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Salem numbers and arithmetic hyperbolic groups [PDF]
Transactions of the American Mathematical Society, 2019 In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we
Vincent Emery +2 more
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Implementation of hyperbolic complex numbers in Julia language
Discrete and Continuous Models and Applied Computational Science, 2022 Hyperbolic complex numbers are used in the description of hyperbolic spaces. One of the well-known examples of such spaces is the Minkowski space, which plays a leading role in the problems of the special theory of relativity and electrodynamics. However,
Anna V. Korolkova +2 more
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Chromatic numbers of hyperbolic surfaces [PDF]
Indiana University Mathematics Journal, 2016 24 pages, 12 ...
Hugo Parlier, Camille Petit
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Applied Sciences, 2022 For dimensions two, three and four, we derive hyperbolic complex algebraic structures on the basis of suitably defined vector products and powers which allow in a standard way a series definitions of the hyperbolic vector exponential function.
Wolf-Dieter Richter
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Salem Numbers and the Spectrum of Hyperbolic Surfaces [PDF]
International Mathematics Research Notices, 2018 We give a reformulation of Salem's conjecture about the absence of Salem numbers near one in terms of a uniform spectral gap for certain arithmetic hyperbolic surfaces.
Emmanuel Breuillard, Bertrand Deroin
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Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers [PDF]
, 2012 A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated.
Alexander Kolpakov
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Representations of Clifford algebras with hyperbolic numbers [PDF]
Advances in Applied Clifford Algebras, 2007 The representations of Clifford algebras and their involutions and anti-involutions are fully investigated since decades. However, these representations do sometimes not comply with usual conventions within physics.
Ulrych, S.
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Relativistic quantum physics with hyperbolic numbers [PDF]
, 2005 A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects.
S. Ulrych
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Hyperbolic Numbers in Modeling Genetic Phenomena
, 2020 The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2n-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures ...
Sergey Petoukhov
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Kolmogorov's axioms for probabilities with values in hyperbolic numbers [PDF]
Advances in Applied Clifford Algebras, 2015 We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov's system of axioms.
Alpay, Daniel +2 more
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