Chirality in gravitational and electromagnetic interactions with matter

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigen-modes of a chirality operator. Complex gravitational pulse solutions to the linearized source-free Einstein equations are classified in terms of their chirality and generate a family of non-stationary real spacetime metrics. Particular members of these families are used as backgrounds in analyzing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

On complex Berwald metrics which are not conformal changes of complex Minkowski metrics

We investigate a class of complex Finsler metrics on a domain D ⊂ ℂn. Necessary and sufficient conditions for these metrics to be strongly pseudoconvex complex Finsler metrics, or complex Berwald metrics, are given. The complex Berwald metrics constructed in this paper are neither trivial Hermitian metrics nor conformal changes of complex Minkowski metrics. We give a characterization of complex Berwald metrics which are of isotropic holomorphic curvatures, and also give characterizations of complex Finsler metrics of this class to be Kähler Finsler or weakly Kähler Finsler metrics. Moreover, in the strongly convex case, we give characterizations of complex Finsler metrics of this class to be projectively flat Finsler metrics or dually flat Finsler metrics.

Methods of Interpreting the Results of Vibration Measurements to Locate Damages in Beams

This paper deals with methods of interpreting the results of vibration measurement to identify structural changes in beam-like structures. We briefly presented an own developed damage assess method, that consider a large number of frequencies for the weak-axis banding vibration modes; it allows first a precise localization and afterwards evaluation of the damages. For the first step, recognition of the damage position, we introduce an algorithm implemented in C++ with the interface done using EXCEL features, indicating by one number the damage probable position, based on the Minkowski metrics. To avoid uncertainties, a graphic representation of all results is also presented. The method is tested for values determined by calculus for a randomly selected location, with and without measurement results debased by noise, proving its reliability.

AN IMPORTANT CLASS OF CONFORMALLY FLAT WEAK EINSTEIN FINSLER METRICS

In this paper, we study conformally flat (α, β)-metrics in the form F = αϕ(β/α), where α is a Riemannian metric and β is a 1-form on a C∞ manifold M. We prove that if ϕ = ϕ(s) is a polynomial in s, the conformally flat weak Einstein (α, β)-metric must be either a locally Minkowski metric or a Riemannian metric. Moreover, we prove that conformally flat (α, β)-metrics with isotropic S-curvature are also either locally Minkowski metrics or Riemannian metrics.