• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권4호
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• pp.271-281
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• 2008

Quarter a century ago, I founded the Colorado Mathematical Olympiad. The Colorado Mathematical Olympiad is the largest essay-type in-person mathematical competition in the United States, with 600 to 1,000 participants competing annually for prizes. In this article, I explain what it is, how it works, give examples of problems and solutions, and share with the reader careers of some of the Olympiad's winners.

• 대한수학회보
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• 제34권3호
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• pp.335-350
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• 1997

In this article, a scattering problem in a nonhomogeneous medium is formulated as an integral equation which contains boundary and volume integrals. The integral equation is solved for sufficiently small $$\mid$$\mid$1-p$\mid$$\mid$,$\mid$$\mid${k_i}^2-k^2$\mid$$\mid$\;and\;$\mid$$\mid${\nabla}p$\mid$$\mid$$ where $k,\;k_i$ and p the wave numbers and the density respectively.

• 대한수학회보
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• 제50권1호
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• pp.201-216
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• 2013

In this note, we consider the Riemann problem for a two-dimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one-dimensional Cauchy problem, which provides a verification that our construction produces the correct global solutions.

• 대한수학회지
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• 제39권2호
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• pp.319-330
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• 2002

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

• East Asian mathematical journal
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• 제27권1호
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• pp.51-65
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• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• 대한수학회보
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• 제52권4호
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• pp.1185-1199
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• 2015

This paper is concerned with the optimal control problem for the viscous weakly dispersive Benjamin-Bona-Mahony (BBM) equation. We prove the existence and uniqueness of weak solution to the equation. The optimal control problem for the viscous weakly dispersive BBM equation is introduced, and then the existence of optimal control to the problem is proved.

• 대한수학회보
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• 제52권4호
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• pp.1149-1167
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• 2015

We get a theorem which shows the existence of at least four $2{\pi}$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.

• East Asian mathematical journal
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• 제34권4호
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• pp.451-462
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• 2018

This study analyzed the learning components of the web-based adaptive math learning programs in order to develop adaptive math learning program using artificial intelligence. The components of the web-based adaptive math learning program set for analysis are classified into learning process presentation, concept learning, problem presentation, problem solving process, and learning result processing then analyzed three programs. As a result of analysis, the typical characteristic of components is that it uses a method of repeatedly presenting the same type of problem in order to learn one concept.

• 대한수학회논문집
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• 제12권3호
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• pp.813-827
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• 1997

Multigrid methods for two first-order system least squares (FOSLS) using bilinear finite elements are developed for the pure traction problem of planar linear elasticity. They are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. In this paper, concentration is given on solving for the gradients of displacement only. Numerical results show that the convergences are uniform even as the material becomes nearly incompressible. Computations for convergence rates are included.

• 대한수학회지
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• 제52권6호
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• pp.1179-1194
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• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.