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.     

DTI at 7 and 3 T: systematic comparison of SNR and its influence on quantitative metrics

Diffusion tensor imaging (DTI) and advanced related methods such as diffusion spectrum and kurtosis imaging are limited by low signal-to-noise ratio (SNR) at conventional field strengths. DTI at 7 T can provide increased SNR; however, B0 and B1 inhomogeneity and shorter T2? still pose formidable challenges. The purpose of this study was to quantify and compare SNR at 7 and 3 T for different parallel imaging reduction factors, R, and TE, and to evaluate SNRs influences on fractional anisotropy (FA) and apparent diffusion coefficient (ADC). We found that R>4 at 7 T and R≥2 at 3 T were needed to reduce geometric distortions due to B0 inhomogeneity. For these R at 7 T, SNR was 70-90 for b=0 s/mm² and 22-28 for b=1000s/mm² in central brain regions. SNR was lower at 3 T (40 for b=0 s/mm² and 15 for b=1000 s/mm²) and in lateral brain regions at 7 T due to B1 inhomogeneity. FA and ADC did not change with MRI field strength, SENSE factor or TE in the tested range. However, the coefficient of variation for FA increased for SNR <15 and for SNR <10 in ADC, consistent with published theoretical studies. Our study demonstrates that 7 T is advantageous for DTI and lays the groundwork for further development. Foremost, future work should further address challenges with B0 and B1 inhomogeneity to take full advantage for the increased SNR at 7 T.     

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.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007