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This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle., Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B"

This paper presents numerical solutions of particular Lemaitre-Tolman models approximating a fractal behaviour along the past light cone, as discussed in paper I (0807.0866) of this series. The initial conditions of the numerical problem are discussed and the algorithm used to carry out the numerical integrations is presented. It was found that the numerical solutions are stiff across the flat-curved interface necessary to obtain the initial conditions of the problem. The spatially homogeneous Friedmann models are treated as special cases of the Lemaitre-Tolman solution and solved numerically. Extending the results of paper II (0807.0869) on the Einstein-de Sitter model, to the $K = \pm 1$ models, it was found that the open and closed Friedmann models also do not appear to remain homogeneous along the backward null cone, with a vanishing volume (average) density as one approaches the Big Bang singularity hypersurface. Fractal solutions, that is, solutions representing an averaged and smoothed-out single fractal, were obtained in all three classes of the Lemaitre-Tolman metric, but only the hyperbolic ones were found to be in agreement with observations, meaning that a possible Friedmann background universe would have to be an open one. The best fractal metric obtained through numerical simulations is also analysed in terms of evolution, homothetic self-similarity, comparison with the respective spatially homogeneous case and the fitting problem in cosmology. The paper finishes with a discussion on some objections raised by some authors against a fractal cosmology., Comment: 57 pages. 22 figures. LaTeX. Paper published in 1993. The numerical code used in this paper is discussed in gr-qc/0205095

This paper studies the spatially homogeneous Einstein-de Sitter cosmological model in the context of a relativistic hierarchical (fractal) cosmology as developed in paper I (0807.0866). The Einstein-de Sitter model is treated as a special case of Lemaitre-Tolman's spacetime, obtained by the appropriate choice of the latter's three arbitrary functions. The observational relations along the past light cone of the model under consideration are calculated, and an investigation of whether or not it has fractal behaviour is performed. It was found that the Einstein-de Sitter model does not seem to remain homogeneous along the geodesic and that it also has no fractal features along the backward null cone., Comment: 13 pages. 1 figure. Paper published in 1992

This work examines a relativistic model for the observed inhomogeneities of the large scale structure where the hypothesis that this structure can be described as being a self-similar fractal system is advanced. The concept of hierarchical clustering is identified with a fractal distribution and the problems raised by the use of fractal ideas in a relativistic model are discussed, as well as their relations to the Copernican and Cosmological Principles. Voids, clusters and superclusters of galaxies are assumed to be part of a smoothed-out fractal structure described by a Lemaitre-Tolman solution. The basic concepts of the Newtonian model presented by Pietronero (1987) are reinterpreted and applied to this inhomogeneous curved spacetime. This fractal system is also assumed to have a crossover to homogeneity which leads to a "Swiss cheese" type model, composed by an interior Lemaitre-Tolman metric and an exterior dust Friedmann solution. The Darmois junction conditions between the two spacetimes are calculated, and the observational relations necessary to compare the model with observations are obtained for the interior region. The differential equations of the interior spacetime are set up and a numerical strategy is devised for finding particular Tolman solutions representing a fractal behaviour along the past light cone., Comment: 22 pages. LaTeX. Paper published in 1992

This work discusses the possible empirical verification of the geometrical concept of homogeneity of the standard relativistic cosmology considering its various definitions of distance. We study the physical consequences of the distinction between the usual concept of spatial homogeneity (SH), as defined by the Cosmological Principle, and the concept of observational homogeneity (OH), arguing that OH is in principle falsifiable by means of astronomical observations, whereas verifying SH is only possible indirectly. Simulated counts of cosmological sources are produced by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes and differential densities are derived with the various cosmological distance definitions in the EdS model. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. Besides, simulated counts with no OH features at low redshift start showing OH characteristics at high redshift. The comoving distance seems to be the only distance definition where both SH and OH appear simultaneously. The results show that observations indicating possible lack of OH do not necessarily falsify the standard Friedmannian cosmology, meaning that this cosmology will not necessarily always produce observable homogeneous densities. The general conclusion is that the use of different cosmological distances in the characterization of the galaxy distribution lead to significant ambiguities in reaching conclusions about the behavior of the large-scale galaxy distribution in the Universe., Comment: 12 pages, 12 figures, LaTeX. Matches the final version sent to the journal. Accepted for publication in "Astronomy and Astrophysics"

This paper discusses how theories can be assessed within the epistemological viewpoint advanced by the Austrian physicist Ludwig E. Boltzmann. It builds upon, and further develops, the perspective of Boltzmann's thinking as advanced by Ribeiro and Videira (1998, arXiv:physics/9806011). Boltzmann's epistemological viewpoint accepts that reality is real and proposes that reality can be described by different points of view because his main philosophical thesis states that scientific theories are images of Nature. We present the historical context that witnessed the genesis of Boltzmann's ideas and expand Ribeiro and Videira's (Ibid.) perspective by arguing that later in his life Boltzmann realized the insufficiency of his thesis as justification for theoretical pluralism and avoidance of dogmatism. Consequently, his thinking went beyond epistemology, the nature of scientific knowledge, to include realism, the nature of the represented objects., Comment: 19 pages. New abstract. Sections 1 and 5 were slightly revised and enlarged. Version v1 was intended as a chapter of a book on Boltzmann, but the publisher cancelled it. This version matches the text appearing in "Interdisciplinary Science Reviews"

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number densities statistics of the galaxy distribution as discussed in Ribeiro (2005), namely the differential density $\gamma$ and the integral differential density $\gamma^\ast$. By applying the theory advanced by Ribeiro and Stoeger (2003), which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts $dN/dz$ are extracted from the LF and used to calculate both $\gamma$ and $\gamma^\ast$ with various cosmological distance definitions, namely the area distance, luminosity distance, galaxy area distance and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey and $\gamma$ and $\gamma^\ast$ are calculated for two cosmological models: Einstein-de Sitter and an $\Omega_{m_0}=0.3$, $\Omega_{\Lambda_0}=0.7$ standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro (2005), as well as showing that plots of $\gamma$ and $\gamma^\ast$ against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power law pattern for redshifts higher than 0.1. These findings bring support to Ribeiro's (2005) theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large scale distribution of galaxies., Comment: LaTeX, 37 pages, 6 tables, 10 figures. Accepted for publication in "The Astrophysical Journal"

This work studies the Zipf Law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in Brazilian cities does follow a power law similar to the ones found in other countries. Estimates of the power law exponent were found to be 2.22 +/- 0.34 for the 1970 and 1980 censuses, and 2.26 +/- 0.11 for censuses of 1991 and 2000. More accurate results were obtained with the maximum likelihood estimator, showing an exponent equal to 2.41 for 1970 and 2.36 for the other three years., Comment: 12 pages, 6 figures, 3 tables, Elsevier LaTeX, accepted for publication in "Physica A". Correction of minor mistyping (eq. 8)

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"

This paper outlines CLEW (collaborative learning environment for the Web). The project combines MUD (Multi-User Dimension), workflow, VRML (Virtual Reality Modeling Language) and educational concepts like constructivism in a learning environment where students actively participate in the learning process. The MUD shapes the environment structure. The workflow system allows the execution and coordination of the course activities. The VRML establishes the presentation format of the courses' virtual worlds. Finally, the educational concepts influence the way the didactic material is published. Topics discussed include: the educational background that guides the environment; the environment components, including the participants, regions, and objects; the six layers of the system architecture--presentation, application, management and control, adaptation, external services, and data; the course development, including structuring a course, and the participant's perspective; and future plans. A diagram of the system architecture is included. Contains 20 references. (Author/DLS)

The study of satellite galaxies can provide information on the merging and aggregation processes which, according to the hierarchical clustering models, form the larger spiral galaxies we observe. With the aim of testing hierarchical models of galaxy formation, we have conducted an observational program which comprises H$\alpha$ imaging for both the parent and the satellite galaxies, taken from the compilation by Zaritsky et al. (1997) that contains 115 galaxies orbiting 69 primary isolated spiral galaxies. We have observed a subsample of 37 spiral and irregular galaxies taken from the compilation mentioned above. The aim of this study is to determine star formation properties of the sample galaxies. In this work we present the preliminary results of this program that we have carried out with the 1.8-m Vatican Telescope (VATT)., Comment: 4 pages, 4 figures. Contribution to the proceedings of "Satellites and Tidal Streams", La Palma, May 26-30, 2003

This paper aims to connect the theory of relativistic cosmology number counts with the astronomical data, practice, and theory behind the galaxy luminosity function (LF). We treat galaxies as the building blocks of the Universe, but ignore most aspects of their internal structures by considering them as point sources. However, we do consider general morphological types in order to use data from galaxy redshift surveys, where some kind of morphological classification is adopted. We start with a general relativistic treatment for a general spacetime, and then link the derived expressions with the LF definition adopted in observational cosmology. Then equations for differential number counts, the related relativistic density per source, and observed and total relativistic energy densities of the universe, and other related quantities are written in terms of the luminosity and selection functions. As an example of how these theoretical/observational relationships can be used, we apply them to test the LF parameters determined from the CNOC2 galaxy redshift survey, for consistency with the Einstein-de Sitter (EdS) cosmology, which they assume, for intermediate redshifts. We conclude that there is a general consistency for the tests we carried out, namely both the observed relativistic mass-energy density, and the observed relativistic mass-energy density per source, which is equivalent to differential number counts, in an EdS Universe. In addition, we find clear evidence of a large amount of hidden mass, as has been obvious from many earlier investigations. At the same time, we find that the CNOC2 LF give differential galaxy counts somewhat above the EdS predictions, indicating that this survey observes more galaxies at 0.1 < z < 0.4 than the model's predictions., Comment: 46 pages, 2 figures, 7 tables, AASTeX. Accepted for publication in "The Astrophysical Journal"

This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown., Comment: 13 pages, 10 figures, LaTeX. Fortran code included with the LaTeX source code (also available at http://www.if.ufrj.br/~mbr/codes). Accepted for publication in "Computer Physics Communications"

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous, and conjecturing that this distribution should follow a fractal pattern in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts reviewing the argument concerning the possibility that the galaxy distribution follows such a scaling pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995: astro-ph/9910145) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z ~ 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist., Comment: 30 pages, 2 figures, LaTeX. This paper is a follow-up to gr-qc/9909093. Accepted for publication in "General Relativity and Gravitation"

The two-point correlation function for the dust distribution in the unperturbed Einstein-de Sitter cosmological model is studied along the past light cone. It was found that this function seems unable to represent the theoretical distribution of dust along the backward null cone of this unperturbed model, which has already been determined in a previous paper as being apparently inhomogeneous at ranges usually considered as local. Such result was revisited in order to determine more precisely the quantitative limits where, in theory, we can detect apparent homogeneity, and it was found that this may only happen up to $z \sim 10^{-2}$. A different statistical analysis proposed by Pietronero is used, and it appears to be able to represent more accurately the theoretical distribution of dust in this cosmology. In the light of these results, it is argued that the usual practice of disregarding relativistic effects in studies of distribution of galaxies, by considering them as being placed on local regions, seems to be valid only on much closer scales than it is commonly believed. In the Einstein-de Sitter cosmology with $H_0=75 km s^{-1} Mpc^{-1}$, that may only happen in redshifts as low as $z \approx 0.04$, which means that the local approximation seems to be valid up to zeroth order of approximation only. As at present there are many redshift surveys which have already probed at deeper ranges, it seems that in order to compare the Friedmann models with observations we have to be very careful when ignoring the past light cone problem in observational cosmology, either in theoretical calculations or in data analysis, due to relativistic effects which produce observable inhomogeneity even in spatially homogeneous cosmological models., Comment: standard LaTeX; 23 pages, 2 tables, 3 LaTeX figures; paper published in 1995 is archived here

This paper advances a general proposal for testing non-standard cosmological models by means of observational relations of cosmological point sources in some specific waveband, and their use in the context of the data provided by the galaxy redshift surveys, but for any cosmological metric. By starting from the general theory for observations in relativistic cosmology the equations for colour, K-correction, and number counts of cosmological point sources are discussed in the context of curved spacetimes. The number counts equation is also written in terms of the selection and luminosity functions, which provides a relativistic generalization of its Euclidean version. Since these observables were not derived in the framework of any specific cosmology, they are valid for any cosmological model. The hypotheses used in such derivation are reviewed, together with some difficulties for the practical use of those observables., Comment: 11 pages, LaTeX. Improved text, typos corrected, references added. Accepted for publication in "The Observatory"

This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a cosmological fractal structure are calculated along the past light cone. If this hypothesis proves, even partially, correct, most, if not all, objections raised against fractals in cosmology may be solved. For instance, under this view the standard cosmology has zero average density, as predicted by an infinite fractal structure, with, at the same time, the cosmological principle remaining valid. The theoretical results which suggest this conjecture are reviewed, as well as possible ways of checking its validity., Comment: 6 pages, LaTeX. Text unchanged. Two references corrected. Contributed paper presented at the "South Africa Relativistic Cosmology Conference in Honour of George F. R. Ellis 60th Birthday"; University of Cape Town, February 1-5, 1999

This paper seeks to check the validity of the "apparent fractal conjecture" (Ribeiro 2001ab: gr-qc/9909093, astro-ph/0104181), which states that the observed power-law behaviour for the average density of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in average density profile determination, are calculated along the past light cone. Implementing these conditions in the proposed set of observational relations profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the average density becomes observationally inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology, change which was already analysed by Ribeiro (1992b, 1993, 1994, 1995: astro-ph/9910145) for a non-perturbed model. Here we derive observational relations in a perturbed Einstein-de Sitter cosmology by means of the perturbation scheme proposed by Abdalla and Mohayaee (1999: astro-ph/9810146), where the scale factor is expanded in power series to yield perturbative terms. The differential equations derived in this perturbative context, and other observables necessary in our analysis, are solved numerically. The results show that our perturbed Einstein-de Sitter cosmology can be approximately described by a decaying power-law like average density profile, meaning that the dust distribution of this cosmology has a scaling behaviour compatible with the power-law profile of the density-distance correlation observed in the galaxy catalogues. These results show that, in the context of this work, the apparent fractal conjecture is correct., Comment: 18 pages, 1 figure, LaTeX. Final version (small changes in the figure plus some references update). Fortran code included with the LaTeX source. To be published in "Fractals"

This work discusses the presence of a dogmatic tendency within modern cosmology, and some ideas capable of neutralizing its negative influence. It is verified that warnings about the dangers of dogmatic thinking in cosmology can be found as early as the 1930's, and we discuss the modern appearance of "scientific dogmatism". The solution proposed to counteract such an influence, which is capable of neutralizing this dogmatic tendency, has its origins in the philosophical thinking of the Austrian physicist Ludwig Boltzmann (1844-1906). In particular we use his two main epistemological theses, scientific theories as representations of nature and theoretical pluralism, to show that once they are embodied in the research practice of modern cosmology, there is no longer any reason for dogmatic behaviours., Comment: 14 pages; LaTeX source

This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications rather than their mathematical side. Then we discuss the standard correlation function analysis of galaxy catalogues and many observational facts that brought increasing doubts about the reliability of this method, paying special attention to the standard analysis implicit assumption of an eventual homogeneity of the distribution of galaxies. Some new statistical concepts for analysing this distribution is presented, and without the implicit assumption of homogeneity they bring support to the hypothesis that the distribution of galaxies does form a fractal system. The Pietronero-Wertz's single fractal (hierarchical) model is presented and discussed, together with the implications of this new approach for understanding galaxy clustering., Comment: 51 pages including 22 figures