Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica.
La presenza del full-text è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 868 prodotti
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QDD145 - 17/01/2013
Barchielli, A.; Gregoratti, M.
Quantum continuous measurements: The stochastic Schroedinger equations and the spectrum of the output | Abstract | | The stochastic Schroedinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties of the output of the measurement. For simplicity we deal only with the di usive case. Firstly, we discuss the quantum stochastic Schroedinger equation, which is based on quantum stochastic calculus, and we show how to transform it into the classical stochastic Schroedinger equation by diagonalization of suitable quantum observables, based on the isomorphism between Fock space and Wiener space. Then, we give the a posteriori state, the conditional system state at time t given the output up to that time and we link its evolution to the classical stochastic Schroedinger equation. Finally, we study the output of the continuous measurement, which is a stochastic process with probability distribution given by the rules of quantum mechanics. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties studied. In particular we show how the Heisenberg uncertainty relations give rise to characteristic bounds on the possible spectra and we discuss how this is related to the typical quantum phenomenon of squeezing. We use a simple quantum system, a two-level atom stimulated by a laser, to discuss the di erences between homodyne and heterodyne detection and to explicitly show squeezing and anti-squeezing and the Mollow triplet in the fluorescence spectrum. |
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QDD144 - 15/01/2013
Baccarin, S.; Marazzina, D.
Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints | Abstract | | We investigate a portfolio optimization problem for an agent who invests in two assets, a risk-free and a risky asset modeled by a geometric Brownian motion. The investor faces both fixed and proportional transaction costs and liquidity constraints. His objective is to maximize the expected utility
from the portfolio liquidation at a terminal finite horizon. The model is formulated as a parabolic impulse control problem and we characterize the value function as the unique constrained viscosity solution of the associated quasi-variational inequality. We compute numerically the optimal
policy by a an iterative finite element discretization technique, presenting extended numerical results in the case of a constant relative risk aversion utility function. Our results show that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buy-and-hold trading strategy where the agent recalibrates his portfolio very few times. This contrasts sharply with the continuous interventions of the Merton s model without transaction costs. |
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QDD143 - 11/01/2013
Gazzola, F.
Hexagonal design for stiffening trusses | Abstract | | We consider the problem of choosing the best design for stiffening trusses of plates, such as bridges. We suggest to cover the plate with regular hexagons which fit side to side. We show that this design has some important advantages when compared with alternative designs. |
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QDD142 - 30/11/2012
Terracini, S.; Verzini, G.; Zilio, A.
Uniform Holder bounds for strongly competing systems involving the square root of the laplacian | Abstract | | For a class of competition-diffusion nonlinear systems involving the square root of the Laplacian, including the fractional Gross-Pitaevskii system, we prove that uniform boundedness implies Holder boundedness for every exponent less than 1/2, uniformly as the interspecific competition parameter diverges. Moreover we prove that the limiting profile is Holder continuous of exponent 1/2. This system arises, for instance, in the relativistic Hartree-Fock approximation theory for mixtures of Bose-Einstein condensates in different hyperfine states. |
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QDD141 - 15/11/2012
Hartshorne, R.; Lella, P.; Schlesinger, E:
Smooth curves specialize to extremal curves | Abstract | | Let H_{d,g} denote the Hilbert scheme of locally Cohen-Macaulay curves of degree d and genus g in projective three space. We show that, given a smooth irreducible curve C of degree d and genus g, there is a rational curve {[C_t]} in H_{d,g} such that C_t for t neq 0 is projectively equivalent to C, while the special fibre C_0 is an extremal curve. It follows that smooth curves lie in a unique connected component of H_{d,g}. We also determine necessary and sufficient conditions for a locally Cohen-Macaulay curve to admit such a specialization to an extremal curve. |
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QDD138 - 12/11/2012
Baccarin, S; Marazzina, D.
Optimal impulse control of a portfolio with a fixed transaction cost | Abstract | | The aim of this work is to investigate a portfolio optimization problem in presence of fixed transaction costs. We consider an economy with two assets, one risky and one risk-free, and an agent fully described by its power utility function. We show how fixed transaction costs influence the agent s behavior, showing when it is optimal to recalibrate his/her portfolio, paying the transaction costs. |
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QDD139 - 12/11/2012
Berchio, E.; Ferrero, A.; Grillo, G.
Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models | Abstract | | We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation - Delta_g u=|u|^{p-1}u in a class of Riemannian models (M,g) of dimension n>2 which includes the classical hyperbolic space H^n as well as manifolds with sectional curvatures unbounded below. Sign properties and asymptotic behavior of solutions are influenced by the critical Sobolev exponent while the so-called Joseph-Lundgren exponent is involved in the stability of solutions. |
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QDD140 - 12/11/2012
Berchio, E.
A family of Hardy-Rellich type inequalities involving the L^2-norm of the Hessian matrices | Abstract | | We derive a family of Hardy-Rellich type inequalities in H^2( Omega) cap H_0^1( Omega) involving the scalar product between Hessian matrices. The constants found are optimal and the existence of a boundary remainder term is discussed. |
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