• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.54-58
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• 2011

In this paper, we use L-fuzzy preopen operator to introduce the degree of pre-separatedness and the degree of preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of preconnectedness are presented in L-fuzzy topological spaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.1
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• pp.16-25
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• 2021

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.49-57
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• 2007

Using the idea of degree of openness and degree of nonopenness, Coker and Demirci [5] defined intuitionistic fuzzy topological spaces in Sostak's sense as a generalization of smooth topological spaces and intuitionistic fuzzy topological spaces. M. N. Mukherjee and S. P. Sinha [10] introduced the concept of fuzzy irresolute maps on Chang's fuzzy topological spaces. In this paper, we introduce the concepts of fuzzy (r,s)-irresolute, fuzzy (r,s)-presemiopen, fuzzy almost (r,s)-open, and fuzzy weakly (r,s)-continuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. Using the notions of fuzzy (r,s)-neighborhoods and fuzzy (r,s)-semineighborhoods of a given intuitionistic fuzzy points, characterizations of fuzzy (r,s)-irresolute maps are displayed. The relations among fuzzy (r,s)-irresolute maps, fuzzy (r,s)-continuous maps, fuzzy almost (r,s)-continuous maps, and fuzzy weakly (r,s)-cotinuous maps are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.6
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• pp.853-859
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• 2001

This paper describes the extended topological clean up procedures to improve the quality of unstructured triangular meshes. As a postprocessing step, topological improvement procedures are applied both for elements that are interior to the mesh and for elements connected to the boundary and then Laplacian-like smoothing is used by default. Previous clean up algorithms are limited to eliminate the nodes of degree 3,4,8,9,10 and pairs of nodes of degree 5. In this study, new clean up algorithms which minimize the triple connection structures combined with degree 5 and 7 (ie ; 5-7-5, 7-7-5, 7-5-7 etc) are added. The suggested algorithms are applied to two example meshes to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.101-109
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• 2011

We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-44
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• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• Proceedings of the Korean Information Science Society Conference
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• 2006.10d
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• pp.135-139
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• 2006

Today's social networking services have tens of millions of users, and are growing fast. Their sheer size poses a significant challenge in capturing and analyzing their topological characteristics. Snowball sampling is a popular method to crawl and sample network topologies, but requires a high sampling ratio for accurate estimation of certain metrics. In this work, we evaluate how close topological characteristics of snowball sampled networks are to the complete network. Instead of using a synthetically generated topology, we use the complete topology of Cyworld ilchon network. The goal of this work is to determine sampling ratios for accurate estimation of key topological characteristics, such as the degree distribution, the degree correlation, the assortativity, and the clustering coefficient.

• Journal of the Korean Geographical Society
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• v.35 no.1
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• pp.17-38
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• 2000

The marine terraces often offer come important clues to understand the topographic development during the Quaternary and the present landforms in korea. We examined the mechanism of the marine terraces formation along the coast from Samjung-Ri(community), Guryongpo-Eup(county) to Haseo-Ri, Yangnam-Myun(county), Gyungju-Si(city). Among the various but unique factors of the given coastal environment, which should contribute to the marine terraces formation together, we focused on five possible factors for the present stydy. Geologic difference in bedrocks, protrusion degree of coastiline, topological relief of sea-bottom, fluvial characteristics on land, and pattern of the waves appeared to act cooperatibely on the terrace formation of Southeastem coast in korea, while the fluvial characteristics seemed play a significant but localized role in it. Wide distribution of middle surfaces on the coast of Samjungri-Janggilri could be due to the concentration of the high waves and the weakness of the Tertiary volcanic rocks. For the sporadic distribution of the terraces on the coast of Gupungri-Gyewonri, it seemed attributable to the erosion -susceptible weak bedrock, the coastline of inner bay, shallow sea-bottom with the gentle relief, and other fluvial characteristics with the low divides. Together with the geologic difference in bedrock, other factors including protrusion degree of coast, topological relief of sea-bottom, and the transportation loads by the stream Daejongchon are believed to act cooperatively on the mechanism of the marine terraces formation on the coast of Duwonri-Upchonri.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.307-315
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• 2018

Let G be a simple connected graph with n vertices and m edges, with a sequence of vertex degrees $d_1{\geq}d_2{\geq}{\cdots}{\geq}d_n$ > 0. A vertex-degree topological index, referred to as harmonic index, is defined as $H={\sum{_{i{\sim}j}}{\frac{2}{d_i+d_j}}$, where i ~ j denotes the adjacency of vertices i and j. Lower and upper bounds of the index H are obtained.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.77-89
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• 2002

In this paper, we define for a component $X_{0}$ of a nonsingular compact real algebraic surface X the complex genus of $X_{0}$, denoted by gc($X_{0}$), and use this to prove the nonexistence of nonzero degree entire rational maps f : $X_{0}$ Y provided that gc(Y) > gc($X_{0}$), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.