252 research outputs found
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 -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 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
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
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