Abstract:
We perform a qualitative analysis of the critical equation associated with a stationary ergodic Hamiltonian through a stochastic version of the metric method, where the notion of closed random stationary set, issued from stochastic geometry, plays a major role. Our purpose is to give an appropriate notion of random Aubry set, to single out characterizing conditions for the existence of exact or approximate correctors, and write down representation formulae for them. For the last task, we make use of a Lax--type formula, adapted to the stochastic environment. This material can be regarded as a first step of a long--term project to develop a random analog of Weak KAM Theory, generalizing what done in the periodic case or, more generally, when the underlying space is a compact manifold.

Abstract:
We adapt the metric approach to the study of stationary ergodic Hamilton-Jacobi equations, for which a notion of admissible random (sub)solution is defined. For any level of the Hamiltonian greater than or equal to a distinguished critical value, we define an intrinsic random semidistance and prove that an asymptotic norm does exist. Taking as source region a suitable class of closed random sets, we show that the Lax formula provides admissible subsolutions. This enables us to relate the degeneracies of the critical stable norm to the existence/nonexistence of exact or approximate critical admissible solutions.

Abstract:
We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of globally strict critical subsolutions concentrates. As in the case of a single equation, we prove the existence of critical subsolutions which are strict and smooth outside the Aubry set. This allows us to derive in a simple way a comparison result among critical sub and supersolutions with respect to their boundary data on the Aubry set, showing in particular that the latter is a uniqueness set for the critical system. We also highlight some rigidity phenomena taking place on the Aubry set.

Abstract:
We prove that the multi--time Hamilton--Jacobi equation in general cannot be solved in the viscosity sense, in the non-convex setting, even when the Hamiltonians are in involution.

Abstract:
We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make up, in addition, a dense subset of all critical subsolutions with respect to a suitable metric. If the Hamiltonian is additionally assumed of Tonelli type, then there exist strict subsolutions of class $\CC^{1,1}$ in $\R^N$. The proofs are based on the use of Lax--Oleinik semigroups and their regularizing properties in the stationary ergodic environment, as well as on a generalized notion of Aubry set.

Abstract:
In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax- Oleinik semigroups. This is equivalent to the solvability of an associated multi- time Hamilton-Jacobi equation. We examine the weak KAM theoretic aspects of the commutation property and show that the two Hamiltonians have the same weak KAM solutions and the same Aubry set, thus generalizing a result recently obtained by the second author for Tonelli Hamiltonians. We make a further step by proving that the Hamiltonians admit a common critical subsolution, strict outside their Aubry set. This subsolution can be taken of class C^{1,1} in the Tonelli case. To prove our main results in full generality, it is crucial to establish suitable differentiability properties of the critical subsolutions on the Aubry set. These latter results are new in the purely continuous case and of independent interest.

Abstract:
We consider a continuous coercive Hamiltonian $H$ on the cotangent bundle of the compact connected manifold $M$ which is convex in the momentum. If $u_\lambda:M\to\mathbb R$ is the viscosity solution of the discounted equation $$ \lambda u_\lambda(x)+H(x,d_x u_\lambda)=c(H), $$ where $c(H)$ is the critical value, we prove that $u_\lambda$ converges uniformly, as $\lambda\to 0$, to a specific solution $u_0:M\to\mathbb R$ of the critical equation $$ H(x,d_x u)=c(H). $$ We characterize $u_0$ in terms of Peierls barrier and projected Mather measures.

Abstract:
This paper completes the research of theadministrative appeal under the Serbian law. Itis preceded by two articles containing normativeanalyses of the general regime of the administrativeappeal as prescribed in the General AdministrativeProceeding Act and administrative remedies inspecial policy domains. The main part of thepaper is an empirical research concerning theef ciency of the administrative appeal. Ef ciencyis understood as a precondition for preventingappellants from seeking judicial protection andthus reducing the workload of the court. Theremaining part is dedicated to the ef ciency oftwo other administrative legal remedies, as well asto the ef ciency of the work of the Ombudsman.The purpose of the latter is to provide material for the consideration of possible amendments to theregime of the administrative appeal, which couldenhance its ef ciency.

Abstract:
The large variety of experimental data around the pion-production threshold are compared with a meson-exchange isobar model which includes the pion-nucleon interaction in s-- and p-waves. Theoretical results obtained with two different NN potentials (Bonn and Paris) indicate that the behavior of the excitation function at threshold is sensitive to the details of the NN correlations. The complete model presented, while developed originally to reproduce the reaction around the Delta resonance, is shown to describe well the integral (Coulomb-corrected) cross-section at threshold along with its angular distribution. At low energies the angular dependence of the analyzing power Ay0 is well reproduced also. Finally, the energy dependence of the analyzing power for theta=90 from threshold up to the Delta resonance is considered and discussed.

Abstract:
Thunderstorms may cause large damages to infrastructures and population, therefore the possible identification of the areas with the highest occurrence of these events is especially relevant. Nevertheless, few extensive studies of these phenomena with high spatial and temporal resolution have been carried out in the Alps and none of them includes North-western Italy. To analyze thunderstorm events, the data of the meteorological radar network of the regional meteorological service of Piedmont region (ARPA Piemonte) have been used in this work. The database analyzed includes all thunderstorms occurred during the warm months (April to September) of a 6-year period (2005–2010). The tracks of each storm have been evaluated using a storm tracking algorithm. Several characteristics of the storms have been analyzed, such as the duration, the spatial and the temporaldistribution, the direction and the distance travelled. Obtained results revealed several important characteristics that may be useful for nowcasting purposes providing a first attempt of radar-based climatology in the considered region.