Thematische Bibliographien / Non-Euclidean spaces

Inhaltsverzeichnis

  1. Zeitschriftenartikel
  2. Dissertationen
  3. Bücher
  4. Buchteile
  5. Konferenzberichte

Auswahl der wissenschaftlichen Literatur zum Thema „Non-Euclidean spaces“

Autor: Grafiati
Veröffentlicht am 28. Juni 2021
Zuletzt aktualisiert am 1. Februar 2022

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Zeitschriftenartikel zum Thema "Non-Euclidean spaces"

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Lally, Nick, und Luke Bergmann. „Mapping dynamic, non-Euclidean spaces“. Abstracts of the ICA 1 (15.07.2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-204-2019.

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<p><strong>Abstract.</strong> Space is often described as a dynamic entity in human geographic theory, one that resists being pinned down to static representations. Co-produced in and through relations between various things and phenomena, space in these accounts is variously described as being contingent, processual, plastic, relational, situated, topological, and uneven. In contrast, most cartographic methods and tools are based on static, Euclidean understandings of space that can be reduced to a simple, mathematical description. In this work, I explore how cartography can deal with space as a dynamic and fluid concept that is entangled with the phenomena and objects being mapped. To those ends, I describe a method for creating animated maps based on relational understandings of space that are always in flux.</p><p>This work builds on research in collaboration with Luke Bergmann, where we suggest a move from Geographic Information Systems (GIS) as we commonly know them to the broader realm of <i>geographical imagination systems (gis)</i> that are informed by spatial theory in human geography. The animated maps here are produced using our prototype <i>gis</i> software Enfolding, which use multidimensional scaling (MDS) to visualize relational spaces, in combination with Blender, an open-source 3D rendering program. Written in JavaScript and available as open source software, Enfolding is our first attempt to make gis an accessible set of tools that expand the possibilities for mapping by providing new grammars for creative cartographic practices.</p><p>In the cartographic workflow presented here, I use Enfolding to produce manifolds from a set of points and user-defined distances between points. Changing those measures of distance &amp;ndash; which might represent travel times, affective connections, communicative links, or any other relationship as defined by a user &amp;ndash; produces shifting manifolds. Using the .obj export option in Enfolding, I then import the manifolds into Blender, using them as animation keyframes. In Figure 1, I have added a digital elevation model (DEM) to the 3D figure, producing an animated visualization of a dynamic and relational space that includes a hillshade.</p><p>This workflow represents only one of many creative possibilities for innovative cartographic practices that engage with space as a matter of concern. With growing interest in 3D cartographic methods comes expanded possibilities for visualizing dynamic and relational spaces. Combining conceptual antecedents in both human and quantitative geography with current cartographic methods allows for new approaches to both mapping and space. The workflow and tools that have emerged from this research are presented here with the hope of spurring creative and exploratory cartographic work that draws from but also contributes to vibrant discussions in spatial theory and creative cartography.</p>
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Courrieu, Pierre. „Function approximation on non-Euclidean spaces“. Neural Networks 18, Nr. 1 (Januar 2005): 91–102. http://dx.doi.org/10.1016/j.neunet.2004.09.003.

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Novello, Tiago, Vincius da Silva und Luiz Velho. „Global illumination of non-Euclidean spaces“. Computers & Graphics 93 (Dezember 2020): 61–70. http://dx.doi.org/10.1016/j.cag.2020.09.014.

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Urban, Philipp, Mitchell R. Rosen, Roy S. Berns und Dierk Schleicher. „Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement“. Journal of the Optical Society of America A 24, Nr. 6 (09.05.2007): 1516. http://dx.doi.org/10.1364/josaa.24.001516.

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BORELL, STEFAN, und FRANK KUTZSCHEBAUCH. „NON-EQUIVALENT EMBEDDINGS INTO COMPLEX EUCLIDEAN SPACES“. International Journal of Mathematics 17, Nr. 09 (Oktober 2006): 1033–46. http://dx.doi.org/10.1142/s0129167x06003795.

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We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into ℂn. In this paper we prove that if the automorphism group of X is a Lie group and there exists a proper holomorphic embedding of X into ℂn, 0 < dim X < n, then for any k ≥ 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X × ℂk ↪ ℂn × ℂk. For k = 0 all embeddings will be proved to satisfy the additional property of ℂn\Φ(X) being (n - dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of ℂk into ℂn whenever 0 < k < n.
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Borisov, A. V., und I. S. Mamaev. „Rigid body dynamics in non-Euclidean spaces“. Russian Journal of Mathematical Physics 23, Nr. 4 (Oktober 2016): 431–54. http://dx.doi.org/10.1134/s1061920816040026.

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Capecchi, Danilo, und Giuseppe Ruta. „Beltrami's continuum mechanics in non-Euclidean spaces“. PAMM 15, Nr. 1 (Oktober 2015): 703–4. http://dx.doi.org/10.1002/pamm.201510341.

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Midler, Jean-Claude. „Non-Euclidean Geographic Spaces: Mapping Functional Distances“. Geographical Analysis 14, Nr. 3 (03.09.2010): 189–203. http://dx.doi.org/10.1111/j.1538-4632.1982.tb00068.x.

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Dörfel, B.-D. „Non-commutative Euclidean structures in compact spaces“. Journal of Physics A: Mathematical and General 34, Nr. 12 (19.03.2001): 2583–94. http://dx.doi.org/10.1088/0305-4470/34/12/306.

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Schwarz, Binyamin, und Abraham Zaks. „Non-Euclidean motions in projective matrix spaces“. Linear Algebra and its Applications 137-138 (August 1990): 351–61. http://dx.doi.org/10.1016/0024-3795(90)90134-x.

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Dissertationen zum Thema "Non-Euclidean spaces"

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Garcia, Domingo Josep Lluís. „Real analysis in non-euclidean spaces: trees and spaces of homogeneous type“. Doctoral thesis, Universitat de Barcelona, 2003. http://hdl.handle.net/10803/2124.

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DE LA TESIS:

El contenido de esta tesis se enmarca dentro del Análisis Real. En particular, trata del estudio de ciertos problemas de la teoría de pesos, (una referencia clásica sobre esta teoría es el libro de J. García-Cuerva y J.L. Rubio de Francia [GR]). Nosotros consideramos, por este orden, tres problemas clásicos diferentes, que abarcan buena parte de la teoría de pesos:

(i) Estudio de las inclusiones para espacios con pesos y acotación de operadores integrales entre estos espacios.

(ii) Estudio de propiedades funcionales de espacios con pesos asociados a una reordenada decreciente de funciones.

(iii) Estudio de la acotación de operadores maximales asociados a regiones de aproximación entre espacios con pesos.

Todos estos problemas han sido tratados extensamente en la literatura. Nuestro enfoque ha sido el de extender estos resultados a espacios con la mínima estructura necesaria. Concretamente, hemos trabajado respectivamente en cada capítulo en los siguientes contextos:

(i) Espacios de medida arbitrarios.

(ii) Árboles.

(iii) Espacios de tipo homogéneo.

Puesto que un árbol puede ser a su vez un espacio de medida, o puesto que su frontera puede ser un espacio de tipo homogéneo, algunos resultados para espacios de medida y espacios de tipo homogéneo han sido aplicados a los árboles (véanse los capítulos primero y tercero). En cambio, en el capítulo segundo trabajamos exclusivamente en árboles.

Los espacios donde hemos desarrollado nuestra teoría no poseen, en general, ningún tipo de estructura algebraica. Por tanto, todos los resultados persiguen un objetivo común: la extensión de la teoría de pesos a espacios no euclidianos.
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Vincent, Hugh. „Using geometric algebra to interactively model the geometry of Euclidean and non-Euclidean spaces“. Thesis, Middlesex University, 2007. http://eprints.mdx.ac.uk/6750/.

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This research interprets and develops the 'conformal model of space' in a way appropriate for a graphics developer interested in the design of interactive software for exploring 2-dimensional non-Euclidean spaces. The conformal model of space extends the standard projective model – instead of adding just one extra dimension to standard Euclidean space, a second one is added that results in a Minkowski space similar to that of relativistic spacetime. Also, standard matrix algebra is replaced by geometric ( i.e. Clifford) algebra. The key advantage of the conformal model is that both Euclidean and non- Euclidean spaces are accommodated within it. Transformations in conformal space are generated by bivectors which are special elements of the geometric algebra. These induce geometric transformations in the embedded non Euclidean spaces. However, the relationship between the bivector generated transformations of the Minkowski modelling space and the geometric transformations they induce is extremely obscure. This thesis provides new analytical tools for determining the nature of this relationship. Their derivation was motivated by the need to successfully solve key implementation problems relating to navigation and in-scene mouse interaction. The analytic approaches developed not only successfully solved these problems but pointed the way to implementing other unplanned features. These include facilities for dynamically altering on-screen geometry as well as using multiple viewports to allow the user to interact with the same objects embedded in different geometries. These new analytical approaches could be powerful tools for solving future and as yet unforeseen implementation problems.
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Schötz, Christof [Verfasser], und Enno [Akademischer Betreuer] Mammen. „The Fréchet Mean and Statistics in Non-Euclidean Spaces / Christof Schötz ; Betreuer: Enno Mammen“. Heidelberg : Universitätsbibliothek Heidelberg, 2021. http://d-nb.info/1232409782/34.

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Haxhi, Karen Kleinschmidt. „The euclidean and hyperbolic geometry underlying M.C. Escher's regular division designs /“. View abstract, 1998. http://library.ctstateu.edu/ccsu%5Ftheses/1491.html.

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Thesis (M.S.) -- Central Connecticut State University, 1998.
Thesis advisor: Dr. Jeffrey McGowan. "...in partial fulfillment of the requirements for the degree of Master of Science." Includes bibliographical references (leaves [78-79]).
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Senger, Steven Iosevich Alex. „Erdős distance problem in the hyperbolic half-plane“. Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/5341.

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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. Title from PDF of title page (University of Missouri--Columbia, viewed on January 14, 2010). Thesis advisor: Dr. Alex Iosevich. Includes bibliographical references.
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Rippy, Scott Randall. „Applications of hyperbolic geometry in physics“. CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1099.

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Bobuľa, Matej. „Neeuklidovské vykreslování ve VR“. Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2021. http://www.nusl.cz/ntk/nusl-445563.

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The main goal of this master's thesis is to research different approaches of rendering geometries and spaces in virtual reality. Learn more about the terms, non-Euclidean geometry and non-Euclidean spaces, their origin and different principles used in video game industry to simulate such geometries or spaces. Based on the research, a selection of an optimal API is needed for the implementation of such application. Application is designed to run on desktop computers with Microsoft Windows operating system. Application, in it's core, is a video game and the main goal of the player is to successfully complete each and every level of the game. These levels are designed in a specific way so that they each individually represent some form of non-Euclidean geometry or space.
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Barfield, Naren Anthony. „Integrated artworks : theory and practice in relation to printmaking and computers, and the influence of 'non-Euclidean geometry' and the 'fourth dimension' on developments in twentieth-century pictoral space“. Thesis, Open University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299913.

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Dhinagar, Nikhil J. „Non-Invasive Skin Cancer Classification from Surface Scanned Lesion Images“. Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1366384987.

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Schmidt, Elvis. „O ensino de geometria projetiva na educação básica: uma proposta para apreensão do conhecimento do mundo tridimensional“. Universidade Tecnológica Federal do Paraná, 2015. http://repositorio.utfpr.edu.br/jspui/handle/1/1371.

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Capes
Na busca por uma melhor representação da realidade tridimensional, as Geometrias não- Euclidianas oferecem uma alternativa ao euclidianismo clássico e um dos destaques e a Geometria Projetiva. Assim, o objetivo deste trabalho e, através de ilustrações, contribuir para a assimilação de definições como perspectiva, projeção e o principio da dualidade. E, a partir de resultados importantes como o Teorema de Desargues, o Teorema de Pappus e o Teorema de Pascal, queremos facilitar a compreensão e a visualização de algumas das técnicas de perspectiva que podem ser adaptadas para o uso na sala de aula pelos professores da Educação B ́ sica. A aplicação de uma oficina de Geometria Projetiva em uma turma do 6o ano do Ensino Fundamental e a avaliação dos resultados revelaram que o tema pode ser desenvolvido de maneira promissora com os estudantes na Educação B ́ sica, obtendo uma melhor compreensão do objeto real e associando-o ao conteúdo matemático envolvido.
In search for a better representation of three-dimensional reality, non-Euclidean Geometries offer an alternative to the classic euclidianism and the Projective Geometry is one of the highlights. The purpose of this word is contribute to the assimilation of definitions such as perspective, projection, and the principle of duality, through illustrations. And, from important results as Desargues’ Theorem, Pappus’ Theorem and Pascal’s Theorem, we want to facilitate understanding and viewing some of the perspective techniques that can be adapted for use in classroom by Basic Education teachers. The application of a workshop of Projective Geometry in a class of 6th grade of elementary school and the evaluation of the results revealed that the theme can be developed in a promising way with students in basic education, getting a better comprehension of the real object and associating it to the mathematical content involved.
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Bücher zum Thema "Non-Euclidean spaces"

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Borwein, Jonathan M. Convex functions: Constructions, characterizations and counterexamples. Cambridge: Cambridge University Press, 2010.

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Jeremy, Gray. Ideas of space: Euclidean, non-Euclidean, and relativistic. 2. Aufl. Oxford: Clarendon Press, 1989.

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Outer billiards on kites. Princeton, N.J: Princeton University Press, 2009.

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Aravinda, C. S. Geometry, groups and dynamics: ICTS program, groups, geometry and dynamics, December 3-16, 2012, CEMS, Kumaun University, Almora, India. Providence, Rhode Island: American Mathematical Society, 2015.

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Bolyai, János. Appendix, the theory of space. Amsterdam: North-Holland, 1987.

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Appendix, the theory of space. Budapest: Akadémiai Kiadó, 1987.

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Rozenfelʹd, Boris Abramovich. A history of non-Euclidean geometry: Evolution of the concept of a geometric space. New York: Springer-Verlag, 1988.

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Jeremy, Gray. János Bolyai, non-Euclidean geometry, and the nature of space. Cambridge, Mass: Burndy Library, 2004.

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Ah istory of non-euclidean geometry: Evolution of the concept of a geometric space. New York: Springer-Verlag, 1987.

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Tazzioli, Rossana. Beltrami e i matematici "relativisti": La meccanica in spazi curvi nella seconda metà dell'Ottocento. Bologna: Pitagora, 2000.

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Buchteile zum Thema "Non-Euclidean spaces"

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Ren, Wei, Yoan Miche, Ian Oliver, Silke Holtmanns, Kaj-Mikael Bjork und Amaury Lendasse. „On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces“. In Lecture Notes in Computer Science, 3–13. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66808-6_1.

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Gorelik, E., J. Lindenstrauss und M. Rudelson. „Uniform Non-Equivalence between Euclidean and Hyperbolic Spaces“. In Geometric Aspects of Functional Analysis, 103–9. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9090-8_10.

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Huckemann, Stephan F. „(Semi-)Intrinsic Statistical Analysis on Non-Euclidean Spaces“. In Contributions to Statistics, 103–18. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11149-0_7.

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Casey, Stephen D. „Harmonic Analysis in Non-Euclidean Spaces: Theory and Application“. In Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, 565–601. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55556-0_6.

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Miche, Yoan, Ian Oliver, Wei Ren, Silke Holtmanns, Anton Akusok und Amaury Lendasse. „Practical Estimation of Mutual Information on Non-Euclidean Spaces“. In Lecture Notes in Computer Science, 123–36. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66808-6_9.

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Bhattacharya, Subhrajit, Robert Ghrist und Vijay Kumar. „Multi-robot Coverage and Exploration in Non-Euclidean Metric Spaces“. In Springer Tracts in Advanced Robotics, 245–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36279-8_15.

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Bhattacharya, Rabi, Lizhen Lin und Victor Patrangenaru. „Fréchet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces“. In Springer Texts in Statistics, 303–15. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-4032-5_12.

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Huckemann, Stephan, und Benjamin Eltzner. „Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces“. In Handbook of Variational Methods for Nonlinear Geometric Data, 317–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31351-7_10.

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Dostert, Maria, und Alexander Kolpakov. „Kissing Number in Non-Euclidean Spaces of Constant Sectional Curvature“. In Trends in Mathematics, 574–79. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83823-2_92.

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Saxena, Chandni, Tianyu Liu und Irwin King. „A Survey of Graph Curvature and Embedding in Non-Euclidean Spaces“. In Neural Information Processing, 127–39. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63833-7_11.

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Konferenzberichte zum Thema "Non-Euclidean spaces"

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Oxburgh, Stephen, Chris D. White, Georgios Antoniou, Lena Mertens, Christopher Mullen, Jennifer Ramsay, Duncan McCall und Johannes Courtial. „Windows into non-Euclidean spaces“. In SPIE Optical Engineering + Applications, herausgegeben von G. Groot Gregory und Arthur J. Davis. SPIE, 2014. http://dx.doi.org/10.1117/12.2061418.

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Zeyen, Max, Tobias Post, Hans Hagen, James Ahrens, David Rogers und Roxana Bujack. „Color Interpolation for Non-Euclidean Color Spaces“. In 2018 IEEE Scientific Visualization Conference (SciVis). IEEE, 2018. http://dx.doi.org/10.1109/scivis.2018.8823597.

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„CLASSIFICATION USING HIGH ORDER DISSIMILARITIES IN NON-EUCLIDEAN SPACES“. In International Conference on Pattern Recognition Applications and Methods. SciTePress - Science and and Technology Publications, 2012. http://dx.doi.org/10.5220/0003779503060309.

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Dyachkov, V. V., Y. A. Zaripova und A. V. Yushkov. „Experimental Foundations of Nuclear Physics in Non-Euclidean Spaces“. In International Symposium on Exotic Nuclei EXON-2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811209451_0055.

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Songhao, Zhu, Hu Juanjuan und Sun Wei. „Image classification using three order statistics in non-Euclidean spaces“. In 2013 25th Chinese Control and Decision Conference (CCDC). IEEE, 2013. http://dx.doi.org/10.1109/ccdc.2013.6560896.

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Chen, Lingling, Songhao Zhu, Zhuofan Li und Juanjuan Hu. „Image classification via learning dissimilarity measure in non-euclidean spaces“. In 2014 33rd Chinese Control Conference (CCC). IEEE, 2014. http://dx.doi.org/10.1109/chicc.2014.6895718.

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Biggs, James D. „Quadratic Hamiltonians on non-Euclidean spaces of arbitrary constant curvature“. In 2013 European Control Conference (ECC). IEEE, 2013. http://dx.doi.org/10.23919/ecc.2013.6669107.

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Hu, Juanjuan, Songhao Zhu und Baojie Fan. „Improving Tagging Quality via Learning Dissimilarity Measure in Non-Euclidean Spaces“. In 2013 2nd IAPR Asian Conference on Pattern Recognition (ACPR). IEEE, 2013. http://dx.doi.org/10.1109/acpr.2013.112.

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Chen, Lingling, und Songhao Zhu. „Improving Image Classification Quality Via Dissimilarity Measure In Non-Euclidean Spaces“. In 2015 International Symposium on Computers and Informatics. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/isci-15.2015.91.

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Ghosh, S., und D. Roy. „A Family of Runge-Kutta Based Explicit Methods for Rotational Dynamics“. In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41396.

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The present paper develops a family of explicit algorithms for rotational dynamics and presents their comparison with several existing methods. For rotational motion the configuration space is a non-linear manifold, not a Euclidean vector space. As a consequence the rotation vector and its time derivatives correspond to different tangent spaces of rotation manifold at different time instants. This renders the usual integration algorithms for Euclidean space inapplicable for rotation. In the present algorithms this problem is circumvented by relating the equation of motion to a particular tangent space. It has been accomplished with the help of already existing relation between rotation increments which belongs to two different tangent spaces. The suggested method could in principle make any integration algorithm on Euclidean space, applicable to rotation. However, the present paper is restricted only within explicit Runge-Kutta enabled to handle rotation. The algorithms developed here are explicit and hence computationally cheaper than implicit methods. Moreover, they appear to have much higher local accuracy and hence accurate in predicting any constants of motion for reasonably longer time. The numerical results for solutions as well as constants of motion, indicate superior performance by most of our algorithms, when compared to some of the currently known algorithms, namely ALGO-C1, STW, LIEMID[EA], MCG, SUBCYC-M.
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