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

Leaded tin bronzes: the effects of casting method on dry sliding behaviour

In metal-to-metal sliding bearing applications, leaded tin bronzes are widely known as materials with excellent seizure resistance. In conditions of boundary or dry lubrication, lead may smear across the sliding surface, preventing surface contact and catastrophic seizure. The aim of this study was to determine the effects of casting method on the dry sliding behaviour of leaded tin bronzes. Continuous cast, centrifugally cast, and sand cast leaded tin bronze samples with varying lead contents were subjected to pin-on-disk- testing. It was found that casting method has a significant effect on the wear behaviour of leaded tin bronzes in dry sliding conditions. With continuous cast samples, the dominant wear mode was rapid, stable microcracking along copper/lead interfacial boundaries. With centrifugally and sand cast samples, wear occurred more slowly and erratically through the formation of transfer layers. The dominant wear mode was found to be connected to the coarseness of the distribution of lead particles in the copper matrix

Generalized Elliptic Integrals and the Legendre M-function

We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwarz-Christoffel conformal mapping from a half-plane to a trapezoid. We obtain sharp monotonicity and convexity results for combinations of these functions, as well as functional inequalities and a linearization property.Comment: 28 page

Observation of nuclear ferromagnetic ordering in silver at negative nanokelvin temperatures

The ferromagnetically ordered state in the nuclear spin system of silver has been reached at negative absolute temperatures by adiabatic nuclear demagnetization at entropies below 0.82 ln2. The ordering, caused by the antiferromagnetic Ruderman-Kittel interaction, was observed below -1.9 nK as a saturation of susceptibility close to -1 and as an increase of the NMR frequencies. Comparison with recent mean-field calculations by Viertiö and Oja suggests a domain configuration. The phase diagram of silver nuclei at T<0 is outlined in the magnetic field versus entropy plane.Peer reviewe

The pressure of deconfined QCD for all temperatures and quark chemical potentials

We present a new method for the evaluation of the perturbative expansion of the QCD pressure which is valid at all values of the temperature and quark chemical potentials in the deconfined phase and which we work out up to and including order g^4 accuracy. Our calculation is manifestly four-dimensional and purely diagrammatic -- and thus independent of any effective theory descriptions of high temperature or high density QCD. In various limits, we recover the known results of dimensional reduction and the HDL and HTL resummation schemes, as well as the equation of state of zero-temperature quark matter, thereby verifying their respective validity. To demonstrate the overlap of the various regimes, we furthermore show how the predictions of dimensional reduction and HDL resummed perturbation theory agree in the regime T~\sqrt{g}*mu. At parametrically smaller temperatures T~g*mu, we find that the dimensional reduction result agrees well with those of the nonstatic resummations down to the remarkably low value T~0.2 m_D, where m_D is the Debye mass at T=0. Beyond this, we see that only the latter methods connect smoothly to the T=0 result of Freedman and McLerran, to which the leading small-T corrections are given by the so-called non-Fermi-liquid terms, first obtained through HDL resummations. Finally, we outline the extension of our method to the next order, where it would include terms for the low-temperature entropy and specific heats that are unknown at present.Comment: 45 pages, 21 figures; v2: minor corrections and clarifications, references added; v3: Fig 16 added, version accepted for publication in PR

Dimensional reduction of the Standard Model coupled to a new singlet scalar field

We derive an effective dimensionally reduced theory for the Standard Model augmented by a real singlet scalar. We treat the singlet as a superheavy field and integrate it out, leaving an effective theory involving only the Higgs and SU(2)(L) x U(1)(y) gauge fields, identical to the one studied previously for the Standard Model. This opens up the possibility of efficiently computing the order and strength of the electroweak phase transition, numerically and nonperturbatively, in this extension of the Standard Model. Understanding the phase diagram is crucial for models of electroweak baryogenesis and for studying the production of gravitational waves at thermal phase transitions.Peer reviewe

The Anabolic Androgenic Steroid Fluoxymesterone Inhibits 11β-Hydroxysteroid Dehydrogenase 2-Dependent Glucocorticoid Inactivation

Anabolic androgenic steroids (AAS) are testosterone derivatives used either clinically, in elite sports, or for body shaping with the goal to increase muscle size and strength. Clinically developed compounds and nonclinically tested designer steroids often marketed as food supplements are widely used. Despite the considerable evidence for various adverse effects of AAS use, the underlying molecular mechanisms are insufficiently understood. Here, we investigated whether some AAS, as a result of a lack of target selectivity, might inhibit 11β-hydroxysteroid dehydrogenase 2 (11β-HSD2)-dependent inactivation of glucocorticoids. Using recombinant human 11β-HSD2, we observed inhibitory effects for several AAS. Whereas oxymetholone, oxymesterone, danazol, and testosterone showed medium inhibitory potential, fluoxymesterone was a potent inhibitor of human 11β-HSD2 (half-maximal inhibitory concentration [IC50] of 60-100nM in cell lysates; IC50 of 160nM in intact SW-620, and 530nM in MCF-7 cells). Measurements with rat kidney microsomes and lysates of cells expressing recombinant mouse 11β-HSD2 revealed much weaker inhibition by the AAS tested, indicating that the adverse effects of AAS-dependent 11β-HSD2 inhibition cannot be investigated in rats and mice. Furthermore, we provide evidence that fluoxymesterone is metabolized to 11-oxofluoxymesterone by human 11β-HSD2. Structural modeling revealed similar binding modes for fluoxymesterone and cortisol, supporting a competitive mode of inhibition of 11β-HSD2-dependent cortisol oxidation by this AAS. No direct modulation of mineralocorticoid receptor (MR) function was observed. Thus, 11β-HSD2 inhibition by fluoxymesterone may cause cortisol-induced MR activation, thereby leading to electrolyte disturbances and contributing to the development of hypertension and cardiovascular diseas