Academic literature on the topic 'Hyperbolisch'

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Journal articles on the topic "Hyperbolisch"

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Gehring, Nicole. "Ein systematischer Backstepping-Zugang zur Regelung gekoppelter ODE-PDE-ODE-Systeme." at - Automatisierungstechnik 68, no. 8 (August 27, 2020): 654–66. http://dx.doi.org/10.1515/auto-2020-0030.

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ZusammenfassungDer systematische Zugang zum Backstepping-Entwurf von Zustandsrückführungen für gekoppelte ODE-PDE-ODE-Systeme, die sich zumeist für verteilt-parametrische Prozesse unter Berücksichtigung der Dynamik von Aktoren und Sensoren ergeben, erlaubt nicht nur die sukzessive und vereinfachte Herleitung von bereits bekannten Backstepping-Reglern sondern ermöglicht auch deren Entwurf für bisher nicht betrachtete Systemklassen. Der Zugang nutzt dabei die diesen Systemen inhärente strenge Rückkopplungsform aus. Wie beim klassischen Integrator-Backstepping wird das ODE-PDE-ODE-System schrittweise durch virtuelle Zustandsrückführungen stabilisiert und der Zustand in Fehlerkoordinaten überführt. Der vorgeschlagene, modulare Entwurf ist dabei im Wesentlichen unabhängig davon, ob der verteilt-parametrische Teil des Systems parabolisch oder hyperbolisch ist.
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Yegin, R., and U. Dursun. "On Submanifolds of Pseudo-Hyperbolic Space with 1-Type Pseudo-Hyperbolic Gauss Map." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 4 (December 25, 2016): 315–37. http://dx.doi.org/10.15407/mag12.04.315.

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Glowacki, Elizabeth M., and Mary Anne Taylor. "Health Hyperbolism: A Study in Health Crisis Rhetoric." Qualitative Health Research 30, no. 12 (May 25, 2020): 1953–64. http://dx.doi.org/10.1177/1049732320916466.

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The Ebola virus had only been in the United States for 2 months before it became a major national health concern. However, while some citizens panicked about the looming health crisis, others remained calm, offering explanations for why a rapid spread of the virus was unlikely. Examining the distinctions between these different reactions can contribute to a better understanding of the coping strategies citizens use when facing a health crisis. We consider how citizens respond to fear by focusing on whether or not hyperbolic rhetoric was used as a means for processing and managing fear. Approximately 400 tweets and Facebook posts from the Centers for Disease Control and Prevention, the White House, and The Alex Jones Show were examined to make conclusions about how citizens respond to messages from these mediated forums. At the intersection of health communication and critical rhetoric, we advance an operational definition of health hyperbolism derived from public response to opinion leaders. Ultimately, we find that health hyperbolism contains language illustrative of distrust, blame, anger, misrepresentation, conspiracy, and curiosity.
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Kostin, A. V., and I. Kh Sabitov. "Smarandache Theorem in Hyperbolic Geometry." Zurnal matematiceskoj fiziki, analiza, geometrii 10, no. 2 (June 25, 2014): 221–32. http://dx.doi.org/10.15407/mag10.02.221.

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López Díaz, L. F. "Bóvedas por arista de paraboloides hiperbólicos asimétricos." Informes de la Construcción 50, no. 458 (December 30, 1998): 31–41. http://dx.doi.org/10.3989/ic.1998.v50.i458.877.

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Mosher, Lee. "A hyperbolic-by-hyperbolic hyperbolic group." Proceedings of the American Mathematical Society 125, no. 12 (1997): 3447–55. http://dx.doi.org/10.1090/s0002-9939-97-04249-4.

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Kuznetsov, S. P. "Generation of Robust Hyperbolic Chaos in CNN." Nelineinaya Dinamika 15, no. 2 (2019): 109–24. http://dx.doi.org/10.20537/nd190201.

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Kuznetsov, S. P. "Some Lattice Models with Hyperbolic Chaotic Attractors." Nelineinaya Dinamika 16, no. 1 (2020): 13–21. http://dx.doi.org/10.20537/nd200102.

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Schochet, Steven. "Hyperbolic-hyperbolic singular limits." Communications in Partial Differential Equations 12, no. 6 (January 1987): 589–632. http://dx.doi.org/10.1080/03605308708820504.

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Bawa, Parveen. "Addition Theorems and Nature of Jacobi Hyperbolic Functions." International Journal of Scientific Research 3, no. 6 (June 1, 2012): 250–53. http://dx.doi.org/10.15373/22778179/june2014/79.

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Dissertations / Theses on the topic "Hyperbolisch"

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Schroll, Hans Joachim. "Konvergenz finiter Differenzverfahren für nichtlineare hyperbolisch-parabolische Systeme /." Zürich, 1993. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10273.

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Henseler, Reiner. "A kinetic model for grain growth." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2007. http://dx.doi.org/10.18452/15676.

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In dieser Arbeit wird eine detaillierte Analysis des konsistenten kinetischen Modells zum Kornwachstum von Fradkov durchgeführt. Dieses Modell beschreibt - basierend auf dem von Neumann--Mullins Gesetz - die Flächenänderung eines Korns abhängig von seiner Topologieklasse, d.h. der Anzahl der Kanten. Topologieänderungen werden durch Kopplungsterme zwischen den Gleichungen für die Anzahldichten der verschiedenen Topologieklassen beschrieben. Daraus resultiert ein unendlich-dimensionales System von Transportgleichungen mit tridiagonaler Kopplungsstruktur. Durch eine spezielle Wahl des Kopplungsgewichts, welche die Gleichungen nichtlinear und räumlich nichtlokal macht, wird das Modell konsistent. Nach einer Einführung wird das Modell von Fradkov im zweiten Kapitel hergeleitet; formale Rechnungen zeigen die Konsistenz des Modells auf. Im dritten Kapitel wird das Kopplungsgewicht a priori beschränkt. Dadurch kann im ersten Teil des vierten Kapitels Existenz und Eindeutigkeit von Lösungen für endlich-dimensionale Systeme gezeigt werden. Weitere Schranken an die Anzahldichten im fünften Kapitel ermöglichen den Grenzübergang hinsichtlich der Anzahl der Gleichungen im zweiten Teil des vierten Kapitels. Die Existenz von Lösungen des unendlich-dimensionalen Systems wird somit über eine geeignete Approximation gezeigt. Energiemethoden liefern Eindeutigkeit und stetige Abhängigkeit von den Daten. Im sechsten Kapitel wird das Langzeitverhalten untersucht. Besonderes Augenmerk liegt dabei auf stationären Lösungen eines reskalierten Systems als Kandidaten für selbstähnliche Lösungen. Abschließend wird das Lewis''sche Gesetz asymptotisch verifiziert.
The subject matter of this thesis is a detailed analysis of the self--consistent kinetic model for grain growth introduced by Fradkov. The model is based on the von Neumann--Mullins law describing the change of area of grains according to their topological class, i.e. the number of edges they have. Topological events are performed by coupling terms between equations for the number densities of different topological classes. The resulting system of transport equations is infinite-dimensional with a tridiagonal coupling structure. Self-consistency of this kinetic model is achieved by introducing a coupling''s weight making the equations nonlinear and nonlocal in space. We start with an introduction in the first chapter. Afterwards in the second chapter we derive Fradkov''s model and carry out formal calculations to illustrate self-consistency. In the third chapter we present a priori calculations mainly allowing us to bound the nonlinearity. This enables us to prove existence and uniqueness of solutions to finite-dimensional systems in the first part of the fourth chapter. Further bounds on the number densities established in the fifth chapter allow for passing to the limit concerning the number of equations in the second part of the fourth chapter. Therefore we prove existence of solutions to the infinite-dimensional system by a suitable approximation procedure. Uniqueness and continuous dependence on the data is then provided by energy methods. The sixth chapter focusses on long-time behaviour and mainly on stationary solutions of a rescaled system as candidates for self-similar solutions. Finally we prove Lewis'' law asymptotically.
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Knott, Gereon. "Oscillatory Solutions to Hyperbolic Conservation Laws and Active Scalar Equations." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-122808.

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In dieser Arbeit werden zwei Klassen von Evolutionsgleichungen in einem Matrixraum-Setting studiert: Hyperbolische Erhaltungsgleichungen und aktive skalare Gleichungen. Für erstere wird untersucht, wann man Oszillationen mit Hilfe polykonvexen Maßen ausschließen kann; für Zweitere wird mit Hilfe von Oszillationen gezeigt, dass es unendlich viele periodische schwache Lösungen gibt.
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Aryasomayajula, Naga Venkata Anilatmaja. "Bounds for Green's functions on hyperbolic Riemann surfaces of finite volume." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16828.

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Im Jahr 2006, in einem Papier in Compositio Titel "Bounds auf kanonische Green-Funktionen" J. Jorgenson und J. Kramer, haben optimale Schranken für den hyperbolischen und kanonischen Green-Funktionen auf einem kompakten hyperbolischen Riemannschen Fläche definiert abgeleitet. Diese Schätzungen wurden im Hinblick auf abgeleitete Invarianten aus hyperbolischen Geometrie der Riemannschen Fläche. Als Anwendung abgeleitet sie Schranken für die kanonische Green-Funktionen durch Abdeckungen und für Familien von Modulkurven. In dieser Arbeit erweitern wir ihre Methoden nichtkompakten hyperbolischen Riemann Oberflächen und leiten ähnliche Schranken für den hyperbolischen und kanonischen Green-Funktionen auf einem nichtkompakten hyperbolischen Riemannschen Fläche definiert.
In 2006, in a paper in Compositio titled "Bounds on canonical Green''s functions", J. Jorgenson and J. Kramer have derived optimal bounds for the hyperbolic and canonical Green''s functions defined on a compact hyperbolic Riemann surface. These estimates were derived in terms of invariants coming from hyperbolic geometry of the Riemann surface. As an application, they deduced bounds for the canonical Green''s functions through covers and for families of modular curves. In this thesis, we extend their methods to noncompact hyperbolic Riemann surfaces and derive similar bounds for the hyperbolic and canonical Green''s functions defined on a noncompact hyperbolic Riemann surface.
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Persson, Anna. "Grundläggande hyperbolisk geometri." Thesis, Karlstad University, Faculty of Technology and Science, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-211.

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I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet.

Huvudresultatet i uppsatsen är Gauss – Bonnét´s sats för hyperboliska trianglar.


In this thesis we present fundamental concepts in hyperbolic geometry. The thesis is divided into two chapters. In the first chapter we study Möbiustransformations on the Riemann sphere. The second part of the thesis deal with hyperbolic geometry in the upper half-plane. This model of hyperbolic geometry was created by Poincaré in 1880.

The main result of the thesis is Gauss – Bonnét´s theorem for hyperbolic triangles.

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Steckelberg, Torben. "Hyperbolische Bewegungen auf Lorentz-Boosts /." Hamburg, 2009. http://opac.nebis.ch/cgi-bin/showAbstract.pl?sys=000252297.

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Koch, Tino. "Hyperbolische einfach-punktierte Torus-Bündel." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=957665474.

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Hawksley, Ruth. "Hyperbolic monopoles." Thesis, University of Edinburgh, 1998. http://hdl.handle.net/1842/14019.

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A Euclidean SU(2) monopole consists of a connection and Higgs field on an SU(2) bundle over π3, satisfying certain partial differential equations. Monopoles may equivalently be described in terms of holomorphic vector bundles on twistor space, algebraic curves in twistor space, rational maps, or solutions to Nahm's equations (a set of ODEs for matrix-valued functions), all satisfying some further conditions. Research by Atiyah, Donaldson, Hitchin, Nahm and others has provided a beautiful and relatively complete picture of these different viewpoints and the links between them. Monopoles have also been studied on hyperbolic space π3, although the corresponding picture in this case is less well understood. One difficulty is that the conditions which must be imposed in order for all the various correspondences to be valid have not yet been completely determined. A partial answer is given in Chapter 2, where it is proved that any hyperbolic monopole arising from a spectral curve satisfies a certain natural boundary condition. The proof uses the algebraic geometry of the spectral curve and is similar to Hurtubise's proof of the analogous result in the Euclidean case. A large part of this thesis concentrates on the "Braam-Austin" description of hyperbolic monopoles. This is the hyperbolic version of Nahm's description of Euclidean monopoles; a monopole corresponds to a pair of discrete matrix-valued functions satisfying some difference equations. Euclidean monopoles appear as limits of hyperbolic monopoles as the curvature of π3 tends to zero. This "Euclidean limit" is described geometrically and is studied in terms of Braam-Austin data. Explicit conditions are given for such a sequence to have a subsequence converging to a Euclidean monopole. The result depends on a conjecture (§ 4.5) about properties of Braam-Austin monopole solutions.
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Lê, Nguyên Khoa 1975. "Time-frequency analyses of the hyperbolic kernel and hyperbolic wavelet." Monash University, Dept. of Electrical and Computer Systems Engineering, 2002. http://arrow.monash.edu.au/hdl/1959.1/8299.

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Vlamis, Nicholas George. "Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces." Thesis, Boston College, 2015. http://hdl.handle.net/2345/bc-ir:104137.

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Thesis advisor: Martin J. Bridgeman
Thesis advisor: Ian Biringer
The first part of this dissertation is on the quasiconformal homogeneity of surfaces. In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for the associated quasiconformal homogeneity constants across all closed hyperbolic surfaces in several cases, including the Torelli group, congruence subgroups, and pure cyclic subgroups. Further, we introduce a counting argument providing a possible path to exploring a uniform lower bound for the nonrestricted quasiconformal homogeneity constant across all closed hyperbolic surfaces. We then move on to identities on hyperbolic manifolds. We study the statistics of the unit geodesic flow normal to the boundary of a hyperbolic manifold with non-empty totally geodesic boundary. Viewing the time it takes this flow to hit the boundary as a random variable, we derive a formula for its moments in terms of the orthospectrum. The first moment gives the average time for the normal flow acting on the boundary to again reach the boundary, which we connect to Bridgeman's identity (in the surface case), and the zeroth moment recovers Basmajian's identity. Furthermore, we are able to give explicit formulae for the first moment in the surface case as well as for manifolds of odd dimension. In dimension two, the summation terms are dilogarithms. In dimension three, we are able to find the moment generating function for this length function
Thesis (PhD) — Boston College, 2015
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Books on the topic "Hyperbolisch"

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Hyperbolic geometry and applications in quantum chaos and cosmology. Cambridge, UK: Cambridge University Press, 2012.

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Coornaert, M. Géométrie et théorie des groupes: Les groupes hyperboliques de Gromov. Berlin: Springer, 1990.

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Anderson, James W. Hyperbolic geometry. London: Springer, 1999.

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Hyperbolic geometry. Cambridge: Cambridge University Press, 1992.

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Anderson, James W. Hyperbolic Geometry. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-3987-4.

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Kuznetsov, Sergey P. Hyperbolic Chaos. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23666-2.

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Beckh, Matthias. Hyperbolic structures. Chichester, UK: John Wiley & Sons, Ltd, 2015. http://dx.doi.org/10.1002/9781118932711.

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Beckh, Matthias. Hyperbolic structures. Chichester, West Sussex, United Kingdom: John Wiley & Sons Inc., 2014.

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Barot, Michael. Einführung in die hyperbolische Geometrie. Wiesbaden: Springer Fachmedien Wiesbaden, 2019. http://dx.doi.org/10.1007/978-3-658-25813-9.

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Georgiev, Vladimir. Semilinear hyperbolic equations. Tokyo: Mathematical Society of Japan, 2000.

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Book chapters on the topic "Hyperbolisch"

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Rosebrock, Stephan. "Hyperbolische Gruppen." In Anschauliche Gruppentheorie, 191–210. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-60787-9_10.

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Agricola, Ilka, and Thomas Friedrich. "Hyperbolische Geometrie." In Elementargeometrie, 149–87. Wiesbaden: Springer Fachmedien Wiesbaden, 2014. http://dx.doi.org/10.1007/978-3-658-06731-1_3.

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Hanke-Bourgeois, Martin. "Hyperbolische Erhaltungsgleichungen." In Mathematische Leitfäden, 769–821. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-94877-9_19.

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Wagner, Jürgen. "Hyperbolische Geometrie." In Einblicke in die euklidische und nichteuklidische Geometrie, 235–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-54072-5_5.

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Hengst, Jochen. "Hyperbolische Metapher." In Ansätze zu einer Archäologie der Literatur, 259–303. Stuttgart: J.B. Metzler, 2000. http://dx.doi.org/10.1007/978-3-476-02740-5_8.

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Rosebrock, Stephan. "Hyperbolische Gruppen." In Geometrische Gruppentheorie, 151–71. Wiesbaden: Vieweg+Teubner Verlag, 2004. http://dx.doi.org/10.1007/978-3-322-99649-7_9.

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Denk, Robert, and Reinhard Racke. "Hyperbolische Gleichungen." In Kompendium der ANALYSIS - Ein kompletter Bachelor-Kurs von Reellen Zahlen zu Partiellen Differentialgleichungen, 263–72. Wiesbaden: Vieweg+Teubner Verlag, 2012. http://dx.doi.org/10.1007/978-3-8348-2123-2_24.

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Sonar, Thomas. "Hyperbolische Erhaltungsgleichungen." In Mehrdimensionale ENO-Verfahren, 18–39. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-322-90842-1_2.

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Marsal, Dietrich. "Hyperbolische Gleichungen." In Finite Differenzen und Elemente, 89–111. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-49948-7_5.

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Berchtold, Florian. "Hyperbolische Geometrie." In Geometrie, 81–113. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49954-2_4.

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Conference papers on the topic "Hyperbolisch"

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Narimanov, Evgenii E. "Hyperbolic Metamaterials." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2013. http://dx.doi.org/10.1364/cleo_qels.2013.qtu2a.1.

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Narimanov, Evgenii, and Ishii Satoshi. "Hyperbolic metamaterials." In 2015 11th Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR). IEEE, 2015. http://dx.doi.org/10.1109/cleopr.2015.7376050.

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Gomez-Diaz, J. Sebastian, Mykhailo Tymchenko, and Andrea Alu. "Hyperbolic metasurfaces." In 2015 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2015. http://dx.doi.org/10.1109/aps.2015.7304825.

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Easley, Glenn R., Demetrio Labate, and Vishal M. Patel. "Hyperbolic shearlets." In 2012 19th IEEE International Conference on Image Processing (ICIP 2012). IEEE, 2012. http://dx.doi.org/10.1109/icip.2012.6467393.

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KHRENNIKOV, ANDREI, and GAVRIEL SEGRE. "HYPERBOLIC QUANTIZATION." In Proceedings of the 26th Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770271_0028.

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Chira-Oliva, Pedro, and João Carlos R. Cruz. "Seismic stacking methods: hyperbolic and non-hyperbolic traveltime approximations." In 13th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 26-29 August 2013. Society of Exploration Geophysicists and Brazilian Geophysical Society, 2013. http://dx.doi.org/10.1190/sbgf2013-262.

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Zhang, Chengkun, and Junbin Gao. "Hype-HAN: Hyperbolic Hierarchical Attention Network for Semantic Embedding." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/552.

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Hyperbolic space is a well-defined space with constant negative curvature. Recent research demonstrates its odds of capturing complex hierarchical structures with its exceptional high capacity and continuous tree-like properties. This paper bridges hyperbolic space's superiority to the power-law structure of documents by introducing a hyperbolic neural network architecture named Hyperbolic Hierarchical Attention Network (Hype-HAN). Hype-HAN defines three levels of embeddings (word/sentence/document) and two layers of hyperbolic attention mechanism (word-to-sentence/sentence-to-document) on Riemannian geometries of the Lorentz model, Klein model and Poincaré model. Situated on the evolving embedding spaces, we utilize both conventional GRUs (Gated Recurrent Units) and hyperbolic GRUs with Möbius operations. Hype-HAN is applied to large scale datasets. The empirical experiments show the effectiveness of our method.
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Durach, Maxim, and David W. Keene. "Hyperbolic Tamm Plasmons." In Frontiers in Optics. Washington, D.C.: OSA, 2014. http://dx.doi.org/10.1364/fio.2014.fth3e.3.

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Zayats, Anatoly V. "Nonlinear hyperbolic metamaterials." In 2014 8th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS). IEEE, 2014. http://dx.doi.org/10.1109/metamaterials.2014.6948585.

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Kotlyar, V. V., and A. A. Kovalev. "Hyperbolic Airy beams." In 2013 International Conference on Advanced Optoelectronics and Lasers (CAOL). IEEE, 2013. http://dx.doi.org/10.1109/caol.2013.6657568.

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Reports on the topic "Hyperbolisch"

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Chu, Isaac, Gregory Fu, Mark Steffen, and Matthias Sherwood. Hyperbolic Analysis. Web of Open Science, April 2020. http://dx.doi.org/10.37686/ejai.v1i1.29.

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Ungar, Abraham A. Hyperbolic Geometry. GIQ, 2014. http://dx.doi.org/10.7546/giq-15-2014-259-282.

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Ungar, Abraham A. Hyperbolic Geometry. Jgsp, 2013. http://dx.doi.org/10.7546/jgsp-32-2013-61-86.

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Stannard, Casey R., and Paul Callahan. Hyperbolic Honeycomb. Ames: Iowa State University, Digital Repository, November 2016. http://dx.doi.org/10.31274/itaa_proceedings-180814-1635.

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Ungar, Abraham A. The Hyperbolic Triangle Defect. GIQ, 2012. http://dx.doi.org/10.7546/giq-5-2004-225-236.

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Shearer, Michael. Nonlinear Hyperbolic Conservation Laws. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada184963.

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Keyfitz, Barbara L. Nonstrictly Hyperbolic Conservation Laws. Fort Belvoir, VA: Defense Technical Information Center, November 1989. http://dx.doi.org/10.21236/ada218525.

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Hyman, J., M. Shashikov, B. Swartz, and B. Wendroff. Multidimensional methods for hyperbolic problems. Office of Scientific and Technical Information (OSTI), April 1996. http://dx.doi.org/10.2172/224954.

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Ungar, Abraham A. The Relativistic Hyperbolic Parallelogram Law. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-249-264.

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Steinhardt, Allan O. Hyperbolic Transforms in Array Processing. Fort Belvoir, VA: Defense Technical Information Center, February 1991. http://dx.doi.org/10.21236/ada247061.

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