Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups

We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G).     

17O and 14N spectroscopy of 17O-labeled nucleic acid bases

Oxygen-17 and nitrogen-14 nuclear magnetic resonance techniques have been utilized in studying liquid-state hydrogen bonding interactions between nucleic acid bases and between the bases and solvent. The bases uracil and thymine have been labeled with ¹⁷O at positions 2 and 4, cytosine at position 2 and thymine riboside at position 4. The ¹⁷O chemical shift was found to be a sensitive structural probe and to provide information concerning the resonance forms that contribute to the total wave function. The chemical shift of the oxygen of thymine and uracil at position 2 was detected at a higher field than that of oxygen at position 4, presumably owing to an increased contribution of single bonded-oxygen valence bond structures at position 2. The ¹⁷O and ¹⁴N chemical shifts of cytosine were found to be strongly pH dependent, and the results have been interpreted in terms of predominant cytosine resonance structures contributing to the aqueous cation and anion. The ¹⁷O line width of cytosine in aqueous solution indicates the presence of hydrogen bonded dimers between neutral and cationic forms.     

Spectral methods for growth curve clustering

Central European Journal of Operations Research - The growth curve clustering problem is analyzed and its connection with the spectral relaxation method is described. For a given set of growth...     

Correlating Structure and KA2 Catalytic Activity of ZnII Hydrazone Complexes

Two new Zn(II) complexes bearing tridentate hydrazone-based ligands with NNO or NNS donor atoms were synthesised and characterised by elemental analysis, infrared (IR) and nuclear magnetic resonance (NMR) spectroscopies, and single crystal X-ray diffraction methods. These complexes, together with four previously synthesised analogues, having hydrazone ligands with a NNO donor set of atoms, were successfully employed as catalysts in the ketone-amine-alkyne (KA²) coupling reaction, furnishing tetrasubstituted propargylamines, compounds with unique applications in organic chemistry. DFT calculations at the CAM-B3LYP/TZP level of theory were performed to elucidate the electronic structure of the investigated Zn(II) complexes, excellently correlating the structure of the complexes to their catalytic reactivity.     

Detection of protein deposits using NIR spectroscopy

The aim of this study was to determine if it is possible to distinguish between the groups of spoiled and unspoiled soft contact lenses using near-infrared spectroscopy and new analytical approach – Aquaphotomics. Using the principal component analysis, it was established that the absorbance spectra of worn and new contact lenses are differed at water absorption band related to hydration of proteins. Detection of proteins thus was performed indirectly by using vibrations of water molecules. This exploratory study showed that near-infrared spectroscopy and Aquaphotomics have potential for non-invasive, chemical-free detection of protein deposits on hydrated soft contact lenses.     

Classification of framed links in 3-manifolds

We present a short and complete proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in detail. Let M be a connected oriented closed smooth 3-manifold, L ₁(M) be the set of framed links in M up to a framed cobordism, and deg: L ₁(M) → H ₁(M; ℤ) be the map taking a framed link to its homology class. Then for each α ∈ H ₁(M; ℤ) there is a one-to-one correspondence between the set deg⁻¹ α and the group ℤ_2d(α), where d(α) is the divisibility of the projection of α to the free part of H ₁(M; ℤ).     

Autoxidation of lipids in parchment

Historic parchment is a macromolecular material, which is complex due to its natural origin, inhomogeneity of the skin structure, unknown environmental history and potential localised degradation. Most research into its stability has so far focussed on thermal and structural methods of analyses.Using gas chromatographic analysis of the atmosphere surrounding parchment during oxidation, we provide the experimental evidence on the production of volatile aldehydes, which can be the products of lipid autoxidation. Oxidation of parchment with different aldehyde emissions was additionally followed in situ using chemiluminometry and the same techniques were used to evaluate the oxidation of differently delipidised parchment. It was shown that the production of peroxides and the emission of aldehydes from the material decrease with lower lipid content. Building on this evidence, we can conclude that the presence of lipids (either initially present in the skin or resulting from conservation intervention) leads to oxidative degradation of collagen and that the non-destructive analysis of the emission of volatiles could be used as a quick tool for evaluation of parchment stability.     

List Ramsey numbers

We introduce a list‐coloring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and where they are far apart. For $?$‐uniform cliques we prove that the list Ramsey number is bounded by an exponential function, while it is well known that the Ramsey number is superexponential for uniformity at least 3. This is in great contrast to the graph case where we cannot even decide the question of equality for cliques.