Results 201 to 210 of about 8,394 (239)

n-Dimensional hyperbolic complex numbers

Advances in Applied Clifford Algebras, 1998
In 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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Hyperbolic double-complex numbers

AIP Conference Proceedings, 2009
The 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, K. I. Krastev, B. Kiradjiev, George Venkov, Ralitza Kovacheva, Vesela Pasheva   +5 more
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Hyperbolic complex numbers and nonlinear sigma models

International Journal of Theoretical Physics, 1987
We show that the hyperbolic complex numbers or double numbers can be used to generate solutions of two-dimensional Minkowskian sigma models with values on noncompact manifolds.
Lambert, Dominique, TOMBAL,, Philippe
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Complex and Hyperbolic Numbers

2012
The 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.
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ON THE NUMBER OF COMPLEX HYPERBOLIC MANIFOLDS OF BOUNDED VOLUME

International Journal of Mathematics, 2005
We give an effective bound on the number of n-dimensional complex hyperbolic manifolds of volume bounded by v > 0 in terms of n ≥ 2 and v, using effective methods of algebraic geometry, related to adjunction theory and complexity of Chow varieties.
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Intersection numbers and the hyperbolicity of the curve complex

Journal für die reine und angewandte Mathematik (Crelles Journal), 2006
Summary: We give another proof of the result of Masur and Minsky that the complex of curves associated to a compact orientable surface is hyperbolic. Our proof is more combinatorial in nature and can be expressed mostly in terms of intersection numbers. We show that the hyperbolicity constant is bounded above by a logarithmic function of the complexity
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HILBERT SPACE OVER COMPLEX HYPERBOLIC NUMBERS AND HYPER-TRIGONOMETRIC INTERFERENCE

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2009
This note is devoted to extension of quantum probability calculus to generalizations of complex Hilbert space. Starting with Hilbert space over complex hyperbolic numbers, we derive general hyper-trigonometric interference of probabilities.
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The number theory of a system of hyperbolic complex numbers.

1949
[...] Although much has been written and a great deal of elegent theory developed for numbers of the form x + iy, where i2 = -1 and x and y are real numbers, viz, the ordinary complex numbers; very little has been said concerning an analogous system of numbers of the form x + jy where j2 = 1.
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On the Betti numbers of finite volume real- and complex-hyperbolic manifolds

Journal of Differential Geometry
In [\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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Complex and hyperbolic Fibonacci numbers and phyllotaxis

Symmetry: Culture and Science, 2022
S.V. Petoukhov, E.S. Petukhova, V.I. Svirin   +2 more
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