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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QDD136 - 10/29/2012
Zucca, F.
Persistent and susceptible bacteria with individual deaths | Abstract | | The aim of this paper is to study two models for a bacterial population subject to antibiotic treatments.
It is known that some bacteria are sensitive to antibiotics. These bacteria are in a state called persistence and each bacterium can switch from this state to a non-persistent (or susceptible) state and back.
Our models extend those introduced in [6] by adding a (random) natural life cycle for each bacterium and
by allowing bacteria in the susceptible state to escape
the action of the antibiotics with a fixed probability
1-p (while every bacterium in a persistent state survives with
probability 1). In the first model we inject the antibiotics in the system at fixed, deterministic times while in the second one the time intervals are random.
We show that, in order to kill eventually the whole bacterial population, these time intervals cannot be too large . The maximum admissible length is increasing with respect to
p and it decreases rapidly when p<1.
While in the case p=1 switching back and forth to the persistent state is the only chance of surviving
for bacteria, when p<1 and the death rate in the persistent case is positive then switching state is not always a good strategy from the bacteria point of view.
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QDD133 - 10/04/2012
Grillo, G.; Muratori, M.; Punzo, F.
Conditions at infinity for the inhomogeneous filtration equation | Abstract | | We investigate existence and uniqueness of solutions to the
filtration equation with an inhomogeneous density in ${ mathbb R}^N$, approaching at infinity a given continuous datum of Dirichlet type. |
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QDD134 - 10/04/2012
Grillo, G.; Muratori, M.
Sharp short and long time L^ infty bounds for solutions to porous media equations with homogeneous Neumann boundary conditions | Abstract | | We study a class of nonlinear diffusion equations whose model is the classical porous media equation on euclidean domains, with homogeneous Neumann boundary conditions. We improve the known results in such model case, proving sharp uniform regularizing properties of the evolution for short time and sharp long time bounds for convergence of solutions to their mean value. The generality of the discussion allows to consider, almost at the same time, weighted versions of the above equation provided an appropriate weighted Sobolev inequality holds. In fact, we show that the validity of such weighted Sobolev inequality is equivalent to the validity of a suitable regularizing bound for solutions to the associated weighted porous media equation.
The long time asymptotic analysis relies on the assumed weighted Sobolev inequality only, and allows to prove uniform convergence to the mean value, with the rate predicted by linearization, in such generality. |
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QDD130 - 10/02/2012
Barbatis, G; Gazzola, F.
Higher order linear parabolic equations | Abstract | | We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the updated state of art and we suggest several open problems. |
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QDD131 - 10/02/2012
Bramanti, M.; Cupini, G.; Lanconelli, E.; Priola, E.
Global L^{p} estimates for degenerate Ornstein Uhlenbeck operators with variable coefficients | Abstract | | We consider a class of degenerate Ornstein-Uhlenbeck operators A in R^N, where A is the sum of a principal part in
nondivergence form, with uniformly continuous and bounded entries, which is uniformly elliptic on R^s (s
( drift ) which is linear in x and such that if we freeze the principal part at any point x_0 we get a hypoelliptic operator. For this class of operators we prove global L^p estimates (1
the previous estimates as a byproduct of analogous estimates for the corresponding evolution operator of Kolmogorov-Fokker-Planck type,
A-D_t, on a strip R^N x[-T,T], when the coefficients of the principal part depend on (x,t).
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QDD132 - 10/02/2012
Bramanti, M.; Fanciullo, M. S.
BMO estimates for nonvariational operators with discontinuous coefficients structured on Hörmander s vector fields on Carnot groups | Abstract | | We consider a class of nonvariational linear operators formed by homogeneous left invariant Hormander s vector fields with respect to a structure of Carnot group. The bounded coefficients of the operators belong to the vanishing logarithmic mean oscillation class with respect to the distance induced by the vector fields (in particular they can be discontinuous). We prove local estimates in local BMO spaces intersected with the Lebesgue spaces. Even in the uniformly elliptic case our estimates improve the known results. |
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QDD129 - 07/23/2012
Cipriani F.; Sauvageot J.L.
Variations in Noncommutative Potential Theory: finite-energy states, potentials and multipliers | Abstract | | In this work we undertake an extension of various aspects of the potential theory of Dirichlet forms from locally compact spaces to noncommutative C-star-algebras with trace. In particular we introduce finite-energy states, potentials and multipliers of Dirichlet spaces. We prove several results among which the celebrated Deny s embedding theorem and the Deny s inequality, the fact that the carre du champ of bounded potentials are finite-energy functionals and the relative supply of multipliers. |
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QDD128 - 07/21/2012
Sesana, D.; Marazzina, D.; Fusai, G.
Pricing Exotic Derivatives Exploiting Structure | Abstract | | In this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring is applied. The algorithm is general and is examined in detail with reference to the CEV (Constant Elasticity of Variance) process, for which up to date no efficient procedures are available. The approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed-up of the recursion. The algorithm is applied to different exotic derivatives, such as Asian, barrier, Bermudan, lookback and step options. Extensive numerical experiments confirm the theoretical results.
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