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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QDD77 - 11/20/2010
Raffaella Pavani
About the numerical conservation of first integral by a class of symmetric methods | Abstract | | We present a class of symmetric methods which are particularly suitable
for general conserving systems. Numerical evidence for numerical conservation of first
integral within a requested accuracy is provided. |
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QDD78 - 11/20/2010
Gazzola, F.; Grunau, H.C., Sweers, G.
Polyharmonic boundary value problems | Abstract | | This monograph covers higher order linear and nonlinear elliptic boundary value problems in
bounded domains, mainly with the biharmonic or polyharmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or – since, in contrast to second order equations, a general form of a comparison principle does not exist – on “almost positivity.”
The required kernel estimates are also presented in detail.
As for nonlinear problems, several techniques well-known from second order equations
cannot be utilised and have to be replaced by new and different methods. Subcritical, critical
and supercritical nonlinearities are discussed and various existence and nonexistence results
are proved. The interplay with the positivity topic from the first part is emphasised and, moreover, a far-reaching Gidas-Ni-Nirenberg-type symmetry result is included. Finally, some recent progress on the Dirichlet problem for Willmore surfaces under symmetry assumptions is discussed. |
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QDD79 - 11/20/2010
Gazzola, F.; Weth, T.
Remainder terms in a higher order Sobolev inequality | Abstract | | For higher order Hilbertian Sobolev spaces, we improve the embedding inequality for the critical Lp-space by adding a remainder term with a suitable weak norm. |
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QDD80 - 11/20/2010
Fragalà, I.; Gazzola, F.; Pierre, M.
On an isoperimetric inequality for capacity conjectured by Polya and Szego | Abstract | | We study a conjecture by Polya and Szego on the approximation of the electrostatic capacity of convex bodies in terms of their surface measure. We prove that a “local version” of this conjecture holds true and we give some results which bring further evidence to its global validity. |
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QDD81 - 11/20/2010
Barucci, E.; Gazzola, F.
Prices in the utility function and demand monotonicity | Abstract | | We analyze utility functions when they depend both on the quantity of the goods consumed by the agent and on the prices of the goods. This approach allows us to model price effects on agents’ preferences (e.g. the so-called Veblen effect and the Patinkin formulation). We provide sufficient conditions to observe demand monotonicity and substitution among goods. Power utility functions are investigated: we provide examples of price dependent utility functions that cannot be written as an increasing transformation of a classical utility function dependent only upon quantities. |
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QDD72 - 10/27/2010
Barchielli A.; Pellegrini C.
Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation | Abstract | | The correlated-projection technique has been successfully applied to derive a large class of highly non Markovian dynamics, the so called non Markovian generalized Lindblad type equations or Lindblad rate equations. In this article, general unravellings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unravelling can be interpreted in terms of measurements continuous in time, but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and we discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory. |
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QDD73 - 10/27/2010
Castro Santis R.; Barchielli A.
Quantum stochastic differential equations and continuous measurements: unbounded coefficients | Abstract | | A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of Hudson-Parthasarathy equations with bounded coefficients. By using some results on Hudson-Parthasarathy equations with unbounded coefficients, we are able to extend the theory of quantum continuous measurements to cases in which unbounded operators on the system space are involved. A significant example of a quantum optical system (the degenerate parametric oscillator) is shown to fulfill the hypotheses
introduced in the general theory. |
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QDD69 - 10/22/2010
Pirola, G.P.;Rizzi,C.;Schlesinger, E.
A new curve algebraically but not rationally uniformized by radical | Abstract | | We give a new example of a curve C algebraically, but not rationally, uniformized by radicals.
This means that C has no map onto P^1 with solvable Galois group, while there exists
a curve C that maps onto C and has a finite morphism to P^1 with solvable Galois group.
We construct such a curve C of genus 9 in the second symmetric product of a general curve of genus 2. It is also an example of a genus 9 curve that does not satisfy condition S(4,2,9) of Abramovich and Harris. |
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