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.     

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.     

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).     

Computational complexity of isothermic DNA sequencing by hybridization

In the paper, the computational complexity of several variants of the problem of isothermic DNA sequencing by hybridization, is analyzed. The isothermic sequencing is a recent method, in which isothermic oligonucleotide libraries are used during the hybridization with an unknown DNA fragment. The variants of the isothermic DNA sequencing problem with errors in the hybridization data, negative ones or positive ones, are proved to be strongly NP-hard. On the other hand, the polynomial time algorithm for the ideal case with no errors is proposed.     

Tocochromanols composition in kernels recovered from different apricot varieties: RP-HPLC/FLD and RP-UPLC-ESI/MSn study

Composition of tocochromanols in kernels recovered from 16 different apricot varieties (Prunus armeniaca L.) was studied. Three tocopherol (T) homologues, namely α, γ and δ, were quantified in all tested samples by an RP-HPLC/FLD method. The γ-T was the main tocopherol homologue identified in apricot kernels and constituted approximately 93% of total detected tocopherols. The RP-UPLC-ESI/MSⁿ method detected trace amounts of two tocotrienol homologues α and γ in the apricot kernels. The concentration of individual tocopherol homologues in kernels of different apricots varieties, expressed in mg/100 g dwb, was in the following range: 1.38–4.41 (α-T), 42.48–73.27 (γ-T) and 0.77–2.09 (δ-T). Moreover, the ratio between individual tocopherol homologues α:γ:δ was nearly constant in all varieties and amounted to approximately 2:39:1.