Let V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using methods based on incidence structures known as the Kramer-Mesner matrices. These structures are induced by particular group actions on the collection of subspaces of the vector space V. Subsequently, we discuss and use computational techniques for solving certain linear problems of the form AX = B, where A is a large integral matrix and X is a {0,1} solution. These techniques involve (i) lattice basis-reduction, including variants of the LLL algorithm, and (ii) linear programming. Inspiration came from the 2013 work of Braun, Kohnert, Ostergard, and Wassermann, [17], who produced the first nontrivial large set of geometric designs with t ≥ 2. Bal Khadka and Michael Epstein provided the know-how for using the LLL and linear programming algorithms that we implemented to construct the large sets. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

by Lo Kam Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 107-111). / Chapter 1 --- Introduction --- p.7 / Chapter 1.1 --- The Goal --- p.8 / Chapter 1.2 --- The Work of the Thesis --- p.9 / Chapter 1.3 --- Layout of Thesis --- p.9 / Chapter 2 --- The Unit Commitment Problem --- p.11 / Chapter 2.1 --- What is UCP? --- p.11 / Chapter 2.1.1 --- Why is UCP difficult? --- p.12 / Chapter 2.1.2 --- Costs --- p.12 / Chapter 2.1.3 --- Constraints --- p.13 / Chapter 2.2 --- Mathematical Formulation --- p.15 / Chapter 2.3 --- Literature Review --- p.19 / Chapter 2.3.1 --- Exhaustive Enumeration --- p.19 / Chapter 2.3.2 --- Priority List --- p.20 / Chapter 2.3.3 --- Langragian Relaxation --- p.21 / Chapter 2.3.4 --- Neural Network --- p.21 / Chapter 2.3.5 --- Genetic Algorithms --- p.22 / Chapter 2.3.6 --- Dynamic Programming --- p.22 / Chapter 3 --- Genetic Algorithms --- p.24 / Chapter 3.1 --- Introduction --- p.24 / Chapter 3.1.1 --- Outline of Traditional GA --- p.25 / Chapter 3.2 --- Basic elements --- p.26 / Chapter 3.2.1 --- Coding --- p.26 / Chapter 3.2.2 --- Fitness Function --- p.26 / Chapter 3.2.3 --- Selection and Reproduction --- p.26 / Chapter 3.2.4 --- Mutation --- p.28 / Chapter 3.2.5 --- Replacement --- p.29 / Chapter 3.2.6 --- Epistasis --- p.29 / Chapter 3.2.7 --- A Simple Example --- p.30 / Chapter 3.3 --- Exploration vs Exploitation --- p.33 / Chapter 3.4 --- Constraints Handlings --- p.34 / Chapter 3.4.1 --- Penalty Function --- p.35 / Chapter 3.4.2 --- Proper Encoding --- p.36 / Chapter 3.4.3 --- Repair Algorithms --- p.36 / Chapter 4 --- Dynamic Programming --- p.37 / Chapter 4.1 --- Introduction --- p.37 / Chapter 4.1.1 --- Decomposition --- p.38 / Chapter 4.2 --- Mathematical Formulation --- p.43 / Chapter 4.3 --- A Simple Example --- p.44 / Chapter 5 --- DP Crossover Operator (DPX) --- p.50 / Chapter 5.1 --- Why DP is chosen as the crossover operator --- p.50 / Chapter 5.2 --- What is DPX? --- p.51 / Chapter 5.2.1 --- A Simple Example --- p.51 / Chapter 5.2.2 --- Mechanism of DPX --- p.58 / Chapter 5.3 --- Properties of DPX --- p.63 / Chapter 5.3.1 --- Number of parents --- p.63 / Chapter 5.3.2 --- Crossover Sites --- p.65 / Chapter 5.3.3 --- Perservation of Feasibility --- p.66 / Chapter 6 --- Implementation --- p.69 / Chapter 6.1 --- GA Construction --- p.69 / Chapter 6.1.1 --- Coding --- p.69 / Chapter 6.1.2 --- Fitness Function --- p.70 / Chapter 6.1.3 --- Selection --- p.72 / Chapter 6.1.4 --- Crossover --- p.76 / Chapter 6.1.5 --- Mutation Rate --- p.76 / Chapter 6.1.6 --- Replacement --- p.77 / Chapter 6.2 --- Algorithm --- p.77 / Chapter 6.3 --- Optimal Power Generations for Fuel Costs --- p.80 / Chapter 6.3.1 --- The Simple Scheduling Method --- p.80 / Chapter 7 --- Experimental Results --- p.84 / Chapter 7.1 --- Experiment Details --- p.84 / Chapter 7.2 --- Problem A --- p.86 / Chapter 7.2.1 --- Data Results --- p.86 / Chapter 7.2.2 --- Graphical Results --- p.90 / Chapter 7.2.3 --- Analysis --- p.90 / Chapter 7.3 --- Problem B --- p.92 / Chapter 7.3.1 --- Data Results --- p.92 / Chapter 7.3.2 --- Graphical Results --- p.94 / Chapter 7.3.3 --- Analysis --- p.96 / Chapter 8 --- Conclusion and Future Work --- p.97 / Chapter 8.1 --- Conclusion --- p.97 / Chapter 8.2 --- Future Work --- p.98 / Chapter A --- Problems Parameters --- p.100 / Chapter A.1 --- Problem A --- p.100 / Chapter A.1.1 --- Parameters of Generating Units --- p.101 / Chapter A.2 --- Problem B --- p.103 / Chapter A.2. --- 1 Parameters of Generating Units --- p.104

Graph Isomorphism is one of the very few classical problems in NP of unsettled complexity status. The families of highly regular structures, for example Steiner 2-designs, strongly regular graphs and primitive coherent configurations, have been perceived as difficult cases for graph isomorphism. These highly regular structures arise naturally as obstacles for both the classical group theory and combinatorial approaches for the graph isomorphism problem. In this thesis we investigate the isomorphism problem of highly regular structures. We present new results to understand the combinatorial structure of highly regular structures, and propose some new algorithms to compute the canonical forms (and thus isomorphism testing) of highly regular structures based on the structural theorems. We also give an algorithm solving the isomorphism problem of two unknown graphs in the property testing setting. Our new algorithm has sample complexity matching the information theoretical lower bound up to some multiplicative subpolynomial factor.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-09-12T20:25:13Z No. of bitstreams: 1 PabloImperio.pdf: 1334880 bytes, checksum: 04f05e0c6089e9173666f70f591bba35 (MD5) / Made available in DSpace on 2017-09-12T20:25:13Z (GMT). No. of bitstreams: 1 PabloImperio.pdf: 1334880 bytes, checksum: 04f05e0c6089e9173666f70f591bba35 (MD5) Previous issue date: 2017-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work uses GeoGebra software (version 5.0.328.0-3D) as a tool to solve counting problems. Some elements of combinatorial analysis and insertion of objects in the software are presented, motivating its use in solving counting problems and including practical classroom applications in classroom. In order to obtain data about problem solving, classes were taught with and without the use of GeoGebra in two different classes and also the results were compared. It was verified that the use of the software helps to understand the concepts, since it works the dynamicity, allowing the student to modify the results and draw conclusions. / Este trabalho utiliza o software GeoGebra (versão 5.0.328.0-3D) como ferramenta na resolução de problemas de contagem. São apresentados alguns elementos de análise combinatória e inserção de objetos no software, motivando sua utilização na resolução de problemas de contagem e incluindo aplicações prática em sala de aula. Para obtenção de dados sobre a resolução de problemas, foram ministradas aulas com e sem o uso do GeoGebra em duas turmas distintas e comparados os resultados. Verificou-se que a utilização do aplicativo ajuda a compreender os conceitos, visto que trabalha a dinamicidade, possibilitando ao aluno modificar os resultados e tirar conclusões.

Submitted by Daniella Santos (daniella.santos@ufma.br) on 2017-11-23T11:57:53Z No. of bitstreams: 1 MAKEBENIGNO.pdf: 503602 bytes, checksum: 341b1fad0eebf1c68b8ab490776354c0 (MD5) / Made available in DSpace on 2017-11-23T11:57:53Z (GMT). No. of bitstreams: 1 MAKEBENIGNO.pdf: 503602 bytes, checksum: 341b1fad0eebf1c68b8ab490776354c0 (MD5) Previous issue date: 2017-03-06 / This work will present the importance of combinatorial analysis, both in middle school and elementary school. We will list several exemples of problems involving combinatorial analysis and we will see how the subject and matter is charged in Enem and mathematics Olympics. Basic, we present some of the main difficulties of some students and combinatoy, shows how the teacher can teach through the solution of the problems, basic that we will present the situation of mathematical education in Brazil and its packaging of basic education. / Este trabalho tem como objetivo apresentar a importância da análise combinatória, tanto no Ensino Médio como no Ensino Fundamental. Listaremos vários exemplos de problemas envolvendo análise combinatória e veremos como esse assunto é cobrado no ENEM e em olimpíadas de matemática. Além disso, apresentamos algumas das principais dificuldades dos alunos em combinatória, e como o professor poderá ensinar por meio da resolução de problemas, além disso apresentaremos a situação da educação matemática no Brasil e seus impactos no ensino básico.

Segmented polyurethaneureas (SPUU) are thermoplastic elastomers with excellent elastic properties, high abrasion resistance and tear strength, making them very useful in numerous industrial applications ranging from microelectronics (slurry pad) to biomedical (artificial heart vessels) applications. The elastic and mechanical properties of these materials are strongly influenced by their two phase morphology. The factors that influence phase separation include difference in polarity between the hard and soft phases, composition and temperature. In general good phase separation results in materials with superior mechanical and elastic properties. Due to the immense potential applications of SPUU elastomers, there is a need for materials with higher strength. However, higher strength is not desired at the detriment of elasticity. If fact, stronger materials with enhanced elasticity are desired. In this thesis, high-strength SPUU elastomers were synthesized by incorporating reactive Laponite particles with surface-active free amine. The synthesis of pure SPUU is very complex, and addition of a reactive silicate further increases the complexity. To remedy this challenge, combinatorial methods and high-throughput screening techniques were used to optimize the diamine concentration and cure temperature. It was determined that pure SPUU elastomers prepared at a diamine stoichiometry of 85 100 mole %, and cured at 90 95 oC produced materials with higher strength and elongation at break. SPUU nanocomposites were prepared by maintaining the overall diamine stoichiometry at 95 mole %, and cured at 90 oC. Uniaxial tensile strength was optimized at a particle weight fraction of 1 wt. %, with a nearly 200 % increase in tensile strength and a 40 % increase in elongation at break, compared to pristine SPUU.

Electric propulsion has recently become a viable technology for spacecraft, enabling shorter flight times, fewer required planetary gravity assists, larger payloads, and/or smaller launch vehicles. With the maturation of this technology, however, comes a new set of challenges in the area of trajectory design. Because low-thrust trajectory optimization has historically required long run-times and significant user-manipulation, mission design has relied on expert-based knowledge for selecting departure and arrival dates, times of flight, and/or target bodies and gravitational swing-bys. These choices are generally based on known configurations that have worked well in previous analyses or simply on trial and error. At the conceptual design level, however, the ability to explore the full extent of the design space is imperative to locating the best solutions in terms of mass and/or flight times. Beginning in 2005, the Global Trajectory Optimization Competition posed a series of difficult mission design problems, all requiring low-thrust propulsion and visiting one or more asteroids. These problems all had large ranges on the continuous variables - launch date, time of flight, and asteroid stay times (when applicable) - as well as being characterized by millions or even billions of possible asteroid sequences. Even with recent advances in low-thrust trajectory optimization, full enumeration of these problems was not possible within the stringent time limits of the competition. This investigation develops a systematic methodology for determining a broad suite of good solutions to the combinatorial, low-thrust, asteroid tour problem. The target application is for conceptual design, where broad exploration of the design space is critical, with the goal being to rapidly identify a reasonable number of promising solutions for future analysis. The proposed methodology has two steps. The first step applies a three-level heuristic sequence developed from the physics of the problem, which allows for efficient pruning of the design space. The second phase applies a global optimization scheme to locate a broad suite of good solutions to the reduced problem. The global optimization scheme developed combines a novel branch-and-bound algorithm with a genetic algorithm and an industry-standard low-thrust trajectory optimization program to solve for the following design variables: asteroid sequence, launch date, times of flight, and asteroid stay times. The methodology is developed based on a small sample problem, which is enumerated and solved so that all possible discretized solutions are known. The methodology is then validated by applying it to a larger intermediate sample problem, which also has a known solution. Next, the methodology is applied to several larger combinatorial asteroid rendezvous problems, using previously identified good solutions as validation benchmarks. These problems include the 2nd and 3rd Global Trajectory Optimization Competition problems. The methodology is shown to be capable of achieving a reduction in the number of asteroid sequences of 6-7 orders of magnitude, in terms of the number of sequences that require low-thrust optimization as compared to the number of sequences in the original problem. More than 70% of the previously known good solutions are identified, along with several new solutions that were not previously reported by any of the competitors. Overall, the methodology developed in this investigation provides an organized search technique for the low-thrust mission design of asteroid rendezvous problems.

The implementation of two different algorithms for generating compact codes of some size N are presented. An analysis of both algorithms is given. in an attempt to prove whether or not the algorithms run in constant amortized time. Meta-Fibonacci sequences are also investigated in this paper. Using a particular numbering on k-ary trees, we find that a group of meta-Fibonacci sequences count the number of nodes at the bottom level of these k-ary trees. These meta-Fibonacci sequences are also related to compact codes. Finally, generating functions are proved for the meta-Fibonacci sequences discussed.

This thesis contains several results concerning the combinatorics of partially ordered sets (posets) which are either of enumerative or extremal nature. <br><br> The first concerns conjectures of Friedland and Kahn, which state that the (extremal) d-regular graph on N vertices containing both the maximal number of matchings and independent sets of a fixed size is the graph consisting of disjoint union of appropriate number of complete bipartite d-regular graphs on 2d vertices. We show that the conjectures are true in an asymptotic sense, using entropy techniques. <br><br> As a second result, we give tight bounds on the size of the largest Boolean family which contains no three distinct subsets forming an "induced V" (i.e. if A,B,C are all in our family, if C is contained in the intersection of A B, A must be a subset of B). This result, though similar to known results, gives the first bound on a family defined by an induced property. <br><br> We pose both Dedekind-type questions concerning the number of antichains and a Stanley-type question concerning the number of linear extensions in generalized Boolean lattices; namely, products of chain posets and the poset of partially defined functions. We provide asymptotically tight bounds for these problems. <br><br> A Boolean function, f, is called cherry-free if for all triples x,y,z where z covers both x and y, f(z)=1 whenever both f(x)=1 and f(y)=1. We give bounds on the number of cherry-free functions on bipartite regular posets, with stronger results for bipartite posets under an additional co-degree hypotheses. We discuss applications of these functions to Boolean Horn functions and similar structures in ranked regular posets.

Humboldt-Univ., Habil.-Schr.--Berlin. / Literaturverz. S. [100] - 109.