We prove some properties of the first eigenvalue of nonlinear weighted problems.
In particular, the first eigenvalue is shown to be isolated. Moreover, existence and
non existence results of solutions in W^{1,p}_0(\Omega) for nonlinear weighted
equations with exponential growth are obtained.
Nonlinear weighted problems
First eigenvalue
Existence and non-existence of solutions
General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. (C) 2004 Elsevier Ltd. All rights reserved.
Multidimensional extensions of the Bernoulli and Appell polynomials are defined generalizing the corresponding generating functions, and using the Hermite-Kampe de Feriet (or Gould-Hopper) polynomials. Furthermore the differential equations satisfied by the corresponding 2D polynomials are derived exploiting the factorization method, introduced in [15].
A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in
it is studied numerically. Based on the assumption of long wavelength and small amplitude of the
pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear
fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is
coupled with a six compartment lumped parameter model, which accounts for the global circulatory
features and provides boundary conditions. The differential equations are first linearized to investigate
the nature of the propagation phenomena. The full non-linear equations are then approximated with a
numerical finite difference method on a staggered grid.
Some numerical simulations show the characteristics of the wave propagation. The dependence of
the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been
highlighted. The importance of the axial deformation is evidenced by its variation in correspondence
of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to
a compliance jump due to prosthetic implantations are finally studied.
We describe a model for the optimization of the issuances of Public Debt securities developed together with the Italian Ministry of Economy and Finance. The goal is to find the composition of the portfolio issued every month which minimizes a specific cost function. Mathematically speaking, this is a stochastic optimal control problem with strong constraints imposed by national regulations and the Maastricht treaty. The stochastic component of the problem is represented by the evolution of interest rates. At this time the optimizer employs classic Linear Programming techniques. However more sophisticated techniques based on Model Predictive Control strategies are under development.
Linear programming
public debt
stochastic control
term structure evolution
ESA95
In this paper we propose a simple and effective way to improve the classical Shape from Shading (SFS) problem exploiting light projection information contained in the image data. Edges of concave regions can be split in projecting and the projected points. The geometrical relation between these points allows us to introduce a constraint on the SFS solution. To show the potentialities of our model, we present an application to a Cultural Heritage problem such as the extraction of the boundaries of the degradation zones. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.
We prove some properties of the first eigenvalue of the problem
\begin{array}{ll}
-{\cal A}_p u \colon = - \hbox{\rm div\ } \Big( (A\D u, \D
u)^{(p-2)/2}A\D u\Big)= \lambda V(x) |u|^{p-2} u & \hbox{\rm in\
} \O
\\
\quad u=0 & \hbox{\rm on\ } \partial \O .
\end{array}
In particular, the first eigenvalue is shown to be isolated. Moreover, existence and non existence results
of solutions in W^{1, p}_0(\Omega) for nonlinear weighted equations with exponential growth are obtained.
A comparison between A(1) and A(2) processes, when used for describing the evolution in time of the global rate of return on investments made by an insurance company, is proposed. In particular, we compare the two processes analysing the parameter sensibility to the size of the sampling interval. An application shows the results. Finally the impact on the global riskiness of a whole life annuity portfolio is evaluated for both the two models.
A(1) and A(2) models
covariance equivalence principle
investment risk
total riskiness of a life insurance portfolio
whole life annuity portfolio
