Twisting type-N vacuum fields with a group H2H_2

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two non-commuting Killing vectors. We study the case when the homothetic parameter $\phi$ takes the value -1, which is shown to admit a reduction to a third-order real ordinary differential equation for this problem, similar to that previously obtained by one of us when two Killing vectors are present.Comment: LaTeX, 11 pages. To be published in Classical and Quantum Gravit

New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential equation is given. Alternatively, the mentioned first integral can be used in order to provide a first integral of the second-order complex equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in Class. Quantum Gra

Exterior Differential System for Cosmological G2 Perfect Fluids and Geodesic Completeness

In this paper a new formalism based on exterior differential systems is derived for perfect-fluid spacetimes endowed with an abelian orthogonally transitive G2 group of motions acting on spacelike surfaces. This formulation allows simplifications of Einstein equations and it can be applied for different purposes. As an example a singularity-free metric is rederived in this framework. A sufficient condition for a diagonal metric to be geodesically complete is also provided.Comment: 27 pages, 0 figures, LaTeX2e, to be published in Classical and Quantum Gravit

New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields

A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting the Weyl tensor to type D produces a set of equations which can be solved, and a range of new techniques are introduced to simplify the problem. Imposing the further condition that the solution is asymptotically flat yields the Kerr solution uniquely. The implications of this result for the no-hair theorem are discussed. The techniques developed here have many other applications, which are described in the conclusions.Comment: 30 pages, no figure

Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea

Charge without charge, regular spherically symmetric solutions and the Einstein-Born-Infeld theory

The aim of this paper is to continue the research of JMP 46, 042501 (2005) of regular static spherically symmetric spacetimes in Einstein-Born-Infeld theories from the point of view of the spacetime geometry and the electromagnetic structure. The energy conditions, geodesic completeness and the main features of the horizons of this spacetime are explicitly shown. A new static spherically symmetric dyonic solution in Einstein-Born-Infeld theory with similar good properties as in the regular pure electric and magnetic cases of our previous work, is presented and analyzed. Also, the circumvention of a version of "no go" theorem claiming the non existence of regular electric black holes and other electromagnetic static spherically configurations with regular center is explained by dealing with a more general statement of the problem.Comment: Figures in Int J Theor Phys (Online First

FAbry STabilization indEX (FASTEX) : an innovative tool for the assessment of clinical stabilization in Fabry disease

Two disease severity scoring systems, the Mainz Severity Score Index (MSSI) and Fabry Disease Severity Scoring System (DS3), have been validated for quantifying the disease burden of Fabry disease. We aimed to develop a dynamic mathematical model [the FASTEX (FAbry STabilization indEX)] to assess the clinical stability. A multidisciplinary panel of experts in Fabry disease first defined a novel score of severity [raw score (RS)] based on three domains with a small number items in each domain (nervous system domain: pain, cerebrovascular events; renal domain: proteinuria, glomerular filtration rate; cardiac domain: echocardiography parameters, electrocardiograph parameters and New York Heart Association class) and evaluated the clinical stability over time. The RS was tested in 28 patients (15 males, 13 females) with the classic form of Fabry disease. There was good statistical correlation between the newly established RS and a weighted score (WS), with DS3 and MSSI (R (2) = 0.914, 0.949, 0.910 and 0.938, respectively). In order to refine the RS further, a WS, which was expressed as a percentage value, was calculated. This was based on the relative clinical significance of each item within the domain with the panel agreeing on the attribution of a different weight of clinical damage to a specific organ system. To test the variation of the clinical burden over time, the RS was repeated after 1 year. The panel agreed on a cut-off of a 20% change from baseline as the clinical WS to define clinical stability. The FASTEX model showed good correlation with the clinical assessment and with clinical variation over time in all patients

On tuning passive black-box macromodels of LTI systems via adaptive weighting

This paper discusses various approaches for tuning the accuracy of rational macromodels obtained via black-box identification or approximation of sampled frequency responses of some unknown Linear and Time-Invariant system. Main emphasis is on embedding into the model extraction process some information on the nominal terminations that will be connected to the model during normal operation, so that the corresponding accuracy is optimized. This goal is achieved through an optimization based on a suitably defined cost function, which embeds frequency-dependent weights that are adaptively refined during the model construction. A similar procedure is applied in a postprocessing step for enforcing model passivity. The advantages of proposed algorithm are illustrated on a few application examples related to power distribution networks in electronic system