Results 41 to 50 of about 180 (135)
Properties of the Ammann–Beenker Tiling and its Square Periodic Approximants
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.This review article is intended for those seeking to understand the geometrical properties of one well‐known two‐dimensional quasiperiodic tiling, namely the Ammann‐Beenker tiling. This eight‐fold symmetric tiling has been a preferred starting point for studies of electronic properties of quasicrystals, due to its relatively simple structure as ...
Anuradha Jagannathan, Michel Duneau
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Canonical‐Cell Tilings and their Atomic Decorations
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract The canonical cell tiling is a geometrical framework that uses four kinds of basic polyhedra, called the canonical cells, to model the packing of atoms and clusters in icosahedral quasicrystals and related periodic approximants. Over the past three decades, it has become increasingly clear that this framework is the most sensible approach to ...
Nobuhisa Fujita +2 more
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Super Fibonacci Graceful Graphs and Fibonacci Cubes [PDF]
Control Systems and Computers, 2020 The popularity of Fibonacci cubes is due to their wide range of uses. In mathematical chemistry, this concept is used in the study of hexagonal graphs. In computer science, Fibonacci cubes are interesting from an algorithmic point of view. V. Hsu introduced them in 1993 to simulate the connections of multiprocessor computer networks.
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Pure Point Diffraction and Almost Periodicity
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical concept of Bohr almost periodicity and how it fits into the classes of mean, Besicovitch and Weyl almost periodic point sets.
Daniel Lenz +2 more
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Substitutions and their Generalisations
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and potentials.
Neil Mañibo
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Strong divisibility sequences and sieve methods
Mathematika, Volume 70, Issue 4, October 2024.Abstract We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods.
Tim Browning, Matteo Verzobio
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Advanced Theory and Simulations, Volume 7, Issue 6, June 2024.The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. The 3D surface computed from precise atomic coordinates can be represented as either a voxelized point cloud or a mathematically exact surface. Sphractal is a Python package that estimates the fractal dimensions of such surfaces by computing their box ...
Jonathan Yik Chang Ting +2 more
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p-th order generalized Fibonacci cubes and maximal cubes in Fibonacci p-cubes
Discrete MathematicsThe Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive 1s. We study a one parameter generalization, p-th order Fibonacci cubes $Γ^{(p)}_n$, which are subgraphs of $Q_n$ induced by strings without p consecutive 1s. We show the link between vertices of $Γ^{(p)}_n$ and compositions of integers with parts in
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The eccentricity sequences of Fibonacci and Lucas cubes
Discrete Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aline Castro, Michel Mollard
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Image Encryption Using Quantum 3D Mobius Scrambling and 3D Hyper-Chaotic Henon Map. [PDF]
Entropy (Basel), 2023 Wang L, Ran Q, Ding J.
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