• Journal of Institute of Control, Robotics and Systems
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• v.18 no.3
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• pp.218-223
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• 2012

Maintenance and improvement of the graph connectivity is very important for decentralized multi-agent systems. Although the CBBA (Consensus-Based Bundle Algorithm) guarantees suboptimal performance and bounded convergence time, it is only valid for connected graphs. In this study, we apply a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimation, we design a decentralized gradient controller to maintain the graph connectivity while agents are traveling to perform assigned tasks. Simulation result for fully-actuated first-order agents that move in a 2-D plane are presented.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2019.05a
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• pp.37-40
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• 2019

On this paper, we show the way of forming graph data structure via setting an edge between Korean actors if they appeared in the same movie. From this graph, we calculate the 'centralities' (which declared on this paper) for each actor, then examine distribution by ranking the actors of the centralities and analyze the change of the actor who is/was center on the graph by years. Finally, we suggest the way that sets the numerically Range limits on social group.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.321-330
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• 2023

Let G = (V, E) be a graph. Consider the group S₃. Let g : V (G) → S₃ be a function. For each edge xy assign the label 1 if ${\lceil}{\frac{o(g(x))+o(g(y))}{2}}{\rceil}$ is odd or 0 otherwise. g is a group S₃ mean cordial labeling if |v_g(i) - v_g(j)| ≤ 1 and |e_g(0) - e_g(1)| ≤ 1, where vg(i) and e_g(y)denote the number of vertices labeled with an element i and number of edges labeled with y (y = 0, 1). The graph G with group S₃ mean cordial labeling is called group S₃ mean cordial graph. In this paper, we discuss group S3 mean cordial labeling for star related graphs.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.127-133
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• 1997

In order to study the limits of sequences appearing in, for example, stochastic process, A. V. Skorokhod has defined new function space topologies. We compare these topologies with the topology of compact convergence, the topology of pointwise convergence and others.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.264-273
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• 2002

This paper focuses on disassembly sequencing, which is the problem of determining the optimum disassembly level and the corresponding disassembly sequence for a product at its end-of-life with the objective of maximizing the overall profit. In particular, sequence-dependent operation times, which frequently occur in practice due to tool-changeover, part reorientation, etc, are considered in the parallel disassembly environment. To represent the problem, a modified directed graph of assembly states is suggested as an extension of the existing extended process graph. Based on the directed graph, the problem is transformed into the shortest path problem and formulated as a linear programming model that can be solved straightforwardly with standard techniques. A case study on a photocopier was done and the results are reported.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.12
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• pp.1021-1026
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• 2016

The graph-based SLAM (Simultaneous Localization and Mapping) approach has been gaining much attention in SLAM research recently thanks to its ability to provide better maps and full trajectory estimations when compared to the filtering-based SLAM approach. Even though graph-based SLAM requires batch processing causing it to be computationally heavy, recent advancements in optimization and computing power enable it to run fast enough to be used in real-time. However, data association problems still require large amount of computation when building a pose graph. For example, to find loop closures it is necessary to consider the whole history of the robot trajectory and sensor data within the confident range. As a pose graph grows, the number of candidates to be searched also grows. It makes searching the loop closures a bottleneck when solving the SLAM problem. Our approach to alleviate this bottleneck is to sample a limited number of pose nodes in which loop closures are searched. We propose a heuristic for sampling pose nodes that are most advantageous to closing loops by providing a way of ranking pose nodes in order of usefulness for closing loops.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.665-668
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• 2012

For a given graph G we consider a set S(G) of all symmetric matrices A = [$a_{ij}$] whose nonzero entries are placed according to the location of the edges of the graph, i.e., for $i{\neq}j$, $a_{ij}{\neq}0$ if and only if vertex $i$ is adjacent to vertex $j$. The minimum rank mr(G) of the graph G is defined to be the smallest rank of a matrix in S(G). In general the computation of mr(G) is complicated, and so is that of the maximum multiplicity MaxMult(G) of an eigenvalue of a matrix in S(G) which is equal to $n$ - mr(G) where n is the number of vertices in G. However, for trees T, there is a recursive formula to compute MaxMult(T). In this note we show that this recursive formula for MaxMult(T) also computes the path cover number $p$(T) of the tree T. This gives an alternative proof of the interesting result, MaxMult(T) = $p$(T).

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.977-986
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• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.749-762
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• 2017

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.