art machine learning model rooted in structural risk minimization. SVM is underestimated with regards to its application to real world problems because of the difficulties associated with its use. We aim at showing that the performance of SVM highly depends on which kernel function to use. To achieve these, after providing a summary of support vector machines and kernel function, we constructed experiments with various benchmark datasets to compare the performance of various kernel functions. For evaluating the performance of SVM, the F1-score and its Standard Deviation with 10-cross validation was used. Furthermore, we used taylor diagrams to reveal the difference between kernels. Finally, we provided Python codes for all our experiments to enable re-implementation of the experiments.

• Journal of Korean Society for Quality Management
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• v.34 no.3
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• pp.62-65
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• 2006

We can use the ridge regression as a means for stabilizing the coefficient estimators in the fitted model when performing experiments in highly constrained regions causes collinearity problems in mixture experiments. But there is no theory available on which to base statistical inference of ridge estimators. The bootstrap could be used to seek the confidence intervals of ridge estimators.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.759-766
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• 2000

In order to design fractional factorial experiments which include some debarred combinations, we should select defining contrasts so that those combinations are to be excluded. Choi(1999) presented a method of selectign defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations. In this paper, we extend Choi's method to general p-level fractional factorial experiments to select defining contrasts which cold exclude some debarred combinations.