Results 41 to 50 of about 11,503 (148)

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
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New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
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On Transcendental Numbers: New Results and a Little History

Axioms, 2018
Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π , and ...
Solomon Marcus, Florin F. Nichita
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Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras

Nonlinear Analysis, 2022
The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
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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-Ces&agrave;ro's, Melham's
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Kissing number in hyperbolic space

, 2019
This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $\mathbb{H}^n$, for $n\geq 2$. For that purpose, the kissing number is replaced by the kissing function $ (n, r)$ which depends on the radius $r$.
Dostert, Maria, Kolpakov, Alexander
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On scaled hyperbolic numbers induced by scaled hyperbolic rings

, 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
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On Mersenne Numbers and their Bihyperbolic Generalizations

Annales Mathematicae Silesianae
In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers.
Bród Dorota, Szynal-Liana Anetta
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Algebraic numbers, hyperbolicity, and density modulo one

Journal of Number Theory, 2012
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.
Gorodnik, A, Kadyrov, S
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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. A few simple examples are presented, which point out that the hyperbolic numbers can close this gap.
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