Schatten classes for Toeplitz operators with Hilbert space windows on modulation spaces

We prove that if ω, ω₁, ω₂, v₁, v₂ are appropriate, , j=1,2, and ωa∈Lp, then the Toeplitz operator Tph₁,h₂(a) from to belongs to the Schatten-von Neumann class of order p. From this property we prove convolution properties between weighted Lebesgue spaces and Schatten-von Neumann classes of symbols in pseudo-differential calculus.     

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.     

Atmospheric chemistry of a model biodiesel fuel, CH3C(O)O(CH2)2OC(O)CH3: kinetics, mechanisms, and products of Cl atom and OH radical initiated oxidation in the presence and absence of NOx

Relative rate techniques were used to study the kinetics of the reactions of Cl atoms and OH radicals with ethylene glycol diacetate, CH3C(O)O(CH2)2OC(O)CH3, in 700 Torr of N2/O2 diluent at 296 K. The rate constants measured were k(Cl + CH3C(O)O(CH2)2OC(O)CH3) = (5.7 +/- 1.1) x 10(-12) and k(OH + CH3C(O)O(CH2)2OC(O)CH3) = (2.36 +/- 0.34) x 10(-12) cm3 molecule-1 s-1. Product studies of the Cl atom initiated oxidation of ethylene glycol diacetate in the absence of NO in 700 Torr of O2/N2 diluent at 296 K show the primary products to be CH3C(O)OC(O)CH2OC(O)CH3, CH3C(O)OC(O)H, and CH3C(O)OH. Product studies of the Cl atom initiated oxidation of ethylene glycol diacetate in the presence of NO in 700 Torr of O2/N2 diluent at 296 K show the primary products to be CH3C(O)OC(O)H and CH3C(O)OH. The CH3C(O)OCH2O* radical is formed during the Cl atom initiated oxidation of ethylene glycol diacetate, and two loss mechanisms were identified: reaction with O2 to give CH3C(O)OC(O)H and alpha-ester rearrangement to give CH3C(O)OH and HC(O) radicals. The reaction of CH3C(O)OCH2O2* with NO gives chemically activated CH3C(O)OCH2O* radicals which are more likely to undergo decomposition via the alpha-ester rearrangement than CH3C(O)OCH2O* radicals produced in the peroxy radical self-reaction.     

Atmospheric chemistry of CF3CH=CH2 and C4F9CH=CH2: products of the gas-phase reactions with Cl atoms and OH radicals

FTIR-smog chamber techniques were used to study the products of the Cl atom and OH radical initiated oxidation of CF3CH=CH2 in 700 Torr of N2/O2, diluent at 296 K. The Cl atom initiated oxidation of CF3CH=CH2 in 700 Torr of air in the absence of NOx gives CF3C(O)CH2Cl and CF3CHO in yields of 70+/-5% and 6.2+/-0.5%, respectively. Reaction with Cl atoms proceeds via addition to the >C=C< double bond (74+/-4% to the terminal and 26+/-4% to the central carbon atom) and leads to the formation of CF3CH(O)CH2Cl and CF3CHClCH2O radicals. Reaction with O2 and decomposition via C-C bond scission are competing loss mechanisms for CF3CH(O)CH2Cl radicals, kO2/kdiss=(3.8+/-1.8)x10(-18) cm3 molecule-1. The atmospheric fate of CF3CHClCH2O radicals is reaction with O2 to give CF3CHClCHO. The OH radical initiated oxidation of CxF2x+1CH=CH2 (x=1 and 4) in 700 Torr of air in the presence of NOx gives CxF2x+1CHO in a yield of 88+/-9%. Reaction with OH radicals proceeds via addition to the >C=C< double bond leading to the formation of CxF2x+1C(O)HCH2OH and CxF2x+1CHOHCH2O radicals. Decomposition via C-C bond scission is the sole fate of CxF2x+1CH(O)CH2OH and CxF2x+1CH(OH)CH2O radicals. As part of this work a rate constant of k(Cl+CF3C(O)CH2Cl)=(5.63+/-0.66)x10(-14) cm3 molecule-1 s-1 was determined. The results are discussed with respect to previous literature data and the possibility that the atmospheric oxidation of CxF2x+1CH=CH2 contributes to the observed burden of perfluorocarboxylic acids, CxF2x+1COOH, in remote locations.     

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.     

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.     

Gabor pairs,and a discrete approach to wave-front sets

We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of “continuous type”. This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f.     

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.