Abstract:
We prove a Gamma-convergence result for an energy functional related to some fractional powers of the Laplacian operator, with two singular perturbations (one in the interior and one on the boundary).

Abstract:
we study the electronic properties (density of states, conductivity and thermopower) of some nearly-freeelectron systems: the liquid alkali metals and two liquid alloys, li-na and na-k. the study has been performed within the self-consistent second order renormalized propagator perturbation expansion (rpe) for the self-energy. the input ionic pseudopotentials and static correlation functions are derived from the neutral pseudoatom method and the modified hypernetted chain theory of liquids, respectively. reasonable agreement with experiment is found for na, k, rb and na-k, whereas for li and cs and li-na the agreement is less satisfactory.

Abstract:
We study the electronic properties (density of states, conductivity and thermopower) of some nearly-freeelectron systems: the liquid alkali metals and two liquid alloys, Li-Na and Na-K. The study has been performed within the self-consistent second order Renormalized Propagator Perturbation Expansion (RPE) for the self-energy. The input ionic pseudopotentials and static correlation functions are derived from the neutral pseudoatom method and the modified hypernetted chain theory of liquids, respectively. Reasonable agreement with experiment is found for Na, K, Rb and Na-K, whereas for Li and Cs and Li-Na the agreement is less satisfactory.

Abstract:
We study the electronic properties (density of states, conductivity and thermopower) of some nearly--free--electron systems: the liquid alkali metals and two liquid alloys, Li-Na and Na-K. The study has been performed within the self-consistent second order Renormalized Propagator Perturbation Expansion (RPE) for the self-energy. The input ionic pseudopotentials and static correlation functions are derived from the neutral pseudoatom method and the modified hypernetted chain theory of liquids, respectively. Reasonable agreement with experiment is found for Na, K, Rb and Na-K, whereas for Li and Cs and Li-Na the agreement is less satisfactory

Abstract:
We study numerically the crossover between organized and disorganized states of three non-equilibrium systems: the Poisson/coalesce random walk (PCRW), a one-dimensional spin system and a quasi one-dimensional lattice gas. In all cases, we describe this crossover in terms of the average spacing between particles/domain borders $< S(t) >$ and the spacing distribution functions $p^{(n)}(s)$. The nature of the crossover is not the same for all systems, however, we found that for all systems the nearest neighbor distribution $p^{(0)}(s)$ is well fitted by the Berry-Robnik model. The destruction of the level repulsion in the crossover between organized an disorganized states is present in all systems. Additionally, we found that the correlations between domains in the gas and spin systems are not strong and can be neglected in a first approximation but for the PCRW the correlations between particles must be taken into account. To find $p^{(n)}(s)$ with $n>1$, we propose two different analytical models based on the Berry-Robnik model. Our models give us a good approximation for the statistical behavior of these systems in their crossover and allow us to quantify the degree of order/disorder of the system.

Abstract:
This paper presents results on both the kernel and cokernel of the S-capitulation map C_{F,S}\ra C_{K,S}^{G} for arbitrary finite Galois extensions K/F (with Galois group G) and arbitrary finite sets of primes S of F (assumed to contain the archimedean primes in the number field case)

Abstract:
Let $k$ be a perfect field and let $p$ be a prime number different from the characteristic of $k$. Let $C$ be a smooth, projective and geometrically integral $k$-curve and let $X$ be a Severi-Brauer $C$-scheme of relative dimension $p-1$ . In this paper we show that $CH^{d}(X)_{{\rm{tors}}}$ contains a subgroup isomorphic to $CH_{0}(X/C)$ for every $d$ in the range $2\leq d\leq p$. We deduce that, if $k$ is a number field, then $CH^{d}(X)$ is finitely generated for every $d$ in the indicated range.

Abstract:
This version is a significant improvement of the original paper. It includes a new section where we discuss norm tori in some detail. The new abstract is the following: In this paper we obtain Chevalley's ambiguous class number formula for an arbitrary torus T over a global field. The classical formula of C.Chevalley may be recovered by setting T=G_{m} in our formula. As an illustration of the general result, we discuss norm tori in detail. A key ingredient of the proof of our main theorem is the work of X.Xarles on groups of components of Neron-Raynaud models of tori.