Optimal Besov Differentiability for Entropy Solutions of the Eikonal Equation

In this paper we study the eikonal equation in a bounded planar domain. We prove the equivalence among optimal Besov regularity, the finiteness of every entropy production, and the validity of a kinetic formulation. © 2019 Wiley Periodicals, Inc.     

The New Fluorescent Membrane Probe Ahba: A Comparative Study with the Largely Used Laurdan

Lipid bilayers have been largely used as model systems for biological membranes. Hence, their structures, and alterations caused on them by biological active molecules, have been the subject of many studies. Accordingly, fluorescent probes incorporated into lipid bilayers have been extensively used for characterizing lipid bilayer fluidity and/or polarity. However, for the proper analysis of the alterations undergone by a membrane, a comprehensive knowledge of the fluorescent properties of the probe is fundamental. Therefore, the present work compares fluorescent properties of a relative new fluorescent membrane probe, 2-amino-N-hexadecyl-benzamide (Ahba), with the largely used probe 6-dodecanoyl-N,N-dimethyl-2-naphthylamine (Laurdan), using both static and time resolved fluorescence. Both Ahba and Laurdan have the fluorescent moiety close to the bilayer surface; Ahba has a rather small fluorescent moiety, which was shown to be very sensitive to the bilayer surface pH. The main goal was to point out the fluorescent properties of each probe that are most sensitive to structural alterations on a lipid bilayer. The two probes were incorporated into bilayers of the well-studied zwitterionic lipid dimyristoyl phosphatidylcholine (DMPC), which exhibits a gel-fluid transition around 23 °C. The system was monitored between 5 and 50 °C, hence allowing the study of the two different lipid structures, the gel and fluid bilayer phases, and the transition between them. As it is known, the fluorescent emission spectrum of Laurdan is highly sensitive to the bilayer gel-fluid transition, whereas the Ahba fluorescence spectrum was found to be insensitive to changes in bilayer structure and polarity, which are known to happen at the gel-fluid transition. However, both probes monitor the bilayer gel-fluid transition through fluorescence anisotropy measurements. With time-resolved fluorescence, it was possible to show that bilayer structural variations can be monitored by Laurdan excited state lifetimes changes, whereas Ahba lifetimes were found to be insensitive to bilayer structural modifications. Through anisotropy time decay measurements, both probes could monitor structural bilayer changes, but the limiting anisotropy was found to be a better parameter than the rotational correlation time. It is interesting to have in mind that the relatively small fluorophore of Ahba (o-Abz) could possibly be bound to a phospholipid hydrocarbon chain, not disturbing much the bilayer packing and being a sensitive probe for the bilayer core.     

Zur Trennung des Thalliums vom Antimon

Ohne Zusammenfassung     

Thallium

Ohne Zusammenfassung     

Normal subgroups in the Cremona group

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane $ \mathbb{P}_{\mathbf{k}}^2 $ is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory and algebraic geometry to produce elements in the Cremona group that generate non-trivial normal subgroups.     

Spherical Particle in Nematic Liquid Crystal Under an External Field: The Saturn Ring Regime

We consider a nematic liquid crystal occupying the exterior region in \({\mathbb {R}}^3\) outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to an external field, modeled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough, we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn ring defect around the particle, rather than a dipolar director field typical of a point defect.     

Synthesis of a fluoroalkene peptidomimetic precursor of N-acetyl-l-glutamyl-l-alanine

Fluoroolefin peptidomimetics of the dipeptide N-acetyl-Glu-Ala were synthesized via an Evans asymmetric aldol reaction and an Overman rearrangement. This dipeptide is the N-terminal of an octapeptide implicated in the signal transduction via PKCε.     

Determination of soluble lignin and proteins in the presence of each other

Several methods for the differential determination of lignin and of proteins solubilized together in the same solution are compared. It is shown that lignin is best determined by spectrophotometry at 280 nm, the absorptivity of the polymer being an order of magnitude greater than those of proteins. In contrast, a turbidimetric method applied to acid-precipitated lignin is strongly influenced by both the nature and the amounts of the proteins present in the mixture. Ninhydrin reagents permits the determination of proteins without interference from soluble lignin. Phenol and Coomassie Blue reagents react strongly with lignin, thus masking their interaction with proteins. The soluble lignin preparations used were solubilized from stake lignin in buffers adjusted to different pH values. They were analysed by exclusion chromatography and the results suggest that the lignin fragments obtained at higher pH are larger than those solubilized at lower pH. Turbidimetry showed that these larger soluble fragments form larger aggregates after acid precipitation.