• Communications of Mathematical Education
• /
• v.23 no.1
• /
• pp.109-128
• /
• 2009

This study aimed to investigate students' learning process by examining their perception process of problem structure and mathematization, and further to suggest an effective teaching and learning of mathematics to improve students' problem-solving ability. Using the qualitative research method, the researcher observed the collaborative learning of two middle school students by providing problem-posing activities of five lessons and interviewed the students during their performance. The results indicated the student with a high achievement tended to make a similar problem and a new problem where a problem structure should be found first, had a flexible approach in changing its variability of the problem because he had advanced algebraic thinking of quantitative reasoning and reversibility in dealing with making a formula, which related to developing creativity. In conclusion, it was observed that the process of problem posing required accurate understanding of problem structures, providing students an opportunity to understand elements and principles of the problem to find the relation of the problem. Teachers may use a strategy of simplifying external structure of the problem and analyzing algebraical thinking necessary to internal structure according to students' level so that students are able to recognize the problem.

• Journal of Korean Institute of Industrial Engineers
• /
• v.17 no.1
• /
• pp.127-130
• /
• 1991

The multi-divisional knapsack problem is defined as a binary knapsack problem where each of mutually exclusive divisions has its own capacity. We consider the relaxed LP problem and develop a transformation which converts the multi-divisional linear knapsack problem into smaller size linear knapsack problems. Solution procedures and a numerical example are presented.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.647-654
• /
• 2017

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.439-450
• /
• 2009

In this note we give a connection between the truncated moment problem and the 2-variable subnormal completion problem.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.685-692
• /
• 2009

We consider the linearized (approximated) problem for differentiable vector optimization problem, and then we establish equivalence results between a differentiable vector optimization problem and its associated linearized problem under the proper efficiency.

• East Asian mathematical journal
• /
• v.31 no.3
• /
• pp.371-377
• /
• 2015

We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

• Journal of Elementary Mathematics Education in Korea
• /
• v.16 no.2
• /
• pp.269-293
• /
• 2012

This study is intended to figure out how the 6th grade students carry out newly added standards regard to the problem solving in the revised mathematics curriculum in 2007 and 2009, which are 'finding useless information in a given problem', 'finding insufficient information in a given problem', and 'posing new problem by changing conditions of the given problem.' In order to achieve this goal, we examined the characteristics of 200 elementary students' problem posing. We constructed and used the survey sheet which consisted of 6 items relevant to 'finding useless information in a given problem', 'finding insufficient information in a given problem', and 'posing new problem by changing conditions of the given problem.'

• Journal of the Korean Institute of Intelligent Systems
• /
• v.22 no.4
• /
• pp.414-424
• /
• 2012

Finding or automatically generating problem instance is useful for algorithm analysis/test. The topic has been of interest in the field of hardware/software engineering and theory of computation. We apply objective value-distance correlation analysis to problem spaces, as previous researchers applied it to solution spaces. According to problems, we define the objective function by (1) execution time of tested algorithm or (2) its optimality; this definition is interpreted as difficulty of the problem instance being solved. Our correlation analysis is based on the following aspects: (1) change of correlation when we use different algorithms or different distance functions for the same problem, (2) change of that when we improve the tested algorithm, (3) relation between a problem instance space and the solution space for the same problem. Our research demonstrates the way of problem instance space analysis and will accelerate the problem instance space analysis as an initiative research.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.39 no.1
• /
• pp.56-63
• /
• 2016

We consider a satellite mission scheduling problem, which is a promising problem in recent satellite industry. This problem has various considerations such as customer importance, due date, limited capacity of energy and memory, distance of the location of each mission, etc. Also we consider the objective of each satellite such as general purpose satellite, strategic mission and commercial satellite. And this problem can be modelled as a general knapsack problem, which is famous NP-hard problem, if the objective is defined as to maximize the total mission score performed. To solve this kind of problem, heuristic algorithm such as taboo and genetic algorithm are applied and their performance are acceptable in some extent. To propose more efficient algorithm than previous research, we applied a particle swarm optimization algorithm, which is the most promising method in optimization problem recently in this research. Owing to limitation of current study in obtaining real information and several assumptions, we generated 200 satellite missions with required information for each mission. Based on generated information, we compared the results by our approach algorithm with those of CPLEX. This comparison shows that our proposed approach give us almost accurate results as just less than 3% error rate, and computation time is just a little to be applied to real problem. Also this algorithm has enough scalability by innate characteristic of PSO. We also applied it to mission scheduling problem of various class of satellite. The results are quite reasonable enough to conclude that our proposed algorithm may work in satellite mission scheduling problem.

• Hwankyungkyoyuk
• /
• v.20 no.3
• /
• pp.113-124
• /
• 2007

The purpose of this study is to investigate the direction of how to educate water shortage problem to middle school students. In the reality that many people of the world have been painful of the water shortage problem, Korea is classified as 'water shortage country'. Here, we investigated the awareness of middle school students about the contents related to the water shortage problem by surveying with the questionnaires developed in this study. And we analyzed how water shortage problem appeared in the environmental textbook of middle school. Based on these, we examined the direction of environmental education in middle school on the theme of the water shortage problem. The results of the survey showed that students revealed difference of knowledge and experience, and also revealed difference of knowledge and feeling related to the water shortage problem. The students had the knowledge about water shortage problem but they did not have experience in their real lives. Also, the results of the survey showed that students had attitude of waste in water use, even though they had awareness and knowledge about the importance of water resources. And the students did not have enough knowledge related to the water shortage problem. From the analysis of the textbooks, We found that the contents were not composed to enhance deep understanding of the students about the water shortage problem. Based on the analysis of the results, the directions of middle school environmental education in Korea about water shortage problem were extracted in this research.