• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.347-361
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• 2022

Two virtual knot diagrams are said to be equivalent, if there is a sequence S of Reidemeister moves and virtual moves relating them. The difference of writhes of the two virtual knot diagrams gives a lower bound for the number of the first Reidemeister moves in S. In previous work, we introduced a polynomial q_K(t) for a virtual knot diagram K which gave a lower bound for the number of the third Reidemeister moves in the sequence S. In this paper we define a new polynomial from a coloring of a virtual knot diagram. Using this polynomial, we give a lower bound for the number of the second Reidemeister moves in S. The polynomial also suggests the design of the sequence S.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.145-161
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• 2017

If a virtual knot diagram can be transformed to another virtual one by a finite sequence of crossing changes, Reidemeister moves and virtual moves then the two virtual knot diagrams are said to be homotopic. There are infinitely many homotopy classes of virtual knot diagrams. We give necessary conditions by using polynomial invariants of virtual knots for two virtual knots to be homotopic. For a sequence S of crossing changes, Reidemeister moves and virtual moves between two homotopic virtual knot diagrams, we give a lower bound for the number of crossing changes in S by using the affine index polynomial introduced in [13]. In [10], the first author gave the q-polynomial of a virtual knot diagram to find Reidemeister moves of virtually isotopic virtual knot diagrams. We find how to apply Reidemeister moves by using the q-polynomial to show homotopy of two virtual knot diagrams.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.87-96
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• 1998

Using the concept of cellular manufacturing systems(CMS) in job shop manufacturing system is one of the most innovative approaches to improving plant productivity. However. several constraints in machine duplication cost, machining capability, cell space capacity, intercell moves and exceptional elements(EEs) are main problems that prevent achieving the goal of maintaining an ideal CMS environment. Minimizing intercell part traffics and EEs are the main objective of the cell formation problem because it is a critical point that improving production efficiency. Because the intercell moves could be changed according to the sequence of operation, it should be considered in assigning parts and machines to machine ceil. This paper presents a method that eliminates EEs under the constraints of machine duplication cost and ceil space capacity attaining two goals of minimizing machine duplications and minimizing intercell moves simultaneously. Developing an algorithm that calculates the machine duplications by cell-machine incidence matrix and part-machine Incidence matrix, and calculates the exact intercell moves considering the sequence of operation. Based on the number of machine duplications and exact intercell moves, the goal programming model which satisfying minimum machine duplications and minimum intercell moves is developed. A linear programming model is suggested that could calculates more effectively without damaging optimal solution. A numerical example is provided to illustrate these methods.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.263-266
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• 1998

Several constraints in machine duplication cost, machining capability, cell space capacity, intercell moves and exceptional elements(EEs) are main problems that prevent achieving the goal of ideal Cellular Manufacturin System (CMS) environment. Minimizing intercell part traffics and EEs are the main objective of the cell formation problem as it's a critical point that improving production efficiency. Because the intercell moves could be changed according to the sequence of operation, it should be considered in assigning parts and machines to machine cells. This paper presents a method that eliminates EEs under the constraints of machine duplication cost and cell space capacity attaining two goals of minimizing machine duplications and minimizing intercell moves simultaneously. Developing an algorithm that calculates the machine duplications by cell-machine incidence matrix and part-machine incidence matrix, and calculates the exact intercell moves considering the sequence of operation. Based on the number of machine duplications and exact intercell moves, the goal programming model which satisfying minimum machine duplications and minimum intercell moves is developed. A linear programming model is suggested that could calculates more effectively without damaging optimal solution. A numerical example is provided to illustrate these methods.

• Journal of Korea Game Society
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• v.18 no.5
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• pp.77-82
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• 2018

Go is the most complex board game in which the computer can not search all possible moves using an exhaustive search to find the best one. Prior to AlphaGo, all powerful computer Go programs have used the Monte-Carlo Tree Search (MCTS) to overcome the difficulty in positional evaluation and the very large branching factor in a game tree. In this paper, we tried to find the best sequence of moves using an MCTS on a very small Go board. We found that a $2{\times}2$ Go game would be ended in a tie and the size of Komi should be 0 point; Meanwhile, in a $3{\times}3$ Go Black can always win the game and the size of Komi should be 9 points.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.485-506
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• 2015

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.449-461
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• 2006

Generalizing twist moves of classical knots, we introduce $t(a_1,{\cdots},a_m)$-moves of virtual knots for an $m$-tuple ($a_1,{\cdots},a_m$) of nonzero integers. In [4], M. Goussarov, M. Polyak and O. Viro introduced finite type invariants of virtual knots and Gauss diagram formulae giving combinatorial presentations of finite type invariants. By using the Gauss diagram formulae for the finite type invariants of degree 2, we give a necessary condition for a virtual long knot K to be transformed to a virtual long knot K' by a finite sequence of $t(a_1,{\cdots},a_m)$-moves for an $m$-tuple ($a_1,{\cdots},a_m$) of nonzero integers with the same sign.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.619-622
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• 2000

In this paper, we propose a method for generating graphic objects having realistic shadows inserted into video sequence for the enhanced augmented reality. Our purpose is to extend the work of [1], which is applicable to the case of a static camera, to video sequence. However, in case of video, there are a few challenging problems, including the camera calibration problem over video sequence, false shadows occurring when the video camera moves and so on. We solve these problems using the convenient calibration technique of [2] and the information from video sequence . We present the experimental results on real video sequences.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.183-202
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• 2018

${\Delta}-moves$ are closely related with a Vassiliev invariant of degree 2. For classical knots, M. Okada showed that the second coefficients of the Conway polynomials of two knots differ by 1 if the two knots are related by a single ${\Delta}-move$. The first author extended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knots of type 2 which is induced from the Kauffman polynomial of a virtual knot. The arrow polynomial is a generalization of the Kauffman polynomial. We will generalize this result by using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knot and give a lower bound for the number of ${\Delta}-moves$ transforming $K_1$ to $K_2$ if two virtual knots $K_1$ and $K_2$ are related by a finite sequence of ${\Delta}-moves$.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1247-1257
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• 2016

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.