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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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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QDD70 - 10/22/2010
Berchio, E.; Cassani, D.; Gazzola, F.
Hardy-Rellich inequalities with boundary remainder terms and applications | Abstract | | We prove a family of Hardy-Rellich inequalities with optimal constants and additional boundary
terms. These inequalities are used to study the behavior of extremal solutions to biharmonic
Gelfand-type equations under Steklov boundary conditions. |
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QDD71 - 10/22/2010
Conti, M.; Marchini, E.M.; Pata, V.
Approximating infinite delay with finite delay | Abstract | | Equations with infinite delay commonly face the philosophical objection of being unphysical ,
since a memory of infinite duration conflicts with
reality. Indeed, besides common sense, experimental observations on concrete physical
models tell that effects from the far past cannot possibly influence the current dynamics of a given system. On the other hand, infinite delay arises quite naturally in the mathematical description of several relevant phenomena. In this note, we propose a possible conceptual solution, showing that infinite delay can be recovered as a limiting case of finite delay on a large time-scale, along with a quantitative control of the discrepancy. |
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QDD67 - 10/21/2010
Bramanti, M.; Brandolini, L.; Pedroni, M.
Basic properties of nonsmooth Hormander s vector fields and Poincare s inequality | Abstract | | We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander s rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander s vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow s connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare s inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander s vector fields. |
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QDD68 - 10/21/2010
Bramanti, M.; Brandolini, L.; Pedroni, M.
On the lifting and approximation theorem for nonsmooth vector fields | Abstract | | We prove a version of Rothschild-Stein s theorem of lifting and approximation and some related results in the context of nonsmooth Hormander s vector fields for which the highest order commutators are only Holder continuous. The theory explicitly covers the case of one vector field having weight two while the others have weight one. |
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QDD74 - 10/20/2010
Maddalena, F.; Percivale, D.; Tomarelli, F.
Adhesive flexible material structures | Abstract | | We study variational problems modeling the adhesion interaction with a rigid substrate for elastic strings and rods. We produce conditions characterizing bonded and detached states as well as optimality properties with respect to loading and geometry. We show Euler equations for minimizers of the total energy outside self-contact and secondary contact points with the substrate. |
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QDD66 - 10/19/2010
Boccellari, T.; Tomarelli, F.
Generic uniqueness of minimizer for Blake & Zisserman functional | Abstract | | Blake-Zisserman functional achieves a finite minimum for any pair of contrast parameters alpha, beta such that 0
Uniqueness of minimizer does not hold in general.
Nevertheless, in the 1D case uniqueness of minimizer is a generic property for in the sense that it holds true for almost all gray levels data g and parameters alpha, beta: here we prove that, whenever alpha/beta is irrational, the minimizer is unique for any g belonging to a G_delta subset of L^2 which depends on alpha and beta.
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