Teichm\"uller's problem in space

Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a spatial analogue of a classical result due to Teichm\"uller. Unlike Teichm\"uller's result, our bounds are explicit. Explicit bounds are based on two sharp well-known distortion results: the quasiconformal Schwarz lemma and the bound for linear dilatation. Moreover, Bernoulli type inequalities and asymptotically sharp bounds for special functions involving complete elliptic integrals are applied to simplify the computations. Finally, we discuss the behavior of the quasihyperbolic metric under quasiconformal maps and prove a sharp result for quasiconformal maps of R^n \ {0} onto itself.Comment: 25 pages, 2 figure

The Geroch group in the Ashtekar formulation

We study the Geroch group in the framework of the Ashtekar formulation. In the case of the one-Killing-vector reduction, it turns out that the third column of the Ashtekar connection is essentially the gradient of the Ernst potential, which implies that the both quantities are based on the ``same'' complexification. In the two-Killing-vector reduction, we demonstrate Ehlers' and Matzner-Misner's SL(2,R) symmetries, respectively, by constructing two sets of canonical variables that realize either of the symmetries canonically, in terms of the Ashtekar variables. The conserved charges associated with these symmetries are explicitly obtained. We show that the gl(2,R) loop algebra constructed previously in the loop representation is not the Lie algebra of the Geroch group itself. We also point out that the recent argument on the equivalence to a chiral model is based on a gauge-choice which cannot be achieved generically.Comment: 40 pages, revte

Efficiency of different methods and forms of microelements application in function of n fertilizer in apple trees

In order to achieve a high yield and quality of apple fruit, more effective ways of fertilization are required in the modern, high density apple orchards. The objective of this research was to determine the efficiency (partial nutrient balance, PNB) of different methods (foliar and fertrigation) and forms (chelates and salts) of microelements application in relation to the levels of N fertilization in apple orchard cultivar (‘Golden Delicious’). The combined effects of these fertilizers on the number of apple fruits per tree and on the yield per tree were also studied. Foliar application of Mn, Zn and Fe had significantly higher partial nutrient balance values compared to the soil application in both years of the experiment. However, most of the PNB values were below 10% indicating relatively low efficiency of the applied fertilizers with microelements

Robust, Universal Tree Balance Indices

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet existing indices are not defined for all rooted trees, are unreliable for comparing trees with different numbers of leaves, and are sensitive to the presence or absence of rare types. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless’ index but can account for population sizes, are defined for trees with any degree distribution, and enable meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalised reciprocal of Sackin’s index. Hence we both unify and generalise the two most popular existing tree balance indices. Our indices are intrinsically normalised and can be computed in linear time. We conclude that these more widely applicable indices have potential to supersede those in current use

Effects of L-ascorbic acid and alpha-tocopherol on biochemical parameters of swimming-induced oxidative stress in serum of guinea pigs

Background: The purpose of this study is to determine the effect of L-ascorbic acid and alpha-tocopherol as well as combination of these vitamins with or without exposure to physical exercise on intensity of lipid peroxidation, activity of xanthine oxidase, activity of total antioxidative system, concentration of glutathione, and activity of catalase in the serum of guinea pigs.Materials and Methods: The experimental measurements of intensity of lipid peroxidation, activity of xanthine oxidase, activity of total antioxidative system, concentration of glutathione, and activity of catalase were done in the serum of guinea pigs. The animals were exposed to the test load to achieve exhaustion and the test was terminated when the animal for the third time to sink into the water.Results: The results of this study demonstrated that endurance exercise of guinea pigs induced oxidative stress response in terms of increased lipid peroxidation and activity of xanthine oxidase in the serum of experimental animals. Our study investigated the antioxidant activity of L-ascorbic acid and alpha-tocopherol also measuring three protective markers in the serum: total antioxidant activity, content of glutathione and activity of catalase. The results obtained show that the vitamins influence the concentrations of above mentioned biochemical parameters, which points out their protective effect of swimming-induced oxidative stress.Conclusion: Single or combined administration of L-ascorbic acid and alpha-tocopherol caused significant inhibition of these markers indicating the important antioxidant activity of the vitamins. Results lead to conclude that the combined treatments with vitamins with or without exposure to physical exercise showed the clear synergistic effect.Key words: L-ascorbic acid, alpha-tocopherol, guinea pigs, oxidative stress,  biochemical parameter

Gravitational waves and dragging effects

Linear and rotational dragging effects of gravitational waves on local inertial frames are studied in purely vacuum spacetimes. First the linear dragging caused by a simple cylindrical pulse is investigated. Surprisingly strong transversal effects of the pulse are exhibited. The angular momentum in cylindrically symmetric spacetimes is then defined and confronted with some results in literature. In the main part, the general procedure is developed for studying weak gravitational waves with translational but not axial symmetry which can carry angular momentum. After a suitable averaging the rotation of local inertial frames due to such rotating waves can be calculated explicitly and illustrated graphically. This is done in detail in the accompanying paper. Finally, the rotational dragging is given for strong cylindrical waves interacting with a rotating cosmic string with a small angular momentum.Comment: Scheduled to appear in Class. Quantum Grav. July 200

Vascular anatomy of the thenar eminence: its relevance to a pedicled or free thenar flap

Background: The aim of this study was to clarify the arterial supply of the skin covering the prominent part of the thenar eminence in order to describe the possibility and potential for harvesting a pedicled or a free flap from the thenar eminence. Materials and methods: The arteries were studied in 30 post-mortem specimens of human hands; 3 previously perfused with 4% formaldehyde solution, and injected with black India ink, and 27 injected with methyl-methacrylate and afterwards corroded in 40% potassium hydroxide solution. Results: In all hands we found two little palmar arteries coming from the anatomical snuff-box portion of the radial artery. We labelled the first (proximal) branch as the middle thenar artery, because it supplies the middle third of the thenar eminence skin. Its diameter varied from 0.25 to 0.55 mm (mean 0.4 mm). The distal, more prominent branch of the radial artery, vascularised the lateral third of the thenar eminence skin, and was named the lateral thenar artery; its diameter ranged from 0.40 to 0.90 mm (mean 0.67 mm). The superficial palmar branch of the radial artery, always present, was classified as: hypoplastic, average or prominent, with a diameter ranging from 0.8 to 2.7 mm (mean 1.47 mm). Conclusions: Three individually developed branches of the radial artery supplied the skin of the thenar eminence. Cutaneous branches of these three arteries were interconnected via anastomotic vessels

The effect of ovariectomy on thyroid c cells of adult rats

The structure and function of C cells of adult female rats after ovariectomy (Ovx) were investigated. Intact control and Ovx rats were i.p. treated with sterile olive oil for 4 weeks. Peroxidase-antiperoxidase (PAP) immunohistochemical procedure was applied to localize calcitonin (CT) in thyroid C cells while its serum content was determined by RIA method. Morphometric analyses of the C cells volume, that of their nuclei and relative volume density included stereological method with the multipurpose test system M42. Also, the average number of C cells number per mm2 was calculated. Ovx led to a significant increase in body weight (21%; p<0.005). At the same time the C cells of Ovx rats had a significantly decreased cell volume (13%; p<0.005) and their number per mm2 was increased by 59% (p<0.001) in comparison with the controls. Ovx resulted in reduction of serum CT level by 45% comparing to the corresponding controls. Based on these data it can be concluded that Ovx inhibits both the structure and function of the C cells.U ovom radu ispitivana je struktura i funkcija C ćelija adultnih ženki pacova posle ovarijektomije (Ovx). Intaktne kontrolne i Ovx životinje su tretirane i.p. sterilnim maslinovim uljem u trajanju od četiri nedelje. Za lokalizaciju kalcitonina (CT) u C ćelijama štitaste žlezde korišćena je imunohistohemijska metoda peroksidaze- antiperoksidaze (PAP). Nivo CT-a u serumu određen je RIA metodom. Morfometrijska ispitivanja volumena C ćelija, njihovih jedara i relativne volumenske gustine ćelija vršena su višenamenskim testnim sistemom M42. Takođe je izračunat broj C ćelija po mm2. Statistička obrada podataka vršena je Studentovim t-testom. Posle Ovx-a telesna masa životinja značajno je povećana za 21% (p<0.005). Volumen C ćelija Ovx pacova značajno je smanjen za 13% (p<0.005), njihov broj po mm2 povećan za 59% (p<0.001), a nivo CT-a u serumu smanjen za 45% u poređenju sa intaktnom kontrolom. Na osnovu dobijenih rezultata možemo zaključiti da Ovx deluje inhibitorno na strukturu i funkciju C ćelija štitaste žlezde kod pacova