Cosmological Distances and Fractal Statistics of Galaxy Distribution

This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density $\gamma$ and the integral differential density $\gamma^\ast$} of the dust distribution in the Einstein-de Sitter cosmology. The main results are as follows: (1) the choice of distance plays a crucial role in determining the scale where relativistic corrections must be taken into account, as both $\gamma$ and $\gamma^\ast$ are strongly affected by such a choice; (2) inappropriate distance choices may lead to failure to find evidence of a galaxy fractal structure when one calculates those quantities, even if such a structure does occur in the galaxy distribution; (3) the comoving distance and the distance given by Mattig's formula are unsuitable to probe for a possible fractal pattern as they render $\gamma$ and $\gamma^\ast$ constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100Mpc (z \~ 0.03) may only be found if those statistics are calculated with the luminosity or redshift distances, as they are the ones where $\gamma$ and $\gamma^\ast$ decrease at higher redshifts; (5) C\'el\'erier and Thieberger's (2001) critique of Ribeiro's (1995: astro-ph/9910145) earlier study are rendered impaired as their objections were based on misconceptions regarding relativistic distance definitions.Comment: 14 pages, 4 figures, A&A LaTeX macro. Minor linguistic changes to match the version sent to the publisher. Accepted for publication in "Astronomy and Astrophysics

Alternative efficiency measures for multiple-output production

This paper has two main purposes. Firstly, we develop various ways of defining efficiency in the case of multiple-output production. Our framework extends a previous model by allowing for nonseparability of inputs and outputs. We also specifically consider the case where some of the outputs are undesirable, such as pollutants. We investigate how these efficiency definitions relate to one another and to other approaches proposed in the literature. Secondly, we examine the behavior of these definitions in two examples of practically relevant size and complexity. One of these involves banking and the other agricultural data. Our main findings can be summarized as follows. For a given efficiency definition, efficiency rankings are found to be informative, despite the considerable uncertainty in the inference on efficiencies. It is, however, important for the researcher to select an efficiency concept appropriate to the particular issue under study, since different efficiency definitions can lead to quite different conclusions

Complex scaling of the hyper-spheric coordinates and Faddeev equations

We implement complex scaling of Faddeev equations using hyper-spheric coordinates and adiabatic expansion. Complex scaling of coordinates allows convenient calculations of three-body resonances. We derive the necessary equations and investigate the adiabatic spectrum at large distances. We illustrate the viability of the implementation by calculations of several three-body resonances: a $0^+$ resonance in a model benchmark system of three identical bosons; the $2^+$ resonance in the $^6$He nucleus within the $\alpha+n+n$ model; and the two $0^+$ resonances in $^{12}$C within the three-$\alpha$ model.Comment: 20 pages, 10 figure