On-line arbitrarily vertex decomposable suns

We give a complete characterization of on-line arbitrarily vertex decomposable graphs in the family of unicycle graphs called suns. A sun is a graph with maximum degree three, such that deleting vertices of degree one results in a cycle. This result has already been used in another paper to prove some Ore-type conditions for on-line arbitrarily decomposable graphs.     

A conformational study of bis-, tris- and tetrakis-pyrazolylmethane. Crystallography, L.S.R., dipole moments and theoretical calculations

Theoretical calculations (MM2 and MNDO) have been carried out on several conformations of bis-, tris- and tetrakispyrazolylmethane. The potential surface thus obtained has been compared with experimental results both in solution (lanthanide shift reagents, dipole moments) and in the solid state (crystallography). The structure of tetrakispyrazolylmethane (3) was determined by X-ray diffraction. The compound crystallizes in the C2/c space group, with a cell of dimensions 29.5117(14), 6.9815(2), 13.8903(4) Å and 105.237(3)°. The molecule presents an approximate S₄( ) axis such as N12, N22, N32 and N42 form a distorted tetrahedron. The calculated conformations of minimum energy are consistent with dielectric measurements. The structure of 3 in the solid state lies 5.0 kcal.mol-1 above the minimum as a result of the crystal field. To explain the LSR results, a coordination with two pyrazole nuclei has to be assumed. The presence of a metal (LSR, organometallic complexes) strongly modifies the conformation: in these conditions, bidentated and tridentated structures are observed.     

Identification of indigoid dyes in natural organic pigments used in historical art objects by high-performance liquid chromatography coupled to electrospray ionization mass spectrometry

Pigments are among the most important components of historical paintings and textiles and their nature provides the unique character of color. They can be divided into two main groups: inorganic and organic, extracted from plants or animals. Their identification is a necessary stage in the conservation of art objects. Reversed-phase liquid chromatography with electrospray ionization mass spectrometry (ESI-MS) and UV/visible spectrophotometric methods were elaborated for the identification of indigoid (indigo, indirubin, isoindigo, isoindirubin) color components of natural dyestuffs and their natural or synthetic precursors (indican, isatin, indoxyl, 2-indolinone). ES-MS offers detection limits in the range 0.03-5.00 microg ml(-1) for the color compounds examined. The method developed made it possible to identify indigo and its isomers in genuine Indian indigo, indigo from woad and Tyrian Purple. It was applied to the identification of natural dyes on fiber from a 19th century Japanese tapestry, 'Cranes in the landscape'. A procedure based on freezing and grinding of a sample before the extraction of dyes from the textile was developed. The components of the extract obtained were identified after acidic hydrolysis as indigotin and methylene blue.     

Screening for Oral Cancer Using Electrochemical Telomerase Assay

Electrochemical telomerase assay (ECTA) developed by our group was evaluated in an oral cancer screening using exfoliated oral cells and tissues obtained from patients of oral cancer, mucosa associated disease, or healthy volunteers. Telomerase activity from ECTA is correlated with hTERT mRNA expression level using a real‐time PCR and was increasing in the following order: healthy volunteer group<mucosa associated disease group<oral cancer group. Sensitivity and specificity of ECTA were 88 % and 72 %, respectively when used 17 % of the threshold value based on the receiver operating characteristic curve in ECTA data.     

Rigidity of products

We give an example of two rigid sets in Euclidean spaces, with nonrigid product. Moreover we give a criterion of rigidity of products for dimensionally homogeneous sets and define a multiplicative class of rigid sets.Supported by KBN grant 2.1092.91.01.     

Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

In this paper, we consider dividend problem for an insurance company whose risk evolves as a spectrally negative Lévy process (in the absence of dividend payments) when a Parisian delay is applied. An objective function is given by the cumulative discounted dividends received until the moment of ruin, when a so-called barrier strategy is applied. Additionally, we consider two possibilities of a delay. In the first scenario, ruin happens when the surplus process stays below zero longer than a fixed amount of time. In the second case, there is a time lag between the decision of paying dividends and its implementation.     

Steiner almost self-complementary graphs and halving near-Steiner triple systems

We show that for every admissible order v≡0 or there exists a near-Steiner triple system of order v that can be halved. As a corollary we obtain that a Steiner almost self-complementary graph with n vertices exists if and only if n≡0 or .     

On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

Quantitative analysis of amphiphilic <Emphasis Type="Italic">N</Emphasis>-alkyloxypyridinecarboximidamide by liquid chromatography–tandem mass spectrometry

LC–MS/MS method to determine hydrophobic N-alkyloxy substituted amidines: N-(2-ethylhexyloxy)pyridine-2-carboximidamide, N-(2-ethylhexyloxy)pyridine-3-carboximidamide, N-(2-ethylhexyloxy)pyridine-4-carboximidamide, N-decyloxy pyridine-2-carboximidamide, N-decyloxypyridine-3-carboximidamide and N-decyloxypyridine-4-carboximidamide was developed and validated in terms of linearity, precision and accuracy. The developed method was successfully applied to monitor and control the synthesis process. The experimental data points indicated that the straight chain alkyl bromide reacted most rapidly than branched alkyl bromide and the enhancement of the reaction efficiency strongly depended on reaction temperature.     

1,2,3-propanetriol radicals formed during oxidative stress

The presented results attempt to approximate the proper structure of the radical formed as a result of the oxidation of 1,2,3-propanetriol. To fulfil the aim unstable radical originated in 1,2,3-propanetriol was trapped by PBN. Resulted spin adduct was measured using EPR spectroscopy and the isotropic hyperfine coupling constants a_iso(¹⁴N) and a_iso(¹H) were obtained by simulation of the EPR spectrum. The next step consisted of conducting a comparative analysis of EPR parameters, based on the calculations conducted at the DFT and MP2 methods level in open-shell formalism including solvent effects. For comparison, calculations were also carried out at the level of combined methods (UB3LYP/QCISD and UMP2/QCISD) in terms of the ONIOM formalism. Comparison of the experimental EPR data of the isotropic hyperfine coupling constants a_iso(¹⁴N) and a_iso(¹H) with the calculated parameters indicate that oxidation of 1,2,3-propanetriol leads to a carbon centred radical where unpaired electron is situated on the second (middle) carbon of 1,2,3-propanetriol. What is important, this conclusion could be made regardless of the chosen calculation method. However, it could be stated that for calculation of the isotropic hyperfine coupling constants a_iso(¹⁴N) and a_iso(¹H) of PBN/gly• adducts, UMP2 polarisable conductor calculation model with two ethanol molecules is explicitly defined.