• Bulletin of the Korean Chemical Society
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• v.16 no.11
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• pp.1046-1056
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• 1995

A topological theory has been introduced to evaluate the degree of complexation and the viscosity of polymer complexes by extending the theory of Iliopoulos and Audebert for aqueous polymer solutions. The previous theory of Iliopoulos and Audebert has offered only a semiquantitative theoretical model for polymer complex systems, whereas our present work gives a general theoretical model applicable to all the polymer complex systems. Their theories considered only the physical property term caused by the displacement of complexed points between polymer solute chains, while our theory deals with all the physical effects, caused by the displacement of complexed points entangled points in polymer solute chains. There have been predicted the characteristics of physical properties from the expression. It is exposed that the predictive values show good agreement with the experimental data for polymer complexes.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.659-675
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• 2023

Let K be an algebraically closed field of characteristic 0 and let f be a non-fibered planar quadratic polynomial map of topological degree 2 defined over K. We assume further that the meromorphic extension of f on the projective plane has the unique indeterminacy point. We define the critical pod of f where f sends a critical point to another critical point. By observing the behavior of f at the critical pod, we can determine a good conjugate of f which shows its statue in GIT sense.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.333-346
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• 2002

Let $F={F^v:S^1->S^1,v\in\; V$ and $g={G^v:S^1->S^1,v\in\; V$ be disjoint flows defined on the unit circle $S^1$, that is such flows that each their element either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial abelian group). The aim of this paper is to give a necessary and sufficient codition for topological conjugacy of disjoint flows i.e., the existence of a homeomorphism $\Gamma:S^1->S^1$ satisfying $$\Gamma\circ\ F^v=G^v\circ\Gamma,\; v\in\; V$$ Moreover, under some further restrictions, we determine all such homeomorphisms.

• East Asian mathematical journal
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• v.34 no.2
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• pp.177-189
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• 2018

Recently, Topological Data Analysis (TDA) has attracted attention among various techniques for analyzing big data. Mapper algorithm, which is one of TDA techniques, is used to visualize the cluster diagram. In this study, students were clustered according to the characteristics and degree of mathematics anxiety using a mapper, and students were visualized according to mathematics anxiety. In order to do this, Mathematical Anxiety Scale (Ko & Yi, 2011) in the aspect of mathematical instability in terms of teaching - learning, ie, Nature of Mathematics, Learning Strategy, Test/Performance is used. And the number of questions that measure the anxiety of mathematics can be extracted by extracting the most relevant items among the items that measure the anxiety of mathematics.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.901-913
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• 2000

This is a summary of results involving the development of a theory of an index of an isolated critical point for densely defined nonlinear operators of type (S(sub)+)(sub)0,L. This index theory is associated with a degree theory, for such operators, whch has been recently developed by the authors.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.3
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• pp.1030-1050
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• 2021

The edges with "bridge characteristic" play the role of connecting the communication between regions in power optical cable network. To solve the problem of mining edges with "bridge characteristic" in provincial power optical cable network, the complex power optical cable network model is constructed. Firstly, to measure the generated potential energy of all nodes in n-level neighborhood local structure for one edge, the n-level neighborhood local structure topological potential is designed. And the minimum connected chain attenuation is designed to measure the attenuation degree caused by substituted edges. On the basis of that, the minimum connected chain attenuation topological potential based measurement is designed. By using the designed measurement, a bridge-edges mining algorithm is proposed to mine edges with "bridge characteristic". The experiments are conducted on the physical topology of the power optical cable network in Jilin Province. Compared with that of other three typical methods, the network efficiency and connectivity of the proposed method are decreased by 3.58% and 28.79% on average respectively. And the proposed method can not only mine optical cable connection with typical "bridge characteristic" but also can mine optical cables without obvious characteristics of city or voltage, but it have "bridge characteristic" in the topology structure.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.425-434
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• 2015

In this paper, a two-point fractional boundary value problem at resonance is considered. By using the coincidence degree theory some existence results of solutions are established.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.327-335
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• 2011

Explicit formulas are given for the first and second Zagreb index, degree-distance and Wiener-type invariants of splice and link of graphs. As a consequence, the first and second Zagreb coindex of these classes of composite graphs are also computed.

• Journal of Korean Society of Rural Planning
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• v.7 no.1 s.13
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• pp.37-48
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• 2001

The purpose of this study is to suggest the landscape potential index for visualizing landscape information in the conservation of hilly landscape in urban fringe. For the visual and quantitative approach to topological landscape assessment, numerical entity data of DEM(digital elevation model) were processed with CAD-based utilities that we developed and were mainly focused on analysis of visibility and visual sensitivity. Some results, with reference in assessing greenbelt area of Eodeung Mt. in Gwangju, proved to be considerable in the landscape assessment of suburban hilly landscapes. 1) Since the viewpoints and viewpoint fields were critical to landscape structure, randomized 194 points(spatially 500m interval) were applied to assessing the generalized visual sensitivity, we called. Because there were similar patterns of distribution comparing to those by 56 points and 18 Points given appropriately, it could be more efficient by a few viewpoints which located widely. 2) Regressional function was derived to represent the relationships between probabilities of visibility frequency and the topological factors(topological dominance, landform complexity and relational aspect) of target field. 3) Visibility scores of each viewpoint were be calculated by summing the visual sensitivity indices within a scene. The scores to the upper part including ridge line have been more representative to overall distributions of visual sensitivities. Also, with sum of deviations of sensitivity indices from each single point's specific index to the weighting values of view points could be estimated rotationally. 4) The deviational distributions of visual sensitivity classes in the topological unit of target field were proved to represent the visual vulnerability of the landform. 5) Landscape potential indices combined with the visual sensitivity and the DGN(degree of green naturality) were proposed as visualized landscape information distributed by topological unit.