Dissertations / Theses on the topic 'Connection (Mathematics)'
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Komatsubara, Kristin Mie. "The mathematics connection a curriculum promoting mathematical application through the home-school connection /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p1457291.
Full textTitle from first page of PDF file (viewed November 7, 2008). Available via ProQuest Digital Dissertations. Includes bibliographical references (p. 172-176).
Sevgi, Sevim. "The Connection Between School And Student Characteristics With Mathematics Achievement In Turkey." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12611190/index.pdf.
Full textmathematics achievement across Turkey by analyzing the data collected from school questionnaire, student background questionnaire and mathematics achievement test in Trends in International Mathematics and Science Study 2007. The analyzed sample was comprised of 4,498 students in 146 schools. Student level factors were highest level of education of either parent, students speak the language of test at home, students&rsquo
parents born in country, books in home, computer and internet connection, computer use, index of time students spend doing mathematics homework in a normal school week, index of students&rsquo
positive affect toward mathematics, index of students&rsquo
valuing mathematics, index of students&rsquo
self confidence in learning mathematics. School related factors were principals reports on the percentages of students in their schools coming from economically disadvantaged homes, principals report on the percentage of students having the language of test as their native language, index of good attendance, principals time spent on various school related activities, schools encouragement of parental involvement, index of school resources for mathematics instruction, index of principals perception of school climate. Hierarchical Linear Modeling (HLM) was used for analysis. The result of the study showed that 45% of variance between schools, 54.6 % of variance was in schools, 57.33 % of school variance in mathematics achievement accounted by principals&rsquo
report on percentages of students coming from economically disadvantaged homes, parents to volunteer for school programs, school resources for mathematics instruction and principals&rsquo
perception of school climate.
Moens, Theodore Warren Bernelot. "Approaches to procedural adequacy in logic programming using connection graphs." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26499.
Full textScience, Faculty of
Computer Science, Department of
Graduate
Kelley, Diana L. "Music and mathematics--is there a connection? : the effects of participation in music programs on academic achievement in mathematics /." Abstract Full Text (HTML) Full Text (PDF), 2008. http://eprints.ccsu.edu/archive/00000493/02/1949FT.htm.
Full textThesis advisors: S. Louise Gould, Philip P. Halloran, Shelley Jones. " ... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 21-22). Also available via the World Wide Web.
Wang, Shiyun. "Connection between Graphical Potential Games and Markov Random Fields with an Extension to Bayesian Networks." Thesis, California State University, Long Beach, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10785804.
Full textA probabilistic graphical model is a graphical representation of a joint probability distribution, in which the conditional independencies among random variables are specified via an underlying graph. We connect the probabilistic graphical models to some special types of games. Graphical potential games are the intersection of potential games and graphical games. They have characteristics from both of these two classes of games, namely, potential functions of potential games and graphical structure of graphical games. We review that there is a bijection between the normalized graphical potential games and the corresponding Markov Random Fields. We use a similar method to study the structure of Bayesian networks and define two types of games on directed graphs whose nodes are players. One is the directed graphical game, which is defined based on the assumption that the utility of player i only depends on the parent of i in the graph. The other one is the Bayesian-factorable potential game. The potential function of the game gives rise to the probability distribution, which can be factorized as in a Bayesian network. We explore the connections between such games and Bayesian networks.
Prasad, Priya Vinata. "Connection, Motivation, & Alignment: Exploring the Effects of Content-Based Mathematical Professional Development." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/332769.
Full textMichels, Tara Marie. "Towards a Connection between Linear Embedding and the Poincaré Functional Equation." Digital Commons @ East Tennessee State University, 2003. https://dc.etsu.edu/etd/836.
Full textBernergård, Zandra. "Connection between discrete time random walks and stochastic processes by Donsker's Theorem." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48719.
Full textTheeranaew, Wanchat. "STUDY ON INFORMATION THEORY: CONNECTION TO CONTROL THEORY, APPROACH AND ANALYSIS FOR COMPUTATION." Case Western Reserve University School of Graduate Studies / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=case1416847576.
Full textSoudamini, Jidesh. "LIFTED MULTIRELATIONS AND PROGRAM SEMANTICS." Kent State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=kent1164077672.
Full textNorberg, Pernilla. "Design av verklighetsanknuten matematikundervisning." Thesis, Karlstads universitet, Institutionen för språk, litteratur och interkultur, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-36765.
Full textMickutė, Laura. "Apie trečios eilės liestinių sluoksniuočių geometriją." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050623_101559-72938.
Full textHassler, Ryan Scott. "Mathematical comprehension facilitated by situation models: Learning opportunities for inverse relations in elementary school." Diss., Temple University Libraries, 2016. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/410935.
Full textPh.D.
The Common Core State Standards call for more rigorous, focused, and coherent curriculum and instruction, has resulted in students being faced with more cognitively high-demanding tasks which involve forming connections within and between fundamental mathematical concepts. Because mathematical comprehension generally relates back to one’s ability to form connections to prior knowledge, this study sought to examine the extent to which current learning environments expose students to connection-making opportunities that may help facilitate mathematical understanding of elementary multiplicative inverses. As part of an embedded mixed-methods design, I analyzed curriculum materials, classroom instruction, and student assessments from four elementary mathematics teachers’ classrooms. A situation model perspective of comprehension was used for analysis. The aim of this study was thus to determine how instructional tasks, representations, and deep questions are used for connection-making, which is the foundation of a situation model that can be used for inference-making. Results suggest that student comprehension depends more on connection-making opportunities afforded by classroom teachers, rather than on learning opportunities found solely within a curriculum. This included instruction that focused on deeply unpacking side-by-side comparison type examples, situated examples in personal concrete contexts, used semi-concrete representations to illustrate structural relationships, promoted efficiency through the sequence of presented representations, and posed deep questions which supported students’ sense-making and emphasized the interconnectedness of mathematics. By analyzing these key aspects, this study contributes to research on mathematical understanding and provides a foundation for helping students facilitate transfer of prior knowledge into novel mathematical situation.
Temple University--Theses
Moran, Renee Rice, and Monica Billen. "The Reading and Writing Connection: Bridging Two Reciprocal Content Areas in Order to Expand Literacy Learning in the Elementary School Classroom." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etsu-works/3599.
Full textTembo, Kondwelan James. "Hur matematikundervisning som har vardagliga samband påverkar elevernas lärande." Thesis, Malmö universitet, Fakulteten för lärande och samhälle (LS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-29454.
Full textThis study focuses on the problem where most pupils lose interest, motivation and the desire to learn mathematics because they perceive it to be a difficult subject. The purpose of this thesis on the other hand is to investigate how mathematics teaching that has everyday life connections affects pupils' learning. The study also wants to shed light on how teachers work so that the teaching of mathematics will contribute to pupils developing interest in mathematics and confidence in their ability to use mathematics in different contexts. The results are based on an analysis of pupils’ and teachers’ questionnaires. There are twenty (22) pupils and four (4) licensed mathematics teachers that took part in this study. The pupils are in grade six (6) and the teachers teach different grades from grade one (1) to six (6). The questionnaires addressed different issues among them; pupils' interest, motivation and learning using everyday connections. When it comes to motivation, 19 pupils answered that they are more motivated to solve math tasks when they use or work with materials or something that helps them solve the tasks. The same number on the other hand answered that they lose the desire or motivation when the lessons are not connected to things they know or like. On learning/teaching, both pupils and teachers went into the same direction. All the 22 pupils answered that they learn better when the teacher uses everyday connections to solve or explain mathematical problems or concepts while 3 out of 4 teachers answered that their pupils learn mathematics best when the lessons are connected to things they know or like. The results of this study however show that pupils' interest, motivation and performance in mathematics increases when lessons are linked to everyday connections.Keywords: everyday connection, interest, mathematics teaching, motivation, understanding.
Pearson, Esther M. "Mathematics Connections to Current Events." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82960.
Full textRoddy, Mark R. "Mathematics teachers' conceptions of "connections." /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/7838.
Full textKochanskaitė, Diana. "Judesiai n-matėje hiperplokštuminių elementų erdvėje." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20110627_132954-52624.
Full textThe present work analyses movements in n-dimensional space of hyperplaine elements . The received results: 1. It was proved that in the n-dimensional space the maximum number of movement groups parameters, number is parameters 2. It was proved that in the n-dimensional space the maximum number of movement groups parameters with asymmetric linear connection is parameters.
Balčiūnas, Aidas. "Baigtinio tipo g- struktūrų vidinės sietys." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100702_112749-84649.
Full textThe most important part of differential geometry in our days is the theory of smooth G- structures, which started with the analyses of clasical construction of Riemannian space. G-structure in smooth manifold is acquired, when we take reduction of its frame bundle corresponding to subgroup G of non-degeneracy matrix group . It‘s important to note, that G- structures do not exist in every manifold. In this paper are considering intrisic connections only of finite type of G- structures. It is proved, that every finite type of G- structure corresponds to finite type of differential equation on the manifold . The Geometry of G- structures is investigated not traditionally while analyzing differential equations of infetisimal simmetrics of G- structures. There are analysed affine connections of G- structures, also and normal connections. The former haven‘t been investigated in geometry of G- structures.
Rozenblyum, Nikita. "Connections on conformal blocks." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67813.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (p. 66-67).
For an algebraic group G and a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i.e. quasi-coherent sheaves with a flat connection. This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space.
by Nikita Rozenblyum.
Ph.D.
Yang, Baozhong 1975. "Yang-Mills connections with isolated singularities." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/105593.
Full textJenkinson, Justin. "Convex Geometric Connections to Information Theory." Case Western Reserve University School of Graduate Studies / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1365179413.
Full textVieira, Ewerton Rocha 1987. "O complexo de Morse-Witten via sequências espectrais." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307541.
Full textDissertação (mestrado) - Universidade Estadual de Campiknas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Nesse trabalho, estudaremos o complexo de Morse-Witten via sequências espectrais, utilizando a matriz de conexão sobre z que codifica as orbitas de conexão do uso de Morse associado ao complexo. O algoritmo do Método da Varredura aplicado à matriz de conexão sobre z produz uma sequência espectral (Er; dr), que por sua vez nos fornece informações importantes sobre a dinâmica. Dada a necessidade de computarmos os geradores dos -modulos Erp,q e as diferencias drp,q da seqüência espectral, utilizamos o software Sweeping Algorithm,que calcula os Erp,q e drp,q de forma rápida e eficiente. Apresentamos uma forma de estender o complexo de Morse-Witten, conforme [BaC1] e [BaC]. Tal complexo apresenta informações entre pontos críticos não consecutivos, ate então não obtidas pelo complexo de Morse-Witten. Para esse complexo estendido temos também uma seqüência espectral associada, através da qual obtemos informações dinâmicas, conforme os trabalhos [BaC1] e [BaC]
Abstract: In this work, we study the Morse-Witten Complex via spectral sequences, using the connection matrix over z, which codi_es the connecting orbits of the Morse ow associated to the complex. The Sweeping Method algorithm applied to the connection matrix over z produces a spectral sequence (Er; rd), which in turn gives us important information on the dynamics. Given the need to compute the generators of Z-modules Erp,q and the diferentials drp,q of the spectral sequence, we use the software Sweeping Algorithm, calculates Erp,q and drp,q quickly and efficiently. We present a way to extend the Morse-Witten as [BaC1] and [BaC]. This complex exhibits information between non-consecutive critical points, not obtainable using the Morse-Witten complex. For this extended Morse Complex we also have an associated spectral sequence, whereby dynamical information is also obtained as in [BaC1] and [BaC]
Mestrado
Mestre em Matemática
Sadasivan, Sridhar. "Mathematical Modeling of Behavior of T-Stub Connections." University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1092837126.
Full textWashington, Arnita. "THE EFFECTS OF LITERATURE ON STUDENT MOTIVATION AND CONNECTIONS IN MATHEMATICS." Master's thesis, University of Central Florida, 2005. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3708.
Full textM.Ed.;
Department of Teaching and Learning Principles
Education
Mathematics Education
Bischoff, Martin [Verfasser]. "Location of Connection Facilities / Martin Bischoff." Aachen : Shaker, 2008. http://d-nb.info/1162790199/34.
Full textEli, Jennifer Ann. "An exploratory mixed methods study of prospective middle grades teachers' mathematical connections while completing investigative tasks in geometry." Lexington, Ky. : [University of Kentucky Libraries], 2009. http://hdl.handle.net/10225/1146.
Full textTitle from document title page (viewed on May 12, 2010). Document formatted into pages; contains: ix, 219 p. : ill. (some col.). Includes abstract and vita. Includes bibliographical references (p. 170-179).
Wilkins, David Raynor. "Elliptic operators, connections and gauge transformations." Thesis, Durham University, 1985. http://etheses.dur.ac.uk/6841/.
Full textHumbert, Philippe. "Intégrale de Kontsevich elliptique et enchevêtrements en genre supérieur." Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00762209.
Full textRomanovski, Iakov. "Connections between descriptive set theory and HF-logic." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ37160.pdf.
Full textRoche, Austin D. "On a natural variational principle for symplectic connections." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33025.
Full textSmart, Angela. "Undergraduate Students’ Connections Between the Embodied, Symbolic, and Formal Mathematical Worlds of Limits and Derivatives: A Qualitative Study Using Tall’s Three Worlds of Mathematics." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24247.
Full textVolk, Viktorija. "Konformiškai simetrinės sietys." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050622_134553-22886.
Full textCook, Jordan Lacy. "Making connections: teaching and using concept maps in a fourth grade mathematics class." Montana State University, 2012. http://etd.lib.montana.edu/etd/2012/cook/CookJ0812.pdf.
Full textSmith, Ronald William 1945. "Professional development organization and primary mathematics teachers : exploring connections with beliefs and practice." Monash University, Faculty of Education, 2001. http://arrow.monash.edu.au/hdl/1959.1/8624.
Full textSlye, Jeffrey. "UNDERGRADUATE MATHEMATICS STUDENTS’ CONNECTIONS BETWEEN THEIR GROUP HOMOMORPHISM AND LINEAR TRANSFORMATION CONCEPT IMAGES." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/65.
Full textMarkevičienė, Laura. "Koreperių sluoksniuočių glodūs tęsiniai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050620_192041-49606.
Full textNystrom, Michel. "The Ambrose-Palais-Singer theorem in synthetic differential geometry /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66260.
Full textSun, Weiran. "Mathematical Problems Arising When Connecting Kinetic to Fluid Regimes." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8555.
Full textThesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Davis, Simon. "Connections and generalized gauge transformations." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2646/.
Full textAlsaody, Seidon. "Generalisations of the Algebraic Theory of Connective Segmentation." Thesis, Uppsala University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-126074.
Full textVieira, Ewerton Rocha 1987. "Transition matrix theory = Teoria da matriz de transição." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307536.
Full textTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Nessa tese, apresentamos uma unificação da teoria das matrizes de transição algébrica, singular, topológica e direcional ao introduzir a matriz de transição (generalizada), a qual engloba todas as quatros citadas anteriormente. Alguns resultados de existência são apresentados bem como a verificação de que cada matriz de transição supracitada são casos particulares da matriz de transição (generalizada). Além disso, nós abordamos como as aplicações das quatros matrizes de transiçao, na teoria do índice de Conley, se traduzem para a matriz de transição (generalizada). Quando a matriz de transição (generalizada) satisfizer o requerimento adicional de cobrir o isomorfismo do índice de Conley F definido pelo fluxo, pode-se provar propriedades de existência e de conexão de órbitas. Essa matriz de transição com a propriedade de cobrir o isomorfismo F é definida como matriz de transição topológica generalizada e a utilizamos para obter conexões de órbitas num fluxo Morse-Smale sem órbitas periódicas bem como para obter conexões de órbitas numa continuação associada à sequência espectral dinâmica
Abstract: In this thesis, we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well as the verification that each of the previous transition matrices are cases of the (generalized) transition matrix. Furthermore, we address how applications of the previous transition matrices to the Conley Index theory carry over to the (generalized) transition matrix. When this more general transition matrix satisfies the additional requirement that it covers flow-defined Conley-index isomorphisms, one proves algebraic and connection-existence properties. These general transition matrices with this covering property are referred to as generalized topological transition matrices and are used to consider connecting orbits of Morse-Smale flows without periodic orbits, as well as those in a continuation associated to a dynamical spectral sequence
Doutorado
Matematica
Doutor em Matemática
Konecny, Jan. "Isotone fuzzy Galois connections and their applications in formal concept analysis." Diss., Online access via UMI:, 2009.
Find full textIncludes bibliographical references.
Huang, Yenwen. "Predictive equations for bolted connections." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41995.
Full textFor single line bolted connections, the value of the eccentricity coefficient is determined
by several independent variables: NR (number of rows in the bolted connection), B
(distance between two adjacent bolts in a vertical column), Xo (horizontal distance from
centroid to applied load), and 0 (the load angle). From the relationships between the
eccentricity coefficient and the independent variables, it was observed that a mathematical
model of the eccentricity coefficient with respect to the independent variables is hard
to determine. Hence, statistical equations for predicting the eccentricity coefficients were
developed by using the Buckingham's PI-Theorem and regression analysis. The precision
of the statistical equations is discussed, and several ways to improve the precision are
presented in this paper.
Master of Science
Adams, Joseph Allen. "Connecting Galois Representations with Cohomology." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/4124.
Full textNestmann, Franz [Verfasser], and G. [Akademischer Betreuer] Last. "Zentrale Grenzwertsätze im Random Connection Model / Franz Nestmann ; Betreuer: G. Last." Karlsruhe : KIT-Bibliothek, 2019. http://d-nb.info/1184990093/34.
Full textConstantinescu, Alexandru [Verfasser]. "Hilbert Functions : A connection between algebra, geometry and combinatorics / Alexandru Constantinescu." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1219070130/34.
Full textTai, Chih-Che. "Nature of Science, Connections, Visions and Opportunities." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etsu-works/3302.
Full textFreyland, Sara. "The Happy Ending Problem and its connection to Ramsey theory." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-379922.
Full textLima, Dahisy Valadão de Souza 1986. "Dynamical spectral sequences for Morse-Novikov and Morse-Bott complexes." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307538.
Full textTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O tema principal desta tese é o estudo de fluxos gradientes associados a campos vetoriais $-\nabla f$ em variedades fechadas, onde $f$ é uma função do tipo Morse, Morse circular e Morse-Bott. Para obter informações dinâmicas em cada caso, utilizamos ferramentas algébricas e topológicas, tais como sequências espectrais e matrizes de conexão. No contexto de Morse, consideramos um complexo de cadeias $(C,\Delta)$ gerado pelos pontos críticos de $f$ onde $\Delta$ conta (com sinal) o número de linhas do fluxo entre dois pontos críticos consecutivos. Uma análise via sequências espectrais $(E^{r},d^{r})$ é feita para se obter resultados de continuação global em superfícies. Nós relacionamos as diferenciais da $r$-ésima página de $(E^{r},d^{r})$ com cancelamentos dinâmicos entre pontos críticos. No caso de função de Morse circular $f:M \rightarrow S^{1}$, o método da varredura para um complexo de Novikov $(\mathcal{N},\Delta)$ associado $f$ e gerado pelos pontos críticos de $f$ é definido sobre o anel $\mathbb{Z}((t))$. Este método produz a cada etapa matrizes de Novikov. Provamos que a matriz final produzida pelo método da varredura tem entradas polinomiais, o que é surpreendente, já que as matrizes intermediárias podem ter séries infinitas como entradas. Apresentamos resultados que mostram que os módulos e diferenciais de uma sequência espectral associada a $(\mathcal{N},\Delta)$ podem ser recuperados através do método da varredura. Para fluxos gradientes associados a funções de Morse-Bott, as singularidades formam variedades críticas. Usamos a teoria do índice de Conley para obter uma caracterização do conjunto de matrizes de conexão para fluxos Morse-Bott. Obtemos resultados sobre o efeito no conjunto de matrizes de conexão causado por mudanças na ordem parcial e na decomposição de Morse de um conjunto invariante isolado
Abstract: The main theme in this thesis is the study of gradient flows associated to a vector field $-\nabla f$ on closed manifolds, where $f$ is either a Morse function, a circle-valued Morse function or a Morse-Bott function. In order to obtain dynamical information, we make use of algebraic and topological tools such as spectral sequences and connection matrices. In the Morse context, consider a chain complex $(C,\Delta)$ generated by the critical points of $f$, where $\Delta$ counts the number of flow lines between consecutive critical points with signs. A spectral sequence $(E^{r},d^{r})$ analysis is used to obtain results on global continuation of flows on surfaces. A link is established between the differentials on the $r$-th page of $(E^{r},d^{r})$ and cancellation of critical points. In the circle-valued Morse case $f:M \rightarrow S^{1}$, a sweeping algorithm for the Novikov chain complex $(\mathcal{N},\Delta)$ associated to $f$ and generated by the critical points of $f$ is defined over the ring $\mathbb{Z}((t))$. This algorithm produces at each stage Novikov matrices. We prove that the last Novikov matrix has polynomial entries which is quite surprising since the matrices in the intermediary stages may have infinite series entries. We also present results showing that the modules and differentials of the spectral sequence associated to $(\mathcal{N},\Delta)$ can be retrieved through the sweeping algorithm. For gradient flows associated to Morse-Bott functions, the singularities form critical manifolds. We use the Conley index theory for the critical manifolds in order to characterize the set of connection matrices for Morse-Bott flows. Results are obtained on the effects on the set of connection matrices caused by a change in the partial ordering and Morse decomposition of isolated invariant sets
Doutorado
Matematica
Doutora em Matemática