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Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces [PDF]
Analysis and Geometry in Metric Spaces, 2015 We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
Buyalo Sergei, Schroeder Viktor
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Coquaternionic Quantum Dynamics for Two-level Systems [PDF]
Acta Polytechnica, 2011 The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory are investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the Hamiltonian.
D. C. Brody, E. M. Graefe
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HC-SPA: Hyperbolic Cosine-Based Symplectic Phase Alignment for Fusion Optimization [PDF]
SensorsIn multimodal collaborative learning, the gradient dynamics of heterogeneous modalities face significant challenges due to the curvature heterogeneity of parameter manifolds and mismatches in phase evolution.
Wenlong Zhang +3 more
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PLoS ONE, 2022 Animals use odors in many natural contexts, for example, for finding mates or food, or signaling danger. Most analyses of natural odors search for either the most meaningful components of a natural odor mixture, or they use linear metrics to analyze the ...
Majid Ghaninia +5 more
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Quantum Chromodynamics and the Hyperbolic Unitary Group SUh(3)
Axioms, 2023 The paper shows that it is possible to construct quantum chromodynamics as a rigorous theory on the basis of employment of hyperbolic unitary group SUh(3), which is a symmetry group for the three-dimensional complex space of the hyperbolic type.
Nikolay Popov, Ivan Matveev
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Implementation of hyperbolic complex numbers in Julia language
Discrete and Continuous Models and Applied Computational Science, 2022 Hyperbolic complex numbers are used in the description of hyperbolic spaces. One of the well-known examples of such spaces is the Minkowski space, which plays a leading role in the problems of the special theory of relativity and electrodynamics. However,
Anna V. Korolkova +2 more
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Non-hyperbolic complex space with a hyperbolic normalization [PDF]
Proceedings of the American Mathematical Society, 2000 By a result of \textit{M. H. Kwack} [Ann. Math. (2) 90, 9-22 (1969; Zbl 0179.12103)] a normalization of a hyperbolic complex space is also hyperbolic (in the sense of S. Kobayashi). In the present note, the authors show that the converse is not true constructing a non-hyperbolic singular projective surface whose normalization is hyperbolic.
Zaidenberg, M, Kaliman, Shulim
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Hyperbolic matter in electrical circuits with tunable complex phases
Nature Communications, 2023 Hyperbolic lattices emulate particle dynamics equivalent to those in negatively curved space, with connections to general relativity. Here, the authors use electric circuits with a novel complex-phase circuit element to simulate hyperbolic graphene with ...
Anffany Chen +13 more
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Translation-Based Embeddings with Octonion for Knowledge Graph Completion
Applied Sciences, 2022 Knowledge representation learning achieves the automatic completion of knowledge graphs (KGs) by embedding entities into continuous low-dimensional vector space.
Mei Yu +7 more
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Complexity, 2020 Network embedding is a frontier topic in current network science. The scale-free property of complex networks can emerge as a consequence of the exponential expansion of hyperbolic space.
Zongning Wu, Zengru Di, Ying Fan
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