Results 1 to 10 of about 1,694,233 (308)
On Hyperbolic Complex Numbers [PDF]
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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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.
S. Ulrych
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Relativistic quantum physics with hyperbolic numbers [PDF]
Physics Letters B, 2000 A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects.
S. Ulrych
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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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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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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.
C. M. Dikmen
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Kolmogorov’s Axioms for Probabilities with Values in Hyperbolic Numbers [PDF]
, 2015 We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov’s system of axioms.
D. Alpay +2 more
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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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Hyperbolic Numbers in Modeling Genetic Phenomena
, 2019 The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2n-dimensional extensions in modeling some genetic and cultural phenomena.
S. Petoukhov
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Counting Salem Numbers of Arithmetic Hyperbolic 3-Orbifolds [PDF]
Bulletin of the Brazilian Mathematical Society, New Series, 2020 It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon.
M. Belolipetsky +3 more
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