Relevant bibliographies by topics / Peano curves

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  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Peano curves'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Peano curves"

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Massopust, Peter R. "Fractal peano curves." Journal of Geometry 34, no. 1-2 (1989): 127–38. http://dx.doi.org/10.1007/bf01224238.

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Cannon, James W., and William P. Thurston. "Group invariant Peano curves." Geometry & Topology 11, no. 3 (2007): 1315–55. http://dx.doi.org/10.2140/gt.2007.11.1315.

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MOLITOR, DENALI, NADIA OTT, and ROBERT STRICHARTZ. "USING PEANO CURVES TO CONSTRUCT LAPLACIANS ON FRACTALS." Fractals 23, no. 04 (2015): 1550048. http://dx.doi.org/10.1142/s0218348x15500486.

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We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.
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Krupski, P., and H. Patkowska. "Menger curves in Peano continua." Colloquium Mathematicum 70, no. 1 (1996): 79–86. http://dx.doi.org/10.4064/cm-70-1-79-86.

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Younsi, Malik. "Peano Curves in Complex Analysis." American Mathematical Monthly 126, no. 7 (2019): 635–40. http://dx.doi.org/10.1080/00029890.2019.1605800.

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Belov, A. S. "POWER SERIES AND PEANO CURVES." Mathematics of the USSR-Izvestiya 27, no. 1 (1986): 1–26. http://dx.doi.org/10.1070/im1986v027n01abeh001162.

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Bochi, Jairo, and Pedro H. Milet. "Peano curves with smooth footprints." Monatshefte für Mathematik 180, no. 4 (2016): 693–712. http://dx.doi.org/10.1007/s00605-016-0899-8.

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Agadzhanov, А. N. "Peano-type curves, Liouville numbers, and microscopic sets." Доклады Академии наук 485, no. 1 (2019): 7–10. http://dx.doi.org/10.31857/s0869-565248417-10.

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Peano-type curves in multidimensional Euclidean space are considered in terms of number theory. In contrast to curves constructed by D. Hilbert, H. Lebesgue, V. Sierpinski, and others, this paper presents results showing that each such curve is a continuous image of universal (shared by all curves) nowhere dense perfect subsets of the interval [0, 1] with a zero s-dimensional Hausdorff measure that consist of only Liouville numbers. An example of a problem in which a pair of continuous functions controlling the behavior of an oscillating system generates a Peano-type curve in the plane is given.
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Albuquerque, N., L. Bernal-González, D. Pellegrino, and J. B. Seoane-Sepúlveda. "Peano curves on topological vector spaces." Linear Algebra and its Applications 460 (November 2014): 81–96. http://dx.doi.org/10.1016/j.laa.2014.07.029.

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Budagov, A. A. "Peano curves and moduli of continuity." Mathematical Notes of the Academy of Sciences of the USSR 50, no. 2 (1991): 783–89. http://dx.doi.org/10.1007/bf01157562.

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Dissertations / Theses on the topic "Peano curves"

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Granholm, Jonas. "Remarkable curves in the Euclidean plane." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-112576.

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An important part of mathematics is the construction of good definitions. Some things, like planar graphs, are trivial to define, and other concepts, like compact sets, arise from putting a name on often used requirements (although the notion of compactness has changed over time to be more general). In other cases, such as in set theory, the natural definitions may yield undesired and even contradictory results, and it can be necessary to use a more complicated formalization.    The notion of a curve falls in the latter category. While it is intuitively clear what a curve is – line segments, empty geometric shapes, and squiggles like this: – it is not immediately clear how to make a general definition of curves. Their most obvious characteristic is that they have no width, so one idea may be to view curves as what can be drawn with a thin pen. This definition, however, has the weakness that even such a line has the ability to completely fill a square, making it a bad definition of curves. Today curves are generally defined by the condition of having no width, that is, being one-dimensional, together with the conditions of being compact and connected, to avoid strange cases.    In this thesis we investigate this definition and a few examples of curves.
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Albuquerque, Nacib André Gurgel e. "Hardy-Littlewood/Bohnenblust-Hille multilinear inequalities and Peano curves on topological vector spaces." Universidade Federal da Paraí­ba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7448.

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Made available in DSpace on 2015-05-15T11:46:22Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1916558 bytes, checksum: 2a74bd2ee59f2f8ed1aa50acfcc283c4 (MD5) Previous issue date: 2014-12-26<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This work is divided in two subjects. The first concerns about the Bohnenblust-Hille and Hardy- Littlewood multilinear inequalities. We obtain optimal and definitive generalizations for both inequalities. Moreover, the approach presented provides much simpler and straightforward proofs than the previous one known, and we are able to show that in most cases the exponents involved are optimal. The technique used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this thesis to improve the constants for vector-valued Bohnenblust-Hille type inequalities. The second subject has as starting point the existence of Peano spaces, that is, Haurdor spaces that are continuous image of the unit interval. From the point of view of lineability we analyze the set of continuous surjections from an arbitrary euclidean spaces on topological spaces that are, in some natural sense, covered by Peano spaces, and we conclude that large algebras are found within the families studied. We provide several optimal and definitive result on euclidean spaces, and, moreover, an optimal lineability result on those special topological vector spaces.<br>Este trabalho édividido em dois temas. O primeiro diz respeito às desigualdades multilineares de Bohnenblust-Hille e Hardy-Littlewood. Obtemos generalizações ótimas e definitivas para ambas desigualdades. Mais ainda, a abordagem apresentada fornece demonstrações mais simples e diretas do que as conhecidas anteriormente, além de sermos capazes de mostrar que os expoentes envolvidos são ótimos em varias situações. A técnica utilizada combina ferramentas probabilísticas e interpolativas; esta ultima e ainda usada para melhorar as estimativas das versões vetoriais da desigualdade de Bohnenblust-Hille. O segundo tema possui como ponto de partida a existência de espaços de Peano, ou seja, os espaços de Hausdor que são imagem contínua do intervalo unitário. Sob o ponto de vista da lineabilidade, analisamos o conjunto das sobrejecoes contínuas de um espaço euclidiano arbitrário em um espaço topológico que, de certa forma, e coberto por espaços de Peano, e concluímos que grandes álgebras são encontradas nas famílias estudadas. Fornecemos vários resultados ótimos e definitivos em espaços euclidianos, e, mais ainda, um resultado de lineabilidade ótimo naqueles espaços vetoriais topológicos especiais.
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Maia, Francisco Everton Pereira. "Curvas planas : clássicas, regulares e de preenchimento." reponame:Repositório Institucional da UFABC, 2016.

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Orientador: Prof. Dr. Vinicius Cifú Lopes<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.<br>Neste trabalho apresentaremos uma visão sobre os princípios das curvas planas. Iniciamos o desenvolvimento dos estudos com as cônicas: parábola, elipse e hipérbole que são aplicadas no Ensino Médio normalmente usando equações cartesianas. Abordaremos o assunto destas e outras curvas usando equações paramétricas, com intuito de mostrar a vantagem de utilizá-las. Abrangeremos em nossos estudos a catenária, a cicloide e a curva de Bézier, curvas as quais não são estudadas no Ensino Básico, mas poderiam ser apresentadas como um desafio motivador ao estudo da Matemática, explorando suas várias aplicações que acontecem de maneira natural em nosso cotidiano. Apresentaremos propriedades gerais das curvas como: continuidade, parametrização, comprimento de arco, curva suave, curvatura e outras, além de realizar a demonstração do teorema fundamental das curvas planas e para finalizar estudaremos uma curva exótica, conhecida como curva de preenchimento de espaço, construída pela primeira vez pelo matemático italiano Giuseppe Peano.<br>In this work we will present an insight into the principles of flat curves. We start with the conics: parabola, ellipse and hyperbole which are applied in high school usually using Cartesian equations. We will discuss those and other curves using parametric equations, in order to show the advantage of using them. We will cover in our studies the catenary, the cycloid and a Bézier curve, curves which are not studied in basic education, but could be presented as a challenging motivation to the study of Mathematics by exploring their various uses that happen naturally in our everyday lives. We will introduce general properties of curves as: continuity, parameterization, arc length, smooth curve, curvature and others, in addition to the proof of the fundamental theorem of plane curves, and finally we will study an exotic curve, known as space-filling curve, built for the first time by the Italian mathematician Giuseppe Peano.
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Redtwitz, Dennis Alexander. "Densificabilidad: caracterizaciones, extensiones y aplicaciones." Doctoral thesis, Universidad de Alicante, 2015. http://hdl.handle.net/10045/50328.

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En este trabajo, introducimos los conjuntos densificables, una nueva clase de subconjuntos de espacios métricos en los que problemas de optimización global e integración múltiple se pueden reducir a problemas unidimensionales, resolviendo el mismo problema sobre ciertas curvas (llamadas curvas alfa-densas). Para realizar el estudio de los conjuntos densificables en espacios métricos, introducimos las nociones de densificador, pseudo-densificabilidad, aproximabilidad por caminos y aproximabilidad numerable por caminos, que proporcionan propiedades topológicas y métricas de dichos conjuntos. Estos conceptos han permitido caracterizar la clase de subconjuntos densificables de los espacios euclídeos con interior no vacío. Extendemos el concepto de densificabilidad a espacios topológicos en general, introduciendo las nociones de densificabilidad simple, condicional, secuencial y topológica. De esta manera, problemas de optimización global pueden ser simplificados aun en ausencia de una métrica. Además, probamos que una de estas extensiones es óptima, en el sentido que ninguna condición más débil permite la mencionada simplificación utilizando una sucesión prefijada de curvas. Asimismo, comparamos la densificabilidad topológica con la extensión de la densificabilidad ya existente a subconjuntos de espacios vectoriales topológicos. Introducimos la noción de densificabilidad lineal, que combina ventajas de ambos conceptos. Finalmente, presentamos una aplicación de la teoría de curvas alfa-densas al cálculo de la dimensión logarítmica.
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Úbeda, García José Ignacio. "Aspectos geométricos y topológicos de la curvas α-densas". Doctoral thesis, 2006. http://hdl.handle.net/10045/13270.

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Book chapters on the topic "Peano curves"

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Bader, Michael, and Christian Mayer. "Cache Oblivious Matrix Operations Using Peano Curves." In Applied Parallel Computing. State of the Art in Scientific Computing. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75755-9_64.

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Sergeyev, Yaroslav D., Roman G. Strongin, and Daniela Lera. "Approximations to Peano Curves: Algorithms and Software." In SpringerBriefs in Optimization. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8042-6_2.

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Strongin, Roman G., and Yaroslav D. Sergeyev. "Peano-Type Space-Filling Curves as Means for Multivariate Problems." In Global Optimization with Non-Convex Constraints. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4677-1_8.

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Bader, Michael. "Exploiting the Locality Properties of Peano Curves for Parallel Matrix Multiplication." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-85451-7_85.

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Shekhar, Shashi, and Hui Xiong. "Peano Curve." In Encyclopedia of GIS. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_967.

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Schoenberg, I. J. "On the Peano Curve of Lebesgue." In I.J. Schoenberg Selected Papers. Birkhäuser Boston, 1988. http://dx.doi.org/10.1007/978-1-4612-3946-8_13.

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Schoenberg, I. J. "On the Peano Curve of Lebesgue." In I.J. Schoenberg Selected Papers. Birkhäuser Boston, 1988. http://dx.doi.org/10.1007/978-1-4612-3948-2_17.

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Ceterchi, Rodica, Atulya K. Nagar, and K. G. Subramanian. "Chain Code P System Generating a Variant of the Peano Space-Filling Curve." In Membrane Computing. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12797-8_6.

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"Fat curves and Peano curves." In Topology as Fluid Geometry. American Mathematical Society, 2017. http://dx.doi.org/10.1090/mbk/109/05.

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D'Agostino, Susan. "Follow your curiosity, along a space-filling curve." In How to Free Your Inner Mathematician. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.003.0045.

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“Follow your curiosity, along a space-filling curve” tells the story of Italian mathematician Giuseppe Peano’s quest for and discovery of a space-filling curve—a curve that completely fills a space such as a square—that most mathematicians and scientists at the time did not believe existed. For example, Isaac Newton, in his Philosophiae Naturalis Principia Mathematica, tried to ban space-filling curves. The discussion of space-filling curves is enhanced with numerous hand-drawn sketches showing how to construct German mathematician David Hilbert’s space-filling curve. Mathematics students and enthusiasts are encouraged to foster a Peano-like curiosity in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
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Conference papers on the topic "Peano curves"

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Kaur, Gurpinder, Sachin Bagga, and Kulvinder Singh Mann. "Hadoop Approach to Cluster Based Cache Oblivious Peano Curves." In 2017 IEEE 7th International Advance Computing Conference (IACC). IEEE, 2017. http://dx.doi.org/10.1109/iacc.2017.0037.

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McVay, John, and Ahmad Hoorfar. "Miniaturization of top-loaded monopole antennas using Peano-curves." In 2007 IEEE Radio and Wireless Symposium. IEEE, 2007. http://dx.doi.org/10.1109/rws.2007.351816.

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Bagga, Sachin, Akshay Girdhar, Munesh Chandra Trivedi, and Yingzhi Yang. "RMI Approach to Cluster Based Cache Oblivious Peano Curves." In 2016 Second International Conference on Computational Intelligence & Communication Technology (CICT). IEEE, 2016. http://dx.doi.org/10.1109/cict.2016.26.

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Heinecke, Alexander, and Michael Bader. "Towards many-core implementation of LU decomposition using Peano Curves." In the combined workshops. ACM Press, 2009. http://dx.doi.org/10.1145/1531666.1531672.

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Spence, T. G., and D. H. Werner. "Modular broadband planar arrays based on generalized Peano-Gosper curves." In 2008 IEEE Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting. IEEE, 2008. http://dx.doi.org/10.1109/aps.2008.4619360.

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Lambert, Robin A., John P. Chan, and Bruce G. Batchelor. "Segmentation of color images using Peano curves on a transputer array." In Robotics - DL tentative, edited by Bruce G. Batchelor, Michael J. W. Chen, and Frederick M. Waltz. SPIE, 1992. http://dx.doi.org/10.1117/12.58826.

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Schamschula, Marius P., H. John Caulfield, and Avery Brown. "Peano curve modular optics." In OE/LASE '94, edited by Ivan Cindrich and Sing H. Lee. SPIE, 1994. http://dx.doi.org/10.1117/12.178067.

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Yan Wang, Shoushun Chen, and Amine Bermak. "Novel VLSI implementation of Peano-Hilbert curve address generator." In 2008 IEEE International Symposium on Circuits and Systems - ISCAS 2008. IEEE, 2008. http://dx.doi.org/10.1109/iscas.2008.4541458.

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Peng, Zheng Wen, and Xin Lu. "Amplification Matrix Iteration Algorithm to Generate: The Hilbert-Peano Curve." In 2014 IEEE Symposium on Computer Applications and Communications (SCAC). IEEE, 2014. http://dx.doi.org/10.1109/scac.2014.34.

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McVay, John, Ahmad Hoorfar, and Nader Engheta. "Theory and experiments on Peano and Hilbert curve RFID tags." In Defense and Security Symposium, edited by Raghuveer M. Rao, Sohail A. Dianat, and Michael D. Zoltowski. SPIE, 2006. http://dx.doi.org/10.1117/12.666911.

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