• Kyungpook Mathematical Journal
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• 제62권2호
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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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• 제57권1호
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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.

• 한국경영과학회지
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• 제23권4호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1998년도 추계학술대회 논문집
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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.

• 대한교통학회지
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• 제34권2호
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• pp.180-190
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• 2016

차량의 배기가스에는 질소산화물(NOx), 일산화탄소(CO), 이산화탄소($CO_2$), 입자상 물질(PM), 탄화수소(HC)와 같은 대기 오염물질이 포함되어 있다. 이러한 도로이동오염원의 배출량을 산정하기 위하여 한국에서는 평균속도 기반의 배출계수 곡선식을 사용하고 있으며 교통 계획과 교통 정책의 대안 평가에서 환경적 영향을 분석할 때 활용하고 있다. 그러나 최근에는 차량의 동적 운행 특성과 배출량의 관계를 보다 정확하게 반영하여 배출량을 산정할 수 있는 방법론과 이 방법론을 교통 시뮬레이션 모형에 통합하는 것에 대한 관심이 증가하고 있다. MOVES Lite는 MOVES의 간략 버전으로서 교통 시뮬레이션 모형에 통합될 수 있도록 개발된 운행모드 기반 배출량 산정모형이다. 본 연구에서는 한국의 차종, 주행특성, 배출계수, 배출규제등을 반영하여 MOVES Lite를 개량한 MOVES Lite-K를 개발하기 위한 연구를 수행하였고, 국내의 대표적 배출량 산정 방법인 평균속도 기반의 배출계수 곡선식과 MOVES Lite-K의 배출량 산정 특성을 비교하여 두 방법론의 차이와 국내 적용성을 살펴보았다.

• Kyungpook Mathematical Journal
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• 제46권3호
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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.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제24권4호
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• pp.279-311
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• 2021

In this paper, we report the types of teaching moves a mathematics teacher educator attempted in his teaching of third-grade students at an urban elementary school in South Korea over two months. We analyze the lesson videos to find the patterns of teaching moves and speculate the link between the teaching and students' mathematical proficiencies recommended in the Common Core State Standards for Mathematical Practices. Closely related teaching moves to the students' development of a certain mathematical proficiency would imply the exemplary practices that teachers-both inservice and preservice teachers-can implement in their classrooms.

• Kyungpook Mathematical Journal
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• 제55권2호
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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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• 제58권1호
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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 ${\Delta}-moves$.

• 산업공학
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• 제10권3호
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• pp.189-196
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• 1997

This paper presents a cell formation approach for a cellular manufacturing system to minimize the inter-cell moves considering operation sequences. Two new factors are introduced: (1)flow-similarity(FS) for integrating direct/indirect inter-machine flow and similarity (2)machine cell-part moves (CPM) for exactly computing inter-cell moves. FS is used for combining machines and CPM is used for assigning the parts to the preliminary machine cells. In addition, we develop an aggregated heuristic algorithm to form manufacturing machine cells and assign the parts to those cells based on these concepts. We use performance criterion called total inter-cell moves(TICM), which is the total material flow between internal cells and external cells. Results of computational tests on a number of randomly generated test problems show that the suggested heuristic is superior to existing methods.