In a context of heightened requirements for safety-critical embedded systems and ever-increasing costs of verification and validation, this research proposes to advance the state of formal analysis for control software. Formal methods are a field of computer science that uses mathematical techniques and formalisms to rigorously analyze the behavior of programs. This research develops a framework and tools to express and prove high level properties of control law implementations. One goal is to bridge the gap between control theory and computer science. An annotation language is extended with symbols and axioms to describe control-related concepts at the code level. Libraries of theorems, along with their proofs, are developed to enable an interactive proof assistant to verify control-related properties. Through integration in a prototype tool, the process of verification is made automatic, and applied to several example systems.In a context of heightened requirements for safety-critical embedded systems and ever-increasing costs of verification and validation, this research proposes to advance the state of formal analysis for control software. Formal methods are a field of computer science that uses mathematical techniques and formalisms to rigorously analyze the behavior of programs. This research develops a framework and tools to express and prove high level properties of control law implementations. One goal is to bridge the gap between control theory and computer science. An annotation language is extended with symbols and axioms to describe control-related concepts at the code level. Libraries of theorems, along with their proofs, are developed to enable an interactive proof assistant to verify control-related properties. Through integration in a prototype tool, the process of verification is made automatic, and applied to several example systems.

Made available in DSpace on 2014-06-11T19:27:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-02-16Bitstream added on 2014-06-13T19:34:53Z : No. of bitstreams: 1 rafaeli_fr_me_sjrp.pdf: 475737 bytes, checksum: dae8459d8e40a6b31ed9a1e30e8ab905 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho estudamos o Teorema de Sturm para zeros de soluções de equações diferenciais lineares de segunda ordem e suas extensões. Estes resultados clássicos são aplicados para análise de monotonicidade e convexidade de zeros de polinômios ortogonais clássicos. / We study Sturm's theorem on zeros of solution of linear second-order differential equations as well as its extension. These classical results are applied to analyze monotonicity and convexity of zeros of classical orthogonal polynomials.

The notion of fulfilment of a formula by a sequence of numbers, an approximation of truth due to Kripke, is presented and subsequently formalised in the weak arithmetic theory IΣ1, in some detail. After a number of technical results connecting the formalised notion to the meta-theoretical one a version of Gödel’s Incompleteness Theorem, that no consistent, recursively axiomatisable, Σ2-sound extension T of Peano arithmetic is complete, is shown by construction of a true Π2-sentence and a model of T where it is false, yielding its independence from T. These results are then generalised to a more general notion of fulfilment, proving that IΣ1 has no complete, consistent, recursively axiomatisable, Σ2-sound extensions by a similar construction of an independent sentence. This generalisation comes at the cost of some naturality, however, and an explicit falsifying model will only be obtained under additional assumptions. The aim of the thesis is to reproduce in some detail the notions and results developed by Kripke and Quinsey and presented by Quinsey and Putnam. In particular no novel results are obtained.

O principal objetivo desta dissertação é obter um Teorema do Envelope que permita mecanismos não diferenciáveis, preferências arbitrárias e que possa ser aplicado em modelos com múltiplos agentes. Nós alcançamos isto ao expandir a análise de Milgrom e Segal (2002), generalizando seus resultados para espaços de tipos multidimensionais. Dessa forma, continuamos permitindo que a regra de escolha (mecanismo) seja descontínua. Para obter nosso resultado, é necessário o uso do Teorema do Máximo de Berge e, consequentemente, devemos impor compacidade no conjunto de escolha. Inicialmente esta hipótese pode parecer forte, porém argumentamos que em aplicações _e muito improvável termos um conjunto de escolha aberto ou, principalmente, não limitado. Nós também identificamos condições para que a função valor seja absolutamente contínua e mostramos que sua representação integral também é válida para espaços de tipos multidimensionais. Inicialmente propomos uma generalização direta do resultado de Milgrom e Segal (2002), utilizando a hipótese de continuidade absoluta da função de utilidade do agente. Entretanto, esta exigência não possui muito significado econômico e é considerada pouco elegante por parte da literatura. Neste sentido, incorporamos uma hipótese adicional de diferenciabilidade da utilidade em todo o domínio que gera a mesma representação integral e possui uma maior interpretação econômica. Nossos resultados são, em geral, aplicados a modelos com múltiplos agentes, em especial Economia do Setor Público (provisão de bens públicos e taxação ótima) e teoria dos leilões. / The main objective of this dissertation is to obtain an Envelope Theorem that allows non-di erentiable mechanisms, arbitrary preferences, and that can be applied to models with multiple agents. We achieve that by expanding the analysis of Milgrom and Segal (2002) and generalizing their results to multidimensional type spaces. Thus, we continue allowing that the choice rule (mechanism) is discontinuous. For our result, it is necessary to use the Berge's Maximum Theorem and therefore we must impose compactness in the choice set. Initially this assumption may seem strong, but we argue that in applications there is an open or unbounded choice set is very unlikely. We also identify conditions for the value function is absolutely continuous and show that its integral representation is also valid for multidimensional type spaces. Firstly we propose a direct generalization of the Milgrom and Segal (2002)'s result, using the assumption of absolute continuity of the agent's utility function. However, this requirement does not have much economic interpretation and it is considered not very elegant in the literature. In this sense, we incorporate an additional assumption of di erentiability of the utility in all range that generates the same integral representation and it possesses a greater economic interpretation. Our results are generally applied to models with multiple agents, in particular Public Economics (public goods supply and optimal taxation) and auction theory.

SILVA, Danniel Emanuel Bruno. O teorema de Pitágoras: abordagem no cotidiano da educação matemática e suas diversas demonstrações. 2014. 55 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Jessyca Silva (jessyca@mat.ufc.br) on 2017-08-21T19:55:33Z No. of bitstreams: 1 2014_dis_debsilva.pdf: 1316565 bytes, checksum: f9f30b38921af75056aba52ae1360c98 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia, Na folha de aprovação não deve constar as assinaturas dos membros da banca. Rocilda on 2017-08-22T13:51:25Z (GMT) / Submitted by Jessyca Silva (jessyca@mat.ufc.br) on 2017-08-23T14:35:03Z No. of bitstreams: 1 2014_dis_debsilva.pdf: 1008247 bytes, checksum: e15ea5795b214cc268197d35bb86e018 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, encontrei alguns pequenos erros na Dissertação de DANNIEL EMANUEL, e já envie uma cópia do email para ele avisando quais eram os erros. 1 – FOLHA DE ROSTO (centralize o nome Fortaleza e o ano da Dissertação) 2- FICHA CATALOGRÁFICA (o título da Dissertação que aparece na ficha catalográfica deve estar em letra minúscula, só a primeira letra deve ser maiúscula) 3- FOLHA DE APROVAÇÃO (está faltando seu nome na parte superior da folha de aprovação, acima do título da Dissertação) 4- EPÍGRAFE (retire o sublinha que aparece no nome EINSTEIN) 5- NUMERAÇÃO DAS PÁGINAS (coloque a numeração das páginas no CANTO SUPERIOR DIREITO) Atenciosamente, on 2017-08-23T15:50:40Z (GMT) / Submitted by Jessyca Silva (jessyca@mat.ufc.br) on 2017-08-23T19:33:51Z No. of bitstreams: 1 2014_dis_debsilva.pdf: 1008605 bytes, checksum: 92cfe1499970b1c1f1a10d77725f68b3 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-08-25T11:13:23Z (GMT) No. of bitstreams: 1 2014_dis_debsilva.pdf: 1008605 bytes, checksum: 92cfe1499970b1c1f1a10d77725f68b3 (MD5) / Made available in DSpace on 2017-08-25T11:13:24Z (GMT). No. of bitstreams: 1 2014_dis_debsilva.pdf: 1008605 bytes, checksum: 92cfe1499970b1c1f1a10d77725f68b3 (MD5) Previous issue date: 2014 / This work is about the Pythagorean Theorem and its various statements, addressing its importance and as has been shown in mathematics education. We will present some of the history of Pythagoras, as well as on his theorem, and well see a search on their importance, and how students receive this information. We'll talk a bit about how the textbooks, from elementary school to the middle, deal about it, and finally we will see some statements about this theorem seeking to open a lot more range of options for students and lovers of mathematics teachers. These statements are part of the collection assembled by Loomis, who managed to submit more than three hundred statements of the theorem in a publication of 1940. / Este trabalho trata sobre o Teorema de Pitágoras e suas diversas demonstrações, abordando sua importância e como vem sendo apresentado na educação matemática. Apresentaremos um pouco da história de Pitágoras, bem como, sobre o seu teorema, e veremos uma pesquisa sobre a sua importância, e como os alunos recebem essa informação. Falaremos um pouco, sobre como os livros didáticos, tanto do ensino fundamental como no médio, tratam sobre o assunto, e por fim veremos algumas demonstrações sobre este Teorema buscando abrir muito mais o leque de opções para os alunos e professores amantes da matemática. Essas demonstrações fazem parte do acervo reunido por Loomis, que conseguiu apresentar mais de trezentas demonstrações do teorema em uma publicação de 1940.

We study an additive perturbation theorem for substochastic semigroups which is known as Kato's Theorem. There are two previously-known generalisations of Kato's Theorem, namely for abstract state spaces and for KB-spaces. We prove a version of Kato's Theorem for a class of spaces which encompasses both, namely ordered Banach spaces with generating cone and monotone norm. We also study a property of the perturbed semigroup in Kato's Theorem known as honesty of the semigroup. We add a few results to the fairly extensive existing theory of honesty for Kato's Theorem for abstract state spaces. In light of our new generalisation of Kato's Theorem to ordered Banach spaces with monotone norm, we investigate generalising the theory of honesty to these spaces as well. The results for the general case are less complete as many of the results for the case of abstract state spaces depend on the additive norm structure of the space. We also consider some new applications of honesty theory in abstract state spaces. We begin by applying honesty theory to the study of the heat equation on graphs. We prove that honesty of the heat semigroup coincides with a concept known as stochastic completeness of the graph which has been studied independently of honesty. We then look at the application of honesty theory to quantum dynamical semigroups. We show that honesty is the natural generalisation of the concept of conservativity of quantum dynamical semigroups. Conservative quantum dynamical semigroups are known to have certain "nice" properties. We show that similar properties hold for honest semigroups using honesty theory results. Finally, we consider a form of boundary perturbations in the context of transport semigroups. There exists an analogous theory of honesty for this set-up. We formulate a general result from which honesty results of both Kato's Theorem and transport semigroups can be derived.

The main proponent of management of any animal species is habitat management. The ability of habitats to maintain species communities will depend on the variation in both habitat structure and composition. While spatial variation in habitat resources plays a critical role in determining the distribution of species, an equally important consideration that must be accounted for is temporal variation in the needs of the target species. Nutritional requirements, and thus the habitats used to fulfil those nutritional needs, will be different depending on if the individual is breeding, migrating, molting, enduring winter, or establishing a new range. For waterfowl, we currently assume that winter and migration are nutritionally stressful and are consequently the periods most limiting to populations. The theory of ideal free distribution assumes that animals distribute themselves according to the factor most limiting to their fitness. In the case of non-breeding waterfowl, this factor is believed to be food. We assume if habitats with abundant food resources are provided, waterfowl will make use of those habitats. Deviations from an ideal free distribution based on food become problematic for managers since these deviations will keep some areas from being exploited to their potential, while other areas may become over-exploited. Recent observations have made it clear that this assumption may need to be reconsidered for effective waterfowl management. In this dissertation I quantitatively examine the degree to which spring migrating waterfowl conform to, or deviate from, an ideal free distribution based on food. Since food availability was not expected to account for 100% of waterfowl distribution, I further investigated what other potential habitat components influence the distribution of spring migrating waterfowl. In the first chapter of this dissertation, I explicitly tested the influence of food availability on waterfowl distribution. A series of paired 0.42 ha (1 acre) plots were established in various habitat types. One plot in each pair was treated with corn to a density of 2000 kg/ha, while the remaining plot was used as a control. Background food availability was controlled for by taking core samples from each plot, and estimating the natural seed and invertebrate biomass. The abundance each species of waterfowl using the plots was recorded during morning and afternoon observation periods. Linear mixed models were used to assess how variations in food availability influenced distribution of waterfowl. Although the waterfowl community showed a significant preference for treatment plots, our ability to influence abundance was low. Food availability accounted for minimal variation in abundance of the waterfowl community as a whole or for each focal species. Since the results of the first chapter showed food availability to be a poor predictor of waterfowl distribution, in the second chapter I set out to determine other potential habitat variables could be responsible for driving waterfowl distribution during spring migration. After each observation period, a series of habitat structural measurements were made within each paired plot. Habitat measurements included water characteristics, vegetation structure, vegetation type, habitat type, and weather conditions. Linear mixed models and model selection were employed to determine which of the habitat characteristics showed the greatest ability to predict waterfowl abundance on study plots. Models containing precipitation and Wabash River flood stage predictor variables were the best performing, and were the best predictors of waterfowl abundance on study plots. The results from this chapter encouraged investigation into how environmental factors shape the formation of local duck communities are structured from regional pools. In the third chapter of this dissertation I investigate the relationship between local and regional waterfowl community structure and how this relationship is mediated through environmental filters which dictate what proportion of the regional species pool exists at local scales. To address this relationship, I tested three hypotheses: 1) resource availability drives species diversity at local scales; 2) similarity between local and regional habitats will result in a similar species community occurring at both scales, and; 3) increased heterogeneity of local habitat structure will result in more diverse waterfowl communities at local scales. I used Mahalanobis distance and cumulative standard deviation of habitat variables in conjunction with mixed models and model selection to compare hypotheses and determine which had the greatest potential for mediating local community structure from regional pools. Increasing resource abundance appeared to have the greatest influence over local duck diversity, but the model indicated that although species diversity could be increased by increasing food abundance, diversity at local scales would become saturated before becoming representative of the regional community.

vii, 41 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We generalize a theorem of Zhu relating the trace of certain vertex algebra representations and modular invariants to the arena of vertex super algebras. The theorem explains why the space of simple characters for the Neveu-Schwarz minimal models NS( p, q ) is modular invariant. It also expresses negative products in terms of positive products, which are easier to compute. As a consequence of the main theorem, the subleading coefficient of the singular vectors of NS( p, q ) is determined for p and q odd. An interesting family of q -series identities is established. These consequences established here generalize results of Milas in this field. / Adviser: Arkady Vaintrob

O principal objetivo desta dissertação é obter um Teorema do Envelope que permita mecanismos não diferenciáveis, preferências arbitrárias e que possa ser aplicado em modelos com múltiplos agentes. Nós alcançamos isto ao expandir a análise de Milgrom e Segal (2002), generalizando seus resultados para espaços de tipos multidimensionais. Dessa forma, continuamos permitindo que a regra de escolha (mecanismo) seja descontínua. Para obter nosso resultado, é necessário o uso do Teorema do Máximo de Berge e, consequentemente, devemos impor compacidade no conjunto de escolha. Inicialmente esta hipótese pode parecer forte, porém argumentamos que em aplicações _e muito improvável termos um conjunto de escolha aberto ou, principalmente, não limitado. Nós também identificamos condições para que a função valor seja absolutamente contínua e mostramos que sua representação integral também é válida para espaços de tipos multidimensionais. Inicialmente propomos uma generalização direta do resultado de Milgrom e Segal (2002), utilizando a hipótese de continuidade absoluta da função de utilidade do agente. Entretanto, esta exigência não possui muito significado econômico e é considerada pouco elegante por parte da literatura. Neste sentido, incorporamos uma hipótese adicional de diferenciabilidade da utilidade em todo o domínio que gera a mesma representação integral e possui uma maior interpretação econômica. Nossos resultados são, em geral, aplicados a modelos com múltiplos agentes, em especial Economia do Setor Público (provisão de bens públicos e taxação ótima) e teoria dos leilões. / The main objective of this dissertation is to obtain an Envelope Theorem that allows non-di erentiable mechanisms, arbitrary preferences, and that can be applied to models with multiple agents. We achieve that by expanding the analysis of Milgrom and Segal (2002) and generalizing their results to multidimensional type spaces. Thus, we continue allowing that the choice rule (mechanism) is discontinuous. For our result, it is necessary to use the Berge's Maximum Theorem and therefore we must impose compactness in the choice set. Initially this assumption may seem strong, but we argue that in applications there is an open or unbounded choice set is very unlikely. We also identify conditions for the value function is absolutely continuous and show that its integral representation is also valid for multidimensional type spaces. Firstly we propose a direct generalization of the Milgrom and Segal (2002)'s result, using the assumption of absolute continuity of the agent's utility function. However, this requirement does not have much economic interpretation and it is considered not very elegant in the literature. In this sense, we incorporate an additional assumption of di erentiability of the utility in all range that generates the same integral representation and it possesses a greater economic interpretation. Our results are generally applied to models with multiple agents, in particular Public Economics (public goods supply and optimal taxation) and auction theory.

abstract: Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection. Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem. / Dissertation/Thesis / Doctoral Dissertation Statistics 2018