The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

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

Self-Refereeing System in Ultimate during the Joint Junior Ultimate Championship in Three Different Divisions—A Different Way to Promote Fair-Play?

In ultimate games governed by the World Flying Disc Federation (WFDF), all competitors also take on the role of referee. The players discuss disputed calls with each other during the game, and then follow rules designed for these situations to determine how the play continues. The number one rule of the sport is to respect the spirit of the game (SOTG), which encourages competitive play while preserving mutual respect and minimizing the risk of injury. The use of SOTG in ultimate in the framework of self-arbitration as a moral practice aligns well with other tools of critical pedagogy. For this study, the SOTG scores of the WFDF Joint Junior Ultimate Championship (JJUC 2022) were analyzed. A total of 1009 players from 19 countries competed in 434 self-refereed games (29 national teams in the WJUC Under-20 (U20) tournament and 20 teams in the EYUC Under-17 (U17) tournament). All the scores from the individual criteria correlated well with the overall scores, but for the most part, they did not correlate with each other. Our experience with the scoring system has highlighted the importance of participants understanding the meaning of the results and how they may lead to a constructive reflection to improve exceptions, including scores representing fouls and rules knowledge. The findings provide important information for physical education teachers, coaches, and sport consultants and may be of use to design SOTG programs that could foster the experience of sportsmanship and to facilitate the ethical conduct of athletes in either recreative or in competitive contexts

Assessing ethical behavior and self-control in elite ultimate championships: a cross-sectional study using the spirit of the game scoring system

IntroductionImplementing a self-refereeing system presents a unique challenge in sports education, particularly in academic and training settings where officiated sports prevail. However, Ultimate Frisbee stands out by entrusting players with both athlete and referee roles, introducing distinctive ethical complexities. This manuscript is intended to evaluate ethical behavior and self-control within the Spirit of the Game (SOTG) scoring system in Elite Ultimate. To address these, Ultimate employs the (SOTG) scoring system, integral since the sport's inception in the late 1980s. SOTG aims to enhance and evaluate athletes’ ethical conduct. This study evaluates SOTG's effectiveness in elite-level Ultimate, analyzing variations across divisions and age groups in three high-level tournaments.MethodsUsing a cross-sectional design, data were collected from five international Ultimate tournaments in 2022. Teams spanned diverse age groups (under 17 to over 50) and divisions (women's, mixed, open). Post-match, teams assessed opponents’ SOTG in five domains: Rules knowledge, fouls, fairness, attitude/self-control, and communication. Ratings used a 5-point Likert scale (“poor” to “excellent”). An overall SOTG score was calculated by aggregating domain scores.ResultsOur study consistently revealed high SOTG scores, reflecting strong sportsmanship. “Positive attitude and self-control” consistently ranked highest, while “Knowledge and use of the rules” scored lowest. Divisional differences in SOTG were statistically insignificant. Notably, WMUCC2022 (participants aged 30+) had significantly higher SOTG scores, possibly indicating age-related self-control improvement or evolving sport culture. Lower rules knowledge scores may stem from linguistic translation challenges.ConclusionSelf-refereeing promotes ethical behavior across divisions and age groups. SOTG underscores sportsmanship's importance and aligns with International Olympic Committee (IOC) and with Sustainable Development Goals (SDGs), particularly SDG 3, 4, 5 and 16 fostering a fairer, healthier, and more peaceful world

Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2

We present a precise measurement of the deuteron longitudinal spin asymmetry A_1^d and of the deuteron spin-dependent structure function g_1^d at Q^2 < 1 GeV^2 and 4*10^-5 < x < 2.5*10^-2 based on the data collected by the COMPASS experiment at CERN during the years 2002 and 2003. The statistical precision is tenfold better than that of the previous measurement in this region. The measured A_1^d and g_1^d are found to be consistent with zero in the whole range of x.Comment: 17 pages, 10 figure

Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs

We present a determination of the gluon polarization Delta G/G in the nucleon, based on the helicity asymmetry of quasi-real photoproduction events, Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarized muon beam scattered on a polarized 6-LiD target. The helicity asymmetry for the selected events is = 0.002 +- 0.019(stat.) +- 0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3 (GeV}/c)^2.Comment: 10 pages, 3 figure

First Measurement of the Transverse Spin Asymmetries of the Deuteron in Semi-Inclusive Deep Inelastic Scattering

First measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarized 6-LiD target are presented. The data were taken in 2002 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. The Collins asymmetry turns out to be compatible with zero, as does the measured Sivers asymmetry within the present statistical errors.Comment: 6 pages, 2 figure

The Deuteron Spin-dependent Structure Function g1d and its First Moment

We present a measurement of the deuteron spin-dependent structure function g1d based on the data collected by the COMPASS experiment at CERN during the years 2002-2004. The data provide an accurate evaluation for Gamma_1^d, the first moment of g1d(x), and for the matrix element of the singlet axial current, a0. The results of QCD fits in the next to leading order (NLO) on all g1 deep inelastic scattering data are also presented. They provide two solutions with the gluon spin distribution function Delta G positive or negative, which describe the data equally well. In both cases, at Q^2 = 3 (GeV/c)^2 the first moment of Delta G is found to be of the order of 0.2 - 0.3 in absolute value.Comment: fits redone using MRST2004 instead of MRSV1998 for G(x), correlation matrix adde

The Polarised Valence Quark Distribution from semi-inclusive DIS

The semi-inclusive difference asymmetry A^{h^{+}-h^{-}} for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002-2004 using a 160 GeV polarised muon beam scattered off a large polarised ^6LiD target and cover the range 0.006 < x < 0.7 and 1 < Q^2 < 100 (GeV/c)^2. In leading order QCD (LO) the asymmetry A_d^{h^{+}-h^{-}} measures the valence quark polarisation and provides an evaluation of the first moment of Delta u_v + Delta d_v which is found to be equal to 0.40 +- 0.07 (stat.) +- 0.05 (syst.) over the measured range of x at Q^2 = 10 (GeV/c)^2. When combined with the first moment of g_1^d previously measured on the same data, this result favours a non-symmetric polarisation of light quarks Delta u-bar = - Delta d-bar at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario Delta u-bar = Delta d-bar = Delta s-bar = Delta s.Comment: 7 pages, 3 figures, COMPASS, revised: details added, author list update

A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target

New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.Comment: 40 pages, 28 figure

Measurement of the Spin Structure of the Deuteron in the DIS Region

We present a new measurement of the longitudinal spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron in the range 1 GeV^2 < Q^2 < 100 GeV^2 and 0.004< x <0.7. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarised muon beam and a large polarised 6-LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region 0.004 < x < 0.03.Comment: 10 pages, 6 figures, subm. to PLB, revised: author list, Fig. 4, details adde