Measurement of Direct CP Violation by NA48

The NA48 experiment at the CERN SPS aims to search for direct CP violation in the $K^0$ system through the measurement of ${\rm Re}(\epsilon'/ \epsilon)$ with high accuracy. In 1999 the NA48 collaboration has published its first measuremen based on 1997 data. A new result, based on 1998 and 1999 data, is presented in this article. The result, combined with 1997 data, ${\rm Re}(\epsilon'/\epsilon) = (15.3 \pm 2.6)\times 10^{-4}$, contributes to the precise determination of the size of direct CP violation.Comment: 8 pages, 6 figures (in eps) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China URL http://ismd31.ccnu.edu.cn

Physics of Electroweak Interactions with Nuclei

In this series of lectures it is illustrated how one can study the strong dynamics of nuclei by means of the electroweak probe. In particular, the most important steps to derive the cross sections in first order perturbation theory are reviewed. In the derivation the focus is put on the main ingredients entering the hadronic part (response functions), i.e. the initial and final states of the system and the operators relevant for the reaction. Emphasis is put on the electromagnetic interaction with few-nucleon systems. The Lorentz integral transform method to calculate the response functions ab initio is described. A few examples of the comparison between theoretical and experimental results are shown. The dependence of the response functions on the nuclear interaction and in particular on three-body forces is emphasized.Comment: Lectures given at the International Scientific Meeting on Nuclear Physics, La Rabida, Huelva (Spain), July 4-10, 200

Stochastic Maximum Principle for a PDEs with noise and control on the boundary

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a stochastic control problem for an evolution system in an Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equation in infinite dimension, plays a crucial role in the formulation of the maximum principle.Comment: 15pg

Well Posedness of Operator Valued Backward Stochastic Riccati Equations in Infinite Dimensional Spaces

We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. Then the results will be applied to characterize the value function and optimal feedback law for a infinite dimensional, linear quadratic control problem with stochastic coefficients

Infinite Horizon and Ergodic Optimal Quadratic Control for an Affine Equation with Stochastic Coefficients

We study quadratic optimal stochastic control problems with control dependent noise state equation perturbed by an affine term and with stochastic coefficients. Both infinite horizon case and ergodic case are treated. To this purpose we introduce a Backward Stochastic Riccati Equation and a dual backward stochastic equation, both considered in the whole time line. Besides some stabilizability conditions we prove existence of a solution for the two previous equations defined as limit of suitable finite horizon approximating problems. This allows to perform the synthesis of the optimal control

Variable-step finite difference schemes for the solution of Sturm-Liouville problems

We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques. Different test problems are proposed to emphasize the behaviour of the proposed algorithm