Hasse-Schmidt Derivations and Coefficient Fields in Positive Characteristics

We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of Hasse-Schmidt derivationsComment: 14 pages; A gap in the statement of Proposition (2.7) has been fixed and the proof of Theorem (3.14) has been adapte

Pairing Correlations in Finite Systems: From the weak to the strong fluctuations regime

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the Ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.Comment: Submitted to EPJ

A singularity-free space-time

We show that the solution published in Ref.1 is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, causal symmetry and causal stability. A detailed discussion about which assumptions in the singularity theorems are not fulfilled is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.Comment: Latex 2.09, 14 page

On the exposure to mobile phone radiation in trains

This report presents theoretical estimates of the Power Density levels which may be reached inside trains. Two possible sources of high levels of radiation are discussed. The first one arises since the walls of the wagons are metallic and therefore bounce back almost all radiation impinging on them. The second is due to the simultaneous emission of a seemingly large number of nearby telephones. The theoretical study presented here shows that Power Densities stay at values below reference levels always.Comment: 9 pages, 1 figur

Coupled equations for Kähler metrics and Yang-Mills connections

We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, the Mabuchi K-energy and geodesic stability. We finish by giving some examples of solutions.Comment: 61 pages; v2: introduction partially rewritten; minor corrections and improvements in presentation, especially in Section 4; added references; v3: To appear in Geom. Topol. Minor corrections and improvements, following comments by referee