Results 11 to 20 of about 152,450 (318)
Properties of hyperbolic generalized Pell numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers.
Yüksel Soykan, Melih Göcen
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Algebraic Numbers, Hyperbolicity, and Density Modulo One
Journal of Number Theory, 2011 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.
Alexander Gorodnik, Shirali Kadyrov
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Kissing numbers of closed hyperbolic manifolds [PDF]
American Journal of Mathematics, 2019 We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of Parlier for surfaces. We also obtain bounds on the number of primitive closed geodesics with length in a given interval that are uniform for all closed hyperbolic manifolds ...
Maxime Fortier Bourque, Bram Petri
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A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
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
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Hyperbolic Numbers and the Dirac Spinor
, 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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Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics [PDF]
Acta Polytechnica, 2011 We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups.
V. V. Kisil
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On Hyperbolic Generalized Woodall Numbers
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, Yüksel Soykan
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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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Сучасні інформаційні системи, 2022 The goal of the work. Development of methods for performing basic arithmetic operations with interval complex numbers, which are presented in hyperbolic form, their modulus and argument. Results.
Svitlana Gadetska +3 more
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