Název práce: Grupová souvislost graf· Autor: Lucie Mohelníková Katedra: Informatický ústav Univerzity Karlovy Vedoucí diplomové práce: Mgr. Robert 'ámal,Ph.D., Informatický ústav Univerzi- ty Karlovy Abstrakt: Zabývali jsme se grupovou souvislostí graf·, zejména pak Z2 2- a Z4- souvislostí. Implementovali jsme v jazyce C++ test, zda je graf grupově souvislý a pomocí něho hledáme grafy, které jsou grupově souvislé v jedné ze zkoumaných grup a v druhé nikoliv. Zkoumali jsme grafy, které vzniknou podrozdělením hran několika speciálních graf· např. K4 a krychle. Hlavním přínosem této práce je nalezení dvou graf·, které jsou Z4-souvislé a nejsou Z2 2-souvislé. Pomocí druhé nezávislé implementace testu na grupovou souvislost napsané v jazyce Prolog s využitím CSP jsme ověřili, že tyto grafy jsou Z4-souvislé. Analyticky jsme dokázali, že jeden z nalezených graf· není Z2 2-souvislý. Klíčová slova: grupová souvislost, toky, grupa

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, December 2014. / In this thesis the evolution equations of the Yukawa couplings and quark flavour mixings are derived for the one-loop renormalisation group equations in five and six-dimensional models, compactified in different possible ways to yield standard four space-time dimensions. Different possibilities for the matter fields are discussed, such as the case of bulk propagating or brane localized fields. We discuss in both cases the evolution of the Yukawa couplings, the Jarlskog parameter and the Cabibbo-Kobayashi-Maskawa matrix elements, finding that for both scenarios, as we run up to the unification scale, significant renormalisation group corrections are present. We also discuss the results of different observables of the five-dimensional universal extra dimension model in comparison with those of six-dimensional models and the model dependence of the results. We also studied the scaling of the mass ratios and the implications for the mixing angles in these six-dimensional model as well as the 5D Minimal Supersymmetric Standard Model on an S1/Z2 orbifold. The renormalisation group equation evolutions for the Higgs sector and for the neutrino sector in six-dimensional models are also investigated. The recent experimental results of the Higgs boson from the LHC allow, in some scenarios, stronger constraints on the cutoff scale to be placed, from the requirement of the stability of the Higgs potential.

Consider a finite group G and subgroups H;K of G. We say that H and K permute if HK = KH and call H a permutable subgroup if H permutes with every subgroup of G. A group G is called quasi-Dedekind if all subgroups of G are permutable. We can define, for every finite group G, an arithmetic quantity that measures the probability that two subgroups (chosen uniformly at random with replacement) permute and we call this measure the subgroup permutability degree of G. This measure quantifies, among others, how close a finite group is to being quasi-Dedekind, or, equivalently, nilpotent with modular subgroup lattice. The main body of this thesis is concerned with the behaviour of the subgroup permutability degree of the two families of finite simple groups PSL2(2n), and Sz(q). In both cases the subgroups of the two families of simple groups are completely known and we shall use this fact to establish that the subgroup permutability degree in each case vanishes asymptotically as n or q respectively tends to infinity. The final chapter of the thesis deviates from the main line to examine groups, called F-groups, which behave like nilpotent groups with respect to the Frattini subgroup of quotients. Finally, we present in the Appendix joint research on the distribution of the density of maximal order elements in general linear groups and offer code for computations in GAP related to permutability.

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For the exceptional group of Lie type E8(2) a maximal subgroup is either one of a known set or it is almost simple. In this thesis we compile a complete list of almost simple groups that may have a maximal embedding in E8(2) and in many cases it is proved that such an embedding does not exist. For the groups L2(32) and L2(128) we go further and find all conjugacy classes of their embeddings in E8(2). Extensive use is made of the theory of Brauer characters and modular representation theory, and as such include Brauer character tables in characteristic 2 for many small rank simple groups. The work in this thesis relies heavily on the computer package Magma and includes a collection of useful procedures for computational group theory. The results presented are the author's contribution to the ongoing attempt to classify the maximal subgroups of E8(2).

Ren Xueming. / "November 2001." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Lee Wai Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 108-115). / Chapter 1 --- Introduction --- p.8 / Chapter 1.1 --- Introduction to Group Technology --- p.8 / Chapter 1.2 --- Cell design --- p.9 / Chapter 1.3 --- Objectives of the research --- p.11 / Chapter 1.4 --- Organization of thesis --- p.11 / Chapter 2 --- Literature review --- p.13 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.2 --- Standard models --- p.14 / Chapter 2.2.1 --- Array-based methods --- p.16 / Chapter 2.2.2 --- Cluster identification --- p.16 / Chapter 2.2.3 --- Graph-based methods --- p.17 / Chapter 2.2.4 --- Integer programming --- p.17 / Chapter 2.2.5 --- Seed-based --- p.18 / Chapter 2.2.6 --- Similarity coefficient --- p.18 / Chapter 2.2.7 --- Artificial intelligence methods --- p.19 / Chapter 2.3 --- Generalized models --- p.19 / Chapter 2.3.1 --- Machine assignment models --- p.20 / Chapter 2.3.2 --- Part family models --- p.20 / Chapter 2.3.3 --- Cell formation models --- p.21 / Chapter 3 --- Genetic cell formation algorithm --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- TSP formulation for a permutation of machines --- p.23 / Chapter 3.3 --- Genetic algorithms --- p.26 / Chapter 3.3.1 --- Representation and basic crossover operators --- p.27 / Chapter 3.3.2 --- Fitness function --- p.28 / Chapter 3.3.3 --- Initialization --- p.29 / Chapter 3.3.4 --- Parent selection strategies --- p.30 / Chapter 3.3.5 --- Crossover --- p.31 / Chapter 3.3.6 --- Mutation --- p.37 / Chapter 3.3.7 --- Replacement --- p.38 / Chapter 3.3.8 --- Termination --- p.38 / Chapter 3.4 --- Formation of machine cells and part families --- p.39 / Chapter 3.4.1 --- Objective functions --- p.39 / Chapter 3.4.2 --- Machine assignment --- p.42 / Chapter 3.4.3 --- Part assignment --- p.43 / Chapter 3.5 --- Implementation --- p.43 / Chapter 3.6 --- An illustrative example --- p.45 / Chapter 3.7 --- Comparative Study --- p.49 / Chapter 3.8 --- Conclusions --- p.50 / Chapter 4 --- A multi-chromosome GA for minimizing total intercell and intracell moves --- p.55 / Chapter 4.1 --- Introduction --- p.55 / Chapter 4.2 --- The model --- p.57 / Chapter 4.3 --- Solution techniques to the workload model --- p.61 / Chapter 4.3.1 --- Logendran's original approach --- p.62 / Chapter 4.3.2 --- Standard representation - the GA approach --- p.63 / Chapter 4.3.3 --- Multi-chromosome representation --- p.65 / Chapter 4.4 --- Comparative Study --- p.70 / Chapter 4.4.1 --- Problem 1 --- p.70 / Chapter 4.4.2 --- Problem 2 --- p.71 / Chapter 4.4.3 --- Problem 3 --- p.75 / Chapter 4.4.4 --- Problem 4 --- p.76 / Chapter 4.5 --- Bi-criteria Model --- p.79 / Chapter 4.5.1 --- Experimental results --- p.85 / Chapter 4.6 --- Conclusions --- p.85 / Chapter 5 --- Integrated design of cellular manufacturing systems in the presence of alternative process plans --- p.88 / Chapter 5.1 --- Introduction --- p.88 / Chapter 5.1.1 --- Literature review --- p.90 / Chapter 5.1.2 --- Motivation --- p.92 / Chapter 5.2 --- Mathematical models --- p.93 / Chapter 5.2.1 --- Notation --- p.93 / Chapter 5.2.2 --- Objective functions --- p.95 / Chapter 5.3 --- Our solution --- p.96 / Chapter 5.4 --- Illustrative example and analysis of results --- p.98 / Chapter 5.4.1 --- Solution for objective function 1 --- p.101 / Chapter 5.4.2 --- Solution for objective function 2 --- p.102 / Chapter 5.5 --- Conclusions --- p.103 / Chapter 6 --- Conclusions --- p.104 / Chapter 6.1 --- Summary of achievements --- p.104 / Chapter 6.2 --- Future works --- p.106

Chu Pok Nang. / Thesis submitted on: October 2002. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 69-73). / Abstracts in English and Chinese. / Chapter 1. --- Introduction / Group Technology --- p.6 / Purposes of Research --- p.10 / The Outline of this Thesis --- p.13 / Chapter 2. --- Literature Review / Algorithms for Group Technology --- p.14 / Hierarchical Clustering Approaches --- p.17 / Sorting Based Approaches --- p.18 / Heuristic Exchange Approaches --- p.19 / Seed Based Approaches --- p.20 / Simulated Annealing Approaches --- p.20 / Tabu Search Approaches --- p.21 / Genetic Algorithm Approaches --- p.21 / Neural Network Approaches --- p.22 / Cluster Identification Approaches --- p.22 / Chapter 3. --- The Group Technology Problem / Representing a Manufacturing System --- p.25 / Machine-Part Incidence Matrix --- p.26 / Chapter 4. --- The Improved Cluster Identification Algorithm / Cluster Identification --- p.34 / Formulation --- p.35 / Branch-and-Bound Method --- p.37 / Original Cluster Identification Algorithm --- p.39 / Branching Rule --- p.44 / Chapter 5. --- Computational Studies / Plans for Comparative Studies --- p.49 / Comparison with Existing Cluster Identification Approaches --- p.51 / Solutions to Some Well-known Problems --- p.53 / Comparison with an Optimal Method --- p.60 / Chapter 6. --- Conclusion --- p.63 / Reference --- p.69