The von Neumann-Wigner type potentials and the wave functions' asymptotics for the discrete levels in continuum

One to one correspondence between the decay law of the von Neumann-Wigner type potentials and the asymptotic behaviour of the wave functions representing bound states in the continuum is established.Comment: latex, 7 page

Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance

We investigate five-dimensional braneworld setups with broken Lorentz invariance continuing the developments of our previous paper (arXiv:0712.1136), where a family of static self-tuning braneworld solutions was found. We show that several known braneworld models can be embedded into this family. Then we give a qualitative analysis of spectra of field fluctuations in backgrounds with broken Lorentz invariance. We also elaborate on one particular model and study spectra of scalar and spinor fields in it. It turns out that the spectra we have found possess very peculiar and unexpected properties.Comment: 30 pages, 8 figures, minor corrections, references added, note adde

Laplace transform of spherical Bessel functions

We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the Langevin equation in a one-dimensional Debye model.Comment: 5 pages LATEX, no figures. Accepted 2002, Physica Script

On the rationality of the moduli space of L\"uroth quartics

We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space of quartics which can be circumscribed around a complete pentagon of lines modulo the action of PGL_3(CC) is rational, as is the related moduli space of Bateman seven-tuples of points in P^2.Comment: 7 page

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde

Derivation of critical rainfall thresholds for shallow landslides as a tool for debris flow early warning systems

Abstract. Real-time assessment of debris-flow hazard is fundamental for developing warning systems that can mitigate risk. A convenient method to assess the possible occurrence of a debris flow is to compare measured and forecasted rainfalls to critical rainfall threshold (CRT) curves. Empirical derivation of the CRT from the analysis of past events' rainfall characteristics is not possible when the database of observed debris flows is poor or when the environment changes with time. For debris flows and mud flows triggered by shallow landslides or debris avalanches, the above limitations may be overcome through the methodology presented. In this work the CRT curves are derived from mathematical and numerical simulations, based on the infinite-slope stability model in which slope instability is governed by the increase in groundwater pressure due to rainfall. The effect of rainfall infiltration on landside occurrence is modelled through a reduced form of the Richards equation. The range of rainfall durations for which the method can be correctly employed is investigated and an equation is derived for the lower limit of the range. A large number of calculations are performed combining different values of rainfall characteristics (intensity and duration of event rainfall and intensity of antecedent rainfall). For each combination of rainfall characteristics, the percentage of the basin that is unstable is computed. The obtained database is opportunely elaborated to derive CRT curves. The methodology is implemented and tested in a small basin of the Amalfi Coast (South Italy). The comparison among the obtained CRT curves and the observed rainfall amounts, in a playback period, gives a good agreement. Simulations are performed with different degree of detail in the soil parameters characterization. The comparison shows that the lack of knowledge about the spatial variability of the parameters may greatly affect the results. This problem is partially mitigated by the use of a Monte Carlo approach