Results 11 to 20 of about 1,694,233 (308)
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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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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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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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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The Squeeze Principle of the Sequence of Hyperbolic Numbers [PDF]
Transactions on Computational and Applied Mathematics: The hyperbolic numbers have an analogous composition with the complex numbers, which are composed by two real numbers, generating an exchangeable ring. That is to mean, the hyperbolic numbers can be viewed as the generalization of real numbers. In this
Bingyi Lyu, Hengcheng Zhao
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Hyperbolic numbers as Einstein numbers
Journal of Physics: Conference Series, 2020 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.
D. Kulyabov +2 more
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EXTENSIONS OF THE SHANNON ENTROPY AND THE CHAOS GAME ALGORITHM TO HYPERBOLIC NUMBERS PLANE [PDF]
Fractals, 2019 In this paper, we provide extensions to hyperbolic numbers plane of the classical Chaos game algorithm and the Shannon entropy. Both notions connected with that of probability with values in hyperbolic number, introduced by Alpay et al.
G. Téllez-Sánchez, J. Bory‐Reyes
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Chromatic numbers of hyperbolic surfaces [PDF]
Indiana University Mathematics Journal, 2016 24 pages, 12 ...
Hugo Parlier, Camille Petit
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On scaled hyperbolic numbers induced by scaled hyperbolic rings [PDF]
, 2023 In this paper, we generalize the well-known hyperbolic numbers to certain numeric structures scaled by the real numbers. Under our scaling of $\mathbb{R}$, the usual hyperbolic numbers are understood to be our 1-scaled hyperbolic numbers. If a scale $t$ is not positive in $\mathbb{R}$, then our $t$-scaled hyperbolic numbers have similar numerical ...
Daniel Alpay, Ilwoo Cho
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Barycenters and a law of large numbers in Gromov hyperbolic spaces [PDF]
Revista matemática iberoamericana, 2022 We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces.
Shin-ichi Ohta
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