• Title/Summary/Keyword: Moves

### The Second Reidemeister Moves and Colorings of Virtual Knot Diagrams

• Jeong, Myeong–Ju;Kim, Yunjae
• 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 qK(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.

### Polynomials and Homotopy of Virtual Knot Diagrams

• Jeong, Myeong-Ju;Park, Chan-Young;Park, Maeng Sang
• 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.

### A Method of Eliminating Exceptional Elements Attaining Minimum Machine Duplications and Intercell Moves In Cellular Manufacturing Systems (기계중복과 셀간 이동수의 최소화가 가능한 예외적 요소의 제거 방법 : 비용 및 설치대수 제약 고려)

• Jang, Ik;Yun, Chang-Won;Chung, Byung-Hee
• 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.

### A Method of Eliminating Exceptional Elements Attainting Minimum Machine Duplications and Intercell Moves In Cell Manufacturing Systems (기계중복과 셀간 이동수의 최소화가 가능한 예외적 요소의 제거 방법 : 비용 및 설치대수 제약 고려)

• Chang, Ik;Yoon, Chang-Won;Chung, Byeong-Hui
• 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.

### A Study for Developing an Operating Mode-Based Emission Model for Korea (한국형 운행 모드 기반 배출량 산정 모형 개발에 관한 연구)

• HU, Hyejung;FREY, Christopher;YOON, Chunjoo;YANG, Choongheon;KIM, Jinkook
• Journal of Korean Society of Transportation
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• v.34 no.2
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• pp.180-190
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• 2016
• Atmospheric pollutants such as Nitrogen Oxides(NOx), Carbon Monoxide(CO), Carbon Dioxide($CO_2$), Particulate Matter(PM) and Hydrocarbons(HC) come from vehicle exhaust gases. Emission curves based on average travel speeds have been employed for estimating on-road emissions as well as evaluating environmental impacts of transportation plans and policies in Korea. Recently, there is a growing interest in estimation methods of vehicle emissions considering relationship between vehicle dynamic driving characteristics and emissions, and incorporating such emission estimators into traffic simulation models. MOVES Lite, a simplified version of MOVES, is one of the estimation methods. In this study, the authors performed a study to develop an adaptable version of MOVES Lite for Korea, called MOVES Lite-K. Vehicle types, driving characteristics, emission rates, and emission standards of Korea were reflected in MOVES Lite-K. The characteristics of emission calculation of MOVES Lite-K and NIER emission curves were compared and the adaptability of MOVES Lite-K were examined.

### Finite Type Invariants and Virtual Twist Moves of Virtual Knots

• Jeong, Myeong-Ju
• 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.

### Teaching Moves for Students' Mathematical Proficiencies in Multiplication Lessons

• Colen, Jung;Yeo, Sheunghyun;Kwon, Nayoung;Cho, Hoyun;Kim, Jinho
• Research in Mathematical Education
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• v.24 no.4
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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.

### The Forbidden Number of a Knot

• CRANS, ALISSA S.;MELLOR, BLAKE;GANZELL, SANDY
• 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.

### An Efficient Cell Formation Approach for a Cellular Manufacturing System Considering Operation Sequences (작업순서를 고려한 효율적인 제조셀 형성방법)

• Choi, Dong-Soon;Chung, Byung-Hee
• IE interfaces
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• v.10 no.3
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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.

### Thanking and Apologizing Behaviour in Requestive Email of Koreans and Americans

• Yang, Eun-Mi
• English Language & Literature Teaching
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• v.8 no.1
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• pp.125-141
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• 2002
• This paper examines the pragmatic features of the thanking and apologizing moves which appear in requestive email of Korean speakers of English as a foreign language and American English native speakers. It is important for second language learners to behave appropriately in a target language when communicating with other English speakers who have different cultural backgrounds. The result of this study revealed the differences in the use of thanking and apologizing moves in the requestive email between Koreans and Americans. Koreans used fewer moves of thanking and more moves of apologizing than Americans in three different situations. Koreans' underuse of thanking which is a routine and formulaic expression for Americans could be a marked phenomenon to a recipient of the email in English bringing about a minus effect.