• Journal of Gifted/Talented Education
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• v.24 no.6
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• pp.1053-1071
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• 2014

Problem posing is used to develop the creativity program and adaption for the gifted, and to screen the gifted students in the selection process. However existing creativity assessment factors(fluence, flexibility, originality) has been recognized to have it's limitation to assess the mathematical creativity. To improve the creativity assessment, we propose new set of assessment factors for mathematical creativity test through problem posing. For this study, we let 19 mathematically gifted students to pose two good mathematical problems for a limited time after solving a certain problem so called a reference problem. A week late, we let the subjects, pre-service teachers, and experts to evaluate the problems posed by the subjects, and leave the reasons for evaluating highest mark and lowest mark. With this date, we propose fluence, flexibility, originality, anti-similarity, complexity, elaboration as the set of mathematics creativity assessment factors.

• The Mathematical Education
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• v.55 no.1
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• pp.21-39
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• 2016

This research examined the Korean and American $6^{th}$ grade students' mathematical problem solving ability and methods via an intuitive thinking. For this, the survey research was used. The researcher developed the questionnaire which consists of problems with intuitive and algorithmic problem solving in number and operation, figure and measurement areas. 57 Korean $6^{th}$ grade students and 60 American $6^{th}$ grade students participated. The result of the analysis showed that Korean students revealed a higher percentage than American students in correct answers. But it was higher in the rate of Korean students attempted to use the algorithm. Two countries' students revealed higher rates in that they tried to solve the problems using intuitive thinking in geometry and measurement areas. Students in both countries showed the lower percentages of correct answer in problem solving to identify the impact of counterintuitive thinking. They were affected by potential infinity concept and the character of intuition in the problem solving process regardless of the educational environments and cultures.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.493-500
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• 2023

The multiparameter eigenvalue method can be used to solve the damped finite element model updating problems. This method transforms the original problems into multiparameter eigenvalue problems. Comparing with the numerical methods based on various optimization methods, a big advantage of this method is that it can provide all possible choices of physical parameters. However, when solving the transformed singular multiparameter eigenvalue problem, the proposed method based on the generalised inverse of a singular matrix has some computational challenges and may fail. In this paper, more details on the transformation from the dynamic model updating problem to the multiparameter eigenvalue problem are presented and the structure of the transformed problem is also exposed. Based on this structure, the rigorous mathematical deduction gives the upper bound of the number of possible choices of the physical parameters, which confirms the singularity of the transformed multiparameter eigenvalue problem. More importantly, we present a row and column compression method to overcome the defect of the proposed numerical method based on the generalised inverse of a singular matrix. Also, two numerical experiments are presented to validate the feasibility and effectiveness of our method.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1243-1254
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• 2009

The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, $\infty$). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.173-186
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• 2015

In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.441-447
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• 1999

A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

• The Mathematical Education
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• v.48 no.2
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• pp.141-148
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• 2009

The article discusses roles of analysis in problem solving, especially the problem posing. The author shows the procedure of analysis like the presentation of the hypothesis, the reasoning for the necessary conditions and the sufficient condition. Finally the author suggests that the analysis should be reviewed in the school mathematics.

• East Asian mathematical journal
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• v.27 no.5
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• pp.527-538
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of an equilibrium problem, the set of fixed points of nonexpansive mapping and the set of solutions of the generalized variational inequality for ${\alpha}$-inverse strongly g-monotone mapping in a Hilbert space. Under suitable conditions, strong convergence theorems for approximating a common element of the above three sets are obtained.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.59-64
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• 2007

In this paper, we will introduce the generalized operator equlibrium problem and generalized operator quasi-equlibrium problem which generalize operator equlibrium problem due to Kazmi and Raouf into multi-valued and quasi-equlibrium problems. Using a Park's fixed point theorem, we will prove a new existence theorem on generalized operator equlibrium problem which serves as a basic existence theorem for various kinds of nonlinear problems.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.