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Relevant bibliographies by topics / Spectral polytopes

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Academic literature on the topic 'Spectral polytopes'

Author: Grafiati

Published: 30 June 2021

Last updated: 2 February 2022

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Journal articles on the topic "Spectral polytopes"

1

Greenfeld, Rachel, and Nir Lev. "Fuglede’s spectral set conjecture for convex polytopes." Analysis & PDE 10, no. 6 (July 14, 2017): 1497–538. http://dx.doi.org/10.2140/apde.2017.10.1497.

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KIRAT, IBRAHIM, and ILKER KOCYIGIT. "REMARKS ON SELF-AFFINE FRACTALS WITH POLYTOPE CONVEX HULLS." Fractals 18, no. 04 (December 2010): 483–98. http://dx.doi.org/10.1142/s0218348x1000510x.

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Suppose that the set [Formula: see text] of real n × n matrices has joint spectral radius less than 1. Then for any digit set D = {d1, …, dq} ⊂ ℝn, there exists a unique non-empty compact set [Formula: see text] satisfying [Formula: see text], which is typically a fractal set. We use the infinite digit expansions of the points of F to give simple necessary and sufficient conditions for the convex hull of F to be a polytope. Additionally, we present a technique to determine the vertices of such polytopes. These answer some of the related questions of Strichartz and Wang, and also enable us to approximate the Lebesgue measure of such self-affine sets. To show the use of our results, we also give several examples including the Levy dragon and the Heighway dragon.

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Saldanha, Nicolau C., and Carlos Tomei. "Spectra of regular polytopes." Discrete & Computational Geometry 7, no. 4 (April 1992): 403–14. http://dx.doi.org/10.1007/bf02187851.

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Saldanha, Nicolau C., and Carlos Tomei. "Spectra of semi-regular polytopes." Boletim da Sociedade Brasileira de Matem�tica 29, no. 1 (March 1998): 25–51. http://dx.doi.org/10.1007/bf01245867.

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Douai, Antoine. "Global spectra, polytopes and stacky invariants." Mathematische Zeitschrift 288, no. 3-4 (August 22, 2017): 889–913. http://dx.doi.org/10.1007/s00209-017-1918-8.

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Jungers, Raphaël M., Antonio Cicone, and Nicola Guglielmi. "Lifted Polytope Methods for Computing the Joint Spectral Radius." SIAM Journal on Matrix Analysis and Applications 35, no. 2 (January 2014): 391–410. http://dx.doi.org/10.1137/130907811.

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Paluri, Nataraj S. V., and Jayesh J. Barve. "A Reliable Algorithm to Compute the Spectral Set of a Polytope of Polynomials to Prescribed Accuracy." Journal of Dynamic Systems, Measurement, and Control 128, no. 2 (March 28, 2005): 400–405. http://dx.doi.org/10.1115/1.2196416.

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We propose an algorithm to compute the spectral set of a polytope of polynomials. The proposed algorithm offers several key guarantees that are not available with existing techniques. It guarantees that the generated spectral set: (i) contains all the actual points, (ii) is computed to a prescribed accuracy, (iii) is computed reliably in face of all kinds of computational errors, and (iv) is computed in a finite number of algorithmic iterations. A further merit is that the computational complexity of the proposed algorithm is O(n) in contrast to O(n2) for existing techniques, where n is the degree of the polynomial. The algorithm is demonstrated on a few examples.

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Cerone, V. "A fast technique for the generation of the spectral set of a polytope of polynomials." Automatica 33, no. 2 (February 1997): 277–80. http://dx.doi.org/10.1016/s0005-1098(96)00196-3.

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Khatsymovsky, V. M. "Spectrum of area in the Faddeev formulation of gravity." Modern Physics Letters A 31, no. 19 (June 21, 2016): 1650114. http://dx.doi.org/10.1142/s0217732316501145.

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Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual general relativity (GR). Earlier, we have proposed first-order representation of the minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like four-simplices or, say, cuboids into which [Formula: see text] can be decomposed, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR. In the Hamiltonian formalism, the tetrad bilinears are canonically conjugate to the orthogonal connection matrices. We evaluate the spectrum of the elementary areas, functions of the tetrad bilinears. The spectrum is discrete and proportional to the Faddeev analog [Formula: see text] of the Barbero–Immirzi parameter [Formula: see text]. The possibility of the tetrad and metric discontinuities in the Faddeev gravity allows to consider any surface as consisting of a set of virtually independent elementary areas and its spectrum being the sum of the elementary spectra. Requiring consistency of the black hole entropy calculations known in the literature we are able to estimate [Formula: see text].

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Banigan, James R., Anindita Gayen, and Nathaniel J. Traaseth. "Correlating lipid bilayer fluidity with sensitivity and resolution of polytopic membrane protein spectra by solid-state NMR spectroscopy." Biochimica et Biophysica Acta (BBA) - Biomembranes 1848, no. 1 (January 2015): 334–41. http://dx.doi.org/10.1016/j.bbamem.2014.05.003.

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Dissertations / Theses on the topic "Spectral polytopes"

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Winter, Martin [Verfasser], Christoph [Akademischer Betreuer] Helmberg, Christoph [Gutachter] Helmberg, Michael [Gutachter] Joswig, and Egon [Gutachter] Schulte. "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity / Martin Winter ; Gutachter: Christoph Helmberg, Michael Joswig, Egon Schulte ; Betreuer: Christoph Helmberg." Chemnitz : Technische Universität Chemnitz, 2021. http://d-nb.info/1236341031/34.

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Nicolis, Stamatios. "Étude des défauts topologiques dans des structures atomiques désordonnées : influence sur le spectre d'excitations." Paris 11, 1988. http://www.theses.fr/1988PA112045.

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Les verres métalliques peuvent être considérés, dans une bonne approximation, comme des empilements aléatoires de sphères interagissant avec de simples potentiels de paires. C'est raisonnable, d'un point de vue géométrique, puisque l'unité de l'empilement compact à trois dimensions, le tétraèdre, ne remplit pas l'espace euclidien. Il pave un espace courbe, la 3-sphère. La configuration ainsi définie, un polytope, possède un ordre icosaédrique parfait. Dans cette thèse on introduit des défauts dans cette structure pour réduire la courbure à zéro et interpoler ainsi entre la 3-sphère et l'espace réel. Ceci est fait en exploitant les symétries de la structure idéale et on introduit des défauts à courbure négative qui sont localisés sur des membres d'une fibration de la 3-sphère par des grands cercles, la fibration de Hopf. Comme application de la méthode, on construit des polytopes avec deux, trois, quatre, six lignes ainsi qu'un polytope avec des paires de lignes de défauts de courbure négative et positive. On calcule ensuite leurs fonctions de distribution radiale. En exploitant les propriétés de symétrie des polytopes, on arrive à calculer la densité d'états électroniques (pour une bande non-dégénérée) d'une façon très efficace. Il est possible de définir une zone de Brillouin (uni-dimensionnelle) et regrouper les sommets en familles. Enfin, nous étudions l'influence des défauts sur l'ordre orientationnel des liens. Nous passons en revue des développements récents et appliquons ce formalisme pour déduire des résultats exacts et des règles de sélection pour des amas d'intérêt physique et en utilisons pour interpréter les résultats numériques de deux polytopes, qu'on a traités comme exemple de cette approche. On termine en évoquant quelques problèmes ouverts et des voies de recherche ultérieures

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Winter, Martin. "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity." 2021. https://monarch.qucosa.de/id/qucosa%3A75215.

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A spectral graph realization is an embedding of a finite simple graph into Euclidean space that is constructed from the eigenvalues and eigenvectors of the graph's adjacency matrix. It has previously been observed that some polytopes can be reconstructed from their edge-graphs by taking the convex hull of a spectral realization of this edge-graph. These polytopes, which we shall call spectral polytopes, have remarkable rigidity and symmetry properties and are a source for many open questions. In this thesis we aim to further the understanding of this phenomenon by exploring the geometric and combinatorial properties of spectral polytopes on several levels. One of our central questions is whether already weak forms of symmetry can be a sufficient reason for a polytope to be spectral. To answer this, we derive a geometric criterion for the identification of spectral polytopes and apply it to prove that indeed all polytopes of combined vertex- and edge-transitivity are spectral, admit a unique reconstruction from the edge-graph and realize all the symmetries of this edge-graph. We explore the same questions for graph realizations and find that realizations of combined vertex- and edge-transitivity are not necessarily spectral. Instead we show that we require a stronger form of symmetry, called distance-transitivity. Motivated by these findings we take a closer look at the class of edge-transitive polytopes, for which no classification is known. We state a conjecture for a potential classification and provide complete classifications for several sub-classes, such as distance-transitive polytopes and edge-transitive polytopes that are not vertex-transitive. In particular, we show that the latter class contains only polytopes of dimension d <= 3. As a side result we obtain the complete classification of the vertex-transitive zonotopes and a new characterization for root systems.

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VU, NGOC San. "Systèmes intégrables semi-classiques: du local au global." Habilitation à diriger des recherches, 2003. http://tel.archives-ouvertes.fr/tel-00007113.

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Ce mémoire a pour but de présenter un panorama des recherches que j'ai effectuées depuis la soutenance de ma thèse en 1998. J'en ai également profité pour réordonner mes résultats et émailler le texte de réflexions parfois nouvelles afin de tenter de combiner l'introduction au sujet avec la synthèse de mes recherches. Il sera question de systèmes hamiltoniens complètement intégrables, de leur étude locale, de leurs singularités, de leurs aspects globaux et de certains liens qu'il entretiennent avec les variétés toriques, tout ceci du point de vue de la mécanique classique ainsi que de celui de leur quantification semi-classique. Une étude détaillée des singularités dites non-dégénérées sera présentée.

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Conference papers on the topic "Spectral polytopes"

1

Nechita, Stefan-Cristian, Codrin Alexandru Lupascu, and Octavian Pastravanu. "On Spectrum Location of Discrete-Time Systems with Polytopic Uncertainties." In 2017 21st International Conference on Control Systems and Computer Science (CSCS). IEEE, 2017. http://dx.doi.org/10.1109/cscs.2017.14.

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Türkay, Semiha, and Aslı S. Leblebici. "Vibration Control of a Rigid and Flexible High-Speed Railway Vehicle." In 2020 Joint Rail Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/jrc2020-8096.

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Abstract In this paper, the vertical carbody dynamics of the railway vehicle excited by random track inputs are investigated. The multi-objective ℋ∞ controllers for carbody weight of the actual, heavy and a mass confined in a polytopic range have been designed with the aim of reducing the wheel forces, heave, pitch and roll body accelerations of the vehicle. Later, the carbody mass is modelled as a free-free Euler Bernoulli beam and the low frequency flexural vibrations of the train body are examined. An omnibus ℋ∞ controller is synthesized to suppress both the rigid and low frequencies flexible modes of the railway vehicle. The performances of the ℋ∞ controllers are verified by using the passive and active suspension responses on the right and left rail track disturbances that are represented by the power spectral density functions authenticated for the stochastic real track data collected from the Qinhuangdao-Shenyang passenger railway line in China. Simulation results showed that all controllers exhibit a very good performance by effectively reducing the car-body accelerations in vicinity of the resonanat frequencies while keeping the wheel-rail forces in the allowable limit.

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Pastravanu, Octavian, and Mihaela-Hanako Matcovschi. "On a conjecture in stability analysis of polytopic systems — Mimicking spectral radius properties from real to complex matrices." In 2014 18th International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2014. http://dx.doi.org/10.1109/icstcc.2014.6982381.

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