Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Negishi Cross-Coupling Provides Alkylated Tryptophans and Tryptophan Regioisomers

Mild transition-metal catalysed cross-couplings enable direct functionalisation of biocatalytically halogenated tryptophans with alkyl iodides, representing a new alternative for late-stage derivatisations of halogenated aromatic amino acids. Moreover, this strategy enables preparation of (homo)tryptophan regioisomers in a simple two-step synthesis using a Pd-catalysed Negishi cross coupling. This method provides access to non-canonical constitutional surrogates of tryptophan, ready for use in peptide synthesis.     

Comparison of T-piece and concentric mixing systems for continuous flow synthesis of anatase nanoparticles in supercritical isopropanol/water

T-piece and concentric counter-flow mixing systems are compared in continuous flow supercritical solvothermal synthesis of TiO₂ at identical system parameters. The phase pure anatase nanoparticle products were characterized with powder X-ray diffraction (PXRD), transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS), and the particle size, size distribution and absolute crystallinity mapped as a function of temperature, precursor concentration, flow rate and pressure for the two different continuous flow reactors. The particles synthesized with the T-piece geometry are smaller with a narrower size distribution, possibly indicating a more effective mixing, than particles synthesized at the same conditions with concentric counter-flow geometry. In general, an increased synthesis temperature leads to an increase in absolute crystallinity. For the particles synthesized with the concentric reactor geometry crossing of the critical point of the solvent causes a decrease in the particle size and size distribution, and conditions just above the critical temperature are demonstrated to be optimal for continuous solvothermal synthesis of anatase.     

Novel suberin‐based biopolyesters: From synthesis to properties

This article reports the successful synthesis and characterization of two types of completely biobased polymers prepared by the polycondensation or polytransesterification of suberin fragments, isolated by different procedures and from two different vegetable sources. These polymerizations were conducted with different experimental conditions in terms of the type of catalyst, the reaction medium and temperature, as well as the molar ratio between the reactive moieties. The ensuing linear or partly crosslinked polyesters were characterized by conventional spectroscopic techniques, SEC, DSC, XRD, DMA, and TGA. These hydrophobic materials represent an original contribution to the growing field of polymers from renewable resources. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Global Wave-Front Properties for Fourier Integral Operators and Hyperbolic Problems

We illustrate the composition properties for an extended family of \({\text {SG}}\) Fourier integral operators. We prove continuity results on modulation spaces, and study mapping properties of global wave-front sets for such operators. These extend classical results to more general situations. For example, there are no requirements on homogeneity for the phase functions. Finally, we apply our results to the study of the propagation of singularities, in the context of modulation spaces, for the solutions to the Cauchy problems for the corresponding linear hyperbolic operators.     

SYNTHESIS OF SALICYLTHIOAMIDES AND 4 H-1, 3, 2 BENZOXAZAPHOSPHORIN-DERIVATIVES

Abstract

Recent studies have shown that the dimer of p-methoxyphenylthionophosphinesulfide, 1, is a very superior thiation reagent, as ketones, amides, and esters are in most cases quantitatively converted to their thio-analogues.     

Shadow effects in simulated ultrasound images derived from computed tomography images using a focused beam tracing model

Simulation of ultrasound images based on computed tomography (CT) data has previously been performed with different approaches. Shadow effects are normally pronounced in ultrasound images, so they should be included in the simulation. In this study, a method to capture the shadow effects has been developed, which makes the simulated ultrasound images appear more realistic. The method using a focused beam tracing model gives diffuse shadows that are similar to the ones observed in measurements on real objects. Ultrasound images of a cod (Gadus morhua) were obtained with a BK Medical 2202 ProFocus ultrasound scanner (BK Medical, Herlev, Denmark) equipped with a dedicated research interface giving access to beamformed radio frequency data. CT images were obtained with an Aquilion ONE Toshiba CT scanner (Toshiba Medical Systems Corp., Tochigi, Japan). CT data were mapped from Hounsfield units to backscatter strength, attenuation coefficients, and characteristic acoustic impedance. The focused beam tracing model was used to create maps of the transmission coefficient and scattering strength maps. Field II was then used to simulate an ultrasound image of 38.9 × 55.3 × 4.5 mm, using 10(6) point scatterers. As there is no quantitative method to assess quality of a simulated ultrasound image compared to a measured one, visual inspection was used for evaluation.     

Schatten–von Neumann properties for Fourier integral operators with non-smooth symbols,I

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We prove continuity and Schatten–von Neumann properties of such operators when acting on L ².     

Spectral Properties for Matrix Algebras

We consider Banach algebras of infinite matrices defined in terms of a weight measuring the off-diagonal decay of the matrix entries. If a given matrix $A$ is invertible as an operator on $\ell ^2$ we analyze the decay of its inverse matrix entries in the case where the matrix algebra is not inverse closed in ${\mathcal B} (\ell ^2),$ the Banach algebra of bounded operators on $\ell ^2.$ To this end we consider a condition on sequences of weights which extends the notion of GRS-condition. Finally we focus on the behavior of inverses of pseudodifferential operators whose Weyl symbols belong to weighted modulation spaces and the weights lack the GRS condition.