Results 11 to 20 of about 13,449 (301)
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
doaj +2 more sources
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 ...
Alpay, Daniel, Cho, Ilwoo
openaire +4 more sources
Salem Numbers and the Spectrum of Hyperbolic Surfaces [PDF]
International Mathematics Research Notices, 2018 We give a reformulation of Salem's conjecture about the absence of Salem numbers near one in terms of a uniform spectral gap for certain arithmetic hyperbolic surfaces.
Emmanuel Breuillard, Bertrand Deroin
openaire +6 more sources
Two Generalizations of Dual-Hyperbolic Balancing Numbers [PDF]
Symmetry, 2020 In this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic k-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them.
Dorota Bród +2 more
core +6 more sources
Hyperbolic Jacobsthal Numbers [PDF]
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.
Can Murat Dikmen
openaire +4 more sources
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
doaj +2 more sources
On dual hyperbolic generalized Fibonacci numbers [PDF]
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
Yüksel Soykan
openaire +5 more sources
On Hyperbolic Generalized Woodall Numbers [PDF]
Asian Journal of Advanced Research and ReportsIn this study, we introduce the generalized hyperbolic Woodall numbers. As special cases, we study with hyperbolic Woodall, hyperbolic modified Woodall, hyperbolic Cullen numbers and hyperbolic modified Cullen numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers.
Orhan Eren, Yuksel Soykan
openaire +3 more sources
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
openaire +4 more sources
A Study on Hyperbolic Generalized Guglielmo Numbers [PDF]
, 2023 In this paper, we introduce the generalized hyperbolic Guglielmo numbers. We delve into various specific instances, including hyperbolic triangular numbers, hyperbolic triangular-Lucas numbers, hyperbolic oblong numbers, and hyperbolic pentagonal numbers.
Yüksel Soykan, Bahadır Yılmaz
core +1 more source