• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.141-155
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• 2010

In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in ${\mathbf{Z}}^3$ forms a commutative monoid with an operation derived from a digital connected sum, k ${\in}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in ${\mathbf{Z}}^3$ is also proved to be a commutative monoid with the above operation, k ${\in}$ {18,26}.

• Journal of the Korea Society of Computer and Information
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• v.21 no.2
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• pp.17-23
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• 2016

NUI is a motion interface. It uses the body of the user without the use of HID device such as a mouse and keyboard to control the device. In this paper, we use a Pi Camera and sensors connected to it with small embedded board Raspberry Pi. We are using the OpenCV algorithms optimized for image recognition and computer vision compared with traditional HID equipment and to implement a more human-friendly and intuitive interface NUI devices. comparison operation detects motion, it proposed a more advanced motion sensors and recognition systems fused connected to the Raspberry Pi.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.643-651
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• 2005

In the first part of this paper we investigate several statements concerning infinite maximal planar graphs which are equivalent in finite case. In the second one, for a given induced $\theta$-path (a finite induced path whose endvertices are adjacent to a vertex of infinite degree) in a 4-connected VAP-free maximal planar graph containing a vertex of infinite degree, a new $\theta$-path is constructed such that the resulting fan is tight.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.670-672
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• 2002

본 논문에서는 2개의 랩어라운드 에지를 갖는 m$\times$n(m 2, n$\geq$3, n 흘수) 그리드 그래프에서의 해밀톤 성질을 고려한다. 먼저 그리드 그래프가 해밀톤 연결된(hamiltonian-connected)그래프가 되기 위해 추가로 필요한 에지의 수가 2개 이상임을 보인다. 그리고 m$\times$n 그리드 그래프의 첫 행에 랩어라운드 에지를 추가한 그래프의 해밀톤 성질을 보인 후, m$\times$n 그리드 그래프의 첫 행과 마지막 행에 램어라운드 에지를 추가한 그래프가 해밀톤 연결된 그래프임을 보인다.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.2
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• pp.226-232
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• 1999

Graph Coloring Problem(GCP) is a problem of assigning different colors to nodes which are connected by an edge. An extended form of GCP is TCP (T-coloring problem) and, in TCP, edge weights are added to GCP and it is possible to extend GCP's applications. To solve TCP, in this paper, we propose an improved Simulated Annealing(SA) method with search space smoothing. It has been observed that the improved SA method obtains better results than SA does.

• Proceedings of the Korea Information Processing Society Conference
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• 2019.05a
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• pp.498-500
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• 2019

Point cloud is a flexible set of points that can provide a scalable geometric representation which can be applied in different computer graphic task. We propose a method based on EdgeConv and densely connected layers to aggregate the features for better classification. Our proposed approach shows significant performance improvement compared to the state-of-the-art deep neural network-based approaches.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.745-756
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• 2022

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |u_t|^p-1·u_t (p > 1).

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.11
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• pp.2367-2372
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• 2009

Recently, Many studies have been progressing to path-finding adapted dynamic information on the Terminal Based Navigation System(TBNS). The algorithms proposed are based on $A^*$ algorithm. Path-finding algorithms which use heuristic function may occur a problem of the increase of exploring cost. Path-finding with an abstract graph which expresses real road network as a simple graph is proposed for reducing dependency of heuristic and exploring cost. In this paper, two abstract graph that are different method of construction, Homogeneous Node merging($AG^H$) and Connected Node Merging($AG^C$), are implemented. In result of evaluation of performance, $AG^C$ has better performance than $AG^H$ at construction cost and the number of node access but $AG^C$ has worse performance than AGH at exploring cost.

• The Journal of Bigdata
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• v.5 no.1
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• pp.77-88
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• 2020

Recently, many researches habe been done to organize and analyze various complex relationships in real world, represented in the form of graphs. In particular, the computer field literature data system, such as DBLP, is a representative graph data in which can be composed of papers, their authors, and citation among papers. Becasue graph data is very complex in storage structure and expression, it is very difficult task to search, analysis, and visualize a large size of bibliographic big data. In this paper, we develop a graphic user interface tool, called EEUM, which visualizes bibliographic big data in the form of graphs. EEUM provides the features to browse bibliographic big data according to the connected graph structure by visually displaying graph data, and implements search, management and analysis of the bibliographc big data. It also shows that EEUM can be conveniently used to search, explore, and analyze by applying EEUM to the bibliographic graph big data provided by DBLP. Through EEUM, you can easily find influential authors or papers in every research fields, and conveniently use it as a search and analysis tool for complex bibliographc big data, such as giving you a glimpse of all the relationships between several authors and papers.