Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
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QDD94 - 05/06/2011
Bertacchi, D.; Zucca, F.
Recent results on branching random walks | Abstract | | This paper is a collection of recent results on discrete-time and continuous-time branching random walks.
Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival,
the existence of a pure global survival phase and the approximation of branching random walks by means of multitype contact processes or spatially confined branching random walks.
Most results are obtained using a generating function approach: the probabilities of extinction are seen as fixed points of an infinite dimensional power series. Throughout this paper we provide many nontrivial examples and
counterexamples. |
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QDD95 - 05/06/2011
Bonforte, M.; Gazzola, F.; Grillo G.; Vazquez J.L.
Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space | Abstract | | We study the Emden-Fowler equation on the hyperbolic n-dimensional space. We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation is p=(n+2)/(n-2) as in the Euclidean setting, but the properties of the solutions show striking differences with the Euclidean case. |
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QDD96 - 05/06/2011
Bonforte, M.; Grillo, G.; Vazquez, J.L.
Behaviour near extinction for the Fast Diffusion Equation on bounded domains | Abstract | | We consider the Fast Diffusion Equation posed in a bounded smooth domain with homogeneous Dirichlet
conditions. It is known that for in a certain range of the parameter m appearing in the equation all bounded positive solutions of such problem extinguish in a finite time, and also that such solutions approach a separate variable solution. Here, we are interested in describing the behaviour of the solutions near the extinction time. We first show that the convergence takes place uniformly in the relative error norm. Then, we study the question of rates of convergence. For m close to 1 we get such rates by means of entropy methods and weighted Poincarè inequalities. The analysis of the latter point makes an essential use of fine properties of a associated stationary elliptic problem, which has an independent interest. |
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QDD97 - 05/06/2011
Grillo, G.; Kovarik, H.; Pinchover, Y.
Sharp two-sided heat kernel estimates of twisted tubes and applications | Abstract | | We prove sharp on-diagonal bounds for the heat kernel of the Dirichlet Laplacian in locally twisted three-dimensional tubes. Such bounds show that any, suitably regular, local twisting speeds up the decay of the heat kernel with respect to the case of straight (untwisted) tubes. Moreover, the above large time decay is valid for a wide class of subcritical operators defined on a straight tube.
We also discuss some applications of this result, such as Sobolev inequalities and spectral estimates for Schroedinger operators.
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QDD93 - 04/11/2011
de Falco, C.; Porro, M.; Sacco, R.; Verri, M.
Multiscale Modeling and Simulation of Organic Solar Cells | Abstract | | In this article, we continue our mathematical study of organic photovoltaic device models started off in a previous work, focusing on the issue of accurately modeling the impact of the interface morphology on device performance.
To this end, we propose a multi-dimensional model
for bilayer organic solar cell devices with
arbitrary interface geometries derived by averaging the mass balance equations across the interface thickness. This yields a system of incompletely parabolic nonlinear PDEs to describe mass transport in the materials, coupled with ODEs localized at the heterojunction. We perform the numerical approximation of the differential system in stationary conditions and we apply it to the simulation of a variety of devices with different morphologies. |
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QDD92 - 03/29/2011
Bramanti, M.; Zhu, M.
L^{p} and Schauder estimates for nonvariational operators structured on Hörmander vector fields with drift | Abstract | | We consider linear second order nonvariational partial differential operators of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the X_{i} s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfying Hörmander s condition and a_{ij} (i,j=1,2,...,q) are real valued, bounded measurable functions, such that the matrix {a_{ij}} is symmetric and uniformly positive. We prove that if the coefficients a_{ij} are Hölder continuous with respect to the distance induced by the vector fields, then local Schauder estimates on X_{i}X_{j}u, X_{0}u hold; if the coefficients belong to the space VMO with respect to the distance induced by the vector fields, then local L^{p} estimates on X_{i}_{j}u, X_{0}u hold. The main novelty of the result is the presence of the drift term X_{0}, so that our class of operators covers, for instance, Kolmogorov-Fokker-Planck operators. |
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QDD91 - 03/25/2011
Barucci, E.; Cosso, A.
Portfolio choices and VaR constraint with a defaultable asset | Abstract | | Assuming a Constant Elasticity of Variance (CEV) model for the asset price, that is a defaultable asset showing the so called leverage effect (high volatility when the asset price is low), a VaR constraint reevaluated over time induces an agent more risk averse than a logarithmic utility to take more risk than in the unconstrained setting. |
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QDD90 - 03/22/2011
Barucci, E.; Cosso, A.
Does an equity holding tax help to stabilize a VaR regulated financial market? | Abstract | | We investigate the capability of an equity holding tax to stabilize a VaR regulated financial market. We show that a VaR constraint induces high volatility in a distressed
financial market, the phenomenon is not observed in a market with risk averse unregulated traders. A tax on equity holding smoothes the peak of volatility and stabilizes the market at the cost of a generalized higher volatility. |
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