Results 1 to 10 of about 13,449 (301)
On Hyperbolic Complex Numbers [PDF]
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 +3 more sources
Performance of basic arithmetic actions with complex numbers, which are presented in interval hyperbolic form [PDF]
Сучасні інформаційні системи, 2022 The goal of the work. Development of methods for performing basic arithmetic operations with interval complex numbers, which are presented in hyperbolic form, their modulus and argument. Results.
Svitlana Gadetska +3 more
doaj +2 more sources
One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers [PDF]
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
doaj +3 more sources
Space and space-time topologies in a type-II hyperbolic lattice [PDF]
Nature CommunicationsRecent breakthroughs in hyperbolic lattices have expanded the study of topological phases of matter from Euclidean to non-Euclidean spaces. However, prior work has mostly focused on static spatial topological states at the single outer edge of type-I ...
Jingming Chen +5 more
doaj +2 more sources
Hyperbolic Horadam hybrid functions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The aim of this paper is to introduce the hybrid form of the hyperbolic Horadam function and to investigate some of its properties such as the generating function.
Efruz Özlem Mersin
doaj +1 more source
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 +1 more source
Chromatic numbers of hyperbolic surfaces [PDF]
Indiana University Mathematics Journal, 2016 24 pages, 12 ...
Parlier Hugo, Petit Camille
openaire +3 more sources
On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions
Journal of New Theory, 2023 In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions.
Paula Maria Machado Cruz Catarino +2 more
doaj +1 more source
Topological Bihyperbolic Modules
Communications in Advanced Mathematical Sciences, 2021 The aim of this article is introducing and researching hyperbolic modules, bihyperbolic modules, topological hyperbolic modules, and topological bihyperbolic modules.
Merve Bilgin, Soley Ersoy
doaj +1 more source
Quadratic dynamics over hyperbolic numbers: a brief survey [PDF]
Surveys in Mathematics and its Applications, 2022 Hyperbolic numbers, also called split complex or perplex numbers in the literature, are a variation of complex numbers established as a theory primarily by W. Clifford in the nineteenth century who applied them to mechanics.
Sandra Hayes
doaj