• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.12
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• pp.2243-2251
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• 2016

In this paper, we propose a theoretical model for characterization and upper bounds of [1,2]-domination set of network which has tree structure. In detail, we propose a theoretic model for upper bounds on [1,2]-domination set of a tree network which has some typical constrains. To that purpose, we introduce a graph theory to model and analyze the characteristics of tree structure networks. We assume a node subset D of a graph G=(V,E). We define that D is a [1,2]-dominant set if for any node v in set V which is not an element of a set D is adjacent to a node or two nodes of an element in a set D (that is, $1{\leq}{\mid}N({\upsilon}){\bigcap}D{\mid}{\leq}2$ for every node $v{\in}V-D$). The minimum cardinality of a [1,2]-dominating set of G, which is denoted by ${\gamma}_{[1,2]}(G)$, is called the [1,2]-domination number of G. In this paper, we show new upper bounds and characteristics about the [1,2]-domination number of tree.

• Geophysics and Geophysical Exploration
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• v.12 no.1
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• pp.105-113
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• 2009

The interpretation of observed waveform characteristics identified in refraction and wide-angle reflection data increases confidence in the crustal structure model obtained. When calculating traveltimes and raypaths, wavefront methods on a regular grid based on graph theory are robust even with complicated structures, but basically compute only first arrivals. In this paper, we develop new algorithms to compute traveltimes and raypaths not only for first arrivals, but also for fast and later reflection arrivals, later refraction arrivals, and converted waves between P and S, using the modified wavefront method based on slowness network nodes mapped on a multi-layer model. Using the new algorithm, we can interpret reflected arrivals, Pg-later arrivals, strong arrivals appearing behind Pn, triplicated Moho reflected arrivals (PmP) to obtain the shape of the Moho, and phases involving conversion between P and S. Using two models of an ocean-continent transition zone and an oceanic ridge or seamount, we show the usefulness of this algorithm, which is confirmed by synthetic seismograms using the 2D Finite Difference Method (2D-FDM). Characteristics of arrivals and raypaths of the two models differ from each other in that using only first-arrival traveltime data for crustal structure analysis involves risk of erroneous interpretation in the ocean-continent transition zone, or the region around a ridge or seamount.

• Journal of the Korean Chemical Society
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• v.57 no.5
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• pp.640-655
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• 2013

The purpose of this study is to analyze the cognitive demands level of the description about 'changes of state' and 'kinetic theory' on the 'science 1' textbooks by the 2007 revised curriculum. The three types of curriculum analysis taxonomy have been used to analyze the cognitive demands level of those contents on the 6 kinds of 'science 1' textbooks. The most higher level of cognitive demands about the concepts have been discussed here due to the focus of the concepts. The first, the cognitive demand level about 'three states of substances' depending on the motion of their particles in 6 textbooks is a early formal operational stage because of using by the application of kinetic theory. The second, the cognitive demand level about 'diffusion' and 'evaporation' is a early formal operational stage, because the particles move around faster so they can change their position. The third, the cognitive level of the pressure and volume in a gas is a early formal operational stage because of explaining only phenomena in simple correspondence with formal model of kinetic theory. And simple functional relationships beyond linear on the graph of the volume and pressure of gas, the volume and temperature of gas is also a early formal operational stage. The fourth, the cognitive level of the energy of heat by a change of the state is also a early formal operational stage because kinetic theory picture accepted as providing explanation by the change of the state. And functional relationships beyond linear on the graph of the explanation of boiling point of water in water is also a early formal operational stage.

• The Journal of the Korea Contents Association
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• v.20 no.7
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• pp.212-222
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• 2020

The purpose of this study is to understand the current status and trends of the research studies published by the Society for Industrial and Applied Mathematics which is a leader in the field of industrial mathematics around the world. To perform this purpose, titles and abstracts were collected from 6,255 research articles between 2016 and 2019, and the R program was used to analyze the topic modeling model with LDA techniques and a regression model. As the results of analyses, first, a variety of studies have been studied in the fields of industrial mathematics, such as algebra, discrete mathematics, geometry, topological mathematics, probability and statistics. Second, it was found that the ascending research subjects were fluid mechanics, graph theory, and stochastic differential equations, and the descending research subjects were computational theory and classical geometry. The results of the study, based on the understanding of the overall flows and changes of the intellectual structure in the fields of industrial mathematics, are expected to provide researchers in the field with implications of the future direction of research and how to build an industrial mathematics curriculum that reflects the zeitgeist in the field of education.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.1009-1023
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k ) 그래프 이론적 관점에서 고찰하고 정점이 서로소인 경로에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )의 서로 다른 두 노드 v와 w를 잇는 연결도 kappa(G)개의 서로소인 경로의 길이가 두 노드 사이의 거리d(v,w)나 혹은 G(2^m , 2^k )의 지름 \dia(G)에 비해서 얼마나 늘어나는지를 고려한다. 서로소인 경로를 재귀적으로 설계하는데, 그 길이는 k ge2일 때 d(v,w)+2^k-1과 \dia(G)+2^k-1의 최솟값 이하이고, k=1일 때 d(v,w)+3과 \dia(G)\+2의 최솟값 이하이다. 이 연구는 (2^m , 2^k )의 고장 감내 라우팅, 고장 지름이나 persistence의 분석에 이용할 수 있다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties concerned with node-disjoint paths. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . We consider the length increments of {{{{kappa(G)disjoint paths joining arbitrary two nodes v and win G(2^m , 2^k )compared with distance d(v,w)between the two nodes and diameter {{{{\dia(G)of G(2^m , 2^k ), where kappa(G)is the connectivity of G(2^m , 2^k ). We recursively construct disjoint paths of length less than or equal to the minimum of {{{{d(v,w)+2^k-1and \dia(G)+2^k-1for kge2 and the minimum of d(v,w)+3 and \dia(G)+2for k=1. This work can be applied to fault-tolerant routing and analysis of fault diameter and persistence of G(2^m , 2^k )

• KIISE Transactions on Computing Practices
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• v.21 no.2
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• pp.109-114
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• 2015

This paper presents a computational model on the transfer of airborne fine particles to analyze the similarities and influences among the 25 districts in Seoul by quantifying a time series data collected from each district. The properties of each district are driven with the model of a time series of the fine particle concentrations, and the calculation of edge-based weights are carried out with the transfer entropies between all pairs of the districts. We applied a modularity-based graph clustering technique to detect the communities among the 25 districts. The result indicates the discovered clusters correspond to a high transfer-entropy group among the communities with geographical adjacency or high in-between traffic volumes. We believe that this approach can be further extended to the discovery of significant flows of other indicators causing environmental pollution.

• Korean Journal of Social Welfare
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• v.63 no.1
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• pp.137-158
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• 2011

This study explore nonlinear relationship between volunteer time spending and psychosocial well-being among the old adults, on the ground of Socioemotional Selectivity Theory. This is secondary analysis using the 2009 National Old Aging Volunteer Survey data including 645 cases. The simple and multiple line graph method are implemented. As a result, this paper shows a nolinerar relationship which the low level of psychosocial well-being at non volunteer status is increasing to the paticular time spending, and then decreases after high level participation like U-shape. Male, over the 75 and not good health status has showed lower level of volunteer time spending. It can be founded that volunteering activity contributes to improve a psychosocial well-being in old life, but the desirable volunteer time spending is medial about 100-200 yearly not over the 700.

• Journal of the Korean Chemical Society
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• v.28 no.5
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• pp.284-292
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• 1984

This paper aims to predict the substituent and Lewis acid catalysis effect or reactivity on the regioselectivity of (4+2) cycloaddition reaction of the substituted-E-arene-diazocyanides and nitrosobenzenes. Frontier orbital theory (FMO) has been applied to thermal and catalyzed Diels-Alder reaction by means of CNDO/2 and EHT-SPD methods. It has been found that: (1) The above reaction is positive rho(${\rho}$) values in Hammett equation, so it takes normal electron demand reaction, and four-frontier orbitals and Anh methods are identical with experimental major regioisomer.(2) When electron withdrawing radicals are substituted HOMO and LUMO energies of dienophiles are reduced, and the reactivity is increased. (3) The major regioisomer is predicted as B type, as the Lewis acid makes complexes of dienophile, and polaries LUMO coefficients of dienophile in an opposite way. (4) The linear correlation of Hammett is indicated in the graph of stabilized energies(${\Delta}$E) and sigma(${\sigma}$).

• 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 IEEK Conference
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• 2002.07a
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• pp.301-304
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• 2002

Recently, database technologies have been used commonly. But, ordinary technologies aren't suitable to construct a complicated database such as a classical literature database or an archaeological relic's database. Because this kinds of data are semi-structured data that doesn't have regular structures, database schema can't be defined before databases. We have proposed DREAM model for semi-structured databases. In this model, a database consists of five elements and the model has operations similar to operation of set theory. And further we have introduced dynamic schema "shape" showing structure of each element. We have already realized a prototype of DBMS adopting DREAM model (DREAM DBMS) and constructing function of shapes. However, shape is imperfect to describe database structures because it can't explain nested structures of elements. In this paper, we will profuse a "shape graph"that is dynamic schema showing database structures more exactly and extend the DREAM DBMS. Further we will evaluate the performance of constructing function of shapes and shape graphs.