Results 1 to 10 of about 3,036,123 (324)
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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A Study on Dual Hyperbolic Fibonacci and Lucas Numbers [PDF]
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
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Asian Research Journal of Mathematics, 2019 In this paper, we introduce the Hyperbolic Jacobsthal numbers and we present recurrence relations, Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we investgate Lorentzian inner product for the hyperbolic Jacobsthal vectors.
C. M. Dikmen
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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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Probabilities with Values in Scaled Hyperbolic Numbers [PDF]
Advances in Applied Clifford AlgebrasAbstract In this paper, we introduce a notion of a probabilistic measure which takes values in t-scaled hyperbolic numbers for $$t\in \mathbb {R}$$ t ∈ R
Daniel Alpay, Ilwoo Cho
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On dual hyperbolic generalized Fibonacci numbers
Indian Journal of Pure and Applied Mathematics, 2019 In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's
Y. Soykan
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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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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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Hyperbolic numbers as Einstein numbers
Journal of Physics: Conference Series, 2020 Abstract In the special theory of relativity (SR) it is usual to highlight so-called paradoxes. One of these paradoxes is the formal appearance of speed values grater then the light speed. In this paper we show that most of these paradoxes arise due to the incompleteness of relativistic calculus over velocities.
Kulyabov D.S. +2 more
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On Hyperbolic Numbers With Generalized Fibonacci Numbers Components
Communications in Mathematics and Applications, 2021 . In this paper, we introduce the generalized hyperbolic Fibonacci numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Fibonacci and hyperbolic Lucas numbers.
Y. Soykan
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