A Renormalization Group Approach to Relativistic Cosmology

We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG) methods. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the Ricci-Hamilton equations studied in connection with the geometry of three-manifolds. The properties of the Ricci-Hamilton flow make it possible to study a critical behaviour of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheet-like structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant is affected by non-trivial scale dependent shear terms, while the spatial anisotropy of the metric influences significantly the scale-dependence of the matter distribution.Comment: 57 pages, LaTeX, 15 pictures available on request from the Author

Using 3D Stringy Gravity to Understand the Thurston Conjecture

We present a string inspired 3D Euclidean field theory as the starting point for a modified Ricci flow analysis of the Thurston conjecture. In addition to the metric, the theory contains a dilaton, an antisymmetric tensor field and a Maxwell-Chern Simons field. For constant dilaton, the theory appears to obey a Birkhoff theorem which allows only nine possible classes of solutions, depending on the signs of the parameters in the action. Eight of these correspond to the eight Thurston geometries, while the ninth describes the metric of a squashed three sphere. It therefore appears that one can construct modified Ricci flow equations in which the topology of the geometry is encoded in the parameters of an underlying field theory.Comment: 17 pages, Late

Analysis of the impact of sex and age on the variation in the prevalence of antinuclear autoantibodies in Polish population: a nationwide observational, cross-sectional study

The detection of antinuclear autoantibody (ANA) is dependent on many factors and varies between the populations. The aim of the study was first to assess the prevalence of ANA in the Polish adult population depending on age, sex and the cutoff threshold used for the results obtained. Second, we estimated the occurrence of individual types of ANA-staining patterns. We tested 1731 patient samples using commercially available IIFA using two cutoff thresholds of 1:100 and 1:160. We found ANA in 260 participants (15.0%), but the percentage of positive results strongly depended on the cutoff level. For a cutoff threshold 1:100, the positive population was 19.5% and for the 1:160 cutoff threshold, it was 11.7%. The most prevalent ANA-staining pattern was AC-2 Dense Fine speckled (50%), followed by AC-21 Reticular/AMA (14.38%) ANA more common in women (72%); 64% of ANA-positive patients were over 50 years of age. ANA prevalence in the Polish population is at a level observed in other highly developed countries and is more prevalent in women and elderly individuals. To reduce the number of positive results released, we suggest that Polish laboratories should set 1:160 as the cutoff threshold

Oddzialywanie stosowanego nawozenia azotem na wartosc C-N, zawartosc azotanow [V] oraz aktywnosc enzymatyczna badanych gleb

W latach 1996-2004 przeprowadzono badania w oparciu o doświadczenie mikropoletkowe, zlokalizowane na terenie Stacji Badawczej ATR w Wierzchucinku. Określono wartości C/N, zawartości azotanów(V) oraz aktywność enzymów uczestniczących w przemianach azotu (dehydrogenaz i ureazy) w badanych glebach (w warstwie: 0-40 i 40-80 cm) w zależności od zastosowanego zróżnicowanego nawożenia azotem w warunkach doświadczenia mikropoletkowego. Po zastosowaniu zróżnicowanego nawożenia azotem (1996-2004) stwierdzono obniżenie zawartości węgla organicznego i azotu ogółem jedynie w warstwie podornej (40-80 cm). Typ gleby, głębokość pobierania próbek glebowych oraz stosowane zróżnicowane nawożenie azotem istotnie determinowało zawartość azotu azotanowego(V), aktywność dehydrogenaz oraz ureazy w badanych glebach.The studies carried out within 1996-2004 were based on a microfield experiment localized at Wierzchucinek TAU Research Station. The aim of study was to estimate the C/N ratio, nitrate(V) contents and the activity of enzymes acting in nitrogen transformations (dehydrogenase and urease) in the soils depending on diversified nitrogen fertilization. After diversified nitrogen fertilization (1996-2004) the decrease of organic carbon and total nitrogen contents in top soil layer (40-80 cm) were observed. Soil type, the depth of soil sampling and diversified nitrogen fertilization significantly determined the nitrate nitrogen(V) content and the activity of dehydrogenase and urease in tested soils

Thermodynamics of Ising Ferromagnet Studied by the Real-Space Renormalization Group Method

The critical exponents of the 3D Ising model were calculated in the approximation of the fourth-order cumulant expansion. Thermodynamic functions in the high-temperature range are obtained