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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.

fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

History of engineering & technology --- fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes --- fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes