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n-Dimensional hyperbolic complex numbers
Advances in Applied Clifford Algebras, 1998In this contribution is deduced a generalisation of the 2-dimensional complex number system. The construction of a hyperbolic basis is one of the main topics in this paper. By the aid of this basis the authors succeed in a nice description of an \(n\)-dimensional direct product ring of reals.
Fjelstad, Paul, Gal, Sorin G.
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Capstone Studies for Math Majors via Complex and Hyperbolic Numbers
PRIMUS, 2022This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry ...
Rachid Atmai +2 more
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The transformation in the P-Module by hyperbolic numbers
FilomatHyperbolic numbers are one of the well-known number systems, like complex numbers. In this paper, we will talk about some properties of hyperbolic numbers, define the P-modulus, and give some properties of the P-modulus.
Jing Li +4 more
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On the Betti numbers of finite volume real- and complex-hyperbolic manifolds
Journal of Differential GeometryIn [\textit{L. F. Di Cerbo} and \textit{M. Stern}, Commun. Anal. Geom. 30, No. 2, 297--334 (2022; Zbl 1509.53046)], the authors derived the Price inequalities for harmonic forms on Riemannian manifolds without conjugate points and with a negative Ricci upper bound.
Di Cerbo, Luca F., Stern, Mark
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Hyperbolic double-complex numbers
AIP Conference Proceedings, 2009The algebra of bicomplex numbers and the corresponding bicomplex holomorphic functions are well known ([1] and others). The hyperbolic bicomplex numbers were used by Dominic Rochon in different aspects (for instance [2]). The algebra of double‐complex numbers (in the sense of [3]) gives a parallel treatement closely related with the classical theory of
L. N. Apostolova +5 more
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Complex and hyperbolic Fibonacci numbers and phyllotaxis
Symmetry: Culture and Science, 2022S.V. Petoukhov +2 more
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A Use of Elliptic Complex Numbers in Newtonian Gravity
Advances in Applied Clifford Algebras, 2022 In this study, we used the fact that unit circle for elliptic numbers is an ellipse to model motion of a planet around a star. For that purpose we first have given a standard derivation of elliptic orbits in Newtonian two-body problem. Then we translated
Furkan Semih Dündar
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Hybrid Complex Numbers: The Matrix Version
Advances in Applied Clifford Algebras, 2018 In this paper we review the notion of hybrid complex numbers, recently introduced to provide a comprehensive conceptual and formal framework to deal with circular, hyperbolic and dual complex.
G. Dattoli +3 more
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Generalized complex numbers over near-fields
, 2019 The construction of the complex numbers over the reals has been generalized in many ways leading, amongs others, to the 2-dimensional elliptical complex numbers (= ordinary complex numbers), the parabolic complex numbers and the hyperbolic complex ...
S. Veldsman
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On some properties of the solution set of one of Wilker’s inequalities for complex numbers
Involve. A Journal of Mathematics, 2021We state and prove properties of the solution set of the extension of one of Wilker’s inequalities to the field of complex numbers. Wilker’s inequalities are inequalities for real numbers which involve trigonometric or hyperbolic functions.
Aar'on Guill'en-Villalobos +1 more
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