Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

Scrambling of autoinducing precursor peptides investigated by infrared multiphoton dissociation with electrospray ionization and Fourier transform ion cyclotron resonance mass spectrometry

Two synthetic precursor peptides, H₂N-CVGIW and H₂N-LVMCCVGIW, involved in the quorum sensing of Lactobacillus plantarum WCFS1, were characterized by mass spectrometry (MS) with electrospray ionization and 7-T Fourier transform ion cyclotron resonance (ESI-FTICR) instrument. Cell-free bacterial supernatant solutions were analyzed by reversed-phase liquid chromatography with ESI-FTICR MS to verify the occurrence of both pentapeptide and nonapeptide in the bacterial broth. The structural characterization of both protonated peptides was performed by infrared multiphoton dissociation using a continuous CO₂ laser source at a wavelength of 10.6 μm. As their fragmentation behavior cannot be directly derived from the primary peptide structure, all anomalous fragments were interpreted as neutral loss of amino acids from the interior of both peptides, i.e., loss of V, G, VG and M, MC, V, CC, from H₂N-CVGIW and H₂N-LVMCCVGIW, respectively. Mechanisms of this scrambling are proposed. FTICR MS provides accurate masses of all fragment ions with very low absolute mass errors (<1.6 ppm), which facilitated the reliable assignment of their elemental compositions. The resolving power was more than sufficient to resolve closely isobaric product ions with routine subparts per million mass accuracies. Only the occurrence of pentapeptide was found in the cell-free culture of L. plantarum, grown in Waymouth’s medium broth, with a low content of 5.2?±?2.6 μM by external calibration. Most of it was present as oxidized H₂N-CVGIW, that is, the soluble disulfide pentapeptide with a level tenfold higher (i.e., 50?±?4 μM, n?=?3).

A novel amperometric biosensor based on a co-crosslinked l-lysine-α-oxidase/overoxidized polypyrrole bilayer for the highly selective determination of l-lysine

An amperometric biosensor for the determination of l-lysine based on l-lysine-α-oxidase immobilized by co-crosslinking on a platinum electrode previously modified by an overoxidized polypyrrole film is described. The optimization of experimental parameters, such as pH and flow rate, permitted to minimize significantly substrate interferences even using a low specific, commercial enzyme. The relevant biases introduced in the measurement of lysine were just about 1% for l-arginine, l-histidine and l-ornithine, roughly 4% for l-phenylalanine and l-tyrosine. The developed approach allowed linear lysine responses from 0.02 mM up to 2 mM with a sensitivity of 41 nA/(mM × mm²) and a detection limit of 4 μM (S/N = 3). No appreciable loss in lysine sensitivity was observed up to about 40 days. Allowing polypyrrole layer to remove interference from electroactive compounds, the present method revealed suitable to detect l-lysine in a pharmaceutical and cheese sample, showing a good agreement with the expected values.     

2D difference gel electrophoresis reference map of a Fusarium graminearum nivalenol producing strain

Fusarium graminearum is widely studied as a model for toxin production among plant pathogenic fungi. A 2D DIGE reference map for the nivalenol‐producing strain 453 was established. Based on a whole protein extract, all reproducible spots were systematically picked and analyzed by MALDI‐TOF/TOF, leading to the identification of 1102 protein species. The obtained map contributes to the annotation of the genome by identifying previously nondescribed hypothetical proteins and will serve as a reference for future studies aiming at deciphering F. graminearum biology and chemotype diversity.     

Trace elements in sediments and bioaccumulation in European silver eels (Anguilla anguilla L.) from a Mediterranean lagoon (SE Italy)

Samples of surface sediments and tissues (liver and muscle) of commercially available European silver eels (Anguilla anguilla L.) collected from Varano lagoon (Italy) were analysed to determine trace element contents. Univariate and multivariate analyses were performed to highlight both the differences between sampling sites and the influence of channel discharges. Atomic ratios indices for sediment data and biological enrichment factors (BEF) for eel tissues were calculated in order to evaluate the enrichment factor due to human activities. The highest levels of As (11.9?µg?g^?1) and Zn (14.1?µg?g^?1) were observed in the south-eastern zone of the lagoon, which is influenced by urban and agricultural discharges. The low levels of Hg observed in this study (0.04?µg?g^?1) led us to exclude both natural and human local sources of this element. Trace element concentrations of all elements were lower in muscle than in liver tissue. Significant enrichment of Cu and Zn was found in livers.     

Mild Microfluidic Approaches to Oxide Nanoparticles Synthesis

Oxide nanoparticles (oxide NPs) are advanced materials with a wide variety of applications in different fields. The use of continuous flow methods is particularly appealing for their synthesis due to the high control achieved over the reaction conditions and the easy process scalability. The present review focuses on the preparation of oxide NPs using microfluidic setups at low temperature (≤80 °C), since the employment of mild reaction conditions is crucial for developing sustainable and cost-effective processes. A particular emphasis will be put on the improvement over the final product features (e. g., size, shape, and size distribution) given by flow methods with respect to conventional batch procedures. The main issues that arise by treating NPs suspensions in microfluidic systems are product deposition or channel clogging; mitigation strategies to overcome these drawbacks will also be presented and discussed.