50,922 research outputs found
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
- …