Orientador: Maria Sueli Marconi Roversi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T02:57:42Z (GMT). No. of bitstreams: 1 Piccoli_Bibiana_M.pdf: 1524742 bytes, checksum: 4328a3e766798f219a0267cdf6e892b7 (MD5) Previous issue date: 2005 / Resumo: Estudamos um tipo especial de função denominada função ponto a conjunto, que associa a cada elemento de um espaço métrico um único subconjunto não vazio de outro espaço métrico. A noção de continuidade das funções usuais caracterizada por propriedades equivalentes, enun-ciadas em termos de vizinhanças ou em termos de seqüências, deram origem a versões corres-pondentes para as funções ponto a conjunto. As propriedades adaptadas, não mais equivalentes, são conhecidas como semicontinuidade superior e semicontinuidade inferior, respectivamente. Uma condição do tipo Lipschitz e um tipo de continuidade propriamente, obtido munindo-se o contradomínio da métrica de Hausdorff, foram relacionados à semicontinuidade. Algumas propriedades algébricas ou topológicas dos conjuntos imagem foram essenciais para os resulta-dos obtidos. Abordamos adaptações de alguns resultados clássicos da análise funcional como os teoremas da limitação uniforme, da aplicação aberta e do gráfico fechado para as funções ponto a conjunto caracterizadas como processos convexos, que são os análogos dos operadores lineares. Estabelecemos também uma versão do teorema de Schauder sobre pontos fixos para funções ponto a conjunto e também para as do tipo contração / Abstract: We study a mapping called a set-valued map which associates with each point of a metric space a non empty subset of another metric space. In the case of single-valued maps, contin-uous functions are characterized by two equivalent properties: one in terms of neighborhood and other in terms of sequences. These two properties can be adapted to the case of set-valued maps, are no longer equivalent and are called upper semi continuity and lower semi continuity, respectively. We adapt to the set-valued case the concept of Lipschitz applications and also a type of continuity when the range is enjoyed with the Hausdorff metric. We related them with the conditions of semi continuity. Some of the results depends on algebraic or topological prop-erties of the images. We adapt to closed convex process the principIe of uniform boundedness, the Banach open mapping and closed graph theorems. The closed convex processes are the set-valued analogues of continuous linear operators. We also establish two fixed point result for set-valued maps: the first generalizes the Schauder fixed point theorem and the second considers that of contraction type / Mestrado / Matematica / Mestre em Matemática

Cette recherche concerne l’étude de l’efficacité d’outils liés à l’analyse fonctionnelle. Le contexte est celui d’enseignements et d’apprentissages qui visent la compréhension de systèmes techniques en éducation technologique au collège. L’utilisation de ces outils issus de l’industrie dans le système éducatif pose des problèmes d’adaptation. La place de l’analyse fonctionnelle, comme langage technique, est analysée au travers de la genèse instrumentale de l’artefact, de l’activité des élèves et de la transposition des savoirs. La problématique de l’efficacité des outils se pose chez les élèves pour comprendre la globalité d’un système technique et, chez les enseignants pour structurer l’apprentissage. La méthodologie a été menée de manière qualitative et quantitative auprès de ces acteurs. Deux expérimentations ont eu lieu, une première avec les enseignants, basée sur une enquête avec un questionnaire et des entretiens. Une seconde, avec les élèves, s’appuyait sur un test d’entrée puis différents exercices écrits et une manipulation opératoire avec une fabrication via une imprimante 3D. Les résultats d’un groupe initié à l’analyse fonctionnelle sont comparés à ceux d’un groupe non initié. Les analyses des données recueillies abordent la façon dont les compétences et les connaissances qui permettent une approche systémique en éducation technologique sont mises en œuvre. Les principaux résultats indiquent que si les enseignants s’emparent de l’analyse fonctionnelle, la maitrise n’est pas totale. Son enseignement profite plus particulièrement aux élèves ayant des difficultés scolaires. Ces éléments sont explicités, approfondis et mis en perspective dans cette thèse. / This doctoral research concerns the study of the effectiveness of some tools related to the functional analysis. The context is the teaching and learning process of technical systems in technological education in French comprehensive schools. The use of these tools coming from the industry in the educational system poses problems of adaptations. The place of functional analysis as a technical language is analyzed through the instrumental genesis of the artifact, the activity of students and through the transposition of knowledge. The issue of effectiveness of these tools arise among pupils to understand the whole of a technical system and among teachers to structure learning. The methodology was conducted in a qualitative and quantitative manner with these actors. Two experiments took place, with teachers first, based on a survey with a questionnaire and interviews. A second, with students, was based on an entry test and various written exercises and operative manipulation with a manufacture via a 3D printer. The results of a group introduced to functional analysis are compared with those of a group not initiated. Data analyses address the manner in which the skills and knowledge that enable a systemic approach in technological education are implemented. The main results indicate that if teachers take over the functional analysis, control is not total. His teaching mainly benefits to pupils with scholar difficulties. These elements are detailed in-depth and put into perspective in this thesis.

In this thesis we summarise several results in the literature which show the approximation capabilities of multilayer feedforward artificial neural networks. We show that multilayer feedforward artificial neural networks are capable of approximating continuous and measurable functions from Rn to R to any degree of accuracy under certain conditions. In particular making use of the Stone-Weierstrass and Hahn-Banach theorems, we show that a multilayer feedforward artificial neural network can approximate any continuous function to any degree of accuracy, by using either an arbitrary squashing function or any continuous sigmoidal function for activation. Making use of the Stone-Weirstrass Theorem again, we extend these approximation capabilities of multilayer feedforward artificial neural networks to the space of measurable functions under any probability measure.

Orientador: Franco Giuseppe Dedini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T13:27:05Z (GMT). No. of bitstreams: 1 Favaro_MariliaColozio_M.pdf: 8312043 bytes, checksum: 69a749f078255331cf34cee565a81a17 (MD5) Previous issue date: 2014 / Resumo: A metodologia de projeto e as ferramentas de desenvolvimento de produto são aplicadas no desenvolvimento do produto para que se obtenham resultados que sejam positivos tanto para a empresa como para o consumidor. Juntos, formam uma base de conhecimento que auxiliam o designer na busca pela solução ideal que satisfaça uma necessidade humana. Por ser um método flexível e multidisciplinar, seus conceitos podem ser usados no desenvolvimento de diversos produtos. A embalagem tem uma peculiaridade em relação aos demais produtos industriais e deve ser considerada com um todo. Para atender a demanda desse tipo de produto, um entendimento aprofundado da função da embalagem relacionado aos aspectos práticos, estéticos e sociais do uso da mesma, é necessário. Dada a importância da relação entre os conceitos levantados, a presente pesquisa tem como objetivo fazer uma análise da metodologia de projeto e ferramentas de desenvolvimento de produto para o desenvolvimento de embalagens de transporte e comercialização de hortifrúti. Para tanto, baseou-se no estudo da metodologia de projeto existente na literatura para, então, propor um método sugerindo ferramentas de desenvolvimento de produto, a fim de proporcionar maior eficiência e eficácia para as embalagens do setor. Os resultados possibilitaram uma visualização do processo de desenvolvimento de embalagem, de modo sistemático, capaz de propor uma série de ganhos tanto para o consumidor como para indústria. Neste ponto, a presente pesquisa de caráter filosófico e conceitual sugere que o estudo sobre o tema é pertinente, pois é necessário suprir a lacuna deixada pela definição da função da embalagem, agregando ferramentas de desenvolvimento de produto adequadas aos passos iniciais de desenvolvimento da embalagem / Abstract: The design methodology and design tools for product development are applied in product development in order to produce results that are positive for the company and the consumer. Together, the design methodology and the design tools form a knowledge base that assists the designer in finding the optimal solution that satisfies a human need. Because it is a flexible and multidisciplinary method, its concepts can be used in the development of several products. The packaging has a peculiarity in comparison with other industrial products and should be considered as a whole. To meet the demand of this type of product, a detailed understanding of the function related to practical, aesthetic and social aspects of the use of packaging is required. Given the importance of the relationship between the concepts raised, this research aims to analyze the design methodology and product development tools for the development of a packaging. For this, the study was based on the methodology described in the literature and then proposes a method suggesting product development tools in order to provide greater efficiency and effectiveness in the packaging industry. The results allowed a systematic way of producing the packaging able to propose a series of gains for both the consumer and industry. At this point, the present study has a philosophical and conceptual character and suggests that the study on the topic is relevant because it is necessary to fill the gap left by the definition of the function of the package / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestra em Engenharia Mecânica

abstract: C*-algebras of categories of paths were introduced by Spielberg in 2014 and generalize C*-algebras of higher rank graphs. An approximately finite dimensional (AF) C*-algebra is one which is isomorphic to an inductive limit of finite dimensional C*-algebras. In 2012, D.G. Evans and A. Sims proposed an analogue of a cycle for higher rank graphs and show that the lack of such an object is necessary for the associated C*-algebra to be AF. Here, I give a class of examples of categories of paths whose associated C*-algebras are Morita equivalent to a large number of periodic continued fraction AF algebras, first described by Effros and Shen in 1980. I then provide two examples which show that the analogue of cycles proposed by Evans and Sims is neither a necessary nor a sufficient condition for the C*-algebra of a category of paths to be AF. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2020

In 1948, Richard Feynman published the first paper on his new approach to non-relativistic quantum mechanics. Before Feynman's work there were two mathematical formulations of quantum mechanics. Schrödinger's formulation was based on PDE (the Schrödinger equation) and states representation by wave functions, so it was in the framework of analysis and differential equations. The other formulation was Heisenberg's matrix algebra. Initially, they were thought to be competing. The proponents of one claimed that the other was “ wrong. ” Within a couple of years, John von Neumann had proved that they are equivalent. Although Feynman's theory was not fundamentally new, it nonetheless offered an entirely fresh and different perspective: via a precise formulation of Bohr's correspondence principle, it made quantum mechanics similar to classical mechanics in a precise sense. In addition, Feynman's approach made it possible to explain physical experiments, and, via diagrams, link them directly to computations. What resulted was a very powerful device for computing energies and scattering amplitudes - the famous Feynman's diagrams. In his formulation, Feynman aimed at representing the solution to the non-relativistic Schrödinger equation in the form of an “ average ” over histories or paths of a particle. This solution is commonly known as the Feynman path integral. It plays an important role in the theory but appears as a postulate based on intuition coming from physics rather than a justified mathematical object. This is why Feynman's vision has caught the attention of many mathematicians as well as physicists. The papers of Gelfand, Cameron, and Nelson are among the first, and more substantial, attempts to supply Feynman's theory with a rigorous mathematical foundation. These attempts were followed by many others, but unfortunately all of them were not quite satisfactory. The difficulty comes from a need to define a measure on an infinite-dimensional space of continuous functions that represent all possible paths of a particle. This Feynman's measure has to produce an integral with the properties requested by Feynman. In particular, the expression for the Feynman measure has to involve the non-absolutely integrable Fresnel integrands. The non-absolute integrability of the Fresnel integrands makes the measure fail to be positive and to have the countably additive property. Thus, a well-defined measure in the case of the Feynman path integral does not exist. Extensive research has been done on the methods of relating the Feynman path integral to the integral with respect to the Wiener measure. The method of analytic continuation in mass defines the Feynman path integral as a certain limit of the Wiener integrals. Unfortunately, this method can be used as definition for only almost all values of the mass parameter in the Schrödinger equation. For physicists, this is not a satisfactory result and needs to be improved. In this work we examine those questions which originally led to the Feynman path integral. By now we know that Feynman's “ dream ” cannot be realized as a positive and countably additive measure on the path-space. Here, we offer a new way out by modifying Feynman's question, and thereby achieving a solution to the Schrödinger equation via a different kind of averages in the path-space. We give our version of the question that Feynman “ should have asked ” in order to realize the elusive path integral. In our formulation, we get a Feynman path integral as a limit of linear functionals, as opposed to the more familiar inductive limits of positive measures, traditionally used for constructing the Wiener measure, and related Gaussian families. We adapt here an approach pioneered by Patrick Muldowney. In it, Muldowney suggested a Henstock integration technique in order to deal with the non-absolute integrability of the kind of Fresnel integrals which we need in our solution to Feynman's question. By applying Henstock's theory to Fresnel integrals, we construct a complex-valued “ probability distribution functions ” on the path-space. Then we use this “ probability ” distribution function to define the Feynman path integral as an inductive limit. This establishes a mathematically rigorous Feynman limit, and at the same time, preserves Feynman's intuitive idea in resulting functional. In addition, our definition, and our solution, do not place any restrictions on any of the parameters in the Schrödinger equation, and have a potential to offer useful computational experiments, and other theoretical insights.

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第22327号 / 医博第4568号 / 新制||医||1041(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 竹内 理, 教授 江藤 浩之, 教授 生田 宏一 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

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.

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this thesis is to further extend the concept of tensor decomposition through the use of function spaces. In doing so, we address the limitations of PCA to vector and matrix representations and the CP-Decomposition to tensor representations. Lastly, we provide an application in the context of professional stock car racing.

<p>Restricted and repetitive behavior (RRB) is a core feature of autism spectrum disorder (ASD). Research suggests that the severity of RRB may be influenced by both environmental variables (e.g., absence of sensory stimulation input) and neurophysiological activity within the body (e.g., atypical regulatory capacity of the autonomic nervous system). Substantial research efforts have been devoted to the assessment of factors that influence the occurrence of RRB in individuals with ASD, which have led to the development of assessment methodologies, such as functional analysis, to identify specific contexts in which RRB occurs, and measures of heart rate variability (HRV) to index the level of neurophysiological activity for individuals with ASD.</p><p>However, despite the increasing consensus that the assessment and treatment of RRB require a more comprehensive approach due to the complexity and heterogeneity of the neurodevelopmental disorder, there exists a paucity in research that addresses both the functional behavioral and neurophysiological dimensions of RRB. This study aimed to address this gap by (a) designing and evaluating the effects of an integrated function-based assessment on identification of the functional subtypes of RRB and (b) examining the relationship between RRB and HRV as an indicator of neurophysiological functioning. The study included six participants, ages four to seven, with ASD. A single-case alternating treatments design, with two conditions simulating low- and high-stimulation environments, was used for the assessment of functional subtypes within each participant. Dependent variables included the duration of RRB and HRV. RRB was measured using MOOSES, a multi-option observation system for experimental studies. HRV was measured using wearable technology that collects blood volume pulse. Visual analysis of time series data as well as nonparametric analyses of the dependent variables were conducted to determine the functional subtypes of RRB and the association between HRV and RRB across participants.</p><p>Study results suggest that (a) the integrated assessment is effective in identifying specific functional subtypes of RRB and (b) HRV is positively correlated with the rate of RRB. The findings of this study offer new insights on the understanding of how underlying environmental and neurophysiological mechanisms may influence the occurrence of RRB in ASD. Furthermore, the study provides an integrated assessment model that can be feasibly implemented in applied settings.</p>