Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD169 - 01/08/2014
Gal, S.G.; Sabadini, I.
Approximation by polynomials on quaternionic compact sets | Abstract | | In this paper we obtain several extensions to the quaternionic setting of some results concerning the approximation by polynomials of functions continuous on a compact set and slice regular in its interior. The results include approximation on compact starlike sets and compact axially symmetric sets. The cases of some concrete particular sets are described in details, including quantitative estimates too.
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QDD168 - 11/28/2013
Arioli, G.
Teaching mathematics with automatic symbolic computation | Abstract | | Abstract. We discuss how the concept of problem solving is central in current research in mathematics education, and how the difficulties of making computations by hand and the time spent in teaching computational skills can move the focus away from the main issues. We describe an experiment performed with students in Mathematical Engineering which shows how the use of automatic symbolic computation can dramatically improve the teaching of both abstract mathematics and the problem solving skills. |
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QDD166 - 11/15/2013
Barucci, E.; Marazzina, D.
Risk seeking, non convex remuneration and regime switching | Abstract | | We investigate asset management in a regime switching framework when the fund manager aims to beat a certain target for the assets under management either in an infinite horizon or over a finite horizon. We consider both a full information and a partial information setting. In a full information setting, the asset manager tends to take more risk in the good state and less risk in the bad state with respect to the constant parameter environment. Confidence risk induces the agent to increase his risk exposure. |
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QDD163 - 10/31/2013
Escudero, C.; Gazzola, F.; Peral I.
Existence versus blow-up results for a fourth order parabolic PDE involving the Hessian | Abstract | | We consider a partial differential equation that arises in the coarse-grained description of epitaxial growth processes. This is a parabolic equation whose evolution is dictated by the competition among the determinant of the Hessian matrix of the solution and the biharmonic operator. This model might present a gradient flow structure depending on the boundary conditions. We first extend previous results on the existence of stationary solutions to this model for Dirichet boundary conditions. For the evolution problem we prove local existence of solutions for arbitrary data and global existence of solutions for small data. Depending on the boundary conditions and the concomitant presence of a variational structure in the equation as well as on the size of the data we prove blow-up of the solution in finite time and convergence to a stationary solution in the long time limit. |
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QDD164 - 10/31/2013
Escudero, C.; Gazzola, F.; Hakl, R.; Peral I.; Torres P.J.
Existence results for a fourth order partial differential equation arising in condensed matter physics | Abstract | | We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions. |
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QDD162 - 10/30/2013
Verzini, G.; Zilio, A.
Strong competition versus fractional diffusion: the case of Lotka-Volterra interaction | Abstract | | We consider a system of differential equations with nonlinear Steklov boundary conditions, related to a stationary problem for many densities subject to fractional diffusion and strong competition of Lotka-Volterra type.
In the case of 2 densities we develop a quasi-optimal regularity theory in
Holder spaces of any exponent less than the optimal one, uniformly w.r.t. the competition parameter. Moreover we show that the traces of the limiting
profiles (as the competition parameter goes to infinity) are Lipschitz continuous and segregated.
Such results are extended to the case of 3 or more densities, with some restrictions on the parameters of the system.
Since for competition of variational type the optimal regularity is known to be lower, these results mark a substantial difference with the case of standard diffusion, where the two competitions can not be distinguished from each other in the limit. |
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QDD161 - 10/24/2013
Corsaro, S.; Marazzina, D.; Marino, Z.
A parallel wavelet-based pricing procedure for Asian options | Abstract | | In this paper we present a parallel pricing algorithm for Asian options based on the Discrete Wavelet Transform (DWT).
The computational kernel of the pricing model is the solution of integral equations. We obtain a sparse and accurate representation of the kernel of such equations in wavelet functions bases. We moreover discuss the parallelization of the algorithm. Numerical results which show the accuracy and
efficiency of the procedure are reported in the paper.
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QDD160 - 07/29/2013
Ferrero, A.; Gazzola, F.
A partially hinged rectangular plate as a model for suspension bridges | Abstract | | A plate model describing the statics and dynamics of a suspension bridge is suggested. A partially hinged plate subject to nonlinear restoring hangers is considered. The whole theory from linear problems, through nonlinear stationary equations, ending with the full hyperbolic evolution equation is studied. This paper aims to be the starting point for more refined models. |
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