• East Asian mathematical journal
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• v.22 no.1
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• pp.79-91
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• 2006

In this paper, we will show some relations between decomposition series {$\pi^{\alpha}q\;:\;{\alpha}$ is an ordinal} and topological series {$\tau_{\alpha}q\;:\;{\alpha}$ is an ordinal} for a convergence structure q and the formular ${\pi}^{\beta}(\tau_{\alpha}q)={\pi}^{{\omega^{\alpha}\beta}}q$, where $\omega$ is the first limit ordinal and $\alpha$ and $\beta({\geq}1)$ are ordinals.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.153-161
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• 2016

It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.215-220
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• 1992

Using a matrix method, pp. Antosik and C. Swartz have obtained a series of nice properties of bounded multiplier convergent (BMC) series on metric linear spaces ([1],[8],[9]). In this paper, we establish a basic property of BMC series on topological vector spaces which is a generalization of a result due to J. Batt([2], Th.2). From this, we have obtained a kind of inclusion theorem of operator spaces. This theorem yields a nice result on infinite systems of linear equations.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.174-179
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• 2003

Through the simultaneous localization and map building (SLAM) technique, a robot can create maps about its unknown environment while it continuously localizes its position. Grid maps and feature maps have been widely used for SLAM together with application of probability methods and POMDP (partially observed Markov decision process). But this approach based on grid maps suffers from enormous computational burden. Topological maps, however, have drawn more attention these days because they are compact, provide natural interfaces, and are easily applicable to path planning in comparison with grid maps. Some topological SLAM techniques like GVG (generalized Voronoi diagram) were introduced, but it enables the robot to decide only whether the current position is part of GVG branch or not in the GVG algorithm. In this paper, therefore, to overcome these problems, we present a method for updating a global topological map from the local topological maps. These local topological maps are created through a labeled Voronoi diagram algorithm from the local grid map built based on the sensor information at the current robot position. And the nodes of a local topological map can be utilized as the features of the environment because it is robust in light of visibility problem. The geometric information of the feature is applied to the extended Kalman filter and the SLAM in the indoor environment is accomplished. A series of simulations have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can be applied relatively well.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.481-485
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• 1996

Let G be an abelian topological group and $x_{ij} \in G$ for all $i, j \in N$ such that the series $\sum_{j=i}^{\infty} x_{ij}$ is subseries convergent for each i.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.595-608
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• 2013

Let G = (V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V (G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).

• Journal of the Korean housing association
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• v.19 no.1
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• pp.9-16
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• 2008

This study aims to construct the design competence by means of a topological approach. To this end, the linguistic concept of 'competence and performance' in Chomskian sense is borrowed and applied to the study. The usability of this method is then tested against the sample apartment plans from Gangnam-gu area in Seoul, and it is found that this enabled a middle-ground approach to a more productive grammar that overcomes the limits in Glassie's and Stiny's grammar systems. Through a series of analyses on the sample plans, it could be clarified that there appear classificatory levels in the competence that controls the planning of the building, zoning of the unit, and layout of LDK combination. At the end, it is evaluated that the generative grammar, constructed in this research, is the possible world in designers' minds, and this retrospective remodelling of the architectural competence could illuminate the 'design decision flow' that generates the sample plans.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.725-744
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• 2019

In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (a_rtkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙²_∞.

• Proceedings of the KIPE Conference
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• 2001.10a
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• pp.266-270
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• 2001

This paper presents a novel topological prototype of voltage source series quasi-resonant zero current soft-switching pulse frequency modulated dc-dc power converter circuit using IGBTs which incorporates a high-frequency flyback transformer link. Its steady-state operating principle is described on the basis of simulation analysis, along with the open loop controlled power regulation characteristics of the multi-functional coupled inductors linked dc-dc power converter operating under a principle of zero current soft switching commutation.