Topological diagonalizations and Hausdorff dimension

The Hausdorff dimension of a product XxY can be strictly greater than that of Y, even when the Hausdorff dimension of X is zero. But when X is countable, the Hausdorff dimensions of Y and XxY are the same. Diagonalizations of covers define a natural hierarchy of properties which are weaker than ``being countable'' and stronger than ``having Hausdorff dimension zero''. Fremlin asked whether it is enough for X to have the strongest property in this hierarchy (namely, being a gamma-set) in order to assure that the Hausdorff dimensions of Y and XxY are the same. We give a negative answer: Assuming CH, there exists a gamma-set of reals X and a set of reals Y with Hausdorff dimension zero, such that the Hausdorff dimension of X+Y (a Lipschitz image of XxY) is maximal, that is, 1. However, we show that for the notion of a_strong_ gamma-set the answer is positive. Some related problems remain open.Comment: Small update

A note on unbounded strongly measure zero subgroups of the Baer–Specker group

AbstractWe show that it is consistent with ZFC that there exist:(1)An unbounded (with respect to ⩽∗) and strongly measure zero subgroup of ZN, but without the Menger property.(2)An unbounded (with respect to ⩽∗) and strongly measure zero subgroup of ZN with the Menger property which does not have the Rothberger property. This answers the last two problems which remained from a classification project of Machura and Tsaban

Wczesne kompleksowe leczenie pacjenta po urazie wielomiejscowym z użyciem gwoździa śródszpikowego i systemu LCP firmy Medgal

The study presents a case of a 44-year old patient admitted to the Department of Orthopaedics as an emergency to treat a multiple fractures of lower limbs.Successful, several-stages surgical treatment and rehabilitation was performed providing very satisfactory result.A case shows how important is the individual approach to the patient after multiple trauma.W pracy przedstawiono przypadek 44-letniego pacjenta przyjętego do Kliniki Ortopedii w trybie nagłym w celu leczenia operacyjnego wielu złamań kończyn dolnych. Przeprowadzono udane kilkustopniowe leczenie operacyjne i rehabilitacja uzyskując bardzo zadowalający wynik. Przypadek pokazuje, jak ważne jest indywidualne podejście do pacjenta po urazie wielomiejscowym

Early complete surgical treatment of a patient after multiple trauma using intramedullary nail and LCP system from Medgal company

The study presents a case of a 44-year old patient admitted to the Department of Orthopaedics as an emergency to treat a multiple fractures of lower limbs. Successful, several-stages surgical treatment and rehabilitation was performed providing very satisfactory result. A case shows how important is the individual approach to the patient after multiple trauma.W pracy przedstawiono przypadek 44-letniego pacjenta przyjętego do Kliniki Ortopedii w trybie nagłym w celu leczenia operacyjnego wielu złamań kończyn dolnych. Przeprowadzono udane kilkustopniowe leczenie operacyjne i rehabilitacja uzyskując bardzo zadowalający wynik. Przypadek pokazuje, jak ważne jest indywidualne podejście do pacjenta po urazie wielomiejscowym

Effects of baryons on weak lensing peak statistics

Upcoming weak-lensing surveys have the potential to become leading cosmological probes provided all systematic effects are under control. Recently, the ejection of gas due to feedback energy from active galactic nuclei (AGN) has been identified as major source of uncertainty, challenging the success of future weak-lensing probes in terms of cosmology. In this paper we investigate the effects of baryons on the number of weak-lensing peaks in the convergence field. Our analysis is based on full-sky convergence maps constructed via light-cones from $N$-body simulations, and we rely on the baryonic correction model of Schneider et al. (2019) to model the baryonic effects on the density field. As a result we find that the baryonic effects strongly depend on the Gaussian smoothing applied to the convergence map. For a DES-like survey setup, a smoothing of $\theta_k\gtrsim8$ arcmin is sufficient to keep the baryon signal below the expected statistical error. Smaller smoothing scales lead to a significant suppression of high peaks (with signal-to-noise above 2), while lower peaks are not affected. The situation is more severe for a Euclid-like setup, where a smoothing of $\theta_k\gtrsim16$ arcmin is required to keep the baryonic suppression signal below the statistical error. Smaller smoothing scales require a full modelling of baryonic effects since both low and high peaks are strongly affected by baryonic feedback.Comment: 22 pages, 11 figures, JCAP accepte