Results 51 to 60 of about 2,057 (213)
Discrete Mathematics, 1997 AbstractLet Φ be the golden ratio (√5 + 1)/2, fn the nth Fibonacci finite word and f the Fibonacci infinite word. Let r be a rational number greater than (2 + Φ)/2 and u a nondashempty word. If ur is a factor of f, then there exists n ⩾ 1 such that u is a conjugate of fn and, moreover, each occurrence of ur is contained in a maximal one of (fn)s for ...
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Some properties of Fibonacci numbers, Fibonacci octonions, and generalized Fibonacci-Lucas octonions [PDF]
Advances in Difference Equations, 2015 In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
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Machine learning for the classification of serial electron diffraction patterns: synthetic data
Acta Crystallographica Section A, EarlyView.Machine learning based sorting of synthetic serial electron diffraction patterns into 2D zonal patterns and patterns representing intersections of multiple Laue zones is demonstrated. The extracted zonal patterns can be used for the determination of unit‐cell parameters.Serial electron crystallography faces a fundamental challenge due to the flat Ewald
Tatiana E. Gorelik, Evgeny Gorelik
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Neural Two‐Level Monte Carlo Real‐Time Rendering
Computer Graphics Forum, EarlyView.Abstract We introduce an efficient Two‐Level Monte Carlo (subset of Multi‐Level Monte Carlo, MLMC) estimator for real‐time rendering of scenes with global illumination. Using MLMC we split the shading integral into two parts: the radiance cache integral and the residual error integral that compensates for the bias of the first one.
Mikhail Dereviannykh +3 more
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Viewpoint Optimization for 3D Graph Drawings
Computer Graphics Forum, EarlyView.Abstract Graph drawings using a node‐link metaphor and straight edges are widely used to represent and understand relational data. While such drawings are typically created in 2D, 3D representations have also gained popularity. When exploring 3D drawings, finding viewpoints that help understanding the graph's structure is crucial.
S. van Wageningen +2 more
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On Recursive Hyperbolic Fibonacci Quaternions
Communications in Advanced Mathematical Sciences, 2021 Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers.
Ahmet Daşdemir
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From Genes to Shapes: Exploring Local Adaptation in Carpathian Ox‐Eye Daisies
Journal of Biogeography, EarlyView.ABSTRACT Aim Historical processes have shaped the Carpathian biogeography, yet ongoing evolutionary forces continue to drive population differentiation. We aimed to test whether local adaptation in the Carpathian subendemic Leucanthemum rotundifolium correlates with genetic, morphological and environmental factors, and to assess how these patterns ...
Kamil Konowalik, Olga Łuczak
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On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence
International Journal of Mathematics and Mathematical Sciences, 2011 Let Fn be the nth Fibonacci number. The order of appearance z(n) of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, for all n=Fm≥5, we have z(n−1)>z(n)
Diego Marques
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Adaptive Fractional Hybrid Impedance Control of Rotary Series Elastic Actuator in Flat Terrains
Advanced Intelligent Systems, Volume 7, Issue 6, June 2025.This article presents an adaptive fractional hybrid impedance control (AFH‐IC) approach for rotary series elastic actuators operating on flat terrains. The proposed method integrates fractional‐order control, adaptive fuzzy logic, and particle swarm optimization to enhance torque tracking accuracy and robustness.
Muhammed Özdemir, Zafer Bingül
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Spherical GTM: A New Proposition for Visualization of Chemical Data
Molecular Informatics, Volume 44, Issue 5-6, June 2025.The Spherical Generative Topographic Mapping method extends the Generative Topographic Mapping method to a spherical manifold to address known nonflat topology issues. The mathematical formalism of this new approach is described, and its ability to visualize in 2D electron density patterns and a tangible chemical library is showcased.
Farah Asgarkhanova +7 more
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