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1	An Enumerative-Probabilistic Study of Chord Diagrams Acan, Huseyin 03 September 2013 (has links) No description available. Mathematics chord diagrams intersection graphs circle graphs permutations permutation graphs
2	Applications of Lexicographic Breadth-first Search to Modular Decomposition, Split Decomposition, and Circle Graphs Tedder, Marc 31 August 2011 (has links) This thesis presents the first sub-quadratic circle graph recognition algorithm, and develops improved algorithms for two important hierarchical decomposition schemes: modular decomposition and split decomposition. The modular decomposition algorithm results from unifying two different approaches previously employed to solve the problem: divide-and-conquer and factorizing permutations. It runs in linear-time, and is straightforward in its understanding, correctness, and implementation. It merely requires a collection of trees and simple traversals of these trees. The split-decomposition algorithm is similar in being straightforward in its understanding and correctness. An efficient implementation of the algorithm is described that uses the union-find data-structure. A novel charging argument is used to prove the running-time. The algorithm is the first to use the recent reformulation of split decomposition in terms of graph-labelled trees. This facilitates its extension to circle graph recognition. In particular, it allows us to efficiently apply a new lexicographic breadth-first search characterization of circle graphs developed in the thesis. Lexicographic breadth-first search is additionally responsible for the efficiency of the split decomposition algorithm, and contributes to the simplicity of the modular decomposition algorithm. Modular Decomposition Split Decomposition Circle Graphs Lexicographic Breadth-First Search LBFS LexBFS Charging argument Amortized analysis Aggregate analysis Recognition Graph Labelled Trees GLT 0984
3	Applications of Lexicographic Breadth-first Search to Modular Decomposition, Split Decomposition, and Circle Graphs Tedder, Marc 31 August 2011 (has links) This thesis presents the first sub-quadratic circle graph recognition algorithm, and develops improved algorithms for two important hierarchical decomposition schemes: modular decomposition and split decomposition. The modular decomposition algorithm results from unifying two different approaches previously employed to solve the problem: divide-and-conquer and factorizing permutations. It runs in linear-time, and is straightforward in its understanding, correctness, and implementation. It merely requires a collection of trees and simple traversals of these trees. The split-decomposition algorithm is similar in being straightforward in its understanding and correctness. An efficient implementation of the algorithm is described that uses the union-find data-structure. A novel charging argument is used to prove the running-time. The algorithm is the first to use the recent reformulation of split decomposition in terms of graph-labelled trees. This facilitates its extension to circle graph recognition. In particular, it allows us to efficiently apply a new lexicographic breadth-first search characterization of circle graphs developed in the thesis. Lexicographic breadth-first search is additionally responsible for the efficiency of the split decomposition algorithm, and contributes to the simplicity of the modular decomposition algorithm. Modular Decomposition Split Decomposition Circle Graphs Lexicographic Breadth-First Search LBFS LexBFS Charging argument Amortized analysis Aggregate analysis Recognition Graph Labelled Trees GLT 0984
4	Bråktal, decimaltal och procent : En kvalitativ studie om hur sambandet mellan bråktal, decimaltal och procent undervisas i årskurs 4-6 Abdulrasul, Zahraa January 2017 (has links) The aim of this study is to investigate how the connection between fractions, decimals and percent are taught in grade 4-6 with more focuson the fractions. The empirical data was obtained by qualitative methods comprising interviews with four mathematic elementary school teachers, in addition to two observations with two classrooms in grade 6. The data presented is from one school. The theoretical framework is based on Liping Ma profound understanding of fundamental mathematics and theories of subject didactic concepts of Kilborn, Löwing, Karlsson & Kilborn and MacIntosh. The results of the interviews and observations show that the connection between fractions, decimals and percent is being taught without illuminating how the mentioned are connected. The aspect of fractions, which has been taught to show the relation between fractions and decimals, was division as metaphor. While there was no aspect of fractions has been taught to show the relation between it and percent except that a percent is a hundredth. Such as 40% is equal with 40/100. In addition, fractions has been taught by using visual aids, but never taught by using number line. In conclusion the connection between fractions, decimals and percent has not been related clearly with basic concept fractions. Fractions decimals percent connection aspect of fractions circle graphs number line numerator denominator tenth hundredth thousandth decimal mark fractions bar Bråktal decimaltal procent samband bråktals ansikte bråkcirklar tallinje täljare nämnare tiondel hundradel tusendel decimaltecken bråkstreck Mathematics Matematik

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