In this paper we explore coloring theorems for the reals, its quotients, cardinals, and their combinations. This work is done under the scope of the axiom of determinacy. We also explore generalizations of Mycielski's theorem and show how these can be used to establish coloring theorems. To finish, we discuss the strange realm of long unions.

Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks whether a Banach space contains lp provided that every spreading model of a normalized block basic sequence of the basis is isometrically equivalent to lp. Next, using the Hindman-Milliken-Taylor theorem, we prove a new stabilization theorem for spreading models which produces a basic sequence all of whose normalized constant coefficient block basic sequences are good. When the resulting basic sequence is semi-normalized, all the spreading models generated by the above good sequences must be uniformly equivalent to lp or c0. Finally, we investigate the assumption that every normalized block tree on a Banach space has a good branch. This turns out to be a very strong assumption and is equivalent to the space being 1-asymptotic lp. We also show that the stronger assumption that every block basic sequence is good is equivalent to the space being stabilized 1-asymptotic lp.

This research presents a systematic and iterative procedure, as well as theoretical study, on expository sermon construction. The basic approach to sermon design involves the treatment of this subject matter as a design problem, utilizing advanced methodology in engineering design. This includes the modeling technique, the flow-chart method, and the optimization theory. In addition, we use heuristics as the search engine for seeking intelligent and efficient optimum design solutions. The heuristics can best be compared to the "artificial intelligence" or the "wisdom bank," involving six sources of wisdom; these include: talents, gifts, creativity, knowledge, experience and spiritual insights. The results represented in this thesis are believed to have demonstrated original findings in the following areas. First, the subject matter is found to be of a design nature, sharing the common characteristics of a general class of the design discipline, namely, having a 3-stage iterative procedure of the ABA' model. Secondly, a mathematical as well as physical model of the sermon design problem is developed in this study, using both homiletic and hermeneutic principles. The human body is used as the physical model, making it possible for simple visualization of the sermon structure and for performance evaluation. A mathematical model is found to be the "Heuristic Combinatorial Optimization Problem" and consists of eight design variables. Although it is not yet possible to develop a computer-aided protocol to seek solutions, an alternative approach called the "Web-Chart Method" can potentially be adaptable to an interactive computer system in the future. It serves as a two-dimensional "design chart" on paper, in which iterative procedures can be performed manually. The advantage is that the designer can direct his or her heuristic search for optimum solutions with the help of a number of design tools, including the "Insight-Recording Sheet" and the "Analogical Analysis Chart." With these tools, the designer has, at his or her disposal, the ability to search for solutions in sermon design, while still maintaining a global view with all the design variables controlled for. In this research, the principles of combinatorial heuristics applicable to the field of optimum design of expository sermons have been described. They are based on heuristic combinatorial optimization methods in the engineering design field with refinements geared to the homiletic as well as hermeneutic nature of the problem. The approaches represented here would allow a designer to utilize resources that are not otherwise available and/or are not easily manageable. With these research results, one would be able to design sermons innovatively and optimally in a systematic and heuristic-guided manner. Further extension of this work would lead to a new field of research and development in the computer-aided design of expository sermons. Key words: preaching; homiletics; expository preaching; design for preaching; sermon construction; computer-aided sermon design; sermon design optimization; heuristic sermon design; heuristic sermon optimization; heuristic combinatorial optimization. / Practical Theology / D. Th.(Practical Theology)

Made available in DSpace on 2016-04-27T16:57:13Z (GMT). No. of bitstreams: 1 Carlos Eduardo de Campos.pdf: 1683164 bytes, checksum: 1dd97a1301e188ce53dd5d495c3b2f0e (MD5) Previous issue date: 2011-11-09 / Secretaria da Educação do Estado de São Paulo / This dissertation is focused on the teaching and learning of the Combinatorial Analysis, specifically mentioning, Counting Problems. The report is about a documentary research, as a result of the analysis of the coursebook, thus the methodological procedures are the most appropriate to this kind of investigation. The aim of this research is to evaluate the types of Counting Problems, which are included in the student s book, Secondary school second grade third term from the Department of Education of the state of São Paulo, in the view of the combinatorial research, taking into account that is the presupposition of the Curriculum of the state of São Paulo, the resolution of the problems in a teaching approach for the combinatorial concepts. The studied problems are the simple ones, in other words, those which could be solved by using only one combinatorial operation. The yardsticks of the content analysis accomplished in the book are the task variables used by Batanero, Navarro-Pelayo, implicit combinatorial model, combinatorial operation, the nature of the elements to be combined and the values of the parameter m and n. They are supported by the theory of the conceptual fields developed by Vergnaud, in which those concepts couldn t be learnt with the approach of a single type of problem. Our investigation led us to the conclusion that, even working with an important list of issues, many of them involved similar situations. It is because not all the considered variables were found in this list / Esta dissertação tem por foco o ensino e a aprendizagem da Análise Combinatória ou, mais especificamente, dos Problemas de Contagem. Trata-se do relatório minucioso de pesquisa documental de análise de material didático e, sobretudo, os procedimentos metodológicos são os adequados a essa modalidade de investigação. O objetivo da investigação é avaliar os tipos de Problemas de Contagem, que figuram no Caderno do Aluno do 3º bimestre do 2º ano do Ensino Médio, da Rede Estadual Paulista de Ensino, com vistas à formação do raciocínio combinatório, levando em conta o pressuposto da Proposta Curricular em questão que entende a resolução de problemas como uma abordagem de ensino eficaz para os conceitos combinatórios. Os problemas estudados são entendidos e classificados como simples, ou seja, aqueles que podem ser resolvidos usando somente uma operação combinatória. Os balizadores da análise de conteúdo realizada no Caderno são as variáveis de tarefa usadas por Batanero e Navarro-Pelayo: modelo combinatório implícito, operação combinatória, natureza dos elementos que se combinam e valores dados aos parâmetros m e n. Os mesmos são respaldados na Teoria dos Campos Conceituais de Verganaud, para a qual conceitos não podem ser apreendidos com a abordagem de um único tipo de problema. Nossa investigação nos levou a constatar que, mesmo com um elenco importante de problemas, muitos deles envolviam situações semelhantes. Isso se deu porque nem todas as variáveis consideradas foram encontradas nesse rol

O presente trabalho propõe resolver o clássico problema combinatorial conhecido como problema do caixeiro viajante. Foi usado no sistema de otimização de busca do menor caminho uma rede neural recorrente. A topologia de estrutura de ligação das realimentações da rede adotada aqui é conhecida por rede recorrente de Wang. Como regra de treinamento de seus pesos sinápticos foi adotada a técnica de perturbação simultânea com aproximação estocástica. Foi elaborado ainda uma minuciosa revisão bibliográfica sobre todos os temas abordados com detalhes sobre a otimização multivariável com perturbação simultânea. Comparar-se-á também os resultados obtidos aqui com outras diferentes técnicas aplicadas no problema do caixeiro viajante visando propósitos de validação. / This work proposes to solve the classic combinatorial optimization problem known as traveling salesman problem. A recurrent neural network was used in the system of optimization to search the shorter path. The structural topology linking the feedbacks of the network adopted here is known by Wang recurrent network. As learning rule to find the appropriate values of the weights was used the simultaneous perturbation with stochastic approximation. A detailed bibliographical revision on multivariable optimization with simultaneous perturbation is also described. Comparative results with other different techniques applied to the traveling salesman are still presented for validation purposes.

Thin-film solar cell research is central to the electricity production of the near future. Photovoltaic technologies based on silicon have a significant portion of the global market and installed capacity. Thin-film solar cells are port of the emerging photovoltaic technologies that are challenging silicon for a part of the electricity production based on solar power. These thin-film technologies, such as copper indium gallium selenide (CIGS) and cadmium telluride (CdTe), are lower cost and require less energy to produce, but also require rare materials. An alternative to these technologies are thin-film solar cells based on more abundant materials. To develop these new materials at Uppsala University, combinatorial synthesis is used. This method produces a significant amount of data across different measurement methods. The data needs to be analysed and combined to gather information about the characteristics of the materials being developed. To facilitate the analysis and combination of data, a database tool was created in MATLAB. The result is a program that allows its User to combine energy-dispersive X-ray spectroscopy (EDS), Raman spectroscopy and Photoluminescence spectroscopy measurements done on solar cell absorber layers. Absorber layers are the section of solar cells where sun lighet is absorbed, and electron-hole pairs are created. The program provides multiple figures and graphs combining the different data collected, enabling the User to draw conclusions about the characteristics of the sample and its suitability as an absorber layer. The combinatorial synthesis database tool created could be user for combinatorial synthesis analysis of other material samples that are not necessarily absorber layers for thin-film solar cells. This report describes both the development of the tool and the code itself.

O presente trabalho propõe resolver o clássico problema combinatorial conhecido como problema do caixeiro viajante. Foi usado no sistema de otimização de busca do menor caminho uma rede neural recorrente. A topologia de estrutura de ligação das realimentações da rede adotada aqui é conhecida por rede recorrente de Wang. Como regra de treinamento de seus pesos sinápticos foi adotada a técnica de perturbação simultânea com aproximação estocástica. Foi elaborado ainda uma minuciosa revisão bibliográfica sobre todos os temas abordados com detalhes sobre a otimização multivariável com perturbação simultânea. Comparar-se-á também os resultados obtidos aqui com outras diferentes técnicas aplicadas no problema do caixeiro viajante visando propósitos de validação. / This work proposes to solve the classic combinatorial optimization problem known as traveling salesman problem. A recurrent neural network was used in the system of optimization to search the shorter path. The structural topology linking the feedbacks of the network adopted here is known by Wang recurrent network. As learning rule to find the appropriate values of the weights was used the simultaneous perturbation with stochastic approximation. A detailed bibliographical revision on multivariable optimization with simultaneous perturbation is also described. Comparative results with other different techniques applied to the traveling salesman are still presented for validation purposes.

This thesis is divided into six parts, all centered around the development of dynamic (i.e., reversibly interacting) systems of molecules and their applications in dynamic combinatorial chemistry (DCC) and organic synthesis. Part one offers a general introduction, as well as a more detailed description of DCC, being the central concept of this thesis. Part two explores the potential of the nitroaldol reaction as a tool for constructing dynamic systems, employing benzaldehyde derivatives and nitroalkanes. This reaction is then applied in part three where a dynamic nitroaldol system is resolved by lipase-catalyzed transacylation, selecting two out of 16 components. In part four, reaction and crystallization driven DCC protocols are developed and demonstrated. The discovery of unexpected crystalline properties of certain pyridine β-nitroalcohols is used to resolve a dynamic system and further expanded into asynthetic procedure. Furthermore, a previously unexplored tandem nitroaldol-iminolactone rearrangement reaction between 2-cyanobenzaldehyde and primarynitroalkanes is used for the resolution of dynamic systems. It is also coupled with diastereoselective crystallization to demonstrate the possibility to combine several selection processes. The mechanism of this reaction is investigated and a synthetic protocol is developed for asymmetric synthesis of 3-substituted isoindolinones. Part five continues the exploration of tandem reactions by combining dynamic hemithioacetal or cyanohydrin formation with intramolecular cyclization to synthesize a wide range of 3-functionalized phthalides. Finally, part six deals with the construction of a laboratory experiment to facilitate the introduction of DCC in undergraduate chemistry education. The experiment is based on previous work in our group and features an acetylcholinesterase-catalyzed resolution of a dynamic transthioacylation system. / QC 20100628

Combinatorial techniques, which overcome limitations of actual models of material research permitting to effectively address this large amount of variables, are utilized in this work to prepare combinatorial libraries of the blend of the biodegradable polymers Poly(e-caprolactone) and Poly(lactic acid). These libraries present continuous composition and temperature gradients in an orthogonal fashion that permit to obtain multiple surface morphologies with controllable microstructures due to the blends low critical solution phase behavior (LCST). The goal of this study is to investigate the effect of surface morphology (surface chemical patterning and surface topography) on cell behavior. The varied surface topography of the libraries is used as a valuable tool that permits to assay the interaction between MC3T3-E1 cells and hundreds of different values of critical surface properties, namely, surface roughness and microstructure size. The outcome of this tool is a rapid screening of the effect of surface topography on cell behavior that is orders of magnitude faster than the standard 1-sample for 1 measurement techniques. The results obtained show that cells are very sensitive to surface topography, and that the final effect of surface properties on cell function is intimately related with the stage of the cell developmental process. Meaning that, for example, areas with optimal characteristics to elicit enhancement of cell attachment is not necessarily the same that promotes cell proliferation. This study imparts an improved understanding of an often neglected factor in biomaterials performance: surface morphology (particularly surface topography). The results provide a new insight into the importance of taking into consideration both chemistry and physical surface features for superior biomaterial design.

This research presents a systematic and iterative procedure, as well as theoretical study, on expository sermon construction. The basic approach to sermon design involves the treatment of this subject matter as a design problem, utilizing advanced methodology in engineering design. This includes the modeling technique, the flow-chart method, and the optimization theory. In addition, we use heuristics as the search engine for seeking intelligent and efficient optimum design solutions. The heuristics can best be compared to the "artificial intelligence" or the "wisdom bank," involving six sources of wisdom; these include: talents, gifts, creativity, knowledge, experience and spiritual insights. The results represented in this thesis are believed to have demonstrated original findings in the following areas. First, the subject matter is found to be of a design nature, sharing the common characteristics of a general class of the design discipline, namely, having a 3-stage iterative procedure of the ABA' model. Secondly, a mathematical as well as physical model of the sermon design problem is developed in this study, using both homiletic and hermeneutic principles. The human body is used as the physical model, making it possible for simple visualization of the sermon structure and for performance evaluation. A mathematical model is found to be the "Heuristic Combinatorial Optimization Problem" and consists of eight design variables. Although it is not yet possible to develop a computer-aided protocol to seek solutions, an alternative approach called the "Web-Chart Method" can potentially be adaptable to an interactive computer system in the future. It serves as a two-dimensional "design chart" on paper, in which iterative procedures can be performed manually. The advantage is that the designer can direct his or her heuristic search for optimum solutions with the help of a number of design tools, including the "Insight-Recording Sheet" and the "Analogical Analysis Chart." With these tools, the designer has, at his or her disposal, the ability to search for solutions in sermon design, while still maintaining a global view with all the design variables controlled for. In this research, the principles of combinatorial heuristics applicable to the field of optimum design of expository sermons have been described. They are based on heuristic combinatorial optimization methods in the engineering design field with refinements geared to the homiletic as well as hermeneutic nature of the problem. The approaches represented here would allow a designer to utilize resources that are not otherwise available and/or are not easily manageable. With these research results, one would be able to design sermons innovatively and optimally in a systematic and heuristic-guided manner. Further extension of this work would lead to a new field of research and development in the computer-aided design of expository sermons. Key words: preaching; homiletics; expository preaching; design for preaching; sermon construction; computer-aided sermon design; sermon design optimization; heuristic sermon design; heuristic sermon optimization; heuristic combinatorial optimization. / Philosophy, Practical and Systematic Theology / D. Th.(Practical Theology)