Academic literature on the topic 'Group theory. Sets. Permutations'

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Journal articles on the topic "Group theory. Sets. Permutations"

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Niemenmaa, Markku. "Decomposition of Transformation Groups of Permutation Machines." Fundamenta Informaticae 10, no. 4 (1987): 363–67. http://dx.doi.org/10.3233/fi-1987-10403.

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By a permutation machine we mean a triple (Q,S,F), where Q and S are finite sets and F is a function Q × S → Q which defines a permutation on Q for every element from S. These permutations generate a permutation group G and by considering the structure of G we can obtain efficient ways to decompose the transformation group (Q,G). In this paper we first consider the situation where G is half-transitive and after this we show how to use our result in the general non-transitive case.
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Blackburn, Simon R. "Sets of permutations that generate the symmetric group pairwise." Journal of Combinatorial Theory, Series A 113, no. 7 (2006): 1572–81. http://dx.doi.org/10.1016/j.jcta.2006.01.001.

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ALEXANDRU, ANDREI, and GABRIEL CIOBANU. "Uniformly supported sets and fixed points properties." Carpathian Journal of Mathematics 36, no. 3 (2020): 351–64. http://dx.doi.org/10.37193/cjm.2020.03.03.

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The theory of finitely supported algebraic structures is a reformulation of Zermelo-Fraenkel set theory in which every set-based construction is finitely supported according to a canonical action of a group of permutations of some basic elements named atoms. In this paper we study the properties of finitely supported sets that contain infinite uniformly supported subsets, as well as the properties of finitely supported sets that do not contain infinite uniformly supported subsets. Particularly, we focus on fixed points properties.
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Müller, Peter, and Gábor Nagy. "On the non-existence of sharply transitive sets of permutations in certain finite permutation groups." Advances in Mathematics of Communications 5, no. 2 (2011): 303–8. http://dx.doi.org/10.3934/amc.2011.5.303.

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Alexandru, Andrei, and Gabriel Ciobanu. "A Topological Approach in the Extended Fraenkel-Mostowski Model of Set Theory." Annals of the Alexandru Ioan Cuza University - Mathematics 60, no. 2 (2014): 261–77. http://dx.doi.org/10.2478/aicu-2013-0029.

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Abstract Lattices of subgroups are presented as algebraic domains. Given an arbitrary group, we define the Scott topology over the subgroups lattice of that group. A basis for this topology is expressed in terms of finitely generated subgroups. Several properties of the continuous functions with respect the Scott topology are obtained; they provide new order properties of groups. Finally there are expressed several properties of the group of permutations of atoms in a permutative model of set theory. We provide new properties of the extended interchange function by presenting some topological
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Shelah, Saharon, and Simon Thomas. "The cofinality spectrum of the infinite symmetric group." Journal of Symbolic Logic 62, no. 3 (1997): 902–16. http://dx.doi.org/10.2307/2275578.

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AbstractLet S be the group of all permutations of the set of natural numbers. The cofinality spectrum CF(S) of S is the set of all regular cardinals λ such that S can be expressed as the union of a chain of λ proper subgroups. This paper investigates which sets C of regular uncountable cardinals can be the cofinality spectrum of S. The following theorem.is the main result of this paper.Theorem. Suppose that V ⊨ GCH. Let C be a set of regular uncountable cardinals which satisfies the following conditions.(a) C contains a maximum element.(b) If μ is an inaccessible cardinal such thatμ = sup(C ∩
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Lulek, B., T. Lulek, J. Biel, and R. Chatterjee. "Racah–Wigner approach to standardization of permutation representations for finite groups." Canadian Journal of Physics 63, no. 8 (1985): 1065–73. http://dx.doi.org/10.1139/p85-174.

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The problem of equivalence of permutation representations of the finite groups is discussed in terms of transforms by bijections of the carrier sets and by group automorphisms. A formal description of a transformation between equivalent representations is given, and a standard form for an arbitrary permutation representation is proposed. The standardization is achieved through the canonical realization of transitive representations and of imprimitivity sets on the left cosets of the group with respect to an appropriate stability subgroup. The purpose of this paper is to pave the way for a syst
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Howard, Paul E. "Subgroups of a free group and the axiom of choice." Journal of Symbolic Logic 50, no. 2 (1985): 458–67. http://dx.doi.org/10.2307/2274234.

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Nielsen [7] has proved that every subgroup of a free group of finite rank is free. The theorem was later strengthened by Schreier [8] by eliminating the finiteness restriction on the rank. Several proofs of this theorem (known as the Nielsen-Schreier theorem, henceforth denoted by NS) have appeared since Schreier's 1927 paper (see [1] and [2]). All proofs of NS use the axiom of choice (AC) and it is natural to ask whether NS is equivalent to AC. Läuchli has given a partial answer to this question by proving [6] that the negation of NS is consistent with ZFA (Zermelo-Fraenkel set theory weakene
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McKay, J., and E. Regener. "Actions of permutation groups on r-sets." Communications in Algebra 13, no. 3 (1985): 619–30. http://dx.doi.org/10.1080/00927878508823180.

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Cameron, P. J., M. Deza, and P. Frankl. "Sharp sets of permutations." Journal of Algebra 111, no. 1 (1987): 220–47. http://dx.doi.org/10.1016/0021-8693(87)90252-3.

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Dissertations / Theses on the topic "Group theory. Sets. Permutations"

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Ramsay, Denise. "On linearly ordered sets and permutation groups of uncountable degree." Thesis, University of Oxford, 1990. http://ora.ox.ac.uk/objects/uuid:ce9a8b26-bb4c-4c85-8231-78e89ce4109d.

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In this thesis a set, Ω, of cardinality N<sub>K</sub> and a group acting on Ω, with N<sub>K+1</sub> orbits on the power set of Ω, is found for every infinite cardinal N<sub>K</sub>. Let W<sub>K</sub> denote the initial ordinal of cardinality N<sub>K</sub>. Define N := {α<sub>1</sub>α<sub>2</sub> . . . α<sub>n</sub>∣ 0 < n < w, α<sub>j</sub> ∈ w<sub>K</sub> for j = 1, . . .,n, α<sub>n</sub> a successor ordinal} R := {ϰ ∈ N ∣ length(ϰ) = 1 mod 2} and let these sets be ordered lexicographically. The order types of N and R are Κ-types (countable unions of scattered types) which have cardinality N<
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Xuan, Mingzhi. "On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers." Thesis, University of North Texas, 2012. https://digital.library.unt.edu/ark:/67531/metadc149691/.

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In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of closed permutation groups of natural numbers with respect to their universal and surjectively univers
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Justus, Amanda N. "Permutation Groups and Puzzle Tile Configurations of Instant Insanity II." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2337.

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The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or a 5 x 4 puzzle, respectively. We consider the possibilities when we delete a color
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Banister, Melissa. "Separating Sets for the Alternating and Dihedral Groups." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/158.

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This thesis presents the results of an investigation into the representation theory of the alternating and dihedral groups and explores how their irreducible representations can be distinguished with the use of class sums.
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Crespo, Charles J. "The McSweeney's Group: Modernist Roots and Contemporary Permutations in Little Magazines." FIU Digital Commons, 2013. http://digitalcommons.fiu.edu/etd/985.

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The purpose of this project centered on the influential literary magazine Timothy McSweeney’s Quarterly Concern. Using Bruno Latour’s network theory as well as the methods put forth by Robert Scholes and Clifford Wulfman to study modernist little magazines, I analyzed the influence McSweeney’s has on contemporary little magazines. I traced the connections between McSweeney’s and other paradigmatic examples of little magazines—The Believer and n+1—to show how the McSweeney’s aesthetic and business practice creates a model for more recent publications. My thesis argued that The Believer continue
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Jung, JiYoon. "ANALYTIC AND TOPOLOGICAL COMBINATORICS OF PARTITION POSETS AND PERMUTATIONS." UKnowledge, 2012. http://uknowledge.uky.edu/math_etds/6.

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In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent avo
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Chassaniol, Arthur. "Contributions à l'étude des groupes quantiques de permutations." Thesis, Clermont-Ferrand 2, 2016. http://www.theses.fr/2016CLF22709/document.

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Dans cette thèse nous étudions le groupe quantique d’automorphismes des graphes finis, introduit par Banica et Bichon. Dans un premier temps nous montrerons un théorème de structure du groupe quantique d’automorphismes du produit lexicographique de deux graphes finis réguliers, qui généralise un résultat classique de Sabidussi. Ce théorème donne une condition nécessaire et suffisante pour que ce groupe quantique s’exprime comme le produit en couronne libre des groupes quantiques d’automorphismes de ces deux graphes. Dans un deuxième temps, nous expliciterons certaines améliorations de résultat
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Hyde, James Thomas. "Constructing 2-generated subgroups of the group of homeomorphisms of Cantor space." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/11362.

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We study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the group of homeomorphisms of Cantor space. In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we study vigorous subgroups of H[sub]c. A subgroup G of H[sub]c is vigorous if for any non-empty clopen set A with proper non-empty clopen subsets B and C there exists g ∈ G with supp(g) ⊑ A and Bg ⊆ C. It is a corollary of the main theorem of Chapter 3 that all finitely generated simple vigorous subgroups of H[sub]c are in fact 2-generated. We show the family of finitely generate
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Gideon, Frednard. "A study of fuzzy sets and systems with applications to group theory and decision making." Thesis, Rhodes University, 2006. http://eprints.ru.ac.za/269/1/MASTER1.pdf.

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In this study we apply the knowledge of fuzzy sets to group structures and also to decision-making implications. We study fuzzy subgroups of finite abelian groups. We set G = Z[subscript p[superscript n]] + Z[subscript q[superscript m]]. The classification of fuzzy subgroups of G using equivalence classes is introduced. First, we present equivalence relations on fuzzy subsets of X, and then extend it to the study of equivalence relations of fuzzy subgroups of a group G. This is then followed by the notion of flags and keychains projected as tools for enumerating fuzzy subgroups of G. In additi
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Khani, Mohsen. "The first order theory of a dense pair and a discrete group." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/the-first-order-theory-of-a-dense-pair-and-a-discrete-group(01e5c6b4-fe53-49c9-8b88-6c47c0ac2f6f).html.

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In this thesis we have shown that a seemingly complicated mathematical structure can exhibit 'tame behaviour'. The structure we have dealt with is a field (a space in which there are addition and multiplication which satisfy natural properties) together with a dense subset (a subset which has spread in all parts of the this set, as Q does in R) and a discrete subset (a subset comprised of single points which keep certain distances from one another). This tameness is essentially with regards to not being trapped with the 'Godel phenomeonon' as the Peano arithmetic does.
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Books on the topic "Group theory. Sets. Permutations"

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Green, J. A. Sets and groups: A first course in algebra. 2nd ed. Chapman & Hall, 1988.

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Sets and groups: A first course in algebra. 2nd ed. Routledge & K. Paul, 1988.

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Wygralak, Maciej. Cardinalities of Fuzzy Sets. Springer Berlin Heidelberg, 2003.

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Sorting and Sets. Sea to Sea Publications, 2006.

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I, Sushchanskiĭ V., ed. Preobrazovanii͡a︡ i perestanovki. 2nd ed. "Nauka," Glav. red. fiziko-matematicheskoĭ lit-ry, 1985.

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Berry, Minta. Building sets of ten. Crabtree Pub., 2012.

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Stephenson, G. An introduction to matrices, sets, and groups for science students. Dover Publications, 1986.

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Cameron, Peter J. Oligomorphic permutation groups. Cambridge University Press, 1990.

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Green, Susannah. Augustin-Louis Cauchy: His life and his early work of permutations, deteriminants and group theory. Oxford Brookes University, 1999.

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Rodabaugh, Stephen Ernest. Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets. Springer Netherlands, 2003.

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Book chapters on the topic "Group theory. Sets. Permutations"

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Droste, Manfred. "On Ore’s Theorem and Universal Words for Permutations and Injections of Infinite Sets." In Groups, Modules, and Model Theory - Surveys and Recent Developments. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51718-6_12.

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Hegyvári, Norbert. "Additive structure of difference sets." In Combinatorial Number Theory and Additive Group Theory. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8962-8_19.

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Baumslag, Gilbert, and Peter B. Shalen. "Affine Algebraic Sets and Some Infinite Finitely Presented Groups." In Essays in Group Theory. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4613-9586-7_1.

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Frenkel, Elizaveta, Alexei G. Myasnikov, and Vladimir N. Remeslennikov. "Regular Sets and Counting in Free Groups." In Combinatorial and Geometric Group Theory. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9911-5_4.

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Alonso, Sergio, Enrique Herrera-Viedma, Francisco Javier Cabrerizo, Carlos Porcel, and A. G. López-Herrera. "Using Visualization Tools to Guide Consensus in Group Decision Making." In Applications of Fuzzy Sets Theory. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73400-0_10.

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Freiman, Gregory A. "On the detailed structure of sets with small additive property." In Combinatorial Number Theory and Additive Group Theory. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8962-8_17.

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Kuga, Michio. "The First Week: Sets and Maps." In Galois’ Dream: Group Theory and Differential Equations. Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0329-2_2.

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Moerdijk, Ieke. "Bisimplicial Sets and the Group-Completion Theorem." In Algebraic K-Theory: Connections with Geometry and Topology. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2399-7_10.

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Baumslag, Gilbert. "Affine algebraic sets and the representation theory of finitely generated groups." In Topics in Combinatorial Group Theory. Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8587-4_5.

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Elsholtz, Christian. "A survey on additive and multiplicative decompositions of sumsets and of shifted sets." In Combinatorial Number Theory and Additive Group Theory. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8962-8_16.

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Conference papers on the topic "Group theory. Sets. Permutations"

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Ying, ZuBei, Fan Ye, Jing Li, and ZhenJie Hong. "Multiple attribute group decision making with incomplete information based on interval-valued intuitionistic fuzzy sets theory." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002146.

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Lim, Shi Ying Candice, Bradley Adam Camburn, Diana Moreno, Zack Huang, and Kristin Wood. "Design Concept Structures in Massive Group Ideation." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59805.

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Empirical work in design science has highlighted that the process of ideation can significantly affect design outcome. Exploring the design space with both breadth and depth increases the likelihood of achieving better design outcomes. Furthermore, iteratively attempting to solve challenging design problems in large groups over a short time period may be more effective than protracted exploration by an isolated set of individuals. There remains a substantial opportunity to explore the structure of various design concept sets. In addition, many empirical studies cap analysis at sample sizes of
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Haşıloğlu, Selçuk Burak. "Determination of Country of Origin Image with Fuzzy Set Theory." In International Conference on Eurasian Economies. Eurasian Economists Association, 2012. http://dx.doi.org/10.36880/c03.00471.

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As foreign trade has become more spread, the country of production and even the origin of the raw material used in the production has become an important factor. Mentioning the country of origin on the label of the product dates back to World War-I when “Good product sells itself” understanding is dominant. In this study, the image of country of origin was evaluated with fuzzy set theory. Fuzzy sets theory lays foundation for the methods used in the solution of relative and uncertain problems. As image evaluation is a relative issue, these methods were used in our study. The first phase in the
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Gao, Song, and Jichuan Kang. "Group Maintenance Strategy for FPSO Offloading System Based on Reliability Analysis." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-55083.

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Floating Production Storage and Offloading (FPSO) is being widely used in offshore petroleum production. As a key subsystem, the offloading system often fails and causes marine disaster. The aim of this study was to investigate the failure events and failure rate to determine the efficient maintenance strategy, in particular maintenance interval and overhaul cycle. Failure Mode and Effects Analysis (FMEA) method was applied for the reliability analysis of the main failure events and their interrelations. In order to guarantee the accuracy, the analysis is based on four primary subsystem of off
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Sullivan, Gerald A., and Jon-Michael Hardin. "The Can Crusher Project: A Multi-Semester Design Project to Enhance Retention of Engineering Skill Sets." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47417.

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This paper describes a three semester long project which promotes the development and retention of engineering skill-sets by involving students in the design and fabrication of a can-crushing device. The can-crusher project was inspired by spiral learning theory and provides opportunities for students to practice engineering skill sets, including CAD, programming, machining and working with practical electronics. The paper details the implementation of the project and shows how the project addresses skill-set deficits that can occur in conventional curricula. Finally, modifications to the cont
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Zhou, Jiao, Xingyu Peng, and Dongchi Yao. "Quantitative Risk Assessment Techniques Based on Uncertainty Theory for Natural Gas Distribution Station." In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/ipc2018-78260.

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Pipeline stations, as an important part of long-distance pipeline systems, include lots of facilities which are highly concentrated and always operate continuously. Risk assessment is an important foundation work for the risk management of these stations. Since various uncertainties exist during the quantitative risk assessment (QRA), this paper explores the theories and approaches of QRA for station accidents, and also introduces some specific mathematical theories for quantification and dealing with uncertainties. This paper combines uncertainty theory effectively with the QRA for gas distri
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Abreu, Danilo Taverna Martins Pereira de, Joaquim Rocha dos Santos, Carlos Henrique Bittencourt Morais, Marcelo Ramos Martins, and Danilo Colombo. "Application of Fuzzy Logic and Expert Elicitation for Quantitative Offshore Well Integrity Data Collection." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18995.

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Abstract The risk of uncontrolled hydrocarbon releases in oil &amp; gas wells is mitigated through well barrier elements (such as casings, Xmas trees and packers), which are physical components capable of holding the undesired flow of reservoir fluids. Along with operational and management measures, the well barrier elements ensure the well integrity. Typically, these elements compose well barrier sets and, at least, two tested well barrier sets should be in place during the entire life cycle. Currently, limited quantitative failure data regarding well barrier elements exists, and this fact li
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do Carmo, Lucas H. S., Pedro C. de Mello, Edgard B. Malta, et al. "Analysis of a FOWT Model in Bichromatic Waves: An Investigation on the Effect of Combined Wave-Frequency and Slow Motions on the Calibration of Drag and Inertial Force Coefficients." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18239.

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Abstract The choice of drag and inertia coefficients are critical for the evaluation of hydrodynamic loads in slender cylinders using either Morison’s equation or an approach where viscous forces are simply added to the results of potential theory. Many studies available in the literature have considered fixed cylinders under the action of (two dimensional) sinusoidal currents, showing that the average values of drag and added mass coefficients can be correlated with the Keulegan-Carpenter and Reynolds numbers. However, when the semi-empirical models are used for the analysis of Floating Offsh
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Zhou, Jun, XiaoPing Li, Mengya Cheng, Tao Deng, and Jing Gong. "Topology Analysis and Optimization Design of Coal Bed Methane Gathering System in China." In 2014 10th International Pipeline Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/ipc2014-33278.

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China is abundant in coalbed methane (CBM) resource. The unconventional natural gas reserves has reached 36.81*1012 m3. The Qinshui Basin in Shanxi Province is the largest gas field among CBM gas fields in China which are commercially exploited since the year 2003. In order to solve some typical problems in CBM production, this article considered the geographical characteristics of the fields, introduced and analyzed the low pressure gathering and transporting process and facilities, as well as the important techniques. Respectively, this article introduced the surface gathering and transporti
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