Dissertations / Theses on the topic 'Isometrie'

Definizioni e enunciati riguardo al gruppo fondamentale, alle azioni di gruppo, ai rivestimenti, alle varietà topologiche, differenziabili e riemanniane, alle isometrie e ai gruppi discreti di isometrie. Approfondimento riguardo alle superfici connesse, compatte e orientabili con classificazione topologica, definizione di curvatura gaussiana con classificazione delle superfici in base al valore della curvatura, teorema di Killing-Hopf, teorema di uniformizzazione, enunciato del teorema che verrà dimostrato: la sfera è l'unica superficie connessa, compatta e orientabile ellittica, il toro è l'unica piatta, le somme connesse di g tori (g>1) sono iperboliche. Descrizione del piano euclideo con relativa metrica, descrizione delle sue isometrie, teorema di Chasles con dimostrazione, dimostrazione del toro come unica superficie connessa, compatta e orientabile piatta. Descrizione della sfera con relativa metrica, descrizione delle sue isometrie, dimostrazione della semplicità di SO(3), dimostrazione della sfera come unica superficie connessa, compatta e orientabile ellittica. Descrizione di due modelli del piano iperbolico, descrizione delle sue isometrie, dimostrazione del fatto che le somme connesse di g tori (g>1) sono iperboliche. Definizione di gruppo Fuchsiano e di spazio di Teichmuller.

La tesi riporta la sperimentazione in un liceo scientifico di un software di geometria didattica applicato alle isometrie del piano. L'argomento è stato introdotto partendo dalle tassellazioni del piano mostrando immagini relative all'Alhambra in Spagna e dipinti di Escher.

Muskeln oszillieren nachgewiesener Weise mit einer Frequenz um 10 Hz. Doch was geschieht mit myofaszialen Oszillationen, wenn zwei neuromuskuläre Systeme interagieren? Die Dissertation widmet sich dieser Fragestellung bei isometrischer Interaktion. Während der Testmessungen ergaben sich Hinweise für das Vorhandensein von möglicherweise zwei verschiedenen Formen der Isometrie. Arbeiten zwei Personen isometrisch gegeneinander, können subjektiv zwei Modi eingenommen werden: man kann entweder isometrisch halten – der Kraft des Partners widerstehen – oder isometrisch drücken – gegen den isometrischen Widerstand des Partners arbeiten. Daher wurde zusätzlich zu den Messungen zur Interaktion zweier Personen an einzelnen Individuen geprüft, ob möglicherweise zwei Formen der Isometrie existieren. Die Promotion besteht demnach aus zwei inhaltlich und methodisch getrennten Teilen: I „Single-Isometrie“ und II „Paar-Isometrie“. Für Teil I wurden mithilfe eines pneumatisch betriebenen Systems die hypothetischen Messmodi Halten und Drücken während isometrischer Aktion untersucht. Bei n = 10 Probanden erfolgte parallel zur Aufzeichnung des Drucksignals während der Messungen die Erfassung der Kraft (DMS) und der Beschleunigung sowie die Aufnahme der mechanischen Muskeloszillationen folgender myotendinöser Strukturen via Mechanomyo- (MMG) bzw. Mechanotendografie (MTG): M. triceps brachii (MMGtri), Trizepssehne (MTGtri), M. obliquus externus abdominis (MMGobl). Pro Proband wurden bei 80 % der MVC sowohl sechs 15-Sekunden-Messungen (jeweils drei im haltenden bzw. drückenden Modus; Pause: 1 Minute) als auch vier Ermüdungsmessungen (jeweils zwei im haltenden bzw. drückenden Modus; Pause: 2 Minuten) durchgeführt. Zum Vergleich der Messmodi Halten und Drücken wurden die Amplituden der myofaszialen Oszillationen sowie die Kraftausdauer herangezogen. Signifikante Unterschiede zwischen dem haltenden und dem drückenden Modus zeigten sich insbesondere im Bereich der Ermüdungscharakteristik. So lassen Probanden im haltenden Modus signifikant früher nach als im drückenden Modus (t(9) = 3,716; p = .005). Im drückenden Modus macht das längste isometrische Plateau durchschnittlich 59,4 % der Gesamtdauer aus, im haltenden sind es 31,6 % (t(19) = 5,265, p = .000). Die Amplituden der Single-Isometrie-Messungen unterscheiden sich nicht signifikant. Allerdings variieren die Amplituden des MMGobl zwischen den Messungen im drückenden Modus signifikant stärker als im haltenden Modus. Aufgrund dieser teils signifikanten Unterschiede zwischen den beiden Messmodi wurde dieses Setting auch im zweiten Teil „Paar-Isometrie“ berücksichtigt. Dort wurden n = 20 Probanden – eingeteilt in zehn gleichgeschlechtliche Paare – während isometrischer Interaktion untersucht. Die Sensorplatzierung erfolgte analog zu Teil I. Die Oszillationen der erfassten MTG- sowie MMG-Signale wurden u.a. mit Algorithmen der Nichtlinearen Dynamik auf ihre Kohärenz hin untersucht. Durch die Paar-Isometrie-Messungen zeigte sich, dass die Muskeln und die Sehnen beider neuromuskulärer Systeme bei Interaktion im bekannten Frequenzbereich von 10 Hz oszillieren. Außerdem waren sie in der Lage, sich bei Interaktion so aufeinander abzustimmen, dass sich eine signifikante Kohärenz entwickelte, die sich von Zufallspaarungen signifikant unterscheidet (Patchanzahl: t(29) = 3,477; p = .002; Summe der 4 längsten Patches: t(29) = 7,505; p = .000). Es wird der Schluss gezogen, dass neuromuskuläre Komplementärpartner in der Lage sind, sich im Sinne kohärenten Verhaltens zu synchronisieren. Bezüglich der Parameter zur Untersuchung der möglicherweise vorhandenen zwei Formen der Isometrie zeigte sich bei den Paar-Isometrie-Messungen zwischen Halten und Drücken ein signifikanter Unterschied bei der Ermüdungscharakteristik sowie bezüglich der Amplitude der MMGobl. Die Ergebnisse beider Teilstudien bestärken die Hypothese, dass zwei Formen der Isometrie existieren. Fraglich ist, ob man überhaupt von Isometrie sprechen kann, da jede isometrische Muskelaktion aus feinen Oszillationen besteht, die eine per Definition postulierte Isometrie ausschließen. Es wird der Vorschlag unterbreitet, die Isometrie durch den Begriff der Homöometrie auszutauschen. Die Ergebnisse der Paar-Isometrie-Messungen zeigen u.a., dass neuromuskuläre Systeme in der Lage sind, ihre myotendinösen Oszillationen so aufeinander abzustimmen, dass kohärentes Verhalten entsteht. Es wird angenommen, dass hierzu beide neuromuskulären Systeme funktionell intakt sein müssen. Das Verfahren könnte für die Diagnostik funktioneller Störungen relevant werden.
Muscles oscillate with a frequency of about 10 Hz. But what happens with myofascial oscillations if two neuromuscular systems interact? The dissertation is devoted to this question during isometric interaction. The test measurements provide hints for the presence of possibly two different forms of isometric muscle action. When two persons work against each other, each individual can subjectively choose to take up one of two modes: one can either hold isometrically – thus resist the force of the partner – or one can push isometrically – and therefore work against the resistance of the partner. In addition to the measurements to determine the interaction of neuromuscular systems, measurements with single individuals were done to evaluate the question, if probably two forms of isometric muscle action exist. The doctoral thesis consists of two separate parts concerning the content and methodology: I “Single Isometric” and II “Coupled Isometric”. For part I the hypothetical measurement modes - “holding” and “pushing” during isometric muscle action - were examined using a pneumatic system. During the measurements of n = 10 subjects the signal of pressure, force (strain gauge) and acceleration were recorded. Furthermore, the detection of the mechanic muscle oscillations of the following myotendinal structures occurred via Mechanomyo- (MMG) and Mechanotendography (MTG), respectively: triceps brachii muscle (MMGtri), tendon of triceps brachii muscle (MTGtri) and obliquus externus abdominis muscle (MMGobl). Each test person performed at 80 % of MVC six 15-seconds-measurements (three at holding and three at pushing mode, respectively; break: 1 min.) as well as four fatigue measurements (two at holding and two at pushing mode, respectively; break: 2 min.). In order to compare the two measurement modes holding and pushing, the amplitude of the myofascial oscillations as well as the force endurance were used. Significant differences between the holding and the pushing mode appeared especially when looking at the characteristics of fatigue. Subjects in the holding mode yielded earlier than during the pushing one (t(9) = 3.716; p = .005). In the pushing mode the longest isometric plateau amounts 59.4 % of the overall duration of the measurement. During holding it lasted 31.6 % (t(19) = 5.265, p = .000). The amplitudes of the single-isometric-measurements did not differ significantly. But the amplitude of the MMGobl varied significantly stronger during the pushing mode comparing to the holding one. Due to these partly significant differences between both measurement modes, this setting was considered for the second part „Coupled-Isometric“, too. For the coupled-isometric-measurements n = 20 subjects – divided into same-sex couples – were investigated during isometric interaction. The placement of the sensors is analogous to part I. The oscillations of the recorded MMG- and MTG-signals were analyzed regarding their coherence inter alia by algorithms of non-linear dynamics. Through the coupled-isometric-measurements it was shown, that also during isometric interaction the muscles and the tendons of both neuromuscular systems oscillate at the known frequency range of 10 Hz. Moreover, the systems are able to coordinate them in such a manner, that a significant coherence appears. This differed significantly from random pairings (number of patches: t(29) = 3.477; p = .002; Sum of 4 longest patches: t(29) = 7.505; p = .000). Thus it is concluded that neuromuscular complementary partners are able to synchronize themselves in the sense of coherent behavior. Regarding the parameters concerning the possibly existing forms of isometric muscle action, a significant difference at the coupled-isometric-measurements between holding and pushing appeared with respect to the characteristics of fatigue as well as the amplitudes of the MMGobl. The results of both sub studies strengthen the hypothesis that two forms of isometric muscle action exist. It is questionable whether one can talk of isometry at all, since each isometric muscle action consists of fine oscillations. This excludes a by definition postulated isometry. It is proposed to exchange this term with homeometry. The results of the coupled-isometric-measurements show inter alia, that neuromuscular systems are able to coordinate their myotendinal oscillations, so that coherent behavior arises. It is supposed that for this both systems have to be functionally intact. This procedure could become relevant for diagnostics of functional disorders.

I gruppi risolubili sono tra gli argomenti più studiati nella storia dell'algebra, per la loro ricchezza di proprietà e di applicazioni. Questa tesi si prefigge l'obiettivo di presentare tali gruppi, in quanto argomento che esula da quelli usualmente trattati nei corsi fondamentali, ma che diventa fondamentale in altri campi di studio come la teoria delle equazioni. Il nome di tale classe di gruppi deriva infatti dalla loro correlazione con la risolubilità per formule generali delle equazioni di n-esimo grado. Si ha infatti dalla teoria di Galois che un'equazione di grado n è risolubile per radicali se e solo se il suo gruppo di Galois è risolubile. Da questo spunto di prima e grande utilità, la teoria dei gruppi risolubili ha preso una propria strada, tanto da poter caratterizzare tali gruppi senza dover passare dalla teoria di Galois. Qui viene infatti presentata la teoria dei gruppi risolubili senza far uso di tale teoria: nel primo capitolo esporrò le definizioni fondamentali necessarie per lo studio dei gruppi risolubili, la chiusura del loro insieme rispetto a sottogruppi, quozienti, estensioni e prodotti, e la loro caratterizzazione attraverso la serie derivata, oltre all'esempio più caratteristico tra i gruppi non risolubili, che è quello del gruppo simmetrico. Nel secondo capitolo sono riportati alcuni esempi e controesempi nel caso di gruppi non finiti, tra i quali vi sono il gruppo delle isometrie del piano e i gruppi liberi. Infine nel terzo capitolo viene approfondito il caso dei gruppi risolubili finiti, con alcuni esempi, come i p-gruppi, con un’analisi della risolubilità dei gruppi finiti con ordine minore o uguale a 100.

La presente tesi ha come obiettivo lo studio dei gruppi dei fregi e dei gruppi cristallografici piani. L’elaborato si articola in sei capitoli: il primo e il secondo riguardano rispettivamente alcuni richiami sui gruppi e sulle isometrie; il terzo tratta i gruppi finiti e i gruppi discreti di movimenti. Nel quarto sono classificati i gruppi dei fregi e vi è un esempio per ciascuno nell’arte decorativa. Nel quinto vi è la classificazione dei gruppi cristallografici piani. Infine l’ultimo capitolo riguarda l’artista M.C.Escher e sono presenti quindici sue opere, ognuna delle quali rappresenta un gruppo cristallografico piano diverso.

La curvatura gaussiana K(p) di una superficie S dello spazio euclideo tridimensionale in un suo punto p misura di quanto la superficie si discosta dal proprio piano tangente in p e fornisce informazioni sul comportamento di S in un intorno di p. Quando K è costante su tutta la superficie, essa fornisce informazioni globali di notevole rilevanza. L'esempio più semplice di superficie a curvatura costante positiva è la sfera, ma non è l'unico esempio. Un famoso teorema di Liebmann ci dice che se S è una superficie regolare compatta e connessa con curvatura gaussiana K costante, allora S è una sfera. Questo risultato viene spesso citato come un risultato sulla rigidità della sfera. Questa tesi è dedicata allo studio di condizioni su una superficie regolare S che implicano che S è una sfera.

In this thesis we discuss possible ways to give quantitative measurement for two spaces not being quasi-isometric. From this quantitative point of view, we reconsider the definition of quasi-isometries and propose a notion of ''quasi-isometric distortion growth'' between two metric spaces. We revise our article [32] where an optimal upper-bound for Morse Lemma is given, together with the dual variant which we call Anti-Morse Lemma, and their applications.Next, we focus on lower bounds on quasi-isometric distortion growth for hyperbolic metric spaces. In this class, $L^p$-cohomology spaces provides useful quasi-isometry invariants and Poincaré constants of balls are their quantitative incarnation. We study how Poincaré constants are transported by quasi-isometries. For this, we introduce the notion of a cross-kernel. We calculate Poincaré constants for locally homogeneous metrics of the form $dt^2+\sum_ie^{2\mu_it}dx_i^2$, and give a lower bound on quasi-isometric distortion growth among such spaces.This allows us to give examples of different quasi-isometric distortion growths, including a sublinear one (logarithmic).

Ma thèse se situe à l'intersection de \textit {la théorie des groupes géométrique} et \textit{la théorie des groupes mesurée}. Une question majeure dans la théorie des groupes géométrique est d'étudier la classe de quasi-isométrie (QI) et la classe d'équivalence mesurée (ME) d'un groupe, respectivement. $L^p$-équivalence mesurée est une relation d'équivalence qui est définie en ajoutant des contraintes géométriques avec d'équivalence mesurée. En plus, QI est une condition géométrique. Il est une question naturelle, si deux groupes sont QI et ME, si elles sont $L^p$-ME pour certains $p>0$. Dans mon premier article, en collaboration avec R. Tessera, nous répondons négativement à cette question pour $p\geq 1$, montrant que l'extension centrale canonique d'un groupe surface de genre plus élevé ne sont pas $L^1$-ME pour le produit direct de ce groupe de surface avec $\mathbb{Z}$ (alors qu'ils sont à la fois quasi-isométrique et équivalente mesurée).Dans mon deuxième papier, j'ai observé un lien général entre la géométrie des expandeurs, defini comme une séquence des quotients finis ( l'espace de boîte) d'un groupe finiment engendré, et les propriétés mesurée theorique du groupe. Plus précisément, je l'ai prouvé que si deux <> sont quasi-isométrique, les groupes correspondants doivent être <>, une notion qui combine à la fois QI et ME. Je prouve aussi une version de ce résultat pour le plongement grossière, ce qui permet de distinguer plusieurs classe des expandeurs. Par exemple, je montre que les expandeurs associé à $SL(m, \mathbb{Z})$ ne grossièrement plongent à les expandeurs associés à $SL_n(\mathbb{Z})$ si $m>n$
My thesis lies at the intersection of \textit{geometric group theory} and \textit{measured group theory}. A major question in geometric group theory is to study the quasi-isometry (QI) class and the measure equivalence (ME) class of a group, respectively. $L^p$-measure equivalence is an equivalence relation which is defined by adding some geometric constraints with measure equivalence. Besides, quasi-isometry is a geometric condition. It is a natural question if two groups are QI and ME, whether they are $L^p$-ME for some $p>0$. In my first paper, together with R. Tessera, we answer this question negatively for $p\geq 1$, showing that the canonical central extension of a surface group of higher genus is not $L^1$-ME to the direct product of this surface group with $\mathbb{Z}$ (while they are both quasi-isometric and measure equivalent). In my second paper, I observed a general link between the geometry of expanders arising as a sequence of finite quotients (box space) of a finitely generated group, and the measured theoretic properties of the group. More precisely, I proved that if two box spaces' are quasi-isometric, then the corresponding groups must be `uniformly measure equivalent', a notion that combines both quasi-isometry and measure equivalence. I also prove a version of this result for coarse embedding, allowing to distinguish many classes of expanders. For instance, I show that the expanders associated to $SL(m,\mathbb{Z})$ do not coarsely embed inside the expanders associated to $SL_n(\mathbb{Z}$ if $m>n$

Orientador: Claudina Izepe Rodrigues
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-12T05:50:13Z (GMT). No. of bitstreams: 1 Sousa_AlexandrePereira_M.pdf: 2225572 bytes, checksum: cfb663a28dc18e6cca11fb9f1f98c872 (MD5) Previous issue date: 2008
Resumo: Neste trabalho estudamos isometrias e similaridades no espaço Euclidiano de dimensão três com o objetivo de suas classificações. Apresentamos inicialmente alguns fatos históricos referentes à Geometria, e, a seguir, desenvolvemos um estudo sobre isometrias e similaridades usando ferramentas e conceitos de grupos. Finalmente, sugerimos algumas atividades úteis para uma familiarização e desenvolvimento de habilidades na investigação de simetrias de figuras.
Abstract: The objective of this work is to classify isometries and similarities on three dimensional Euclidean space. We present some historic facts about Geometry followed by a study on isometries and similarities using tools and concepts from groups. We also suggest some helpful activities to develop abilities in the investigation of symmetry groups of figures.
Mestrado
Geometria
Mestre em Matemática

In this dissertation we study lattices in quotient spaces. The basic quotient spaces are: (1) n-dimensional euclidean tori, obtained from quotient of Rn by discrete groups of isometries ge- nerated by linearly independent translations and (2) hyperbolic °at g-tori (tori of genus g ¸ 2), obtained from quotient of hyperbolic plane by fuchsian groups. In the euclidean environment, the considered lattices are provided of the additive group Z2; while in the hyperbolic case the studied lattices are the geometrically uniform and the cyclic ones.
Neste trabalho estudamos reticulados em espaços quocientes. Os espaços quocientes considerados foram: (1) toros euclidianos n-dimensionais, obtidos pelo quociente de Rn por grupos discretos de isometrias gerados por translações linearmente independentes e (2) g-toros planos hiperbólicos (g ¸ 2) ; obtidos pelo quociente do plano hiperbólico por grupos fuchsianos. No caso euclidiano, os reticulados considerados foram provenientes de Z2; enquanto que no caso hiperbólico os reticulados estudados foram os geometricamente uniformes e os cíclicos.
Mestre em Matemática

In this dissertation we study a special sub-collection of Polish metric spaces: complete separable ultrametric spaces. Polish metric spaces have been studied for quite a long while, and a lot of results have been obtained. Motivated by some of earlier research, we work on the following two main parts in this dissertation. In the first part, we show the existence of Urysohn Polish R-ultrametric spaces, for an arbitrary countable set R of non-negative numbers, including 0. Then we give point-by-point construction of a countable R-ultra-Urysohn space. We also obtain a complete characterization for the set R which corresponding to a R-Urysohn metric space. From this characterization we conclude that there exist R-Urysohn spaces for a wide family of countable R. Moreover, we determine the complexity of the classification of all Polish ultrametric spaces. In the second part, we investigate the isometry groups of Polish ultrametric spaces. We prove that isometry group of an Urysohn Polish R-ultrametric space is universal among isometry groups of Polish R-ultrametric spaces. We completely characterize the isometry groups of finite ultrametric spaces and the isometry groups of countable compact ultrametric spaces. Moreover, we give some necessary conditions for finite groups to be isomorphic to some isometry groups of finite ultrametric spaces.

Submitted by Ana Paula Inforsato (ana.inforsato@gmail.com) on 2018-05-21T19:31:12Z No. of bitstreams: 1 Ana Paula final.pdf: 2233592 bytes, checksum: 79e4da8a53734795b00c77eb03daa0af (MD5)
Approved for entry into archive by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br) on 2018-05-22T13:00:36Z (GMT) No. of bitstreams: 1 inforsato_ap_me_rcla.pdf: 2232239 bytes, checksum: 6e5ef796e47228af1164f8da713ea8de (MD5)
Made available in DSpace on 2018-05-22T13:00:36Z (GMT). No. of bitstreams: 1 inforsato_ap_me_rcla.pdf: 2232239 bytes, checksum: 6e5ef796e47228af1164f8da713ea8de (MD5) Previous issue date: 2018-05-04
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Neste trabalho tratamos da classificação dos grupos de friso. Para realizar este objetivo abordamos elementos básicos da estrutura algébrica de grupo bem como apresentamos transformações geométricas, entre estas destacamos: translações, reflexões, rotações e reflexão com deslizamento. Além disso, localizamos este assunto como tópico da estrutura curricular do Ensino Fundamental e executamos uma atividade em sala de aula em que os alunos criaram frisos ornamentais.
In this work we deal with the classification of frieze groups. In order to accomplish this objective we approach basic elements of the algebraic group structure as well as present geometric transformations, among which we highlight: translations, reflections, rotations and glide reflection. In addition, we locate this subject as a topic of the curricular structure of Elementary School and perform a classroom activity in which the students created ornamental friezes.

This thesis consists of four papers, all concerning random iteration of isometries. The papers are:

I. Ambroladze A, Ådahl M, Random iteration of isometries in unbounded metric spaces. Nonlinearity 16 (2003) 1107-1117.

II. Ådahl M, Random iteration of isometries controlled by a Markov chain. Manuscript.

III. Ådahl M, Melbourne I, Nicol M, Random iteration of Euclidean isometries. Nonlinearity 16 (2003) 977-987.

IV. Johansson A, Ådahl M, Recurrence of a perturbed random walk and an iterated function system depending on a parameter. Manuscript.

In the first paper we consider an iterated function system consisting of isometries on an unbounded metric space. Under suitable conditions it is proved that the random orbit {Zn} ^∞_n=0, of the iterations corresponding to an initial point Z₀, “escapes to infinity" in the sense that P(Zn Є K) → 0, as n → ∞ for every bounded set K. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point.

In the second paper we let a Markov chain control the random orbit of an iterated function system of isometries on an unbounded metric space. We prove under necessary conditions that the random orbit \escapes to infinity" and we also give a simple geometric description of these conditions in the Euclidean and hyperbolic spaces. The results generalises the results of Paper I.

In the third paper we consider the statistical behaviour of the reversed random orbit corresponding to an iterated function system consisting of a finite number of Euclidean isometries of Rn. We give a new proof of the central limit theorem and weak invariance principles, and we obtain the law of the iterated logarithm. Our results generalise immediately to Markov chains. Our proofs are based on dynamical systems theory rather than a purely probabilistic approach.

In the fourth paper we obtain a suficient condition for the recurrence of a perturbed (one-sided) random walk on the real line. We apply this result to the study of an iterated function system depending on a parameter and defined on the open unit disk in the complex plane.

Orientador: Michelle Ferreira Zanchetta Morgado
Banca: Évelin Meneguesso Barbaresco
Banca: Grazielle Feliciani Barbosa
Resumo: Este trabalho apresenta uma proposta de atividades voltadas ao ensino de isometria utilizando mosaicos, em especial os mosaicos de Escher, que são resultados de pavimentações do plano que possuem um certo padrão. É uma maneira diferenciada de ensinar o conteúdo, pois ao invés de apenas usar o método tradicional de ensino, utiliza materiais diferenciados e lúdicos, além de recursos computacionais, que tornam a aula muito mais atraente e motivadora, fazendo com que o aluno sinta mais interesse em participar das atividades e auxiliando na sua aprendizagem
Abstract: This work presents a proposal of activities aimed at teaching isometry using mosaics, especially the Escher's mosaics, which are results of pavings of the plane that have a certain pattern. It's a different way of teaching content, because instead of just using the traditional method of teaching, uses differentiated and playful materials, in addition to computing resources, which make much more attractive and motivating classroom, making the student feel more interest in participating in activities and assisting in his learning
Mestre

Made available in DSpace on 2015-09-17T15:24:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-12-04. Added 1 bitstream(s) on 2015-09-17T15:47:28Z : No. of bitstreams: 1 000844091.pdf: 3622159 bytes, checksum: 45127ac59a36f28cda96c5dbd1c211fe (MD5)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Este trabalho apresenta uma proposta de atividades voltadas ao ensino de isometria utilizando mosaicos, em especial os mosaicos de Escher, que são resultados de pavimentações do plano que possuem um certo padrão. É uma maneira diferenciada de ensinar o conteúdo, pois ao invés de apenas usar o método tradicional de ensino, utiliza materiais diferenciados e lúdicos, além de recursos computacionais, que tornam a aula muito mais atraente e motivadora, fazendo com que o aluno sinta mais interesse em participar das atividades e auxiliando na sua aprendizagem
This work presents a proposal of activities aimed at teaching isometry using mosaics, especially the Escher's mosaics, which are results of pavings of the plane that have a certain pattern. It's a different way of teaching content, because instead of just using the traditional method of teaching, uses differentiated and playful materials, in addition to computing resources, which make much more attractive and motivating classroom, making the student feel more interest in participating in activities and assisting in his learning

La tesi è incentrata sulle geometrie non euclidee. Al di là della descrizione dei vari modelli, essa si propone di evidenziare e accertare il fatto che tutte le geometrie, euclidee e non, abbiano pari dignità, fatto oggi pienamente condiviso, ma che era messo in dubbio al momento della loro genesi. Il primo è un capitolo introduttivo riguardo alla storia della geometria, che mira a evidenziare il cambio di prospettiva da una geometria intesa come "misura della terra" a una disciplina svincolata da ogni applicazione pratica. Si arriva poi all'opera di Euclide. A una descrizione sommaria degli Elementi, segue un'analisi del V postulato euclideo che, a differenza dei primi quattro postulati, i quali risultavano intuitivamente evidenti, non era così immediato. Molti studiosi per secoli cercarono invano di dedurlo dagli altri quattro assiomi ma, i tentativi sempre falliti, portarono, fra la fine del XVIII e l'inizio del XIX secolo, all'idea di considerare dei modelli che contemplassero solo i primi quattro postulati e una delle due possibili negazioni del V assioma: nacquero così le geometrie non euclidee. Nel terzo capitolo si scopre che tutte e tre le geometrie sono manifestazioni diverse di un unico concetto generale che le trascende tutte: la curvatura. Lo studio delle geometrie non euclidee e la generalizzazione del concetto di curvatura alle dimensioni superiori, hanno consentito di intraprendere, nel quarto capitolo, un'interpretazione geometrica dell'universo, volta a capire quale geometria risulta più adatta per descriverlo, permettendoci di mostrare la naturale interdisciplinarità delle geometrie non euclidee. Il quinto capitolo, infine, considera gli aspetti didattici attraverso un'analisi delle Indicazioni nazionali e dei libri di testo in merito all'argomento, e ai progetti volti a promuovere un approccio maturo e consapevole al moderno sistema assiomatico e alla geometria di Euclide.

Made available in DSpace on 2016-04-27T16:57:04Z (GMT). No. of bitstreams: 1 Mitchell Christopher Sombra Evangelista.pdf: 3875607 bytes, checksum: 0ac2ae3a28c5c0d8e2bd66e9455ae4b2 (MD5) Previous issue date: 2011-04-27
Secretaria da Educação do Estado de São Paulo
The research described here reports on a qualitative research had the purpose to enable high school students in a public school in the Metropolitan Region of São Paulo, implement and develop knowledge of mathematical object Isometric Transformations by Rotation, Translation and Reflection. Were used in this research, as motivating factors, the Ethnomatematics with Sona Geometry of African ethnic group called Cokwe and Dynamic Geometry using the software GeoGebra. The methodology, Design Experiment, enabled the improvement of a sequence of activities and created the final product of research. Levels of development psychogenetic Piaget and Garcia (1983), intrafigural, interfigural and transfigural possibility to observe the relationships between students identify geometric figures, their properties and structures. The development of this study revealed, made after the analysis of the protocols of the proposed activities, which supported the GeoGebra and Ethnomatematics favored the learning of Isometric Transformations
A pesquisa aqui descrita relata uma investigação de caráter qualitativo que teve como proposta possibilitar que alunos de Ensino Médio, de uma escola pública estadual da Região Metropolitana de São Paulo, aplicassem e desenvolvessem o conhecimento do objeto matemático Transformações Isométricas por meio da Rotação, Translação e Reflexão. Foram utilizados, nesta pesquisa, como elementos motivadores, a Etnomatemática com a Geometria Sona do grupo étnico africano chamado Cokwe e a Geometria Dinâmica com o uso do software GeoGebra. A metodologia utilizada, Design Experiment, possibilitou o aprimoramento de uma sequência de atividades e gerou o produto final da pesquisa. Os níveis de desenvolvimento psicogenéticos de Piaget e Garcia (1983), intrafigural, interfigural e transfigural possibilitaram verificar as relações que os alunos identificam entre as figuras geométricas, suas propriedades e estruturas. O desenvolvimento deste trabalho permitiu concluir, após as análises feitas dos protocolos das atividades propostas, que a Etnomatemática, com apoio do GeoGebra, favoreceu a aprendizagem das Transformações Isométricas

Syfte och frågeställningar

Studiens syfte var att undersöka om utförandet av en isometrisk bålstabiliseringsövning/coreövning kunde påverka upplevelsen av smärta i nacke, axlar och skuldror hos kvinnor med kronisk/långvarig idiopatisk smärta. Studiens frågeställningar var: Hur påverkar utförandet av övningen ”plankan” upplevelsen av smärta i nacke, axlar och skuldror hos deltagarna? Förändras den maximala uthålligheten i övningen mellan deltagarnas första och sista träningstillfälle? Kan interventionen fullföljas av deltagarna?

Metod

Fyra kvinnliga deltagare som alla hade kronisk/långvarig smärta i nacke, axlar eller skuldror utförde övningen ”plankan” som hemträningsövning under fyra veckors tid. Mängden träning dokumenterades i en träningsdagbok som deltagarna kontinuerligt fyllde i under träningsperioden. Före samt inom en vecka efter träningsperioden ifylldes en enkät med frågor om upplevd intensitet, frekvens och lokalisation av smärta. Dessutom mättes maximal uthållighet i övningen ”plankan”.

Resultat

Efter träningsperioden uppskattade alla deltagare med smärta i nacken en förbättring med 1-3 skalsteg i en sammanslagning av alla frågor rörande smärta i nacke. Detta innebar att förändringen mellan deltagarnas svar i före- och efterenkäten, där skalan 0-10 användes, slogs samman till ett värde. Smärta i axlarna skattades som markant förbättrad av två deltagare samt som något försämrad respektive inte förändrad av två deltagare. Endast en deltagare uppskattade sig ha smärta i skuldrorna och ingen skillnad i uppskattningen sågs mellan före- och efterenkäten. Maximal uthållighet i övningen mellan första och sista träningstillfället ökade statistiskt signifikant för alla deltagare mätt i både procent och sekunder.

Slutsats

Resultatet i studien tyder på att övningen kan genomföras av individer med långvarig idiopatisk smärta i nacke, axlar och skuldror utan att ökad upplevd smärta eller andra obehag uppstår samt att den maximala uthålligheten i övningen ökar genom att övningen utförs. Hur många gånger övningen måste utföras för att ge resultat på uthållighet är oklart. Trots att flera deltagare upplevde minskad smärta efter träningsperioden så kan inga slutsatser tas då deltagarantalet var litet och resultatet för interventionsgruppen inte jämförts med en kontrollgrupp. Stora variationer i utförandet av hemträningen förekom bland deltagarna och flera faktorer utöver träningsövningen kan ha påverkat förändringen i smärtupplevelse.

Tässä opinnäytetyössä tutkitaan permutaatioryhmiin kuuluvia isometrisia kuvauksia, jotka ovat joukon sisäisiä bijektiivisiä kuvauksia eli permutaatioita. Isometriset kuvaukset säilyttävät kuvattavan joukon alkioiden väliset etäisyydet. Isometrisissa kuvauksissa joukon alkiot joko siirtyvät, kiertyvät pisteen ympäri, peilautuvat suoran suhteen tai kuvautuvat edellä mainittujen kuvausten yhdistelmillä saman joukon alkioiksi. Isometristen kuvausten joukko on kuvattavan joukon permutaatioryhmän aliryhmä. Työssä on tutkittu isometrisia kuvauksia niin lukusuoralla kuin Euklidisessa tasossakin. Työn tärkeimmät lauseet liittyvät erilaisiin isometristen kuvausten joukkojen muodostamiin aliryhmiin. Isometriset kuvaukset lukusuoralla kiteytyvät lauseeseen: mikäli isometrisilla kuvauksilla on sama vaikutus kahteen suoran pisteeseen, niin silloin isometriset kuvaukset ovat samat. Isometrisia kuvauksia Euklidisessa tasossa on käsitelty laajemmassa kontekstissa kuin isometrisia kuvauksia lukusuoralla. Työssä tutkitut Euklidisen tason isometriset kuvaukset ovat tason pisteiden siirto, kierto origon ympäri, peilaus koordinaattiakselin suhteen sekä niiden yhdistelmät. Työssä todistetaan, että mikäli isometrisilla kuvauksilla on sama vaikutus Euklidisen tason kolmeen pisteeseen, jotka eivät ole samalla suoralla, niin silloin isometriset kuvaukset ovat samat. Jokainen Euklidisen tason isometria on todistettavasti esitettävissä siirtona, kiertona, peilauksena tai niiden erilaisina yhdistelminä. Isometrisella siirrolla voidaan siirtää Euklidisen tason origoa eli tason koordinaattiakseleiden leikkauspistettä mielivaltaiseksi tason Euklidisen tason pisteeksi. Yhdistetyillä isometrisilla kuvauksilla on mahdollista kiertää Euklidista tasoa tason mielivaltaisen pisteen ympäri sekä peilata Euklidinen taso tason kahden mielivaltaisen pisteen kautta kulkevan suoran suhteen. Euklidisen tason osajoukon isometristen kuvausten joukko on Euklidisen tason isometristen kuvausten joukon muodostaman ryhmän aliryhmä sekä Euklidisen tason osajoukon symmetriaryhmä. Euklidisen tason osajoukko on symmetrisen muotoinen, mikäli se voidaan kuvata itselleen useammalla kuin yhdellä isometrisella kuvauksella. Vastaavasti Euklidisen tason osajoukko on epäsymmetrisen muotoinen, mikäli se voidaan kuvata itselleen vain ja ainoastaan identiteettikuvauksella. Dihedraaliset kuvaukset ovat säännöllisten monikulmioiden isometrisia kuvauksia, joissa monikulmion kärkipisteet kuvautuvat saman monikulmion kärkipisteiksi. Säännöllisen n-kulmaisen monikulmion isometristen kuvausten joukko on Dihedraaliryhmä.

Orientadores: Marcelo Firer, Luiz Antonio Barrera San Martin
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-05T23:33:46Z (GMT). No. of bitstreams: 1 Talpo_HumbertoLuiz_D.pdf: 1408389 bytes, checksum: b11f884cbf1e05f81138a8e91a5980dc (MD5) Previous issue date: 2006
Resumo: Seja G uma árvore homogênea e Aut(G) seu grupo de automorfismos. Um automorfismo f Î Aut(G) é par se d(f(x),x) º0 mod 2 para todo vértice x Î G, onde d(.,.) é a função distância definida pelo comprimento do menor caminho ligando os vértices. O conjunto Aut+(G) de todos os automorfismos pares é um subgrupo de índice 2 em Aut(G). Definimos uma geodésica g Ì G como um subgrafo isomorfo a Z (onde Z é visto como um grafo que possui arestas unindo inteiros consecutivos). Uma reflexão em uma geodésica g é um automorfismo involutivo f (f² =1) tal que f(x) = x se, e somente se, x Î G. Denotamos por R o conjunto de todas as reflexões em geodésicas. Neste trabalho (Capítulo 2) provamos que, dada uma árvore homogênea de grau par G, o número de cobertura de Aut+(G) pelas reflexões em geodésicas é 11, no seguinte sentido: dado f Î Aut+(G) existem f1, f2,... fk com k £ 11, tais que f(x) = fk °fk-1°...°f1(x) para todo vértice x em G. Além disso, considerando árvores homogêneas, sabemos que o grupo de automorfismos é completo e o subgrupo de automorfismos pares é simples. Flexibilizamos a condição de homogeneidade e conseguimos demonstrar (Capítulo 3) para o caso de árvores semi-homogêneas, que o grupo de automorfismos é simples e completo
Abstract: Let G be a homogeneous tree and Aut(G) its group of automorphism. An automorphism Î Aut(G) is said to be even if d(f(x),x) º0 mod 2 for every vertex x Î G of , where d(.,.) is the canonical distance function defined by the minimum length of paths connecting the vertices. The set Aut+(G) of all even automorphism is a subgroup of index 2 in Aut(G). We define a geodesic g Ì G as a subtree isomorphic to the standard tree of the integers Z, that is, a homogeneous subtree of degree 2. A reflection in a geodesic g is an involutive automorphism f (f² =1) such that f(x) = x if x Î G. We denote by R the set of all reflections in geodesics. In this work (Chapter 2) we prove that, for every even degree tree G, the covering number of Aut+(G) by reflections in geodesics is 11, in the sense that give f Î Aut+(G) there are f1, f2,... fk with k £ 11, such that f(x) = fk °fk-1°...°f1(x) for every vertex x in G.Moreover, if we consider homogeneous trees we know that automorphisms group is complete and the even automorphisms subgroup is simple. We vary the homogeneous condition and we prove that (Chapter 3) for the semi-homogeneous trees, the automorphisms group is simple and complete
Doutorado
Doutor em Matemática

This study is about audio design for the isometric perspective computer game. Many games have an isometric perspective also known as a top-down perspective. Audio plays a large part in modern computers games. In this thesis I have questioned how audio is used in isometric games and if it is possible to implement positional audio in isometric games, which is mostly used with true perspective games. Through an analysis of how three dimensional audio is used and how audio is designed in true perspective video games, I have attempted to find out how audio can be implemented and designed for video games with an isometric perspective. A discussion in audio design has been formulated based on a game called Magicka Wizard Wars, where I have analyzed and theoretically written how audio implementation would be designed for that specific type of game and what potential problems could occur.

Orientadores: Paulo Regis Caron Ruffino, Dorival Leão Pinto Júnior
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-07-31T18:00:12Z (GMT). No. of bitstreams: 1 Souza_MariaLuisaCardoso_M.pdf: 1693258 bytes, checksum: b584d9a0fa10832ad7bcf792cec1809e (MD5) Previous issue date: 2001
Resumo: O objetivo deste trabalho é construir um isomorfismo de espaços de Wiener abstratos (A WS) entre o espaço de Wiener canônico dado pelas trajetórias do movimento browniano (i, BeM, Co[O,I]) e um espaço de Wiener abstrato (i, h. V), definido sobre um espaço vetorial normado dado por um subconjunto do espaço de todas as seqüências de números reais. Além disso, apresentamos uma generalização da construção feita por Paul Lévy da medida de Wiener no espaço de funções contínuas Co[O,I]. Mais precisamente, Paul Lévy construiu a medida de Wiener a partir da integral do sistema ortonormal completo de Haar. No nosso trabalho, tomamos a integral de uma base ortonormal qualquer de L2 ([0,1], B([O,I], m), onde B([O,I] é a a-álgebra de Borel do intervalo [0,1] e m é a medida de Lebesgue
Abstract: In this monograph we construct an isomorphism of abstract Wiener space (A WS) between the canonical Wiener space given by the trajectories of the Brownian motion (i, BeM, Co[O,I]) and the A WS (i, lz, V) defined over a normed vector space given by a subset ofthe space ofsequences ofreal numbers. Moreover, we present a generalization of Paul Levy's Wiener measure in the space of continuous functions Co[O,I]. Precisely, he constructed the Wiener measure from a series of gaussian random variables multiplied by the Haar orthonormal basis of L 2 ([0,1], B([O,I], m), where B([O,I] is the Borel a-algebra in the interval [0,1] and m is the Lebesgue measure, we extend this method to a general orthonormal basis ofthis Hilbert space
Mestrado
Mestre em Matemática

Suivant m. Broue, nous etudions certaines isometries entre groupes de grothendieck de blocs a defaut abelien de groupes symetriques et sporadiques, qui commutent avec les applications de decomposition generalisees

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Carmen Chicone. Vita. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:22:48Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-12-10Bitstream added on 2014-06-13T19:47:20Z : No. of bitstreams: 1 goncalves_accr_me_prud.pdf: 684147 bytes, checksum: a81c4f89900e68d55d13d636f49523a1 (MD5)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
A perda de massa muscular secundária à idade e à inatividade física é clinicamente relevante na população cardíaca, contudo a prescrição do exercício resistido dinâmico para esses pacientes apresenta-se inconclusiva na literatura. Objetivo: Reunir informações sobre a especificidade dos componentes do treinamento resistido prescrito à população cardiopata. Metodologia: Foi realizada busca sistemática de literatura, a partir das bases de dados LILACS, SciELO e PubMed, utilizando os seguintes descritores na língua portuguesa: força muscular, exercício isométrico, esforço físico, cardiopatia e coronariopatia, e seus correspondentes na língua inglesa (muscle strength, isometric exercise, physical effort, heart disease e artery coronary disease), os quais foram...
Loss of muscle mass secondary to age and physical inactivity is clinically relevant in cardiac population, however dynamic resistance exercise prescription to these patients presents inconclusive in literature. Objective: Adjoin information about specific components of resistance exercise prescribed to cardiac population. Methodology: Systematic search was performed, using the data bases LILACS, SciELO and PubMed. The descriptors used were: muscle strength, isometric exercise, physical effort, heart disease and artery coronary disease, which were surveyed separately and combined, considering for this review articles that ... (Complete abstract click electronic access below)

Purpose: To determine the reliability of early force production (50, 100, 150, 200, and 250 ms) relative to peak force (PF) during an isometric mid-thigh pull and to assess the relationships between these variables. Methods:: Male collegiate athletes (N = 29; age 21.1 [2.9] y, height 1.71 [0.07] m, body mass 71.3 [13.6] kg) performed isometric mid-thigh pulls during 2 separate testing sessions. Net PF and net force produced at each epoch were calculated. Within- and between-session reliabilities were determined using intraclass correlation coefficients and coefficient of variation percentages. In addition, Pearson correlation coefficients and coefficient of determination were calculated to examine the relationships between PF and time-specific force production. Results:: Net PF and time-specific force demonstrated very high to almost perfect reliability both within and between sessions (intraclass correlation coefficients .82–.97; coefficient of variation percentages 0.35%–1.23%). Similarly, time-specific force expressed as a percentage of PF demonstrated very high to almost perfect reliability both within and between sessions (intraclass correlation coefficients .76–.86; coefficient of variation percentages 0.32%–2.51%). Strong to nearly perfect relationships (r = .615–.881) exist between net PF and time-specific net force, with relationships improving over longer epochs. Conclusion:: Based on the smallest detectable difference, a change in force at 50 milliseconds expressed relative to PF > 10% and early force production (100, 150, 200, and 250 ms) expressed relative to PF of >2% should be considered meaningful. Expressing early force production as a percentage of PF is reliable and may provide greater insight into the adaptations to the previous training phase than PF alone.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.
Committee Chair: David Anderson; Committee Co-Chair: Alexander Gray; Committee Member: Anthony Yezzi; Committee Member: Hongyuan Zha; Committee Member: Justin Romberg; Committee Member: Ronald Schafer.

Sammanfattning Syfte och frågeställningar Syftet med studien var att i ett test-retest utvärdera tillförlitligheten i den nyutvecklade kraftmätaren ISOP vad gäller isometrisk muskelkraft i handledens tre rörelseplan. Den frågeställning som låg till grund för studien var följande: Föreligger det någon signifikant skillnad i uppmätta värden vid upprepade mätningar av handledskraft vid två separata testtillfällen (s.k. “test-retest”)? Metod Ett test-retest utfördes på 20 stycken testpersoner (tio kvinnor/tio män, ålder 28-48 år, medelvärde 38,6 år), utan tidigare hand- eller handledsskada. Åtta mätningar utfördes i sex olika handledsriktningar: flexion, extension, radialdeviation, ulnardeviation, pronation och supination av dominant hand samt flexion och extension av icke-dominant hand. Varje mätning bestod av tre stycken tryck med maximal kraft i följd, samt i varje rörelseriktning, och resultatet beräknades som ett medelvärde av dessa (test 1). Testprotokollet upprepades identiskt efter en vecka (test 2). Som intern kontroll användes Jamar handdynamometer, vilken är sedan tidigare reliabilitetstestad. Resultat Sambandet mellan test 1 och test 2 analyserades med Pearson’s korrelations koefficient (r) samt Intraclass Correlation Coefficient (ICC) med ett p-värde satt till 0,001. Resultatet av Pearson r visade ett mycket starkt samband för 9 av 10 par med värden mellan 0,84-0,98, och ett starkt samband för det tionde paret med ett värde på 0,77. Sambandet stärks ytterligare av att ICC ligger mellan 0,88-0,99 för samtliga par. Ett beroende student’s t-test utfördes för att påvisa eventuella skillnader mellan testerna men inga signifikanta skillnader hittades och detta stärker sambandet mellan testerna. Signifikanta skillnader om p är mindre än 0,05. Slutsats Den nyutvecklade kraftmätaren ISOP uppvisar god reliabilitet med mycket starka – starka samband vad gäller test-retest. Inga signifikanta skillnader mellan mätningarna kunde påvisas. ISOP kan således anses vara tillförlitligt för bruk vid rehabilitering och utvärdering av handledsfunktion.
Abstract Aim and hypothesis The aim of this study was to evaluate the reliability of ISOP – a new isometric power device with regard to evaluating isometric muscle force in the three planes of wrist motion. The hypothesis was as follows: Is there a significant difference in isometric power when repeated measurements are conducted at two different time-intervals (so called ”test-retest”)? Method A test-retest protocol was performed in 20 volunteers (ten women/ten men, age range 28-48 years, average 38.6), with no prior hand or wrist injury. Eight measurements were done in six different directions of the wrist: flexion, extension, radial deviation, ulnar deviation, pronation and supination of the dominant hand, as well as flexion and extension of the non-dominant hand. Each measurement consisted of three sequential maneuvers using maximum force, and the results were calculated as an average of these (test 1). The exact same protocol was repeated after a week (test 2). As an internal control, the Jamar hand dynamometer was used as it has previously been proven reliable. Results The relationship between test 1 and test 2 were analyzed using Pearson’s correlation coefficient (r) and Intraclass Correlation Coefficient (ICC) with a p-value set at 0.001. The result of Pearson’s r showed a very strong correlation between 9 of 10 pairs tested, with values between 0.84-0.98, and a strong correlation for the tenth pair with a value of 0.77. The strength of the correlations were confirmed by the ICC which showed 0.88-0.99 for all pairs. A dependent t-test was additionally performed to test for possible deviations between the tests, but no significant differences were found (p>0.05) which strengthens the relationship between the tests. Conclusion The new isometric power device, ISOP, has a very strong to strong correlation in a test-retest situation. No significant differences between the measurements could be demonstrated. ISOP may thus be considered a reliable device for use in wrist rehabilitation and evaluation.

In this thesis we generalize the problem of phase retrieval of vector to that of multi-vector. The identification of the multi-vector is done up to some special classes of isometries in the space. We give some upper and lower estimates on the minimal number of multi-linear operators needed for the retrieval. The results are preliminary and far from sharp.

Orientador: Prof. Dr. Daniel Miranda Machado
Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2014.
Este trabalho tem como objetivo de pesquisa fazer um estudo sobre a aplicação da geometria das transformações (em especial das isometrias) e da pavimentação do plano com polgonos regulares em atividades que fazem uso da Geometria Dinâmica como recurso para visualização e manuseio de objetos geometricos. São apresentados inicialmente os pressupostos teoricos dos conceitos envolvidos com algumas de suas principais denic~oes e propriedades. Em seguida, o trabalho de M.C.Escher e exposto para exemplicar o uso da parte teorica nas artes com o intuito de motivar a apreciação do conteudo estudado. Uma situação-problema e colocada como meio para desenvolver a pesquisa atraves do software Geogebra que foi utilizado para auxiliar a execucão das atividades propostas. Atraves do desenvolvimento do presente estudo, foi possvel constatar que ha um interesse muito maior dos alunos e um consenso por parte de todos de que a utilizac~ao de recursos visuais e tecnologicos no ensino de matematica e mais agradavel e estimulante.
This work aims to make a research study on the application of geometry transformations (especially isometries) and paving the plane with regular polygons in activities that make use of Dynamic Geometry as a resource for viewing and handling of geometric objects. The theoretical assumptions of the concepts involved with some of its main denitions and properties are initially presented. Then the work M.C.Escher is exposed to exemplify the use of the theoretical part in the arts in order to motivate the assessment of the content studied. A problem situation is placed as a means to develop the research through the Geogebra software that was used to assist the implementation of the proposed activities. Through the development of this study, it was found that there is a much greater student interest and consensus by all that the use of visual and technological resources in teaching mathematics is more enjoyable and stimulating.

Orientador: Marcelo Firer
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-01T00:34:36Z (GMT). No. of bitstreams: 1 Talpo_HumbertoLuiz_M.pdf: 2253274 bytes, checksum: 021cc39e57ebd85d37ec2b36e293c57d (MD5) Previous issue date: 2002
Resumo: Definimos uma reflexão em grafos como sendo um automorfismo involutivo cujo conjunto de pontos fixos é uma geodésica completa. Utilizando este conceito demonstramos que o produto de duas reflexões é uma isometria elíptica se e somente se os conjuntos de pontos fixos tem intersecção não vazia. Além disto, para o caso de árvores com valência 4k constante, mostramos que o fecho topológico do grupo gerado por reflexões tem índice 2 no grupo de automorfismos da árvore. Exploramos ainda uma possibilidade de inserir este conceito de reflexões em uma teoria axiomática similar a desenvolvida por Hjelmslev
Abstract: We define a reflection in a graph as an involutive automorphism whose set of fixed points is a complete geodesic. Using this concept, we prove that the product of two such reflections is an eliptic isometry if and only if its sets of fixed points has nonempty intersection. Moreover, for the case of a regular tree of valency 4k, we prove that the topological closure of the group generated by reflections has index 2 in the group of automorphisms of the tree. We explore also a possibility to insert this concept of reflection in an axiomatic theory similar to the one developed by Hjelmslev
Mestrado
Mestre em Matemática

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-10-26T19:45:34Z No. of bitstreams: 1 DissLFGP.pdf: 5615571 bytes, checksum: f5636cf5ae2059f71859a66b025ed4cf (MD5)
Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-11-08T18:31:26Z (GMT) No. of bitstreams: 1 DissLFGP.pdf: 5615571 bytes, checksum: f5636cf5ae2059f71859a66b025ed4cf (MD5)
Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-11-08T18:31:35Z (GMT) No. of bitstreams: 1 DissLFGP.pdf: 5615571 bytes, checksum: f5636cf5ae2059f71859a66b025ed4cf (MD5)
Made available in DSpace on 2016-11-08T18:31:41Z (GMT). No. of bitstreams: 1 DissLFGP.pdf: 5615571 bytes, checksum: f5636cf5ae2059f71859a66b025ed4cf (MD5) Previous issue date: 2016-09-17
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
This actual study is an investigation about the importance of using computers and other information and communication technologies (ICTs) in the teaching of Mathematics. We believe in the thesis that ICT can contribute as an educational means for the improvement of teaching and learning situations, and consequently in solving problems such as school failure and school indiscipline. Therefore, we designed and applied a didactic sequence using the Geogebra for the development of Isometries topic in a class of 6th grade of elementary school. The didactic sequence was structured within the perspectives of Didactic Engineering and adopted a qualitative methodology. The results indicate that ICTs contribute significantly in the process of teaching and learning, but some external factors are still obstacles to the effective implementation of this resource in schools.
O presente estudo é uma investigação acerca da importância da utilização de computadores e outras tecnologias de informação e comunicação (as TIC’s) no ensino de Matemática. Acreditamos na tese de que as TIC’s podem contribuir como meio educativo para a melhora das situações de ensino aprendizagem e, consequentemente, na solução de problemas como o fracasso escolar e a indisciplina escolar. Nesse intuito, idealizamos e aplicamos uma sequência didática com o uso do Geogebra para o desenvolvimento do tópico Transformações Geométricas em uma turma do sexto ano do Ensino Fundamental. A sequência didática foi estruturada dentro das perspectivas da Engenharia Didática e seguiu uma metodologia qualitativa. Os resultados indicam que as TIC’s contribuem de forma significativa no processo de ensino e aprendizagem, contudo alguns fatores externos ainda são entraves para a efetiva implementação deste recurso nas escolas.

Apresentamos conceitos da teoria de Grupos de Lie e Ações Próprias e descrevemos a demonstração da Conjectura de Palais-Terng efetuada por Alexandrino. Tal conjectura garante que uma folheação riemanniana singular com distribuição normal é uma folheação riemanniana singular com seções. Adaptamos para o caso particular das ações isométricas.
We present some aspects of the theory of Lie Groups and Proper Actions, and we review the proof of the Palais-Terng Conjecture given by Alexandrino. This theorem assures that a singular Riemannian foliation with integrable normal distribution is a singular Riemannian foliation with section. We adapt the proof for isometric actions.

Starting from the Riemann Mapping Theorem it arises the interest for biholomorphisms over domains in one or several complex variables. Poincar´e showed that there is no analytic isomorphism between the Polydisc and the unit ball already in C^2. The previous fact may suggest that biholomorphic domains are a class of such well-behaved sets that could extend some regularity of the biholomorpshism until their respective boundaries. A very influent approach was faced by Fefferman (published in the year 1974), by proving that every biholomorphism between bounded strongly pseudoconvex domains with smooth boundaries extends as a diffeomorphism to the closures of the domains. In this work is quoted a classical result that presents an isometry respect to the Bergman metric between biholomorphic domains and he noticed an interesting behaviour of geodesics when they are going to the boundary of a considered domain. The first part of this thesis mainly follows Abate’s work aiming to show the homeomorphic extension of a biholomorphism between C^2-smooth strongly pseudoconvex domains. The second part of this thesis mainly follows the work of Bracci, Gaussier and Zimmer aiming to show the homeomorphic extension of a Quasi-Isometric homeomorphisms to the End compactifications of the respective domains. Other consequences are related to extend the Denjoy-Wolff Theorem for domains in several complex variables and present the Denjoy-Wolff behaviour for commuting holomorphic selfmaps with no fixed point in the domain itself.

Made available in DSpace on 2015-09-17T15:24:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-11-12. Added 1 bitstream(s) on 2015-09-17T15:47:40Z : No. of bitstreams: 1 000845667.pdf: 1587770 bytes, checksum: 06f2f0dbd3bebd13ef2348f171410860 (MD5)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Este trabalho tem como objetivo principal estudar as isometrias - no plano e no espaço - dentro da sala de aula. Inicialmente é realizado um breve resgate histórico a respeito da relação entre os conceitos de isometria e beleza, através dos tempos. Algumas das isometrias foram observadas na natureza em animais e plantas, e em obras construídas pelo Homem, como objetos, obras arquitetônicas famosas e obras de arte (quadros e esculturas). Buscamos conceituar e demonstrar os tipos de isometria no plano, bem como suas composições, além de conceituar os tipos de isometrias no espaço. Também apresentamos o Teorema Fundamental das Isometrias que caracteriza todos os tipos de isometrias no plano. Após a fundamentação teórica, descrevemos a realização de atividades em sala de aula utilizando diferentes tipos de malhas e imagens recortadas de revistas e jornais, com o objetivo de levar o aluno a identificar algum tipo de isometria. No final, apresentamos uma análise de como o ensino-aprendizagem de isometrias são abordados em alguns documentos oficiais de ensino no Brasil (PCNs, Currículo do Estado de São Paulo e matrizes de referências do SARESP)
This work has as main objective to study the isometries - in the plane and in the space - inside the classroom. Initially is performed a brief historic rescue about the relation between the concepts of isometry and beauty through the ages. Some of isometries have been observed in nature in animals and plants, and works constructed by mens, such as objects, famous architectural works and artworks (paintings and sculptures). We seek to conceptualize and demonstrate the types of isometries in the plane, as well as their compositions, and conceptualize the types of isometries in space. After the theoretical foundation, we describe the realization of activities in the classroom using different types of grids and pictures cut from magazines and newspapers, with the goal of bringing students to identify some sort of isometry. In the end, we present an analysis of how the teaching and learning of isometries are dealt in some official documents of education in Brazil (PCNs, Curriculum of São Paulo and arrays of references SARESP)

Orientador: Évelin Meneguesso Barbaresco
Banca: Ermínia de Lourdes Campello Fanti
Banca: Francielle Rodrigues de Castro Coelho
Resumo: Este trabalho tem como objetivo principal estudar as isometrias - no plano e no espaço - dentro da sala de aula. Inicialmente é realizado um breve resgate histórico a respeito da relação entre os conceitos de isometria e beleza, através dos tempos. Algumas das isometrias foram observadas na natureza em animais e plantas, e em obras construídas pelo Homem, como objetos, obras arquitetônicas famosas e obras de arte (quadros e esculturas). Buscamos conceituar e demonstrar os tipos de isometria no plano, bem como suas composições, além de conceituar os tipos de isometrias no espaço. Também apresentamos o Teorema Fundamental das Isometrias que caracteriza todos os tipos de isometrias no plano. Após a fundamentação teórica, descrevemos a realização de atividades em sala de aula utilizando diferentes tipos de malhas e imagens recortadas de revistas e jornais, com o objetivo de levar o aluno a identificar algum tipo de isometria. No final, apresentamos uma análise de como o ensino-aprendizagem de isometrias são abordados em alguns documentos oficiais de ensino no Brasil (PCNs, Currículo do Estado de São Paulo e matrizes de referências do SARESP)
Abstract: This work has as main objective to study the isometries - in the plane and in the space - inside the classroom. Initially is performed a brief historic rescue about the relation between the concepts of isometry and beauty through the ages. Some of isometries have been observed in nature in animals and plants, and works constructed by mens, such as objects, famous architectural works and artworks (paintings and sculptures). We seek to conceptualize and demonstrate the types of isometries in the plane, as well as their compositions, and conceptualize the types of isometries in space. After the theoretical foundation, we describe the realization of activities in the classroom using different types of grids and pictures cut from magazines and newspapers, with the goal of bringing students to identify some sort of isometry. In the end, we present an analysis of how the teaching and learning of isometries are dealt in some official documents of education in Brazil (PCNs, Curriculum of São Paulo and arrays of references SARESP)
Mestre