• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.1069-1105
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• 2001

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.629-634
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• 1995

The purpose of this paper is to develop a method of Collision-Free Path Planning (CFPP) for an articulated robot. First, the configuration of the robot is formed by a set of robot joint angles derived fromm robot inverse kinematics. The joint space that is made of the joint angle set, forms a Configuration space (Cspace). Obstacles in the robot workcell are also transformed and mapped into the Cspace, which makes Cobstacles in the Cspace. (The Cobstacles represented in the Cspace is actually the configurations of the robot causing collision.) Secondly, a connected graph, a kind of roadmap, is constructed from the free configurations in the 3 dimensional Cspace, where the configurations are randomly sampled form the free Cspace. Thirdly, robot paths are optimally in order to minimize of the sum of joint angle movements. A path searching algorithm based on A is employed in determining the paths. Finally, the whole procedures for the CFPP method are illustrated with a 3 axis articulated robot. The main characteristics of the method are; 1) it deals with CFPP for an articulated robot in a 3-dimensional workcell, 2) it guarantees finding a collision free path, if such a path exists, 3) it provides distance optimization in terms of joint angle movements. The whole procedures are implemented by C on an IBM compatible 486 PC. GL (Graphic Library) on an IRIS CAD workstation is utilized to produce fine graphic outputs.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.9 no.3
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• pp.85-93
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• 2010

This paper proposes a new dynamic hardware allocation and binding algorithm of a simultaneous allocation and binding for SOC design automation. The proposed algorithm works on scheduled input graph and simultaneously allocates binds functional units, interconnections and registers by considering interdependency between operations and storage elements in each control step, in order to share registers and interconnections connected to functional units, as much as possible. This paper shows the effectiveness of the proposed algorithm by comparing experiments to determine number of function unit in advance or by comparing separated executing allocation and binding of existing system.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1397-1404
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• 2018

For a connected graph G, an r-maximum edge-coloring is an edge-coloring f defined on E(G) such that at every vertex v with $d_G(v){\geq}r$ exactly r incident edges to v receive the maximum color. The r-maximum index $x^{\prime}_r(G)$ is the least number of required colors to have an r-maximum edge coloring of G. In this paper, we show how the r-maximum index is affected by adding an edge or a vertex. As a main result, we show that for each $r{\geq}3$ the r-maximum index function over the graphs admitting an r-maximum edge-coloring is unbounded and the range is the set of natural numbers. In other words, for each $r{\geq}3$ and $k{\geq}1$ there is a family of graphs G(r, k) with $x^{\prime}_r(G(r,k))=k$. Also, we construct a family of graphs not admitting an r-maximum edge-coloring with arbitrary maximum degrees: for any fixed $r{\geq}3$, there is an infinite family of graphs ${\mathcal{F}}_r=\{G_k:k{\geq}r+1\}$, where for each $k{\geq}r+1$ there is no r-maximum edge-coloring of $G_k$ and ${\Delta}(G_k)=k$.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.109-120
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• 2004

This study investigated three pre-service teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of pre- service teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

• Korean Institute of Interior Design Journal
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• v.21 no.6
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• pp.54-61
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• 2012

The aim of this study is to understand the plan characteristics used in unit floor planning mainly with examples of mixed-use residential tall buildings. The study will extract plan characteristics mainly using the graph expressive technique with essential information of the zoning function of residential space, rather than merely analyzing the various construction floor plans by type. The research method involves studying a group of 50-story buildings (over 200 meters) which were built between 2002 and 2008. Among 6 high-rise residential buildings case, we extract the most preferred type from 34 types, And then we simply classify rooms in 3 zoning, the master, living and children's zones. Finally we analyze the correlation among 3 simple zone and then extract some model type. The results of this study revealed three main findings. First, using the 3 functional zones, the shape of the main building and the unit floor plan can be analyzed simply even when they appear to be complicated. Second, we can extract common features when we analyze the unit floor plan from the viewpoint of the penetrability among 3 zoning. Third, we can extract 2 types when we analyze the unit floor plan from the viewpoint of 3 connected functional zoning concepts.

• Journal of the Korean Solar Energy Society
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• v.31 no.6
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• pp.72-77
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• 2011

The purpose for installation of offshore weather station is a measurement of wind resources and so on. If weather station is operated, it will be possible to analysis for wind resource and arrangement of wind farm by using measured data. In this paper, we carried out the development of offshore wind resource measurement system for measuring offshore wind resource. Also, In order to monitor for real-time wind data with 1 Hz, we installed the wireless transmission system. All wind characteristic data are sent to the server PC through the this system is connected outport of DataLogger. Transmitted wind data were used in order to look at in the Web-page and tablet PC on a real time basis in a graph. In this paper, we will introduce about the wind resource measurement and remote monitoring system that is the result of study.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.709-730
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• 2010

The inverse function of a one-to-one correspondence is explained with a graph, a numerical formula or other useful expressions. The purpose of this paper is to know how low achieving students understand the learning contents needed reversible thinking about irrational functions. Low achieving students in this study took paper-pencil test and their written answers were collected. They made various mistakes in solving problems. Their error types were grouped into several classes and identified in this analysis. Most students did not connected concepts that they learned in the lower achieving students to think in reverse order in case of and to visualize concepts of functions. This paper implies that it is very important to take into account students' accommodation and reversible thinking activity.

• Journal of information and communication convergence engineering
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• v.19 no.2
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• pp.114-119
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• 2021

This paper proposes a method to find an optimal T' with the most terminal of the subset of T' trees that can be connected by a given length by improving a memetic genetic algorithm within several constraints, when the set of terminal T is given to the Euclidean plane R². Constraint (1) is that a given length cannot connect all terminals of T, and (2) considers only the rectilinear layout of the edge connecting each terminal. The construction of interconnections has been used in various design-related areas, from network to architecture. Among these areas, there are cases where only the rectilinear layout is considered, such as wiring paths in the computer network and VLSI design, network design, and circuit connection length estimation in standard cell deployment. Therefore, the heuristics proposed in this paper are expected to provide various cost savings in the rectilinear layout.

• Journal of information and communication convergence engineering
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• v.20 no.2
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• pp.90-95
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• 2022

This paper proposes a method to find a tree with the maximum number of terminals that can be connected by a given length when numerous terminals distributed in a cluster form are given to the Euclidean plane R2 with several constraints. First constraint is that a given terminal is distributed in a cluster form, second is that a given length cannot connect all terminals in the tree, and third is that there is no curved connection between each terminal. This paper proposes a method to establish more efficient interconnections within terminals distributed in a cluster form by improving a randomly distributed memetic genetic algorithm. The construction of interconnections has been extensively used in design-related fields, from networking to architecture. Additionally, in real life, the construction of interconnections is mostly distributed in the form of clusters. Therefore, the heuristic algorithm proposed in this paper can be effectively utilized in real life and is expected to provide various cost savings.