Results 1 to 10 of about 423,443 (325)
Hyperbolic complex numbers in two dimensions [PDF]
arXiv, 2000 19 ...
Silviu Olariu
arxiv +5 more sources
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
doaj +5 more sources
Chromatic numbers of hyperbolic surfaces [PDF]
Indiana University Mathematics Journal, 2016 24 pages, 12 ...
Hugo Parlier, Camille Petit
openalex +5 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
openalex +8 more sources
Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ \mathbb{Z}_p $ [PDF]
AIMS Mathematics, 2023 The aim of this paper is to introduce several degenerate hyperbolic functions as degenerate versions of the hyperbolic functions, to evaluate Volkenborn and the fermionic $ p $-adic integrals of the degenerate hyperbolic cosine and the degenerate ...
Taekyun Kim, Hye Kyung Kim , Dae San Kim
doaj +2 more sources
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
openalex +7 more sources
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 determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic ...
Vincent Emery +2 more
openalex +6 more sources
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
doaj +2 more sources