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The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in…
We identify a duality transformation in one-dimensional hopping models that relates propagators in general disordered potentials linked by an up-down inversion of the energy landscape. This significantly generalises previous results for a…
In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.
The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.
An expansion of the Weyl function of a $H$-selfadjoint random matrix with one negative square is provided. It is shown that the coefficients converge to a certain generalization of Catlan numbers. Properties of this generalization are…
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…
A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
This is a review of the properties of spectral fluctations in disordered metals, their relation with Random Matrix Theory and semiclassical picture. We also review the physics of persistent currents in mesoscopic isolated rings, the…
A brief summary on the properties of the so called Joint Spectral Radius
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
A non-standard generalisation of the Bender potentials $x^2(\ii x^\ve)$ is suggested. The spectra are obtained numerically and some of their particular properties are discussed.
Some spectral data analysis methods that are useful for the two-dimensional imaging diagnostics data are introduced. It is shown that the frequency spectrum, the local dispersion relation, the flow shear, and the nonlinear energy transfer…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
In this paper, the spectrum, residual spectrum, point spectrum and spectral radius of weighted conditional type operators are computed. As an application, we give an equivalent condition for weighted conditional type operators to be…
One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it…
Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…