Abstract:
an iterative method based on picard's approach to odes' initial-value problems is proposed to solve first-order quasilinear pdes with matrix-valued unknowns, in particular, the recently discovered variational pdes for the missing boundary values in hamilton equations of optimal control. as illustrations the iterative numerical solutions are checked against the analytical solutions to some examples arising from optimal control problems for nonlinear systems and regular lagrangians in finite dimension, and against the numerical solution obtained through standard mathematical software. an application to the (n + 1)-dimensional variational pdes associated with the n-dimensional finite-horizon time-variant linear-quadratic problem is discussed, due to the key role the lqr plays in two-degrees-of freedom control strategies for nonlinear systems with generalized costs. mathematical subject classification: primary: 35f30; secondary: 93c10.

Abstract:
The process underlying the generation of the EEG signals can be described as a set of current sources within the brain. The potential distribution produced by these sources can be measured on the scalp and inside the brain by means of an EEG recorder. There is a well-known mathematical model that relates the electric potential in the head with the intracerebral sources. In this work, we study and prove some properties of the solutions of the model for known sources. In particular, we study the error in the potential, introduced by considering an approximated shape of the head.

Abstract:
we focus on the forward problem of electroencephalography, discuss a mathematical model and state properties of its weak solutions. a static and a time-dependent model for the source are considered. numerical solutions, obtained by a boundary element method technique, are compared with the analytical ones and with eeg recordings.

Abstract:
We focus on the Forward Problem of electroencephalography, discuss a mathematical model and state properties of its weak solutions. A static and a time-dependent model for the source are considered. Numerical solutions, obtained by a Boundary Element Method technique, are compared with the analytical ones and with EEG recordings.

Abstract:
The screening of point charges in hydrogenated Si quantum dots ranging in diameter from 10 A to 26 A has been studied using first-principles density-functional methods. We find that the main contribution to the screening function originates from the electrostatic field set up by the polarization charges at the surface of the nanocrystals. This contribution is well described by a classical electrostatics model of dielectric screening.

Abstract:
We report semi-empirical pseudopotential calculations of emission spectra of charged excitons and biexcitons in CdSe nanocrystals. We find that the main emission peak of charged multiexcitons - originating from the recombination of an electron in an s-like state with a hole in an s-like state - is blue shifted with respect to the neutral mono exciton. In the case of the negatively charged biexciton, we observe additional emission peaks of lower intensity at higher energy, which we attribute to the recombination of an electron in a p state with a hole in a p state.

Abstract:
Sensitivity analysis can provide useful information when one is interested in identifying the parameter θ of a system since it measures the variations of the output u when θ changes. In the literature two different sensitivity functions are frequently used: the traditional sensitivity functions (TSF) and the generalized sensitivity functions (GSF). They can help to determine the time instants where the output of a dynamical system has more information about the value of its parameters in order to carry on an estimation process. Both functions were considered by some authors who compared their results for different dynamical systems (see Banks and Bihari, 2001; Kappel and Batzel, 2006; Banks et al., 2008). In this work we apply the TSF and the GSF to analyze the sensitivity of the 3D Poisson-type equation with interfaces of the forward problem of electroencephalography. In a simple model where we consider the head as a volume consisting of nested homogeneous sets, we establish the differential equations that correspond to TSF with respect to the value of the conductivity of the different tissues and deduce the corresponding integral equations. Afterward we compute the GSF for the same model. We perform some numerical experiments for both types of sensitivity functions and compare the results.

Abstract:
in this work we present an output feedback algorithm that solves the trajectory tracking problem in control affine nonlinear systems. this algorithm, is an improvement, for this class of systems, of that of (mancilla aguilar et al. 2000a), since it reduces the chattering effect on the control while keeping the original performance. in addition, and via a high gain observer, it deals with discrete output measurements instead of the states, as the original algorithm does.

Abstract:
In this work we present an output feedback algorithm that solves the trajectory tracking problem in control affine nonlinear systems. This algorithm, is an improvement, for this class of systems, of that of (Mancilla Aguilar et al. 2000a), since it reduces the chattering effect on the control while keeping the original performance. In addition, and via a high gain observer, it deals with discrete output measurements instead of the states, as the original algorithm does.