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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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Implementation of hyperbolic complex numbers in Julia language [PDF]
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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Salem numbers and arithmetic hyperbolic groups [PDF]
Transactions of the American Mathematical Society, 2018 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
Emery, Vincent +2 more
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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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A second order differential equation for the relativistic description of electrons and photons [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.
Baylis +43 more
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Hyperbolic band topology with non-trivial second Chern numbers [PDF]
Nature Communications, 2023 To date, studies of topological band theory have mostly dealt with Euclidean space. Here, the authors use classical electric-circuit networks to realize topological insulators in 2D negatively-curved (hyperbolic) space with non-trivial second Chern ...
Weixuan Zhang +4 more
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Julia and Mandelbrot Sets for Dynamics over the Hyperbolic Numbers [PDF]
Fractal and Fractional, 2019 Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of these sets for dynamical systems over the hyperbolic numbers.
Vance Blankers +3 more
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On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components
Fundamental Journal of Mathematics and Applications, 2019 Dual-hyperbolic Fibonacci and Lucas numbers with Fibonacci and Lucas coefficients are introduced by Cihan et al. and some identities and theorems are given regarding modules and conjugates of these numbers.
Mehmet Ali̇ Güngör, Arzu CİHAN
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Counting Salem Numbers of Arithmetic Hyperbolic 3-Orbifolds [PDF]
Bulletin of the Brazilian Mathematical Society = Boletim da Sociedade Brasileira de Matematica, 2021 It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon.
Mikhail Belolipetsky +3 more
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Barycenters and a law of large numbers in Gromov hyperbolic spaces [PDF]
Revista matemática iberoamericana, 2022 We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces.
Shin‐ichi Ohta
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