• ETRI Journal
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• v.35 no.3
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• pp.523-529
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• 2013

Subquadratic space complexity multipliers for optimal normal bases (ONBs) have been proposed for practical applications. However, for the Gaussian normal basis (GNB) of type t > 2 as well as the normal basis (NB), there is no known subquadratic space complexity multiplier. In this paper, we propose the first subquadratic space complexity multipliers for the type 4 GNB. The idea is based on the fact that the finite field GF($2^n$) with the type 4 GNB can be embedded into fields with an ONB.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.1-16
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• 1997

Children should have opportunities to experience problem solving individually with strategies for developing their problem solving abilities. To make an instructional design for individual teaming, problem solving activities were classified into categories like individual activities, individual activities within a group, and team teaching. A flow of teaching and teaming process was designed before, and concrete and semi-concrete materials were used in an experimental teaching, which was analysed in this research.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.69-79
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• 2018

The Euclid metric is well-known and there are many results on the space with that metric. But there are many other metrics which gives more practical and useful results in the plane. In this paper, we introduce new metric function in the plane, which is more useful in city with subway. Finally we generalize to the general metric space and introduce a new metric on ${\mathbb{R}}^n$.

• Research in Mathematical Education
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• v.15 no.3
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• pp.251-259
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• 2011

Metaphor is the main representations of teachers' practical knowledge, which can help students to understand mathematics better. Through the recording and quantitative analysis of video cases of expert teachers in mathematics classroom, there are some results after analysis: 1) Teachers use many metaphors in the classroom and most of that are structural-ontological metaphors, which takes a certain period of time. 2) Teachers use the metaphors mainly in the teaching process of introduce and explore by the form of question-answer. 3) During the process of concept teaching, the metaphors from the real-world examples can promote the students have more motivation to study. During the process of procedure teaching, the metaphors from similar materials can promote the students to understand the operational skill better.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.30-35
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• 2013

Motivated by the emergency scheduling in a transportation network, this paper considers a transportation problem, in which, the truck times and transportation costs are assumed as uncertain variables. To meet the demand in the practical applications, two optimization objectives are considered, one is the total costs and another is the completion times. And then, a multi-objective optimization model is developed according to the situation in applications. Because there are commensurability and conflicting between the two objectives commonly, a solution does not necessarily exist that is best with respective to the two objectives. Therefore, the problem is reduced to a single objective model, which is an uncertain programming with a chance-constrain. After some analysis, its equivalent deterministic form is obtained, which is a nonlinear programming. Based on a stepwise optimization strategy, a solution method is developed to solve the problem. Finally, the computational results are provided to demonstrate the effectiveness of our model and algorithm.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.765-778
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• 2017

Finding an initial feasible solution on the central path is the main difficulty of feasible interior-point methods. Although, some algorithms have been suggested to remedy this difficulty, many practical implementations often do not use perfectly centered starting points. Therefore, it is worth to analyze the case that the starting point is not exactly on the central path. In this paper, we propose a weighted-path following interior-point algorithm for solving the Cartesian $P_{\ast}({\kappa})$-linear complementarity problems (LCPs) over symmetric cones. The convergence analysis of the algorithm is shown and it is proved that the algorithm terminates after at most $O\((1+4{\kappa}){\sqrt{r}}{\log}{\frac{x^0{\diamond}s^0}{\varepsilon}}\)$ iterations.

• Journal of the Korean School Mathematics Society
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• v.7 no.2
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• pp.67-79
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• 2004

Researchers in education intend and aspire to improve education practice. Researches should provide practical knowledge, instruments, teaching/learning skills which are needed in real educational environments. Research should closely related to practice. Design-experiment researches intend to promote and help education innovation. A variety of design experiment researches are presented with their characteristics, methods, goals, principles, case studies, prospects.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.139-159
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• 2000

In this manuscript we study perturbed Newton-like methods for the solution of nonlinear operator equations in a Banach space and their discretized versions in connection with the mesh independence principle. This principle asserts that the behavior of the discretized process is asymptotically the same as that for the original iteration and consequently, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved by others using Newton's method for certain classes of boundary value problems and even more generally by considering a Lipschitz uniform discretization. In some of our earlierpapers we extend these results to include Newton-like methods under more general conditions. However, all previous results assume that the iterates can be computed exactly. This is mot true in general. That in why we use perturbed Newton-like methods and even more general conditions. Our results, on the one hand, extend, and on the other hand, make more practical and applicable all previous results.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• Journal of the Korean School Mathematics Society
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• v.3 no.2
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• pp.133-154
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• 2000

The purpose of this study is to analyze theoretically suggested performance test and find out the actual conditions is math class at high schools and to suggest some devices for improvement for the various problems. To achieve this goal of study, I applied a performance test to the first graders of high school for one semester, and analyzed various phenomena which appeared during its practice. I made several questionnaire based on the materials of an academic seminar, "Several questions and devices for the improvement on mathematics performance test" And through the analysis, I pointed several problems of the performance test and proposed alternative plans. Several practical alternatives can be suggested for the problems appeared in the operation of performance test. The most important thing than any other technical solution in teachers′ diverse endeavor and enthusiastic research attitude to overcome the difficulties. Teachers′ spontaneousness is the foundation to enhance their own specialty and eradicate the propriety of the performance test.