Relevant bibliographies by topics / Isometrie

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Isometrie'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 May 2024

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Journal articles on the topic "Isometrie"

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Mantovani, Lisa. "Achillessehnentendinopathie: Welchen Nutzen hat ein isometrisches Training?" MSK – Muskuloskelettale Physiotherapie 26, no. 03 (July 2022): 141–46. http://dx.doi.org/10.1055/a-1827-2679.

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Isometrisches Training wird seit ein paar Jahren zur Schmerzlinderung bei einer Achillessehnentendinopathie empfohlen. Doch nicht nur Schmerz, auch die reduzierte physische Leistungsfähigkeit sollte in der Therapie adressiert werden, da diese möglicherweise zu Rückfällen führen kann. Kann Isometrie auch die Leistungsfähigkeit beeinflussen?
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Jiménez-Vargas, Antonio, and María Isabel Ramírez. "Algebraic Reflexivity of Non-Canonical Isometries on Lipschitz Spaces." Mathematics 9, no. 14 (July 11, 2021): 1635. http://dx.doi.org/10.3390/math9141635.

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Let Lip([0,1]) be the Banach space of all Lipschitz complex-valued functions f on [0,1], equipped with one of the norms: fσ=|f(0)|+f′L∞ or fm=max|f(0)|,f′L∞, where ·L∞ denotes the essential supremum norm. It is known that the surjective linear isometries of such spaces are integral operators, rather than the more familiar weighted composition operators. In this paper, we describe the topological reflexive closure of the isometry group of Lip([0,1]). Namely, we prove that every approximate local isometry of Lip([0,1]) can be represented as a sum of an elementary weighted composition operator and an integral operator. This description allows us to establish the algebraic reflexivity of the sets of surjective linear isometries, isometric reflections, and generalized bi-circular projections of Lip([0,1]). Additionally, some complete characterizations of such reflections and projections are stated.
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Sun, Yuqi. "On Coarse Isometries and Linear Isometries between Banach Spaces." Axioms 13, no. 3 (February 28, 2024): 157. http://dx.doi.org/10.3390/axioms13030157.

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Let X,Y be two Banach spaces and f:X→Y be a standard coarse isometry. In this paper, we first show a sufficient and necessary condition for the coarse left-inverse operator of general Banach spaces to admit a linearly isometric right inverse. Furthermore, by using the well-known simultaneous extension operator, we obtain an asymptotical stability result when Y is a space of continuous functions. In addition, we also prove that every coarse left-inverse operator does admit a linear isometric right inverse without other assumptions when Y is a Lp(1<p<∞) space, or both X and Y are finite dimensional spaces of the same dimension. Making use of the results mentioned above, we generalize several results of isometric embeddings and give a stability result of coarse isometries between Banach spaces.
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BAKHIT, M. A. "ISOMETRIES ON SOME GENERAL FAMILY FUNCTION SPACES AMONG COMPOSITION OPERATORS." Journal of Mathematical Analysis 13, no. 1 (March 30, 2022): 1–13. http://dx.doi.org/10.54379/jma-2022-1-1.

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In this paper, we discuss the isometries of composition operators on the holomorphic general family function spaces F(p, q, s). First, we classify the isometric composition operators acting on a general Banach spaces. For 1 < p < 2, we display that an isometry of Cφ is caused only by a rotation of the disk. We scrutinize the previous work on the case for p ≥ 2. Also, we characterize many of the foregoing results about all α-Besov-type spaces F(p, αp − 2, s), α > 0. We exhibit that in every classes F(p, αp − 2, s) except for the Dirichlet space D = F(2, 0, 0), rotations are the only that produce isometries.
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Mahmoud, Sid, Muneo ChO, and Ji Lee. "(m,q)-isometric and (m,∞)-isometric tuples of commutative mappings on a metric space." Filomat 34, no. 7 (2020): 2425–37. http://dx.doi.org/10.2298/fil2007425m.

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In this paper, we introduce new concepts of (m,q)-isometries and (m,?)-isometries tuples of commutative mappings on metrics spaces. We discuss the most interesting results concerning this class of mappings obtained form the idea of generalizing the (m,q)-isometries and (m,?)-isometries for single mappings. In particular, we prove that if T = (T1,..., Tn) is an (m,q)-isometric commutative and power bounded tuple, then T is a (1,q)-isometric tuple. Moreover, we show that if T = (T1,...,Td) is an (m,?)- isometric commutative tuple of mappings on a metric space (E,d), then there exists a metric d? on E such that T is a (1,?)-isometric tuple on (E,d?).
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Popov, Vladimir A. "Locally Isometric Riemannian Analytic Spaces." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 4-1 (216-1) (December 28, 2022): 55–64. http://dx.doi.org/10.18522/1026-2237-2022-4-1-55-64.

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Classes of locally isometric Riemannian analytic manifolds are studied. A generalization of the concept of completeness is given. We consider the Lie algebra 𝔤 of all Killing vector fields of a Riemannian analytic manifold, its stationary subalgebra 𝔥 the simply connected Lie group 𝐺 corresponding to the Lie algebra 𝔤, and the subgroup 𝐻 corresponding to the Lie subalgebra 𝔥. In the absence of a center in the algebra 𝔤 the concept of a quasi-complete (compressed) manifold is introduced. An oriented Riemannian analytic manifold whose vector field algebra has zero center is said to be quasi-complete if it is non-extendable and does not admit non-trivial orientation-preserving and all Killing vector fields local isometries to itself. The main property of such a manifold is that it is unique in the class of all locally isometric Riemannian analytic manifolds, and any locally given isometry of this manifold 𝑀 into itself can be analytically extended to an isometry 𝑓: 𝑀 ≈ 𝑀. For an arbitrary class of locally isometric Riemannian analytic manifolds, a definition of a pseudocomplete manifold is given, which is complete if a complete manifold exists in the given class. A Riemannian analytic simply connected manifold M is called pseudocomplete if it has the following properties. 𝑀 is non-extendable. There is no locally isometric covering map f; M→N, where N is a simply connected Riemannian analytic manifold and f (M) is an open subset of N not equal to N.
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Aleman, Alexandru, Peter Duren, María J. Martín, and Dragan Vukotić. "Multiplicative Isometries and Isometric Zero-Divisors." Canadian Journal of Mathematics 62, no. 5 (October 1, 2010): 961–74. http://dx.doi.org/10.4153/cjm-2010-048-7.

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AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.
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Li, Chi-Kwong. "Norms, Isometries, and Isometry Groups." American Mathematical Monthly 107, no. 4 (April 2000): 334. http://dx.doi.org/10.2307/2589178.

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Li, Chi-Kwong. "Norms, Isometries, and Isometry Groups." American Mathematical Monthly 107, no. 4 (April 2000): 334–40. http://dx.doi.org/10.1080/00029890.2000.12005201.

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Cima, Joseph A., and Warren R. Wogen. "Isometric equivalence of isometries on $H^p$." Proceedings of the American Mathematical Society 144, no. 11 (April 27, 2016): 4887–98. http://dx.doi.org/10.1090/proc/13106.

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Dissertations / Theses on the topic "Isometrie"

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Bucciarelli, Chiara. "Geometria e topologia delle superfici." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9725/.

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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.
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Bartolini, Gloria. "Una sperimentazione in un liceo scientifico: le tassellazioni del piano con l'uso di un software di geometria didattica." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2292/.

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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.
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Schaefer, Laura. "Synchronisationsphänomene myotendinöser Oszillationen interagierender neuromuskulärer Systeme : mit Betrachtung einer Hypothese bezüglich unterschiedlicher Qualitäten isometrischer Muskelaktion." Phd thesis, Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7244/.

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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.
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Paolizzi, Michele. "Gruppi risolubili." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8713/.

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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.
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Caravita, Alessandro. "I gruppi dei fregi e i gruppi cristallografici piani." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23478/.

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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.
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De, Lorenzi Diego. "La rigidità della sfera." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18241/.

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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.
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Shchur, Vladimir. "Quasi-isometries between hyperbolic metric spaces, quantitative aspects." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00867709.

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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).
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Gunepin, François-Xavier. "Positionnement isométrique des plasties du ligament croisé antérieur : de la théorie à la pratique (à propos de 24 cas)." Bordeaux 2, 1992. http://www.theses.fr/1992BOR2M141.

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Das, Kajal. "On Uniform and integrable measure equivalence between discrete groups." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN023.

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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 $m>n$
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Sousa, Alexandre Pereira. "Isometrias e similaridades." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306864.

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Orientador: Claudina Izepe Rodrigues
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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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
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Books on the topic "Isometrie"

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Zeichnen, Isometrisches. Isometrisches Papier : Isometrie Zeichenbuch: Isometrisch 3D Zeichnen 120 Seiten. Independently Published, 2019.

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Bücherallerlei, Steve Rueb. Isometrie Isometrisch Zeichnen Isometriepapier DIN A5 120 Seiten: Technisches Zeichnen I Ingenieur Geschenk I Isometriepapier I Isometrie Block I 3D Grafik Zeichnen. Independently Published, 2020.

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Zeichnen, Isometrisch Isometrisch. Isometrisch Zeichnen: DIN A4 Isometriepapier - Isometrieblock Zeichenbuch Mit Isometrie Papier 200 Seiten. Independently Published, 2019.

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Zeichnen, Isometrisch Isometrisch. Isometrisch Zeichnen: DIN A4 Isometriepapier - Isometrieblock Zeichenbuch Mit Isometrie Papier 200 Seiten. Independently Published, 2019.

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Kleingrün, Klara. Isometrisches Papier 3D: 3D Projekte Isometriepapier Isometrieblock Isometrie 3D-Zeichenbuch Isometrisches Zeichnen Architekt. Independently Published, 2019.

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Kleingrün, Klara. Isometrisches Papier 3D: 3D Projekte Isometriepapier Isometrieblock Isometrie 3D-Zeichenbuch Isometrisches Zeichnen Architekten. Independently Published, 2019.

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Kleingrün, Klara. Isometrisches Papier 3D: 3D Projekte Isometriepapiere Isometrieblock Isometrie 3D-Zeichenbuch Isometrisches Zeichnen Architekt. Independently Published, 2019.

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Kleingrün, Klara. Isometrisches Papier 3D: 3D Projekte Isometriepapier Isometrieblock Isometrie 3D-Zeichenbuch Isometrisches Zeichnen Architekt Konstruieren. Independently Published, 2019.

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Publishing, Isometrie Technisches Zeichnen. ISOMETRISCHES PAPIER Für Architektur und Design: Groß Large 150 Seiten 150 Pages Isometric Graph Paper Zeichenbuch Mit Isometrie Papier Dreieck 3D Matrix 0,28 Zoll Gleichseitige Dreiecke. Independently Published, 2019.

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Publishing, Architektur Technisches Zeichnen. ISOMETRISCHES PAPIER Für Architektur und Design: Groß Large 150 Seiten 150 Pages Isometric Graph Paper Zeichenbuch Mit Isometrie Papier Dreieck 3D Matrix 0,28 Zoll Gleichseitige Dreiecke. Independently Published, 2019.

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Book chapters on the topic "Isometrie"

1

Petermann, J., P. Trus, and L. Gotzen. "Untersuchungen zur Isometrie des hinteren Kreuzbandersatzes." In 54. Jahrestagung, 569–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84552-9_398.

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Benedetto, K. P., A. Inderster, and K. H. Künzel. "Faserverlauf und Isometrie der vorderen Kreuzbandbündel — Leichenstudie." In Hefte zur Zeitschrift „Der Unfallchirurg“, 1215–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-78055-4_269.

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Hopf, Heinz. "Ǜber Isometrie und stetige Verbiegung von Flächen." In Collected Papers - Gesammelte Abhandlungen, 607–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-40036-0_34.

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Pullarcot, Sunil. "Piping Isometric Drawings (Isometrics)." In Process Plant Piping, 41–54. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9781003328124-3.

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Lang, Serge, and Gene Murrow. "Isometries." In Geometry, 356–89. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4757-2022-8_12.

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Carlson, Philip. "Isometries." In Solutions Manual for Geometry: A High School Course, 114–27. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0861-7_12.

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Lang, Serge. "Isometries." In Basic Mathematics, 133–72. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1027-6_7.

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Gelca, Răzvan, Ionuţ Onişor, and Carlos Yuzo Shine. "Isometries." In Problem Books in Mathematics, 3–69. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89117-6_1.

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Gelca, Răzvan, Ionuţ Onişor, and Carlos Yuzo Shine. "Isometries." In Problem Books in Mathematics, 249–54. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89117-6_5.

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Gelca, Răzvan, Ionuţ Onişor, and Carlos Yuzo Shine. "Isometries." In Problem Books in Mathematics, 271–367. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89117-6_9.

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Conference papers on the topic "Isometrie"

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Chen, Qiuyi, and Mark D. Fuge. "Characterizing Designs via Isometric Embeddings: Applications to Airfoil Inverse Design." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-116743.

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Abstract Many data analysis and design problems involve reasoning about points in high-dimensional space. A common strategy is to embed points from this high-dimensional space into a low-dimensional one. As we will show in this paper, a critical property of good embeddings is that they preserve isometry — i.e., preserving the geodesic distance between points on the original data manifold within their embedded locations in the latent space. However, enforcing isometry is non-trivial for common Neural embedding models, such as autoencoders and generative models. Moreover, while theoretically appealing, it is not clear to what extent enforcing isometry is really necessary for a given design or analysis task. This paper answers these questions by constructing an isometric embedding via an isometric autoencoder, which we employ to analyze an inverse airfoil design problem. Specifically, the paper describes how to train an isometric autoencoder and demonstrates its usefulness compared to non-isometric autoencoders on both simple pedagogical examples and for airfoil embeddings using the UIUC airfoil dataset. Our ablation study illustrates that enforcing isometry is necessary to accurately discover latent space clusters — a common analysis method researchers typically perform on low-dimensional embeddings. We also show how isometric autoencoders can uncover pathologies in typical gradient-based Shape Optimization solvers through an analysis on the SU2-optimized airfoil dataset, wherein we find an over-reliance of the gradient solver on angle of attack. Overall, this paper motivates the use of isometry constraints in Neural embedding models, particularly in cases where researchers or designer intend to use distance-based analysis measures (such as clustering, k-Nearest Neighbors methods, etc.) to analyze designs within the latent space. While this work focuses on airfoil design as an illustrative example, it applies to any domain where analyzing isometric design or data embeddings would be useful.
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Rosa, Gustavo Henrique de Mello, Guilherme Henrique Moretto, Kelly Zhang, and João Eduardo de Araujo. "Modification of palmar grip strength induced by overflow contralateral to hip contraction." In XIV Congresso Paulista de Neurologia. Zeppelini Editorial e Comunicação, 2023. http://dx.doi.org/10.5327/1516-3180.141s1.404.

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Introduction: Neurofunctional rehabilitation often employs various approaches to enhance recruitment and muscle strength through overflow, a phenomenon that amplifies the motor response of homologous muscles in the contralateral segment. overflow has been well documented in the literature, particularly in techniques like FNP and cross-education. The phenomenon of overflow is known to facilitate muscle activity in muscles that are not actively stimulated, resulting in unintentional contractions during a resisted isometric activity. Objectives: The objective of this study was to investigate the overflow mechanisms of non-homologous contralateral muscles of the lower limb during an instructed handgrip task. Methods: A total of 90 individuals, with a motor preference for their right upper limb (RUL), were divided into control (CG) and resisted isometry group (RIG) and underwent a protocol involving three maximal hand grip contractions with their RUL and LUL. In assessment 2, the CG performed the same protocol as baseline, while the RIG group performed three maximal isometric contractions of left hip flexion with three maximal contractions of hand flexion with their RUL. statistical analysis was conducted by a multiple comparison analysis of variance with P < 0.05. Results: Observing the data from evaluation 1, both the CG and RIG showed a reduction in strength between the third and first attempt for both the left and right upper limbs (F = 1.07, F = 0.68, respectively). In evaluation 2, the decrease occurred only for the CG in both upper limbs (F = 0.15, F = 1.29, respectively). Conclusion: Our study revealed that maximal muscle strength was maintained in RIG individuals during assessment 2, indicating the existence of overflow when performing an isometric hip flexion task concomitantly with the palmar grip.
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Alamélou, Quentin, Paul-Edmond Berthier, Chloé Cachet, Stéphane Cauchie, Benjamin Fuller, Philippe Gaborit, and Sailesh Simhadri. "Pseudoentropic Isometries." In ASIA CCS '18: ACM Asia Conference on Computer and Communications Security. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3196494.3196530.

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Mathieu, Martin. "Spectral isometries." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-21.

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Yang, Meimei, Pengfei Fang, and Hui Xue. "Expanding the Hyperbolic Kernels: A Curvature-aware Isometric Embedding View." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/497.

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Modeling data relation as a hierarchical structure has proven beneficial for many learning scenarios, and the hyperbolic space, with negative curvature, can encode such data hierarchy without distortion. Several recent studies also show that the representation power of the hyperbolic space can be further improved by endowing the kernel methods. Unfortunately, the known kernel methods, developed in hyperbolic space, are limited by the adaptation capacity or distortion issues. This paper addresses the issues through a novel embedding function. To this end, we propose a curvature-aware isometric embedding, which establishes an isometry from the Poincar\'e model to a special reproducing kernel Hilbert space (RKHS). Then we can further define a series of kernels on this RKHS, including several positive definite kernels and an indefinite kernel. Thorough experiments are conducted to demonstrate the superiority of our proposals over existing-known hyperbolic and Euclidean kernels in various learning tasks, e.g., graph learning and zero-shot learning.
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Safyannikov, Nikolay M., Olga I. Bureneva, Zoya A. Aleksanyan, and Aleksandr E. Chepasov. "Isometric Vector Neuroanalyzer." In 2021 II International Conference on Neural Networks and Neurotechnologies (NeuroNT). IEEE, 2021. http://dx.doi.org/10.1109/neuront53022.2021.9472819.

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Sahillioglu, Yusuf, and Yucel Yemez. "3D Isometric shape correspondence." In 2010 IEEE 18th Signal Processing and Communications Applications Conference (SIU 2010). IEEE, 2010. http://dx.doi.org/10.1109/siu.2010.5651555.

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Dollár, Piotr, Vincent Rabaud, and Serge Belongie. "Non-isometric manifold learning." In the 24th international conference. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1273496.1273527.

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Vasiloglou, Nikolaos, Alexander G. Gray, and David V. Anderson. "Learning Isometric Separation Maps." In 2009 IEEE International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2009. http://dx.doi.org/10.1109/mlsp.2009.5306212.

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Gao, Maolin, Zorah Lahner, Johan Thunberg, Daniel Cremers, and Florian Bernard. "Isometric Multi-Shape Matching." In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2021. http://dx.doi.org/10.1109/cvpr46437.2021.01396.

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Reports on the topic "Isometrie"

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Lee, Hyun. Stochastically Nonnegative Isometries. Web of Open Science, March 2020. http://dx.doi.org/10.37686/emj.v1i1.24.

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Chuang, Wu-yen, and Peng Gao. Flux-induced Isometry Gauging in Heterotic Strings. Office of Scientific and Technical Information (OSTI), January 2007. http://dx.doi.org/10.2172/896927.

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Chartrand, Rick, and Valentina Staneva. Restricted isometry properties and nonconvex compressive sensing. Office of Scientific and Technical Information (OSTI), November 2007. http://dx.doi.org/10.2172/1454956.

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Burns, T. J. CGVIEW: A program to generate isometric and perspective views of combinatorial geometries. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/5065672.

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Burns, T. J. CGVIEW: A program to generate isometric and perspective views of combinatorial geometries. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/10158989.

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Davenport, Mark A., and Michael B. Wakin. Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property. Fort Belvoir, VA: Defense Technical Information Center, August 2009. http://dx.doi.org/10.21236/ada521441.

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Pfander, Goetz E., Holger Rauhut, and Joel A. Tropp. The Restricted Isometry Property for Time-Frequency Structured Random Matrices. Fort Belvoir, VA: Defense Technical Information Center, June 2011. http://dx.doi.org/10.21236/ada563016.

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Williams, Carole A., J. Martin, J. Moffatt, J. E. Douglas, and A. R. Lind. Enhancing the Tolerance to +Gz Acceleration by Optimizing the Use of Isometric Contractions in Combination with Straining Maneuvers. Fort Belvoir, VA: Defense Technical Information Center, August 1990. http://dx.doi.org/10.21236/ada230454.

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Li, Yinghao, Shuoqi Li, Yongqi Wang, Jianming Zhou, Jing Yang, and Jiayuan Ma. Effects of Isometric Resistance Exercise of Lower Limbs on Intraocular Pressure and Ocular Perfusion Pressure of Healthy Adults. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, January 2021. http://dx.doi.org/10.37766/inplasy2021.1.0073.

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Li, Rui, Chen Soon Chee, Tengku Fadilah Tengku Kamalden, Alif Syamim Syazwan Ramli, and Kun Yang. Effects of Blood Flow Restriction Training on Lower Extremity Maximum Dynamic Strength and Isometric Muscle Strength among Athletes: A Systematic Review and meta- analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, September 2023. http://dx.doi.org/10.37766/inplasy2023.9.0051.

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