Embeddable quantum homogeneous spaces

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. Izumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above.     

Reprint of: Application of micro-thin-layer chromatography as a simple fractionation tool for fast screening of raw extracts derived from complex biological,pharmaceutical and environmental samples

The main goal of present paper is to demonstrate the separation and detection capability of micro-TLC technique involving simple one step liquid extraction protocols of complex materials without multi-steps sample pre-purification. In the present studies target components (cyanobacteria pigments, lipids and fullerenes) were isolated from heavy loading complex matrices including spirulina dried cells, birds’ feathers and fatty oils as well as soot samples derived from biomass fuel and fossils-fired home heating systems. In each case isocratic separation protocol involving less that 1 mL of one component or binary mixture mobile phases can be completed within time of 5–8 min. Sensitive detection of components of interest was performed via fluorescence or staining techniques using iodine or phosphomolybdic acid. Described methodology can be applied for fast fractionation or screening of whole range of target substances as well as chemo-taxonomic studies and fingerprinting of complex mixtures, which are present in raw biological or environmental samples.     

Study of ethylic Babassu biodiesel properties at low temperatures

Nowadays the growing fuel deficit requires the development of alternative fuel sources. Biodiesel is a good substitute to the conventional diesel because it is quite similar to the fossil fuel in its main characteristics. However, there are some obstacles, as the properties of cold-flow, to the development of a more useful alternative fuel. In this work we use the X-ray diffraction and differential calorimetry scanning to study low temperature properties of ethylic Babassu biodiesel. Our results show that the nucleation of crystals starts below ?8 °C and the crystallization temperature does not change significantly when the sample was submitted to a winterization process. The higher concentrations of ethyl esters from saturated fat acid are probably responsible for this characteristic. The X-ray diffraction, combined with DSC measurements, was efficiently employed in the characterization of cold-flow biodiesel properties, showing to be very helpful techniques.     

Stereostructure of mycoheptin A2

The absolute configurations of all the stereogenic centers of the antibiotic mycoheptin A₂ were established upon previously elaborated general procedure, consisting of DQF‐COSY, NOESY, ROESY, HSQC and HMBC experiments as major tools. The structure of mycoheptin A₂ without stereochemistry of its aglycone has been reported before. Copyright © 2012 John Wiley & Sons, Ltd.     

Activation and structural and adsorption features of activated carbons with highly developed micro-, meso- and macroporosity

Three sets of activated carbons (ACs) were prepared with the same precursor but activated differently (by CO₂ or water vapour) with various burn-off levels. The ACs demonstrate increased deviation of the pore shape from the slitshaped model with increasing burn-off and contributions of pores of different sizes depending on the activation type. Significant re-arrangement of adsorption complexes, especially of the Van der Waals type characteristic for nonpolar or weakly polar adsorbates (H₂, CH₄, CH₂Cl₂, CHCl₃), occurs in both micropores and mesopores of ACs with decreasing temperature. The behaviour of their mixtures with water and DMSO can strongly differ from that of individual adsorbates.     

Separation of chiral molecules by temperature programmed desorption

The Monte Carlo simulation method was used to model thermal desorption of a pair of enantiomers from a solid surface with a chiral periodic pattern of active sites. The main objective of the study was to determine the optimal number of the active sites and their spatial distribution within the unit cell of the surface to achieve the most efficient separation of the enantiomers. For that purpose we tested the series of chiral patterns which were found previously for the equilibrium adsorption. Temperature programmed desorption spectra were calculated using a square lattice of adsorption sites in which the active sites were distributed spatially according to the candidate patterns. Additionally, influence of relaxation of the adsorbed layer on the relative shift of the TPD peaks of the enantiomers was assessed and the key factors affecting the chiral separation were identified.     

Sard's theorem for mappings in Hölder and Sobolev spaces

We prove various generalizations of classical Sard's theorem to mappings f:M ^m →N ⁿ between manifolds in Hölder and Sobolev classes. It turns out that if f ∈ C ^k,λ (M ^m ,N ⁿ ), then—for arbitrary k and λ—one can obtain estimates of the Hausdorff measure of the set of critical points in a typical level set f ^?1(y). The classical theorem of Sard holds true for f ∈ C ^k with sufficiently large k, i.e., k>max(m?n,0); our estimates contain Sard's theorem (and improvements due to Dubovitskii and Bates) as special cases. For Sobolev mappings between manifolds, we describe the structure of f ^?1(y).     

Ambazone salt with p-aminobenzoic acid

In this study, we obtained a novel salt of ambazone (AMB) with p-aminobenzoic acid (PABA) that exhibits improved solubility and antibacterial activity. The salt was produced by solvent-drop grinding and characterized by powder X-ray diffraction, thermal analysis and Fourier transform infrared spectroscopy. The salt nature of the new form was confirmed by infrared spectroscopy based on the characteristic vibrational band of the protonated amino group. Based on the X-ray powder diffraction data, the compound crystallizes in the triclinic P_-1 space group with the following unit cell parameters: a = 14.294 Å, b = 9.162 Å, c = 8.777 Å, α = 95.90°, β = 100.63°, γ = 91.73°. Thermal analysis reveals the thermal events and different decomposition steps of this solid form as compared to the starting compounds. Powder dissolution measurements showed solubility improvement compared with pure ambazone of 2 and 3.3 times in water and phosphate buffer, respectively. Antibacterial tests showed higher activity of the salt to Gram-negative Escherichia coli and Salmonella bacteria as compared to AMB and PABA. The study demonstrates that the pharmaceutical salt of ambazone with p-aminobenzoic acid (AMB–PABA) can be a possible alternative to ambazone in the treatment of infections with Gram-negative bacteria.