• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.673-687
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• 2022

In this study, we solve the Cayley inclusion problem and the fixed point problem in real Hilbert space using Tseng's technique with inertial extrapolation in order to obtain more efficient results. We provide a strong convergence theorem to approximate a common solution to the Cayley inclusion problem and the fixed point problem under some appropriate assumptions. Finally, we present a numerical example that satisfies the problem and shows the computational performance of our suggested technique.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.209-224
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• 2006

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.391-408
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• 2000

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem form the conventional setting of a planar shock-interface interaction.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.583-605
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• 2016

Problem solving has been consistently emphasized in national mathematics curricula, whereas the foci of such an emphasis have been changed. Given this background, this study traced down major changes in emphasizing problem solving from the first national mathematics curriculum to the most recent 2015 curriculum. In particular, both the 2009 and the 2015 revised curricula were analyzed in detail to figure out the latest emphasis and trends. This paper then investigated whether a series of mathematics textbooks were aligned to the emphases of recent curricula. It finally discussed some issues that we need to reconsider with regards to problems, problem solving strategies, and the process of problem solving. As such, this study is expected to provide textbook developers with detailed implications on how to employ problem solving in new series of textbooks.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.919-928
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• 2018

In this paper, we consider the admissible control problem for the linear systems by using the solution of the Hausdorff moment problem. In addition, we consider the admissible control problem for SIR epidemic model.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.1-23
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• 2005

The decentralized static output feedback design problem is considered. A constrained trust region method is developed that solves this optimal control problem when a complete set of state variables is not available. The considered problem is interpreted as a non-linear (non-convex) constrained matrix optimization problem. Then, a decentralized constrained trust region method is developed for this problem class exploiting the diagonal structure of the problem and using inexact computations. Finally, numerical results are given for the proposed method.

• School Mathematics
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• v.8 no.3
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• pp.341-364
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• 2006

This paper analyzed contents related to problem solving in the 7th elementary mathematics curriculum in conjunction with main changes in the next curriculum under discussion. This paper then provided detailed analyses of textbooks and workbooks in terms of principal contents, problem solving strategies, content areas, and problem types in order to look closely at how such instructional materials would put the vision of the curriculum into action. It is expected that many issues and suggestions stemming from the analyses will serve basic information to develop next curriculum and its concomitant instructional materials in a way to fostering students' problem solving ability.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.175-196
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• 2009

In this paper we analyze Ziv's geometrical differentiated teaching and learning materials using inner structure of mathematics problems. In order to analyze inner structure of mathematics problems we in detail describe problem solving process, and extract main frame from problem solving process. We represent inner structure of mathematics problems as tree including induced relations. As a result, we characterize low-level problems and middle-level problems, and find some differences between low-level problems and middle-level problems.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.123-139
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• 2019

This study analyzed how problem-posing tasks included in Korean middle school mathematics textbooks were distributed in terms of content area, task type, and context of task to investigate that the mathematics textbooks are giving students ample opportunities for problem-posing activities. The analysis of 10 mathematics textbooks for first grade in middle school according to the revised mathematics curriculum in 2015 found that the problem-posing tasks contained in the textbooks are insufficient in quantity and not evenly distributed in terms of content areas. There were also more problem-posing tasks with relatively moderate constraints than those with strong or weak constraints in terms of mathematical constraints. In addition, there were more problem-posing tasks that were not requiring students to make a new context, and more often camouflage contexts were used. Based on this, implications for improving mathematics problem-posing tasks in mathematics textbook were suggested.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.391-399
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• 2005

In this paper we present an algorithm based on network flow techniques which provides a solution for a combinatorial problem. Then, in order to provide all the solutions of this problem, we make use of an algorithm that given the bipartite graph $G=(V_1 {\cup}{V_2},\;E,\;{\omega})$ outputs the enumeration of all bipartite matchings of given cardinality v and cost c.