• Industrial Engineering and Management Systems
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• v.12 no.3
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• pp.198-206
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• 2013

The team orienteering problem (TOP) or the multiple tour maximum collection problem can be considered as a generic model that can be applied to a number of challenging applications in logistics, tourism, and other fields. This problem is generally defined as the problem of determining P paths, in which the traveling time of each path is limited by $T_{max}$ that maximizes the total collected score. In the TOP, a set of N vertices i is given, each with a score $S_i$. The starting point (vertex 1) and the end point (vertex N) of all paths are fixed. The time $t_{ij}$ needed to travel from vertex i to j is known for all vertices. Some exact and heuristics approaches had been proposed in the past for solving the TOP. This paper proposes a new solution methodology for solving the TOP using the particle swarm optimization, especially by proposing a solution representation and its decoding method. The performance of the proposed algorithm is then evaluated using several benchmark datasets for the TOP. The computational results show that the proposed algorithm using specific settings is capable of finding good solution for the corresponding TOP instance.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.2 s.140
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• pp.113-123
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• 2005

A higher order panel method based on B-spline representation for both the geometry and the solution is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then shown to be evaluated using conventional numerical quadrature. By selecting a proper order for numerical quadrature, the accuracy of the present method can be increased to the machine limit. The far- and near-field influences are shown to be evaluated based on the same far-field approximation, but the near-field solution requires subdividing the panels into smaller subpanels continuously, which can be effectively implemented due to the B-spline representation of the geometry. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution on the blade surface, including very close to the tip and trailing edge regions, with far fewer panels than existing low order panel methods.

• 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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.2
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• pp.375-389
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• 2015

An improved boundary element method is presented for numerical analysis of hydrodynamic behavior of marine structures. A new algorithm for numerical solution of the finite depth free-surface Green function in three dimensions is developed based on multiple series representations. The whole range of the key parameter R/h is divided into four regions, within which different representation is used to achieve fast convergence. The well-known epsilon algorithm is also adopted to accelerate the convergence. The critical convergence criteria for each representation are investigated and provided. The proposed method is validated by several well-documented benchmark problems.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.185-195
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• 2010

In the unified field theory(UFT), in order to find a solution of the Einstein's equation it is necessary and sufficient to study the torsion tensor. The main goal in the present paper is to obtain, using a given torsion tensor (3.1), the complete representation of a particular solution of the Einstein's equation in terms of the basic tensor $g_{{\lambda}{\nu}}$ in even-dimensional UFT $X_n$.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• Journal of Digital Contents Society
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• v.18 no.2
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• pp.347-356
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• 2017

It is well-known that the face recognition method via sparse representation has been proved very robust and showed good performance. Its weakness is, however, that its time complexity is very high because it should solve $L_1$-minimization problem to find the sparse solution. In this paper, we propose to use the ROMP(Regularized Orthogonal Matching Pursuit) method for the sparse solution, which solves the $L_2$-minimization problem with regularization condition using the greed strategy. In experiments, we shows that the proposed method is comparable to the existing best $L_1$-minimization solver, Homotopy, but is 60 times faster than Homotopy. Also, we proposed C-SCI method for classification. The C-SCI method is very effective since it considers the sparse solution only without reconstructing the test data. It is shown that the C-SCI method is comparable to, but is 5 times faster than the existing best classification method.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.3
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• pp.427-440
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• 1996

Constraint networks are a major approach to knowledge representation in Concurrent Engineering (CE) systems. The networks model various factors in CE as constraints linked by shared variables. Many systems have been developed to assist constraint network processing. While these systems can be useful, their underlying assumption that a solution must simultaneously satisfy all the constraints is often unrealistic and hard to achieve. Proposed in this paper is a hierarchical representation of constraint networks using priorities, namely Prioritized Constraint Network (PCN). A mechanism to propagate priorities is developed, and a new satisfiability definition taking into account the priorities is described. Strength of constraint supporters can be derived from the propagated priorities. Several properties useful for investigating PCN's and finding effective solving strategies ore developed.

• Korean Institute of Interior Design Journal
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• no.37
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• pp.48-54
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• 2003

This study investigates great potential of architectural representation drawings for architects as well as designers to realize their design concept into visual forms. In 1988, an exhibition called "Deconstruction in Architecture" at Modern Art Museum, New York, was an important turning point in design representation. The study examines design drawings of architects of deconstructivism to analyze new attitudes toward building forms and programs in contemporary architecture. The study found in the drawings that initially, collages in many different types are often utilized to express simultaneous time and space. Secondly, section drawings become more important to explain ambiguous and complex floor system than before. Thirdly, cinematic montages are utilized to express indeterminate or loose programs. Fourthly, diagrams are utilized to visualize initial conditions and clues of design solution. The study concludes that design drawings are not only representation media admitting of changes and progress but also tools of design creation. creation.