Thematische Bibliographien / Dimensión de Frobenius-Perron

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Auswahl der wissenschaftlichen Literatur zum Thema „Dimensión de Frobenius-Perron“

Autor: Grafiati

Veröffentlicht am 17. September 2021

Zuletzt aktualisiert am 9. Februar 2022

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Zeitschriftenartikel zum Thema "Dimensión de Frobenius-Perron"

Dong, Jingcheng, Sonia Natale und Leandro Vendramin. „Frobenius property for fusion categories of small integral dimension“. Journal of Algebra and Its Applications 14, Nr. 02 (19.10.2014): 1550011. http://dx.doi.org/10.1142/s0219498815500115.

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Let k be an algebraically closed field of characteristic zero. In this paper, we prove that fusion categories of Frobenius–Perron dimensions 84 and 90 are of Frobenius type. Combining this with previous results in the literature, we obtain that every weakly integral fusion category of Frobenius–Perron dimension less than 120 is of Frobenius type.

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Drobot, Vladimir, und John Turner. „Hausdorff dimension and Perron-Frobenius theory“. Illinois Journal of Mathematics 33, Nr. 1 (März 1989): 1–9. http://dx.doi.org/10.1215/ijm/1255988801.

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Metz, Volker. „Nonlinear Perron–Frobenius theory in finite dimensions“. Nonlinear Analysis: Theory, Methods & Applications 62, Nr. 2 (Juli 2005): 225–44. http://dx.doi.org/10.1016/j.na.2005.02.116.

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Dong, Jingcheng, Libin Li und Li Dai. „Integral almost square-free modular categories“. Journal of Algebra and Its Applications 16, Nr. 06 (12.04.2017): 1750104. http://dx.doi.org/10.1142/s0219498817501043.

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We study integral almost square-free modular categories; i.e., integral modular categories of Frobenius–Perron dimension [Formula: see text], where [Formula: see text] is a prime number, [Formula: see text] is a square-free natural number and [Formula: see text]. We prove that, if [Formula: see text] or [Formula: see text] is prime with [Formula: see text], then they are group-theoretical. This generalizes several results in the literature and gives a partial answer to the question posed by the first author and Tucker. As an application, we prove that an integral modular category whose Frobenius–Perron dimension is odd and less than [Formula: see text] is group-theoretical.

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Dong, Jingcheng, und Henry Tucker. „Integral Modular Categories of Frobenius-Perron Dimension pq n“. Algebras and Representation Theory 19, Nr. 1 (29.07.2015): 33–46. http://dx.doi.org/10.1007/s10468-015-9560-9.

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Etingof, Pavel. „Frobenius-Perron Dimensions of Integral $\mathbb {Z}_{+}$-rings and Applications“. Algebras and Representation Theory 23, Nr. 5 (07.11.2019): 2059–78. http://dx.doi.org/10.1007/s10468-019-09924-1.

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Fox, Colin, Li-Jen Hsiao und Jeong-Eun (Kate) Lee. „Solutions of the Multivariate Inverse Frobenius–Perron Problem“. Entropy 23, Nr. 7 (30.06.2021): 838. http://dx.doi.org/10.3390/e23070838.

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We address the inverse Frobenius–Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map; that is, a map under which the uniform distribution on the d-dimensional hypercube is invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via one-dimensional examples, and then use the factorization to present solutions in one and two dimensions induced by a range of uniform maps.

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Bruillard, Paul, Cásar Galindo, Seung-Moon Hong, Yevgenia Kashina, Deepak Naidu, Sonia Natale, Julia Yael Plavnik und Eric C. Rowell. „Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2“. Canadian Mathematical Bulletin 57, Nr. 4 (01.12.2014): 721–34. http://dx.doi.org/10.4153/cmb-2013-042-6.

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AbstractWe classify integral modular categories of dimension pq4 and p2q2, where p and q are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension 4q2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara–Yamagami categories and quantum groups. We show that a non-grouptheoretical integral modular category of dimension 4q2 is either equivalent to one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising froma certain quantum group.

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MAULDIN, R. D., und M. URBAŃSKI. „Parabolic iterated function systems“. Ergodic Theory and Dynamical Systems 20, Nr. 5 (Oktober 2000): 1423–47. http://dx.doi.org/10.1017/s0143385700000778.

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In this paper we introduce and explore conformal parabolic iterated function systems. We define and study topological pressure, Perron–Frobenius-type operators, semiconformal and conformal measures and the Hausdorff dimension of the limit set. With every parabolic system we associate an infinite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical features (properly defined invariant measures for example) of the limit set.

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Duvall, P., und J. Keesling. „The dimension of the boundary of the Lévy Dragon“. International Journal of Mathematics and Mathematical Sciences 20, Nr. 4 (1997): 627–32. http://dx.doi.org/10.1155/s0161171297000872.

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In this paper we describe the computations done by the authors in determining the dimension of the boundary of the Lévy Dragon. A general theory was developed for calculating the dimension of a self-similar tile and the theory was applied to this particular set. The computations were challenging. It seemed that a matrix which was215×215would have to be analyzed. It was possible to reduce the analysis to a752×752matrix. At last it was seen that ifλwas the largest eigenvalue of a certain734×734matrix, thendimH(K)=ln(λ)ln((2))Perron-Frobenius theory played an important role in analyzing this matrix.

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Dissertationen zum Thema "Dimensión de Frobenius-Perron"

Pacheco, Rodríguez Edwin Fernando. „Grafos de Frobenius-Perron para categorías de fusión“. Doctoral thesis, 2015. http://hdl.handle.net/11086/2805.

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Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, 2015.
Sea C una categoría de fusión íntegra, en este trabajo se estudian algunos grafos, llamados el grafo primo y el grafo común divisor, relacionados con las dimensiones de Frobenius-Perron de los objetos simples de C. Estos grafos generalizan los grafos correspondientes asociados a los caracteres irreducibles y a los órdenes de las clases de conjugación en un grupo finito. Se describen los grafos en distintos casos específicos, entre otros, cuando C es una equivariantización bajo la acción de un grupo finito, una categoría 2-pasos nilpotente, y la categoría de representaciones de un doble de Drinfeld torcido de un grupo finito. Se demuestran generalizaciones al contexto de las categorías de fusión íntegras de resultados sobre el número de componentes conexas de los grafos correspondientes para grupos finitos. En particular, se prueba que si C es una categoría íntegra trenzada no degenerada, entonces el grafo primo de C tiene a lo sumo 3 componentes conexas, y tiene a lo sumo 2 componentes conexas si C es además resoluble. Como aplicación de los resultados principales, se demuestra un resultado de clasificación para categorías de fusión débilmente íntegras tales que las dimensiones de sus objetos simples son todas potencias de números primos.
Let C be an integral fusion category. In this work, we study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects of C. This graphs extend the corresponding graphs associated to the irreducible character degrees and the conjugacy class sizes of a nite group. We describe these graphs in several cases, among others, when C is an equivariantization under the action of a nite group, a 2-step nilpotent fusion category, and the representation category of a twisted quantum double. We prove generalizations of known results on the number of connected components of the corresponding graphs for nite groups in the context of braided fusion categories. In particular, we show that if C is any integral nondegenerate braided fusion category, then the prime graph of C has at most 3 connected components, and it has at most 2 connected components if C is in addition solvable. As an application we prove a classi cation result for weakly integral braided fusion categories all of whose simple objects have prime power Frobenius- Perron dimension.

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Czenky, Agustina Mercedes. „Sobre las categorías modulares de dimensión impar“. Bachelor's thesis, 2019. http://hdl.handle.net/11086/11747.

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Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.
El objetivo de este trabajo es presentar de la manera más autocontenida posible a las categorías modulares de dimensión impar, sus propiedades e invariantes. En la primera parte se exponen las nociones de categorías tensoriales y categorías de fusión. Se presentan construcciones útiles, como la graduación y la equivariantización por grupos finitos, y clases distinguidas de categorías: punteadas, de tipo grupo, nilpotentes, solubles, entre otras. En una segunda parte se aborda el estudio de las categorías modulares y se tratan algunos de sus invariantes: S-matriz, T -matriz, Sumas de Gauss e Indicadores de Frobenius-Schur. Finalmente se discuten algunos problemas actuales y nuevas herramientas, como el Teorema de Cauchy para categorías de fusión esféricas, la clasificación de categorías modulares de dimensión impar de rango pequeño y la clasificación de categorías modulares casi libres de cuadrados de dimensión impar. Se presentan además algunos resultados propios vinculados a dichos problemas y técnicas.
The main goal of this work is to present, in the most comprehensive way we can achieve, odd dimensional modular categories, their properties and invariants. The first part sets out the notions of tensor and fusion categories. Useful constructions are included, such as grading and equivariantization by finite groups, and distinguished classes of categories are introduced: pointed, group-theoretical, nilpotent and solvable, among others. A second part approaches the study of modular categories and some of their invariants: S-matrix, T -matrix, Gauss Sums and Frobenius-Schur Indicators. Finally, some current problems and new techniques are discussed, such as the Cauchy Theorem for spherical fusion categories, the classification of odd dimensional modular categories of small rank and the classification of odd dimensional almost square-free modular categories. Some original results related to the mentioned problems and techniques are exhibited.

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Buchteile zum Thema "Dimensión de Frobenius-Perron"

Takeo, F. „Hausdorff Dimension of Some Fractals and Perron-Frobenius Theory“. In Contributions to Operator Theory and its Applications, 177–95. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8581-2_11.

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