Results 11 to 20 of about 423,443 (325)
Quadratic Dynamics Over Hyperbolic Numbers [PDF]
arXiv, 2020 Hyperbolic numbers are a variation of complex numbers, but their dynamics is quite different. The hyperbolic Mandelbrot set for quadratic functions over hyperbolic numbers is simply a filled square, and the filled Julia set for hyperbolic parameters inside the hyperbolic Mandelbrot set is a filled rectangle.
Sandra Hayes
openalex +3 more sources
Algebraic Numbers, Hyperbolicity, and Density Modulo One
Journal of Number Theory, 2011 We prove the density of the sets of the form ${ _1^m _1^n _1 +...+ _k^m _k^n _k : m,n \in \mathbb N}$ modulo one, where $ _i$ and $ _i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups.
Alexander Gorodnik, Shirali Kadyrov
openalex +6 more sources
Kissing numbers of closed hyperbolic manifolds [PDF]
American Journal of Mathematics, 2019 We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of Parlier for surfaces. We also obtain bounds on the number of primitive closed geodesics with length in a given interval that are uniform for all closed hyperbolic manifolds ...
Maxime Fortier Bourque, Bram Petri
openalex +4 more sources
A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers.
Cihan Arzu +3 more
doaj +5 more sources
Properties of hyperbolic generalized Pell numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers.
Yüksel Soykan, Melih Göcen
openalex +2 more sources
Radix form in hyperbolic and dual numbers [PDF]
arXiv, 2022 We investigate number systems for the ring of integers of hyperbolic and dual numbers. We characterize all canonical number systems providing radix form for hyperbolic and dual numbers. Our approach allows us to get suitable bases by means of Banach lattice algebra structure.
openaire +3 more sources
Hyperbolic Numbers and the Dirac Spinor
, 1998 A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over the hyperbolic number system. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the transformation properties of the complex Dirac spinor.
F. Antonuccio
openalex +4 more sources
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 +1 more source
Aggressive Behavior, Volume 49, Issue 1, Page 85-95, January 2023., 2023 Abstract The past two decades have produced extensive evidence on the manifold and severe outcomes for victims of aggression exposure in the workplace. However, due to the dominating individual‐centered approach, most findings miss a social network perspective.
Alexander Herrmann +2 more
wiley +1 more source
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