• Education of Primary School Mathematics
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• v.25 no.1
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• pp.81-100
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• 2022

The purpose of this study is to develop a framework for analyzing the solution spaces of open-ended task and to explore their usefulness and applicability based on the analysis of solution spaces constructed by students. Based on literature reviews and previous studies, researchers developed a framework for analyzing solution spaces (OMR-framework) organized into subspaces of outcome spaces, method spaces, representation spaces which could be used in structurally analyzing students' solutions of open-ended tasks. In our research, we developed open-ended tasks which had various outcomes and methods that could be solved by using the concepts of factors and multiples and assigned the tasks to 181 elementary school fifth and sixth graders. As a result of analyzing the student's solution spaces by applying the OMR-framework, it was possible to systematically analyze the characteristics of students' understanding of the concept of factors and multiples and their approach to reversible and constructive thinking. In addition to formal mathematical representations, various informal representations constructed by students were also analyzed. It was revealed that each space(outcome, method, and representation) had a unique set of characteristics, but were closely interconnected to each other in the process. In conclusion, it can be said that method of analyzing solution spaces of open-ended tasks of this study are useful for systemizing and analyzing the solution spaces and are applicable to the analysis of the solutions of open-ended tasks.

• Education of Primary School Mathematics
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• v.27 no.4
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• pp.435-462
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• 2024

This study aims to derive educational implications for fostering mathematical creativity in elementary students. To achieve this, proportional distribution problems were presented as multiple-solution tasks, and students' problem-solving processes were analyzed from the perspective of mathematical creativity. The study involved 100 sixth-grade elementary students who were given proportional distribution problems as multiple-solution tasks to analyze their problem-solving methods. The students were grouped based on teacher variables, and the groups were assessed in terms of fluency, originality, and flexibility in mathematical creativity. The characteristics of the collective solution spaces were identified by comparing the frequency of various problem-solving strategies and representation types. The study found that teachers significantly influence mathematical creativity within collective solution spaces. Depending on the teacher, differences in fluency and originality were observed. Collective solution spaces with less reliance on formulaic approaches and higher use of diverse representations scored higher in creativity. Conversely, heavy reliance on symbolic representations was associated with lower creativity. These findings highlight the importance of encouraging various problem-solving strategies and representations within collective solution spaces to foster creativity. The study confirms that teachers play a crucial role in fostering mathematical creativity. Differences in creativity between groups based on teacher variables indicate that teachers impact students' problem-solving approaches. Additionally, relying solely on symbolic representations does not naturally lead to mathematical creativity, underscoring the need to provide students with opportunities to explore diverse mathematical representations. Creating an educational environment that encourages students to experiment with various strategies and representations is essential for nurturing their creativity.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.6
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• pp.445-452
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• 2014

This paper discusses the multifrontal direct solution method with out of core storage for large scale structural analysis in a limited computing resource. Large scale structural analysis requires huge amount of memory space and computation, so out of core solution method is needed in limited computing resource. In this research, out of core multifrontal solution algorithm which utilize the small size of physical memory and minimize the amount of access of low speed out of core storage is introduced. Three ideas, which are stack space in lower trianglar part of square factorization matrix, inverse stack data structure and selective data caching and recovery by data block size, are proposed.

• Tunnel and Underground Space
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• v.10 no.3
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• pp.257-270
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• 2000

사물의 거동, 현상에 대한 해석을 실시함에 있어 해석적 해법에 대비한 수치적 해법의 장점은 재질의 성질이 불균질하고 이방성이며 구조물의 형태가 기하학적으로 복잡할 뿐만 아니라 경계조건이 복잡하여 수학적인 표현이 어려울 때 그 해석을 가능케 해 주는 것이라고 볼 수 있다. 이러한 수치 해석법의 대표적인 것으로 유한요소법과 경계 요소법을 들 수 있다.(중략)

• School Mathematics
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• v.19 no.3
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• pp.481-494
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• 2017

Tasks of multiple solutions have been said to be suitable for the cultivation of mathematical creativity. However, studies on the fact that multiple solutions presented by students are useful or meaningful, and students' thoughts while finding multiple solutions are very short. In this study, we set goals to confirm the qualitative differences among the multiple solutions presented by the students and, if present, from the viewpoint of mathematical creativity. For this reason, after presenting the set of tasks of the two versions to eight mathematically gifted students of the second-grade middle school, we analyzed qualitative differences that appeared among the solutions. In the study, there was a difference among the solution presented first and the solutions presented later, and qualitatively substantial differences in terms of flexibility and creativity. In this regard, it was concluded that the need to account for such qualitative differences in designing and applying multiple solutions should be considered.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.159-174
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• 2015

Dragomiretskiy and Zosso (2014) developed a new decomposition method, termed variational mode decomposition (VMD), which is efficient for handling the tone detection and separation of signals. However, VMD may be inefficient in the presence of missing data since it is based on a fast Fourier transform (FFT) algorithm. To overcome this problem, we propose a new approach based on a novel combination of VMD and hierarchical (or h)-likelihood method. The h-likelihood provides an effective imputation methodology for missing data when VMD decomposes the signal into several meaningful modes. A simulation study and real data analysis demonstrates that the proposed method can produce substantially effective results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.6
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• pp.36-44
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• 2003

In this paper, an analytic solution method is proposed to overcome the numerical problems when the slewing dynamics of hybrid coordinate systems is investigated via time finite element analysis. It is shown that the dynamics of the hybrid coordinate systems is governed by the coupled dual differential equations for both slewing and structural modes. Structural modes are transformed into the time-based modal coordinates and analytic spatial propagation equations are derived for each space-dependent time mode. Slew angle history is obtained analytically by appropriate applications of the boundary conditions and structural propagation is re-calculated using the slew angle. Numerical examples are demonstrated to validate the proposed analytic method in comparison to the existing state transition matrix method.

• Proceedings of the Korean Society of Computer Information Conference
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• 2011.06a
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• pp.381-384
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• 2011

본 논문은 사용자 및 동적환경의 변화를 파악하고 분석된 정보를 바탕으로 최적화된 경로를 제공하기 위한 시스템을 멀티에이전트를 이용하여 해결하고자 하였다. 멀티에이전트를 통해 설정된 목표를 찾아가는 먹이추적 문제에 적용하였고 현실 세계와 흡사한 무한 공간 환경에서 알고리즘의 성능을 실험하였다. 적용된 환경의 모델은 순환구조(circular)형 격자 공간이라는 새로운 실험 공간으로 방향 벡터 함수 알고리즘을 통해 새롭게 멀티에이전트의 목표를 획득하기 위한 해법이다. 기존의 연구와 비교하여 먹이의 효율적 포획, 에이전트간의 충돌문제 해결에 대한 새로운 해법을 제시할 수 있었다.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1999.10a
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• pp.18-18
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• 1999

IRR형태의 액체 램제트 추진기관의 공기 흡입구 유동과 내부 연소 유동을 파악하기 위한 수치적 해석을 수행하였다. 해석은 다원 혼합기체에 대한 압축성 Navier-Stoke 방정식과 공기/Kerosene에 대한 화학 반응을 고려하였으며, 결합된 형태의 k-$\omega$/k-$\varepsilon$ 2 방정식 난류모델을 이용하였다. 기본 유동 해법으로는 고차의 시간 및 공간 정확도를 가지는 근사 Riemann 해법과 LU-SGS 방법을 이용하였다.

• Journal of the Korean Society of Safety
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• v.8 no.4
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• pp.201-206
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• 1993

A space-time finite element method was presented for time dependent problem. The method which treat both the space and time unformly were proposed and numerically tested. The weighted residual process was used to formulate a finite element method in a space-time domain based upon continuous Galerkin method. This method leads to a conditional stabie high-order accurate solver.