Results 251 to 260 of about 132,757 (287)

The Integral and Limit Exchange Theorem for Hyperbolic Complex Columns

Highlights in Science Engineering and Technology
This paper delves into hyperbolic numbers and their generalizations like bicomplex and hyperbolic complex numbers. By analyzing prior studies, it explores their mathematical properties, including basic concepts, function sequences, and integral ...
R. Guo, Meiyi Shan, Renjie Tong
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Laplace Theorem for hyperbolic complex determinants

Highlights in Science Engineering and Technology
This paper studies the Laplace theorem for hyperbolic complex determinants, aiming to explore the algebraic properties of hyperbolic complex numbers and their applications in analysis.
Haitao Ye, Jie Zhang, Shiyu Fu
semanticscholar   +1 more source

Research on the Computation and Properties of the Hyperbolic Complex Determinant

Highlights in Science Engineering and Technology
  In this paper, the calculation results and properties of determinants under hyperbolic complex numbers are studied. The hyperbolic complex number is a commutative ring consisting of two real numbers with zero divisors.
Jie Zhang, Yajing Ma, Kai Jin
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A Study On Hyperbolic Generalized Edouard Numbers

Asian Journal of Probability and Statistics
In this study, we introduce the generalized hyperbolic Edouard numbers, a novel class of sequences governed by fourth-order recurrence relations, which extend traditional frameworks through enriched algebraic and combinatorial structures.
Emine Esra Ayrılma, Y. Soykan
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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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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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Convexity Theorem for Hyperbolic Functions in Complex Analysis

Highlights in Science Engineering and Technology
This paper studies the convexity of hyperbolic complex functions, where hyperbolic numbers are commutative rings that contain zero divisors and are composed of two real numbers.
Yizhe Feng, Xinyue Huang, Luowei Cui
semanticscholar   +1 more source

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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Capstone Studies on Roots of Hyperbolic Numbers

PRIMUS - Problems, Resources, and issues in mathematics undergraduate studies
To help students develop a more creative and inquisitive mathematical mindset, we present capstone-style explorations on finding roots of hyperbolic numbers, a generalization of the complex numbers. We include pedagogical reflections, informed by our use
N. Easley, Barbara A. Shipman
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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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