• Education of Primary School Mathematics
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• v.7 no.1
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• pp.43-56
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• 2003

In late 19C, German mathematician Felix Klein declaired "Erlangen program" to reform mathematics education in Germany. The main ideas of "Erlangen program" contain the importance of instructing the concepts of functions and groups in school mathematics. After one century from that time, the importance of concepts of groups revived by Bourbaki in the sense of the algebraic structure which is the most important structure among three structures of mathematics - algebraic structure. ordered structure and topological structure. Since then, many mathematicians and mathematics educators devoted to work with the concepts of group for school mathematics. This movement landed on Korea in 21C, and now, the concepts of groups appeared in element mathematics text as plane rigid motion. In this paper, we state the rigid motions centered the symmetry - an important notion in group theory, then summarize the results obtained from some classroom activities. After that, we discuss the responses of children to concepts of groups.of groups.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.231-241
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• 2013

On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ norm. We first show, using the special topological properties of the $p$-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.899-912
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• 2011

We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.10a
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• pp.912-915
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• 2003

To support emerging group applications such as network games and Internet live-casting efficiently. IP multicast mechanism is highly needed. But IP multicast still has not been deployed in the current Internet because of its difficulty to manage. Overlay multicast mechanisms are proposed to serve group communications more effectively in the current unicast oriented Internet. In this paper we categorize the proposed ones into topological view point.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.1-9
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• 1989

In 1980 and 1983, it was proved that P $D^{2}$-groups are surface groups ([2], [3]). Since then, topologists have been positively studying about P $D^{n}$ -groups (or $D^{n}$ -groups). For example, let a topological space X have a right .pi.-action, where .pi. is a multiplicative group. If each x.memX has an open neighborhood U such that for each u.mem..pi., u.neq.1, U.cap. $U_{u}$ =.phi., this right .pi.-action is said to be proper. In this case, if X/.pi. is compact then (1) .pi.$_{1}$(X/.pi).iden..pi.(X:connected, .pi.$_{1}$: fundamental group) ([4]), (2) if X is a differentiable orientable manifold with demension n and .rho.X (the boundary of X)=.phi. then $H^{k}$ (X;Z).iden. $H_{n-k}$(X;Z), ([6]), where Z is the set of all integers.s.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.5
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• pp.1199-1206
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• 2015

This paper introduces an algorithm for computing similarity between two poses in the motion capture data with different scale of skeleton, different number of joints and different joint names. The proposed algorithm first performs the topological analysis on the skeleton hierarchy for classifying the joints into more meaningful groups. The global joints positions of each joint group then are aggregated into a point cloud. The number of joints and their positions are automatically adjusted in this process. Once we have two point clouds, the algorithm finds an optimal 2D transform matrix that transforms one point cloud to the other as closely as possible. Then, the similarity can be obtained by summing up all distance values between two points clouds after applying the 2D transform matrix. After some experiment, we found that the proposed algorithm is able to compute the similarity between two poses regardless of their scale, joint name and the number of joints.

• Spatial Information Research
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• v.2 no.2
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• pp.147-163
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• 1994

This paper presents three methods of generating the transportation network data out of the topological geographic database in the hope that the conversion of the geographic database file containing the topology to the conventional node-link type trans¬portation network file may facilitate the integration between transportation planning mod¬els and GIS by alleviating the inherent problems of both computing environments. One way of the proposed conversion method is to use the conversion software that allows the bi-directional conversion between the UTPS (Urban Transportation Planning System) type transportation planning model and GIS. The other two methods of data structure conversion approach directly transform the GIS's user-level topology into the transportation network data topology, and have been introduced with codes programmed with FORTRAN and AML (Arc Macro Language) of ARC/INFO. If used successfully, any approach would not only improve the efficiency of transportation planning process and the associated decision-making activities in it, but enhance the productivity of trans¬portation planning agencies.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.22 no.2
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• pp.29-43
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• 2023

It is necessary to grasp the characteristics of traffic flow passing through a specific road section and the topological structure of the road in advance in order to quickly prepare a movement management strategy in the event of a disaster or disaster. It is because it can be an essential basis for road managers to assess vulnerabilities by microscopic road units and then establish appropriate monitoring and management measures for disasters or disaster situations. Therefore, this study presented spatial density, time occupancy, and betweenness centrality index to evaluate vulnerabilities by road link in the city department and defined spatial-temporal and topological vulnerabilities by clustering analysis based on distance and density. From the results of this study, road administrators can manage vulnerabilities by characterizing each road link group. It is expected to be used as primary data for selecting priority control points and presenting optimal routes in the event of a disaster or disaster.

• Biomaterials and Biomechanics in Bioengineering
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• v.2 no.1
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• pp.15-22
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• 2015

Poly(ethylene glycol) end-capped with pentafluorophenyl group(s) in ABA (FP-PEG-FP) and AB (mPEG-FP) types were prepared. Even though they were similar in composition, the lower critical solution temperature (LCST) of FP-PEG-FP was observed at $23^{\circ}C$, whereas that of mPEG-FP was observed at $65^{\circ}C$. To understand the large difference in solution behaviour of the two polymers, UV-VIS spectroscopy, microcalorimetry, 1H-NMR spectroscopy, and dynamic light scattering were used. FP-PEG-FP has two hydrophobic pentafluorophenyl groups at the ends of hydrophilic PEG (1000 Daltons), whereas mPEG-PF has a highly dynamic PEG (550 Daltons) block that are anchored to a hydrophobic pentafluorophenyl group. PF-PEG-PF not only has a smaller conformational degree of freedom than mPEG-PF but also can form extensive intermolecular aggregates, therefore, PF-PEG-PF exhibits a significantly lower LCST than mPEG-PF. This paper suggests that topological control is very important in designing a temperature-sensitive polymer.