• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.267-280
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• 2023

In this article, we show that the family of all 𝓘^𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘^𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘^𝒦-convergence and the relationship between 𝓘^𝒦-continuity and 𝓘^𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘^𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘^𝒦-sequential space.

• Journal of Korean Society for Geospatial Information Science
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• v.9 no.1 s.17
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• pp.27-38
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• 2001

The GIS construction project using the Digital Map has been progressed actively since the enforcement of NGIS project in 1995. But, the Digital Map actually can't use directly in building GIS because of many defects of the digital map such as geometric features errors(the overshoot/undershoot of line or the opening of polygon), non-topology etc. Many advanced countries in GIS has provided users Framework Data which is generated topology defined spatial relationships and used as a basic data of national geospatial information. In this study, we proposed the definition and the scope of Framework Data as a basemap of the Nation Geospatial Information and studied for the management and construction of the Transportation/Road Framework Data which is a core and basic data among them.

• Journal of Digital Convergence
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• v.9 no.3
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• pp.235-247
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• 2011

The Mind is a still vastly vague and unknown notion. But the more we view this phenomenon with multi-faceted viewpoints and depth, the more we discourse of the Mind with profundity and develop the concept of the Mind with more objectivity which will become that much more perfect. This article proposes to capture the Theory of the Mind, to some extent, in various academic fields and in parallel studies to organize the whole perspectives of the Mind in form of a digital knowledge Mind Map and present a thinkable model of the topology of the Mind.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.761-790
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• 2021

For given spaces X and Y, let map(X, Y) and map_*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map_*(X, Y ; g) be the path component of map(X, Y) containing f and map_*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane π^n+m(ΣⁿℂP²) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣⁿℂP², S^m) up to homotopy equivalence. We also determine the generalized Gottlieb groups G_n(ℂP², S^m). Finally, we compute homotopy groups of mapping spaces map(ΣⁿℂP², S^m; f) for all generators [f] of [ΣⁿℂP², S^m], and Gottlieb groups of mapping components containing constant map map(ΣⁿℂP², S^m; *).

• Journal of Korean Society for Geospatial Information Science
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• v.17 no.3
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• pp.13-21
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• 2009

Digital map should have the up-to-dateness as well as the accuracy to perform a role as the national spatial data. As digital mapping process require aerial photograph, surveying, and field working, it consumes a lot of time and cost. So there is a limit to maintain the up-to-dateness. If we updates the digital map frequently by using the as-built drawings, we can prevent the waste of national budget by reuse of existing drawings and make accuracy updates from existing survey results. In spite of this advantages, due to insufficiency of CAD drawing standard, inconsistency of file types of as-built drawings and digital maps, and topology relations between input features and original features, so the frequent updates using the as-built drawings is on the difficult situation to perform. In this research, first, CAD features extracted from as-built drawings land the new/update whether original features exist or not and generate topology from spatial relation of features. Second, suggest the efficient partial-update-plan performing integrity test. As a result, guarantee the accuracy and the up-to-dateness of digital map.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.793-806
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• 2002

Feature-based similarity retrieval become an important research issue in image database systems. The features of image data are useful to discrimination of images. In this paper, we propose the highspeed k-Nearest Neighbor search algorithm based on Self-Organizing Maps. Self-Organizing Maps (SOM) provides a mapping from high dimensional feature vectors onto a two-dimensional space. The mapping preserves the topology of the feature vectors. The map is called topological feature map. A topological feature map preserves the mutual relations (similarity) in feature spaces of input data. and clusters mutually similar feature vectors in a neighboring nodes. Each node of the topological feature map holds a node vector and similar images that is closest to each node vector. In topological feature map, there are empty nodes in which no image is classified. We experiment on the performance of our algorithm using color feature vectors extracted from images. Promising results have been obtained in experiments.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.5
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• pp.385-391
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• 2013

Big Data is data of big size which is not processed, collected, stored, searched, analyzed by the existing database management system. The parallel genetic algorithm using the Hadoop for BigData technology is easily realized by implementing GA(Genetic Algorithm) using MapReduce in the Hadoop Distribution System. The previous study that the genetic algorithm using MapReduce is proposed suitable transforming for the GA by MapReduce. However, they did not show good performance because of frequently occurring data input and output. In this paper, we proposed the MRPGA(MapReduce Parallel Genetic Algorithm) using improvement Map and Reduce process and the parallel processing characteristic of MapReduce. The optimal solution can be found by using the topology, migration of parallel genetic algorithm and local search algorithm. The convergence speed of the proposal method is 1.5 times faster than that of the existing MapReduce SGA, and is the optimal solution can be found quickly by the number of sub-generation iteration. In addition, the MRPGA is able to improve the processing and analysis performance of Big Data technology.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.47 no.2
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• pp.1-10
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• 2010

Mapping virtual process topology to physical processor topology is one of the most important design issues in parallel programming. However, the mapping problem is complicated due to the topology irregularity and routing complexity. This paper proposes a new process mapping scheme called adjacency-based mapping (AM) for irregular cluster systems assuming that the two-dimensional mesh process topology is specified as an interprocess communication pattern. The cluster systems have been studied and developed for many years since they provide high interconnection flexibility, scalability, and expandability which are not attainable in traditional regular networks. The proposed AM tries to map neighboring processes in virtual process topology to adjacent processors in physical processor topology. Simulation study shows that the proposed AM results in better mapping quality and shorter interprocess latency compared to the conventional approaches.

• The Transactions of the Korea Information Processing Society
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• v.7 no.4
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• pp.1193-1200
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• 2000

A network topology has been an important factor for an efficient network management, but data collection for the network configuration has been done manually or semi automatically by a network administrator or an expert. Requirements to generate an intro-domain network topology ar usually either all IP addresses with subne $t^ernet mask or the network identification of all IP addresses. The amounts of traffic are generally high in the semi-automatic system due to using large number of low-level protocols and commands to get rather simple data. In this paper, we propose an algorithm which can be executed with only publicly available input. It can find all IP addresses as well as the network boundary of an intra-domain by using an intelligent method developed in this algorithm. The collected data will be used to draw a network map automatically by using a proposed network topology generation algorithm.hm.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.1-27
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• 2008

We introduce a new concept of convex spaces and a multimap class K having certain KKM property. From a basic KKM type theorem for a K-map defined on an convex space without any topology, we deduce ten equivalent formulations of the theorem. As applications of the equivalents, in the frame of convex topological spaces, we obtain Fan-Browder type fixed point theorems, almost fixed point theorems for multimaps, mutual relations between the map classes K and B, variational inequalities, the von Neumann type minimax theorems, and the Nash equilibrium theorems.