Implicit-explicit multistep methods for quasilinear parabolic equations

Summary. Efficient combinations of implicit and explicit multistep methods for nonlinear parabolic equations were recently studied in [1]. In this note we present a refined analysis to allow more general nonlinearities. The abstract theory is applied to a quasilinear parabolic equation. Received March 10, 1997 / Revised version received March 2, 1998     

On integrability of certain rank 2 sub-Riemannian structures

We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows.     

Elimination of motion,pulsatile flow and cross-talk artifacts using blade sequences in lumbar spine MR imaging

The purpose of this study is to evaluate the ability of T2 turbo spin echo (TSE) axial and sagittal BLADE sequences in reducing or even eliminating motion, pulsatile flow and cross-talk artifacts in lumbar spine MRI examinations. Forty four patients, who had routinely undergone a lumbar spine examination, participated in the study. The following pairs of sequences with and without BLADE were compared: a) T2 TSE Sagittal (SAG) in thirty two cases, and b) T2 TSE Axial (AX) also in thirty two cases. Both quantitative and qualitative analyses were performed based on measurements in different normal anatomical structures and examination of seven characteristics, respectively. The qualitative analysis was performed by experienced radiologists. Also, the presence of image motion, pulsatile flow and cross-talk artifacts was evaluated. Based on the results of the qualitative analysis for the different sequences and anatomical structures, the BLADE sequences were found to be significantly superior to the conventional ones in all the cases. The BLADE sequences eliminated the motion artifacts in all the cases. In our results, it was found that in the examined sequences (sagittal and axial) the differences between the BLADE and conventional sequences regarding the elimination of motion, pulsatile flow and cross-talk artifacts were statistically significant. In all the comparisons, the T2 TSE BLADE sequences were significantly superior to the corresponding conventional sequences regarding the classification of their image quality. In conclusion, this technique appears to be capable of potentially eliminating motion, pulsatile flow and cross-talk artifacts in lumbar spine MR images and producing high quality images in collaborative and non-collaborative patients.     

Comparison of PD BLADE with fat saturation (FS), PD FS and T2 3D DESS with water excitation (WE) in detecting articular knee cartilage defects

The purpose of this study, is to compare the sequences: 1) proton density (PD) BLADE (BLADE is a PROPELLER-equivalent implementation of the Siemens Medical System) with fat saturation (FS) coronal (COR), 2) PD FS COR, 3) multi-planar reconstruction (MPR) with 3 mm slice thickness and 4) multi-planar reconstruction (MPR) with 1.5 mm slice thickness, both from the T2 3D-double-echo steady state (DESS) with water excitation (WE) sagittal (SAG), regarding their abilities to identify changes in the femorotibial condyle cartilage in knee MRI examinations. Thirty three consecutive patients with osteoarthritis (18 females, 15 males; mean age 56 years, range 37–71 years), who had been routinely scanned for knee examination using the previously mentioned image acquisition techniques, participated in the study. A quantitative analysis was performed based on the relative contrast (ReCON) measurements, which were taken both on normal tissues as well as on pathologies. Additionally, a qualitative analysis was performed by two radiologists. Motion and pulsatile flow artifacts were evaluated. The PD BLADE FS COR sequence produced images of higher contrast between Menisci and Cartilage, Fluid and Cartilage, Pathologies and Cartilage as well as of the Conspicuousness Superficial Cartilage and it was found to be superior to the other sequences (p < 0.001). The sequences T2 3D DESS 1.5 mm and T2 3D DESS 3 mm were significantly superior to the PD BLADE FS COR and the PD FS COR sequences in the visualization of Bone and Cartilage and the Conspicuousness Deep Surface Cartilage. This pattern of results is also confirmed by the quantitative analysis. PD FS BLADE sequences are ideal for the depiction of the cartilage pathologies compared to the conventional PD FS and T2 3D DESS sequences.     

Hydrophilic interaction ultra performance liquid chromatography retention prediction under gradient elution

The development and application of new separation mechanisms such as hydrophilic interaction chromatography (HILIC) is of high importance for the simultaneous analysis of polar molecules such as primary metabolites. However the retention mechanism in HILIC is not fully understood and as a result retention prediction tools are not at hand for this chromatographic approach. In the present report we study the utility of a simple algorithm, based on a simple linear and/or a simple logarithmic retention model, for retention prediction in HILIC gradient separation of a mixture of 23 selected compounds including (poly)amines, amino acids, saccharides, and other molecules. Utilizing two types of gradient elution programs with or without an isocratic part, retention data were collected in order to build prediction models. Starting from at least three gradient runs the prediction of analyte retention was very satisfactory for all gradient programs tested, providing useful evidence of the value of such retention time prediction methodologies.     

Magnetic anisotropy axis reorientation at ultrathin FePt films

Ultrathin FePt films (thickness between 1 nm and 5 nm) were studied for non‐volatile memories applications. The films were magnetron sputtered on monocrystalline MgO?001? substrates at 500 °C. The films are polycrystalline, except the 1 nm thick film which is not continuous. It is shown that films with thickness higher than 2.7 nm have L1₀ structure and perpendicular magnetic anisotropy, while a transition to in‐plane anisotropy occurs for thinner films. The out‐of‐plane coercivity drops from 16 kOe at the thicker film to 0.5 kOe at the thinner one.

Hysteresis cycles of FePt films as a function of film thickness.     

Hořava–Lifshitz cosmology

The cosmological equations suggested by the non-relativistic renormalizable gravitational theory proposed by Hořava are considered. It is pointed out that the early universe cosmology has features that may give an alternative to inflation and the theory may be able to escape singularities.     

Enhanced sonochemical degradation of bisphenol-A by bicarbonate ions

Sonochemical elimination of organic pollutants can take place through two degradation pathways. Molecules with relatively large Henry’s law constants will be incinerated inside the cavitation bubble, while nonvolatile molecules with low Henry’s law constants will be oxidised by the OH ejected from the bubble of cavitation. Taking bisphenol-A as a model pollutant, this study points out an alternate degradation route, mediated by bicarbonate ions, which is significant for the elimination of micro-pollutants at concentrations present in natural waters. In this process, OH radicals react with bicarbonate ions to produce the carbonate radical, which, unlike the OH radical, can migrate towards the bulk of the solution and therefore induce the degradation of the micro-pollutants present in the bulk solution. As a consequence, initial degradation rate is increased by a factor 3.2 at low concentration of bisphenol-A (0.022 μmol l⁻¹) in presence of bicarbonate in water.