On quantum stochastic dynamics and noncommutative\mathbb{L}_p spaces

We show that using the thermodynamic limit, one can give a simple and natural construction of noncommutative spaces for quantum systems on a lattice. Within this framework, we discuss the construction and ergodicity properties of stochastic dynamics of spin flip and diffusion type.     

Efficient Palladium(0)-Catalyzed Synthesis of Alkenyl 1-Thioglycosides and Thiodisaccharides

ABSTRACT

Unsaturated thiodisaccharides are obtained in good yields by alkylation of ethyl α-O-?²-glycosides, having a leaving group at C-4, with various thiocarbohydrates in the presence of a catalytic amount of palladium(0). The reaction is regio- and stereospecific for the α-erythro enoside, and only stereospecific in the case of the α-threo enoside, alkylation occurring at C-4 and C-2. In all cases, only the β-anomer is formed.     

DIRECTIONAL DO-NOTHING CONDITION FOR THE NAVIER-STOKES EQUATIONS

The numerical solution of flow problems usually requires bounded domains although the physical problem may take place in an unbounded or substantially larger domain. In this case, artificial boundaries are necessary. A well established artificial boundary condition for the Navier-Stokes equations diseretized by finite elements is the “do-nothing” condition. The reason for this is the fact that this condition appears automatically in the variational formulation after partial integration of the viscous term and the pressure gradient. This condition is one of the most established outflow conditions for Navier-Stokes but there are very few analytical insight into this boundary condition. We address the question of existence and stability of weak solutions for the Navier-Stokes equations with a “directional do-nothing” condition. In contrast to the usual “do-nothing” condition this boundary condition has enhanced stability properties. In the case of pure outflow, the condition is equivalent to the original one, whereas in the case of inflow a dissipative effect appears. We show existence of weak solutions and illustrate the effect of this boundary condition by computation of steady and non-steady flows.     

Simultaneous treatment of polymer surface by EUV radiation and ionized nitrogen

In this paper chemical modification of a poly(vinylidene fluoride) surface by extreme ultraviolet (EUV) irradiation in a presence of ionized nitrogen was demonstrated for the first time. Nitrogen gas, injected into an interaction region, was ionized and excited by the EUV radiation from a laser-plasma source. The ionization degree and excited states of nitrogen were investigated using EUV spectrometry and the corresponding spectra are presented. Chemical modification of polymer after combined EUV and ionized nitrogen treatment was investigated using X-ray photoelectron spectroscopy. A?significant contribution of nitrogen atoms in near-surface layer of the polymer after the treatment was demonstrated.     

Effect of stationary phase polarity on the retention of ionic liquid cations in reversed phase liquid chromatography

Chromatographic analysis of ionic liquids on different types of packings offers interesting possibility to determine their retention mechanism. As a consequence, the major interactions between stationary phase ligands and analyzed chemical entities can be defined. The main aim of this work was to analyze cations of ionic liquids on chemically bonded stationary phases with specific structural properties. The attempt to predict the main interactions between positive ions of ionic liquids and stationary phase ligands was undertaken. For that purpose, butyl, octyl, octadecyl, phenyl, aryl, mixed, alkylamide, and cholesterolic packings were chosen and applied to the analysis of six most commonly used ionic liquids' cations. Obtained results indicate mainly dispersive and pi-pi type of interaction part in the retention mechanism of analyzed compounds.     

Detection of T2 changes in an early mouse brain tumor

The aim of the study was to determine the effect of early tumor growth on T₂ relaxation times in an experimental glioma model. A 9.4-T magnetic resonance imaging (MRI) system was used for the investigations. An animal model (n=12) of glioma was established using an intracranial inoculation of U87MGdEGFRvIII cells. The imaging studies were performed from Day 10 through Day 13 following tumor inoculation. Tumor blood vessel density was determined using quantitative immunochemistry. Tumor volume was measured daily using MR images. T₂ values of the tumor were measured in five areas across the tumor and calculated using a single exponential fitting of the echo train. The measurements on Days 10 and 13 after tumor inoculation showed a 20% increase in T₂. The changes in T₂ correlated with the size of the tumor. Statistically significant differences in T₂ values were observed between the edge of the tumor and the brain tissue on Days 11, 12 and 13 (P=.014, .008, .001, respectively), but not on Day 10 (P=.364). The results show that T₂-weighted MRI may not detect glioma during an early phase of growth. T₂ increases in growing glioma and varies heterogenously across the tumor.     

Asymmetric palladium-catalyzed annulation of benzene-1,2-diol and racemic secondary propargylic carbonates bearing two different substituents

The palladium-catalyzed cyclization of benzene-1,2-diol with various racemic secondary propargyl carbonates having no acetylenic hydrogen in the presence of (R)-Binap as the chiral ligand afforded the two regioisomers of the corresponding 2,3-dihydro-1,4-dioxin derivatives in quite good yields, and also in enantioselectivities going from 40 to 97%. The cyclization of benzene-1,2-diol with methyl (R)-1-methyl-3-phenylpro-2-yn-1-yl carbonate in the presence of dppb as the achiral ligand afforded 2-benzylidene-3-methyl-2,3-dihydro-1,4-benzodioxine as the major product with 15% ee. The use of (R)-Binap as the chiral ligand afforded the (+) cyclized compound in 45% ee, when the (−) enantiomer was obtained with 77% ee in the presence of (S)-Binap. All the results suggest that in this case the enantioselective step is the diastereoselective protonation of the palladium-carbene intermediates.     

B1 transmit phase gradient coil for single-axis TRASE RF encoding

Purpose

TRASE (Transmit Array Spatial Encoding) MRI uses RF transmit phase gradients instead of B₀ field gradients for k-space traversal and high-resolution MR image formation. Transmit coil performance is a key determinant of TRASE image quality. The purpose of this work is to design an optimized RF transmit phase gradient array for spatial encoding in a transverse direction (x- or y- axis) for a 0.2 T vertical B₀ field MRI system, using a single transmitter channel. This requires the generation of two transmit B₁ RF fields with uniform amplitude and positive and negative linear phase gradients respectively over the imaging volume.

Materials and Methods

A two-element array consisting of a double Maxwell-type coil and a Helmholtz-type coil was designed using 3D field simulations. The phase gradient polarity is set by the relative phase of the RF signals driving the simultaneously energized elements.

Results

Field mapping and 1D TRASE imaging experiments confirmed that the constructed coil produced the fields and operated as designed. A substantially larger imaging volume relative to that obtainable from a non-optimized Maxwell-Helmholtz design was achieved.

Conclusion

The Maxwell (sine)–Helmholtz (cosine) approach has proven successful for a horizontal phase gradient coil. A similar approach may be useful for other phase-gradient coil designs.