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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.
S. Ulrych
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On Dual Hyperbolic Guglielmo Numbers
Journal of Advances in Mathematics and Computer ScienceIn this research, the generalized dual hyperbolic Guglielmo numbers are introduced. Various special cases are explored (including dual hyperbolic triangular numbers, dual hyperbolic triangular-Lucas numbers, dual hyperbolic oblong numbers, and dual hyperbolic pentagonal numbers).
Bahadır Yılmaz, Yüksel Soykan
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Quadratic Dynamics Over Hyperbolic Numbers [PDF]
, 2020 Hyperbolic numbers are a variation of complex numbers, but their dynamics is quite different. The hyperbolic Mandelbrot set for quadratic functions over hyperbolic numbers is simply a filled square, and the filled Julia set for hyperbolic parameters inside the hyperbolic Mandelbrot set is a filled rectangle.
Sandra Hayes
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Hyperbolic Numbers and the Dirac Spinor [PDF]
, 1998 A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over the hyperbolic number system. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the transformation properties of the complex Dirac spinor.
F. Antonuccio
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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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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. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures ...
Sergey Petoukhov
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Kolmogorov’s Axioms for Probabilities with Values in Hyperbolic Numbers [PDF]
, 2016 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.
Daniel Alpay +2 more
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Hyperbolic Horadam hybrid functions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The aim of this paper is to introduce the hybrid form of the hyperbolic Horadam function and to investigate some of its properties such as the generating function.
Efruz Özlem Mersin
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AIMS Mathematics, 2023 The aim of this paper is to introduce several degenerate hyperbolic functions as degenerate versions of the hyperbolic functions, to evaluate Volkenborn and the fermionic $ p $-adic integrals of the degenerate hyperbolic cosine and the degenerate ...
Taekyun Kim, Hye Kyung Kim , Dae San Kim
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Implementation of hyperbolic complex numbers in Julia language
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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