Quasi-elementary <Emphasis Type="Italic">H</Emphasis>-Azumaya Algebras Arising from Generalized (Anti) Yetter-Drinfeld Modules

Let H be a Hopf algebra with bijective antipode, α, β ∈ Aut _Hopf (H) and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k, H), the Brauer group of H.     

Distortion of the Poisson Bracket by the Noncommutative Planck Constants

In this paper we introduce a kind of “noncommutative neighbourhood” of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of generators indexed by planar binary leaf-labelled trees. The associated graded algebra (the classical shadow) is interpreted as a “distortion” of the algebra of classical observables of a physical system. It is proven that there exists a q-analogue of the Weyl quantization, where q is a matrix of formal variables, which induces a nontrivial noncommutative analogue of a Poisson bracket on the classical shadow.     

Anti-diffusion method for interface steepening in two-phase incompressible flow

In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.     

Aldehyde oxidase assay by capillary electrophoresis: From off‐line,online up to immobilized enzyme reactor

Capillary electrophoresis is a modern separation technique characterized by many benefits, which qualify it also for enzyme assays and the study of enzyme kinetics during drug development. Homogeneous or heterogeneous approaches can be followed for the enzymatic incubation. In this study, an immobilization procedure of aldehyde oxidase on magnetic particles was developed considering their integration with capillary electrophoresis. A number of magnetic nano/microparticle types were tested for this purpose, showing that aldehyde oxidase was most active when immobilized on bare silica magnetic nanoparticles. Primarily, the reusability of the enzyme immobilized on bare silica nanoparticles was tested. Three consecutive incubations with substrate could be performed, but the activity considerably dropped after the first incubation. One reason could be an enzyme detachment from the nanoparticles, but no release was detected neither at 4°C nor at 37°C during 5 h. The drop in enzymatic activity observed in consecutive incubations, could also be due to inactivation of the enzyme over time at given temperature. For the immobilized enzyme stored at 4°C, the activity decreased to 83% after 5 h, in contrast with a steep decrease at 37°C to 37%.     

Development of a Mild and Versatile Directed Cycloaddition Approach to Pyridines

The aza‐Diels–Alder cycloaddition of 1,2,4‐triazines with alkynes offers a rapid and convenient method for the synthesis of highly substituted pyridines, but often requires harsh conditions and long reaction times. The present study offers a solution to these limitations by use of a temporary tether established by a Lewis acid–base complexation of in situ generated alkynylboranes and triazines bearing a Lewis basic donor. The cycloaddition reactions take place within 20 min at 40 °C and provide direct access to a broad range of pyridines with complete and predictable regiocontrol. The carbon?boron bond can be further functionalised by cross‐coupling allowing further functionality to be introduced after cycloaddition.     

Magnetically Aligned Supramolecular Hydrogels

The magnetic‐field‐induced alignment of the fibrillar structures present in an aqueous solution of a dipeptide gelator, and the subsequent retention of this alignment upon transformation to a hydrogel upon the addition of CaCl₂ or upon a reduction in solution pH is reported. Utilising the switchable nature of the magnetic field coupled with the slow diffusion of CaCl₂, it is possible to precisely control the extent of anisotropy across a hydrogel, something that is generally very difficult to do using alternative methods. The approach is readily extended to other compounds that form viscous solutions at high pH. It is expected that this work will greatly expand the utility of such low‐molecular‐weight gelators (LMWG) in areas where alignment is key.     

H NMR and C-IRMS analyses of acetic acid from vinegar, O-IRMS analysis of water in vinegar: International collaborative study report

An international collaborative study of isotopic methods applied to control the authenticity of vinegar was organized in order to support the recognition of these procedures as official methods. The determination of the ²H/¹H ratio of the methyl site of acetic acid by SNIF-NMR (site-specific natural isotopic fractionation-nuclear magnetic resonance) and the determination of the ¹³C/¹²C ratio, by IRMS (isotope ratio mass spectrometry) provide complementary information to characterize the botanical origin of acetic acid and to detect adulterations of vinegar using synthetic acetic acid. Both methods use the same initial steps to recover pure acetic acid from vinegar. In the case of wine vinegar, the determination of the ¹⁸O/¹⁶O ratio of water by IRMS allows to differentiate wine vinegar from vinegars made from dried grapes. The same set of vinegar samples was used to validate these three determinations.The precision parameters of the method for measuring δ¹³C (carbon isotopic deviation) were found to be similar to the values previously obtained for similar methods applied to wine ethanol or sugars extracted from fruit juices: the average repeatability (r) was 0.45 ‰, and the average reproducibility (R) was 0.91‰. As expected from previous in-house study of the uncertainties, the precision parameters of the method for measuring the ²H/¹H ratio of the methyl site were found to be slightly higher than the values previously obtained for similar methods applied to wine ethanol or fermentation ethanol in fruit juices: the average repeatability was 1.34 ppm, and the average reproducibility was 1.62 ppm. This precision is still significantly smaller than the differences between various acetic acid sources (δ¹³C and δ¹⁸O) and allows a satisfactory discrimination of vinegar types. The precision parameters of the method for measuring δ¹⁸O were found to be similar to the values previously obtained for other methods applied to wine and fruit juices: the average repeatability was 0.15‰, and the average reproducibility was 0.59‰. The above values are proposed as repeatability and reproducibility limits in the current state of the art.On the basis of this satisfactory inter-laboratory precision and on the accuracy demonstrated by a spiking experiment, the authors recommend the adoption of the three isotopic determinations included in this study as official methods for controlling the authenticity of vinegar.     

Development and validation of a liquid chromatographic method for the analysis of capreomycin sulfate and its related substances

A gradient LC method for the analysis of capreomycin sulfate and its related substances was developed. The chromatographic conditions include the use of a Hypersil base deactivated C₁₈ (250 mm × 4.6 mm, 5 μm) column maintained at 25 °C, a mobile phase containing acetonitrile, phosphate buffer pH 2.3 and 0.025 M hexanesulfonate at a flow rate of 1.0 mL/min and UV detection performed at 268 nm. Good separation of the four active components of capreomycin and eleven unknown impurities was achieved. A system suitability test to check the quality of the separation is specified. The method shows good repeatability, linearity and robustness.     

Limit cycles near hyperbolas in quadratic systems

In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.