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

On moduli of rings and quadrilaterals: algorithms and experiments

Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by K\"uhnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new $hp$-FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the $hp$-FEM algorithm applies to the case of non-polygonal boundary and report results with concrete error bounds

Lifelong guidance policy and practice in the EU

A study on lifelong guidance (LLG) policy and practice in the EU focusing on trends, challenges and opportunities. Lifelong guidance aims to provide career development support for individuals of all ages, at all career stages. It includes careers information, advice, counselling, assessment of skills and mentoring

On Jordan type inequalities for hyperbolic functions

This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.Comment: 16 page

Nuclear antiferromagnetism in rhodium metal at positive and negative nanokelvin temperatures

We have measured the dynamic susceptibility of polycrystalline rhodium foils down to 280 pK and up to -750 pK. These record-low and -high nuclear spin temperatures were reached by adiabatic demagnetization using initial polarizations of 83 and -60%. At T>0, the static susceptibility, integrated from NMR spectra, displays an antiferromagnetic Curie-Weiss law, with θ=-1.8±0.3 nK. At T<0, a crossover from ferro- to antiferromagnetic tendency is found around -6 nK. We obtain Jnn/h=-17±3 Hz and Jnnn/h=10±3 Hz if only nearest and next nearest neighbor interactions are assumed.Peer reviewe

Spin dynamics in highly polarized silver at negative absolute temperatures

We have studied the spin dynamics of highly polarized silver nuclei at negative absolute temperatures up to inverted polarizations p≃-70%. The measured NMR spectra at B=0.4 and 0.8 mT display a clear inverted suppression-enhancement effect, arising from an interaction between the two spin species, 107Ag and 109Ag. The averaged interaction-field description accounts well for the intensity ratio of the isotopic NMR lines. The frequency difference of the absorption maxima has been used to study the merging and repulsion of the NMR modes at large negative polarizations. At B=0.2 mT, our spectra display only a single exchange-merged line, indicating that the two isotopes act as like spins. The transition from a single NMR line to two separate lines proceeds in a similar fashion as at positive temperatures. No effects attributable to the tendency of ferromagnetic alignment of spins at T<0 were observed.Peer reviewe

Polymerase Chain Reaction Assay With Urine Specimens in the Diagnosis of Acute Chlamydia trachomatis Infection in Women

Objective: The purpose of this study was to evaluate the benefits achievable by Amplicor polymerase chain reaction (PCR) (F. Hoffmann-LaRoche Ltd., Basel, Switzerland) with urine specimens in addition to PACE 2 (Gen-Probe, Inc., San Diego, California) assay with cervical swab specimens in the diagnosis of Chlamydia trachomatis in women

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