Results 121 to 130 of about 2,049,760 (173)
Classification of Hyperbolic Dehn fillings II: Quadratic case [PDF]
arXivThis paper is subsequent to [4]. In this paper, we complete the classification of hyperbolic Dehn fillings with sufficiently large coefficients of any $2$-cusped hyperbolic $3$-manifold by addressing the remaining case not covered in [4].
arxiv
The Parabolic and Hyperbolic Origins of the Number Line
This study explores the intrinsic structure of the number line, governed by the parabolic and hyperbolic properties of integer divisors. By introducing the Modular Hyperbolic Lattice (MHL), a geometric framework grounded in modular arithmetic, we uncover a dual behavior that organizes integer divisors in parabolic patterns and hyperbolically.
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On the Betti numbers of a hyperbolic manifold
Geometric and Functional Analysis, 1992 openaire +2 more sources
On the first Betti numbers of hyperbolic surfaces
Duke Mathematical Journal, 1991 openaire +3 more sources
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On the Dual Hyperbolic Numbers and the Complex Hyperbolic Numbers
Journal of Computer Science & Computational Mathematics, 2018In this study, we will introduce arithmetical operations on dual hyperbolic numbers w x y ju jv and hyperbolic complex numbers w x iy ju ijv which forms a commutative ring.
Şahin, Serdal +2 more
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Hyperbolic Numbers, Genetics and Musicology
2020The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic extensions in the form of 2n-dimensional hyperbolic numbers in bioinformatics, algebraic biology and musicology. These applications reveal hidden interconnections between structures of different biological phenomena.
S. Petoukhov
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Bicomplex and Hyperbolic Numbers
2014The main properties of bicomplex and hyperbolic numbers are considered, in particular, the three conjugations on them generate the corresponding moduli of a bicomplex number which are not real valued: two of them are complex valued and one is hyperbolic valued. The notion of a positive hyperbolic number allows to introduce a partial order on the set of
Daniel Alpay +3 more
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Complex and Hyperbolic Numbers
2012The complex numbers were grudgingly accepted by Renaissance mathematicians because of their utility in solving the cubic equation.1 Whereas the complex numbers were discovered primarily for algebraic reasons, they take on geometric significance when they are used to name points in the plane.
G. Sobczyk
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CANTOR-TYPE SETS IN HYPERBOLIC NUMBERS
Fractals, 2016The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane.
A. S. BALANKIN +3 more
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Geometrical Representation of Hyperbolic Numbers
2011A relevant property of Euclidean geometry is the Pythagorean distance between two points. From this definition the properties of analytical geometry follow. In a similar way the analytical geometry in Minkowski plane is introduced, starting from the invariant quantities of Special Relativity.
Dino Boccaletti +4 more
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