• Research in Mathematical Education
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• v.14 no.1
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• pp.33-50
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• 2010

The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

• Tunnel and Underground Space
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• v.28 no.1
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• pp.25-37
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• 2018

Burger's model was used to analyze creep characteristics of unconsolidated rock. Burger's model should determine four physical parameters from two pairs of data. In this study, physical parameters of Burger's model were determined by applying mathematical concept solution. Creep was accelerated for three years using the determined physical parameters of the Burger's model for unconsolidated rocks. As a result, the creep behavior showed a continuous deformation behavior without convergence. Therefore, in this mine, it is analyzed that the application of U-Beam is more appropriate than roofbolt in terms of stability.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.155-171
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• 2007

One second grader, Junsu, was observed 4 times before and after formal multiplication lesson in Grade 2. This study describes how solution strategies in multiplication problems develop over time and investigates awareness of the relation between situation and computation in simple measurement and partitive division problems as informally experienced. It was found that Junsu used additive calculation for small-number multiplication problems but could not solve large-number multiplication problems and that he did not have concept of mathematical terms at first interview stage. After formal teaching, Junsu learned a variety of multiplication solution strategies and transferred from additive calculation to multiplicative calculation. The cognitive processing load of each strategy was gradually reduced. Junsu experienced measurement division as a dealing strategy and partitive division as a estimate-adjust strategy dealing more than one object in the first round.

• The Mathematical Education
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• v.47 no.3
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• pp.373-386
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• 2008

In highschool probability education, this study analyzed conflicts between intuitive concept and formal definition which originates from the process of establishing the concept of statistical independence. In judging independence, completely different types of problems requiring their own approach was analyzed by dividing them into two types. By doing so, this study researched a way to view independence as an overall idea. That is purposed to suggest a solution to a conflicts between intuitive concept and formal definition and to help not to judge independence out of wrong intuition. This study also suggests that calculation process which leads to precise perception of sample space and event be provided when we prove independence by expressing events with assembly symbols.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.2
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• pp.147-156
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• 1993

Recently a new concept of shadow prices, called average shadow price, has been developed. This paper provides a dual problem and the corresponding duality theorems justifying this new shadow price. The general duality framework is used. As an important secondary result, a new reduced class of price function, the pp. h.-class, has been developed for the general duality theory. This should be distinguished from other known reductions achieved in some specific areas of mathematical programming, in that it sustains the strong duality property in all the mathematical programs. The new general dual problem suggested with this pp. h.-class provides, as an optimal solution, the average shadow prices.

• The Mathematical Education
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• v.43 no.1
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• pp.87-96
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• 2004

For finding the optimal strategy in Blackout game which was introduced in the homepage of popular mono "Beautiful mind", we develope a mathematical proof and an algorithm with a software. We only use the concept of basis and knowledge of basic linear algebra. This process can be extended to the fullsize Go table problem and shows why we have to study mathematics at the college level.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.512-516
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• 1998

Fuzzy mathematical programming (FMP) can be treated an uncertainty condition using fuzzy concept. Further, it can be extended to the multiple objective (or goal) programming problem, naturally. But we feel that FMP have some shortcomings such as the fuzzy number in FMP is the one dimesional possibility set, so it can not be represented the relationship between them, and, in spite of FMP includes some (uncertainty) fuzzy paramenters, many alogrithms are only obtained a crisp solution.In this study, we propose a method of FMS. Our method use the scenario approach (or fuzzy random variables) to represent the relationship between fuzzy numbers, and can obtain the fuzzy solution.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.351-363
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• 2020

We introduce a new concept of Stepanov weighted pseudo almost periodic functions of class r which have been established by recently in [20]. Furthermore, we study the uniqueness and existence of Stepanov weighted pseudo almost periodic mild solutions of partial neutral functional differential equations having the Stepanov pseudo almost periodic forcing terms on finite delay.