• Honam Mathematical Journal
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• v.33 no.4
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• pp.617-628
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• 2011

In relation to the classification of finite topological spaces the paper [17] studied various properties of finite topological spaces. Indeed, the study of future internet system can be very related to that of locally finite topological spaces with some order structures such as preorder, partial order, pretopology, Alexandroff topological structure and so forth. The paper generalizes the results from [17] so that the paper can enlarge topological and homotopic properties suggested in the category of finite topological spaces into those in the category of locally finite topological spaces including ALF spaces.

• ETRI Journal
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• v.29 no.2
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• pp.189-200
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• 2007

This paper addresses the localization and navigation problem in the movement of service robots by using invisible two dimensional barcodes on the floor. Compared with other methods using natural or artificial landmarks, the proposed localization method has great advantages in cost and appearance since the location of the robot is perfectly known using the barcode information after mapping is finished. We also propose a navigation algorithm which uses a topological structure. For the topological information, we define nodes and edges which are suitable for indoor navigation, especially for large area having multiple rooms, many walls, and many static obstacles. The proposed algorithm also has the advantage that errors which occur in each node are mutually independent and can be compensated exactly after some navigation using barcodes. Simulation and experimental results were performed to verify the algorithm in the barcode environment, showing excellent performance results. After mapping, it is also possible to solve the kidnapped robot problem and to generate paths using topological information.

• Journal of the Korean Geographical Society
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• v.41 no.2 s.113
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• pp.188-194
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• 2006

Three-dimensional topological data is essential for 3D modeling and application such as emergency management and 3D network analysis. This paper reviewed current 3D topological data model and developed a method to construct 3D topological node-relation data structure from 2D computer aided design (CAD) data. The method needed two steps with medial axis-transformation and topological node-relation algorithms. Using a medial-axis transformation algorithm, the first step is to extract skeleton from wall data that was drawn polygon or double line in a CAD data. The second step is to build a topological node-relation structure by converting rooms to nodes and the relations between rooms to links. So, links represent adjacency and connectivity between nodes (rooms). As a result, with the conversion method 3D topological data for micro-level sub-unit of each building can be easily constructed from CAD data that are commonly used to design a building as a blueprint.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.1-12
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• 2004

In the Analysis, there have been many cases of confusion on topological structure and uniform structure because they were dealt in metric spaces. The concept of metric spaces is generalized into that of topological spaces but its uniform aspect was much later generalized into the uniform structure by A. Weil. We first investigate Weil's life and his mathematical achievement and then study the history of the uniform structure and its development.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.77-81
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• 2003

SDM (Structural Dynamics Modification) is a tool to improve dynamic characteristics of a structure, more specifically of a base structure, by adding or deleting auxiliary (modifying) structures. In this paper, the goal of the optimal SDM is set to maximize the natural frequency of a base plate structure by attaching serially-connected beam stiffeners. The design variables are chosen as positions of the attaching beam stiffeners, where the number of stiffeners is considered as a design space. The problem of non-matching interface nodes between the base plate and beam stiffeners is solved by using localized Lagrange multipliers, which act to glue the two structures with non-matching interface nodes. As fer the cases of non-matching interface nodes problem, the governing equation of motion of a structure can be considered from the viewpoint of a topological modification, which involves the change of the number of structural members and DOFs. Consequently, the eigenpairs of the beam-stiffened plate structure are obtained by using an eigen reanalysis technique of topological modifications. Evolution Strategies (ES), which is a probabilistic population-based optimization technique that mimics the principles from biological evolution in nature, is utilized as a mean for the optimization.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.647-673
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• 2002

There are many models to study topological $R^2$-planes. Unlike topological $R^2$-planes, it is difficult to find models to study topological R$^3$)-spaces. If an 4-dimensional affine plane intersects with R$^3$, we are able to get a geometrical structure on R$^3$ which is similar to R$^3$-space, and called $R^2$-divisible R$^3$-space. Such spatial geometric models is useful to study topological R$^3$-spaces. Hence, we introduce some classes of topological $R^2$-divisible R$^3$-spaces which are induced from 4-dimensional anne planes.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.39-48
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• 2016

In this paper we extend Takahashi's fixed point theorem on discrete semigroups to general semi-topological semigroups. Next we define the semi-asymptotic non-expansive action of semi-topological semi-groups to give a partial affirmative answer to an open problem raised by A.T-M. Lau.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.33-40
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• 1996

A convergence structure defined by Kent [4] is a correspondence between the filters on a given set X and the subsets of X which specifies which filters converge to points of X. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on X. Thus, a convergence structure may be regarded as a generalization of a topology. With a given convergence structure q on a set X, Kent [4] introduced associated convergence structures which are called a topological modification and a pretopological modification. (omitted)

• Journal of The Korean Society of Agricultural Engineers
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• v.57 no.6
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• pp.59-68
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• 2015

Traditional structure analysis method is based on numerical matrix analysis to use the geometries consisting of the structure. The characteristics require a lot of computer memories and computational time. To avoid these weaknesses, new approach to analyze truss structure was suggested by adopting topological load redistribution method. The axial forces to be not structurely analyzed yet against outside loads were redistributed by using nodal equation of equilibrium randomly at each node without constructing global matrix. However, this method could not calculate the axial forces if structure is statically indeterminate due to degree of many indeterminacies. Therefore, to apply the method suggested in this research, all redundancies of truss structure were replaced by unit loads. Each unit load could make the deformation of a whole structure, and a superposition method was finally adopted to solve the simultaneous equations. The axial forces and deflections agreed with the result of commercial software within the relative error of 1 %, whereas in the case that the axial forces are relatively very smaller than others, the relative errors were increased to 2 %. However, as the values were small enough not to be considered, it was practically useful as a structural analysis model. This model will be used for structural analysis of truss type of large structure such as agricultural farming facility.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.575-589
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• 2011

In order to examine the possibility of some topological structures into the fields of network science, telecommunications related to the future internet and a digitization, the paper studies the Marcus Wyse topological structure. Further, this paper develops the notions of lattice based Marcus Wyse continuity and lattice based Marcus Wyse homeomorphism which can be used for studying spaces $X{\subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.