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present a short note about the perturbative correction to Rydberg energies
under a perturbation cosθ/rμ and discuss the role of SO(4) symmetry.
The complexity of large-scale network systems made of a large number of nonlinearly interconnected components is a restrictive facet for their modeling and analysis. In this paper, we propose a framework of hierarchical modeling of a complex network system, based on a recursive unsupervised spectral clustering method. The hierarchical model serves the purpose of facilitating the management of complexity in the analysis of real-world critical infrastructures. We exemplify this by referring to the reliability analysis of the 380 kV Italian Power Transmission Network (IPTN). In this work of analysis, the classical component Importance Measures (IMs) of reliability theory have been extended to render them compatible and applicable to a complex distributed network system. By utilizing these extended IMs, the reliability properties of the IPTN system can be evaluated in the framework of the hierarchical system model, with the aim of providing risk managers with information on the risk/safety significance of system structures and components.
The theory of frames has been actively developed by many authors
over the past two decades, both for its applications to signal processing, and for its deep connections to other areas of
mathematics such as operator theory. Central to the study of frames is the
frame operator. We initiate an investigation that extends the frame operator to
the bilinear setting.