A multidimensional real Schwarz Lemma for the Hilbert metric

We present a real multidimensional version of the Schwarz Lemma on a bounded convex domain D of ℝ ⁿ endowed with the Hilbert metric. We provide as an application an extension of a Birkhoff’s Theorem on mappings contracting the Hilbert metric.     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

Thermal momentum distribution from path integrals with shifted boundary conditions

For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.     

Real-time digital holographic microscopy of multiple and arbitrarily oriented planes

Digital holographic microscopy is used to numerically refocus a recorded hologram at an arbitrary axial distance. However, as a straightforward property of coherent light fields, image reconstruction on an arbitrary tilted plane could be directly obtained by a rotation in k-space. We demonstrate that this property allows the real-time microscopic inspection of particle distribution over three mutually orthogonal planes at the same time. As a straightforward application we use the proposed technique for real-time monitoring of fluid flow over the three cross sections of a microfluidic channel.     

Spherical and non-spherical bubbles in cosmological phase transitions

The cosmological remnants of a first-order phase transition generally depend on the perturbations that the walls of expanding bubbles originate in the plasma. Several of the formation mechanisms occur when bubbles collide and lose their spherical symmetry. However, spherical bubbles are often considered in the literature, in particular for the calculation of gravitational waves. We study the steady state motion of bubble walls for different bubble symmetries. Using the bag equation of state, we discuss the propagation of phase transition fronts as detonations and subsonic or supersonic deflagrations. We consider the cases of spherical, cylindrical and planar walls, and compare the energy transferred to bulk motions of the relativistic fluid. We find that the different wall geometries give similar perturbations of the plasma. For the case of planar walls, we obtain analytical expressions for the kinetic energy in the bulk motions. As an application, we discuss the generation of gravitational waves.     

Complete minimal hypersurfaces in quaternionic hyperbolic space

We construct new examples of embedded, complete minimal hypersurfaces in quaternionic hyperbolic space and also some minimal foliations. We introduce fans and construct analytic deformations of bisectors.     

Synthesis of Lewis a and Lewis X Pentasaccharides Based on N-Trichloroethoxycarbonyl Protection 1

Abstract

Thexyldimethylsilyl 4,6-O-benzylidene-2-deoxy-2-trichloroethoxycarbonylamino-β-D- glucopyranoside (4), having the 3-hydroxy group unprotected, is a versatile starting material for the synthesis of glucosamine containing oligosaccharides. Thus, reaction with galactosyl donor 5 or fucosyl donor 6 afforded the desired β(1-3)- and α(1-3)-linked disaccharides 7 and 8, respectively, in high yields. Reductive opening of the benzylidene moieties in 7 and 8 gave access to the 4-hydroxy groups in 9 and 10. Ensuing fucosylation of 9 or galactosylation of 10 led to Lewis A (Le^a) and Lewis X (Le^x) trisaccharide building blocks 13 and 14, respectively. Their transformation into glycosyl donors 19 and 20 and subsequent reaction with 3b-O-unprotected lactose derivative 23 as acceptor furnished the Le^a? and Le^x pentasaccharide precursors 24 and 25. Exchange of the N-trichloroethoxycarbonyl group for an N-acetyl group and removal of the O-benzyl and O-acetyl protective groups afforded the desired Le^a? and Le^x? pentasaccharides 1 and 2.

     

Bioreduction of β-carboline imines to amines employing Saccharomyces bayanus

β-Carboline imine reductions mediated by Saccharomyces bayanus have been described achieving moderate to good enantiomeric excesses of the amine products. The enantiomeric excesses of the bioreduction showed a dependence on the imine substituents. Compounds presenting C₁–C₁₁ aliphatic substituent groups afforded amines with an (S)-configuration, whereas C₁₅ and higher aliphatic- and aromatic-substituted β-carboline imines achieved inversion of the configuration in the final (R)-2 amine products. Based on this data, a model for the Saccharomyces reduction is proposed.