Results 1 to 10 of about 157,678 (311)
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
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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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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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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
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Kolmogorov's axioms for probabilities with values in hyperbolic numbers [PDF]
, 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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Systoles and kissing numbers of finite area hyperbolic surfaces [PDF]
, 2015 We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main
Fanoni, Federica, Parlier, Hugo
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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
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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
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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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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
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