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Symmetry and complexity are the focus of a selection of outstanding papers, ranging from pure Mathematics and Physics to Computer Science and Engineering applications. This collection is based around fundamental problems arising from different fields, but all of them have the same task, i.e. breaking the complexity by the symmetry. In particular, in this Issue, there is an interesting paper dealing with circular multilevel systems in the frequency domain, where the analysis in the frequency domain gives a simple view of the system. Searching for symmetry in fractional oscillators or the analysis of symmetrical nanotubes are also some important contributions to this Special Issue. More papers, dealing with intelligent prognostics of degradation trajectories for rotating machinery in engineering applications or the analysis of Laplacian spectra for categorical product networks, show how this subject is interdisciplinary, i.e. ranging from theory to applications. In particular, the papers by Lee, based on the dynamics of trapped solitary waves for special differential equations, demonstrate how theory can help us to handle a practical problem. In this collection of papers, although encompassing various different fields, particular attention has been paid to the common task wherein the complexity is being broken by the search for symmetry.
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Keywords
- asymmetric penalty sparse decomposition (APSD)
- categorical product
- degradation trajectories prognostic
- filtering
- finite difference method
- first multiple Zagreb index
- forced Korteweg-de Vries equation
- fractional differential equations
- fractional dynamical systems
- fractional oscillations (vibrations)
- global mean-first passage time
- harmonic wavelet
- health indicators
- History of engineering & technology
- Kirchhoff index
- Laplacian spectra
- multilevel system
- Nanotubes
- Nonlinear dynamical systems
- numerical stability
- recursive least squares (RLS)
- rolling bearings
- second multiple Zagreb index, hyper-Zagreb index
- spanning tree
- Technology, engineering, agriculture
- Technology: general issues
- trapped solitary wave solutions
- two bumps or holes
- wavelet neural network (WNN)
- Zagreb polynomials
Links
DOI: 10.3390/books978-3-03936-847-1Editions