Orthogonal polynomials in several variables for measures with mass points

Let dν be a measure in ? ^d obtained from adding a set of mass points to another measure dμ. Orthogonal polynomials in several variables associated with dν can be explicitly expressed in terms of orthogonal polynomials associated with dμ, so are the reproducing kernels associated with these polynomials. The explicit formulas that are obtained are further specialized in the case of Jacobi measure on the simplex, with mass points added on the vertices, which are then used to study the asymptotics kernel functions for dν.     

A facile approach to the synthesis of chiral 2-substituted benzofurans

An effective route to chiral optically active 2-substituted benzofurans directly from carboxylic acids is reported. This procedure, which allows the preparation of alpha-alkyl-2-benzofuranmethanamines from N-protected alpha-amino acids without sensible racemization phenomena, proceeds in good yields under mild conditions with the help of microwave irradiation.     

Novel Copper(II) Complexes with Dipinodiazafluorene Ligands: Synthesis,Structure, Magnetic and Catalytic Properties

The reactions of CuX₂ (X = Cl, Br) with dipinodiazafluorenes yielded four new complexes [CuX₂L₁]₂ (X = Cl (1), Br (2), L₁ = (1R,3R,8R,10R)-2,2,9,9-Tetramethyl-3,4,7,8,9,10-hexahydro-1H-1,3:8,10-dimethanocyclopenta [1,2-b:5,4-b’]diquinolin-12(2H)-one) and [(CuX₂)₂L₂]n (X = Cl (3), Br (4), L₂ = (1R,3R,8R,10R,1’R,3’R,8’R,10’R)-2,2,2’,2’,9,9,9’,9’-Octamethyl-1,1’,2,2’,3,3’,4,4’,7,7’,8,8’,9,9’,10,10’-hexadecahydro-1,3:1’,3’:8,10:8’,10’-tetramethano-12,12’-bi(cyclopenta [1,2-b:5,4-b’]diquinolinylidene). The complexes were characterized by IR and EPR spectroscopy, HR-ESI-MS and elemental analysis. The crystal structures of compounds 1, 2 and 4 were determined by X-ray diffraction (XRD) analysis. Complexes 1–2 have a monomeric structure, while complex 4 has a polymeric structure due to additional coordinating N,N sites in L₂. All complexes contain a binuclear fragment {Cu₂(μ-X)_2×2} (X = Cl, Br) in their structures. Each copper atom has a distorted square-pyramidal coordination environment formed by two nitrogen atoms and three halogen atoms. The Cu-N_ax distance is elongated compared to Cu-N_eq. The EPR spectra of compounds 1–4 in CH₃CN confirm their paramagnetic nature due to the d⁹ electronic configuration of the copper(II) ion. The magnetic properties of all compounds were studied by the method of static magnetic susceptibility. For complexes 1 and 2, the effective magnetic moments are µ_eff ≈ 1.87 and 1.83 µ_B (per each Cu²⁺ ion), respectively, in the temperature range 50–300 K, which are close to the theoretical spin value (1.73 µ_B). Ferromagnetic exchange interactions between Cu(II) ions inside {Cu₂(μ-X)₂X₂} (X = Cl, Br) dimers (J/k_B ≈ 25 and 31 K for 1 and 2, respectively) or between dimers (θ′ ≈ 0.30 and 0.47 K for 1 and 2, respectively) were found at low temperatures. For compounds 3 and 4, the magnetic susceptibility is well described by the Curie–Weiss law in the temperature range 1.77–300 K with µ_eff ≈ 1.72 and 1.70 µ_B for 3 and 4, respectively, and weak antiferromagnetic interactions (θ ≈ −0.4 K for 3 and −0.65 K for 4). Complexes 1–4 exhibit high catalytic activity in the oxidation of alkanes and alcohols with peroxides. The maximum yield of cyclohexane oxidation products reached 50% (complex 3). Based on the data on the study of regio- and bond-selectivity, it was concluded that hydroxyl radicals play a decisive role in the oxidation reaction. The initial products in reactions with alkanes are alkyl hydroperoxides.     

Rosa spp. Extracts as a Factor That Limits the Growth of Staphylococcus spp. Bacteria,a Food Contaminant

Due to their richness of bioactive substances, rose hips are a valuable raw material for obtaining extracts with potential antimicrobial activity. The aim of the study was to determine the antagonistic potential of whole pseudo-fruit and flesh extracts of three Rosa sp. varieties against Staphylococcus spp. bacteria isolated as food contaminants. The biological material in this study consisted of seven strains of bacteria from the genus Staphylococcus. Two strains—Staphylococcus aureus ATCC 25923 and Staphylococcus epidermidis DSMZ 3270—were used as reference strains. The other five strains were food-derived isolates—S. epidermidis A5, S. xylosus M5, S. haemolyticus M6, S. capitis KR6, and S. warneri KR2A. The material was the pseudo-fruits of Rosa canina, Rosa pomifera Karpatia, and Rosa rugosa. The polyphenols were extracted from the fleshy part and the whole pseudo-fruit for all rose varieties. The tested preparations differed significantly in their polyphenol composition. The sum of polyphenols ranged from 28 862 to 35 358 mg/100 g of lyophilisate. The main groups of polyphenols found in the preparations were flavanols and ellagitannins. All of the tested extracts inhibited the growth of staphylococci at a concentration of 500 mg/mL. Rosa rugosa fruit extract showed the strongest antimicrobial properties among the studied extracts. For all the strains, the growth inhibition had a diameter of 20.3–29.0 mm. Moreover, six out of the seven tested strains showed the highest inhibition with the use of this extract. The MIC of rose extracts was in the range of 3.125–500 mg/mL and was strictly dependent on the bacterial species, the species of the rose, and the part of the fruit from which the extract was obtained. Correlations were assessed between the main groups of polyphenols in the extracts and their inhibition of bacterial growth. In the case of pseudo-fruit extracts, the inhibitory effect on bacterial growth positively correlated with the content of ellagitannins, and this effect was observed for almost all the tested strains. The results presented herein follow the current trend of minimising the use of chemical preservatives in food; from this point of view, rose extracts are very promising.     

Preparation and characterization of polypyrrole with dispersed metallic rhodium particles

Polypyrrole (PPy) with dispersed metallic Rh particles has been prepared by all‐chemical route, i.e. reduction of Rh³⁺ ions existing in RhCl₃ aqueous solutions with sodium borohydride (NaBH₄) carried out in the presence of the previously obtained PPy doped with chloride ions (PPyCl). PPy–Rh composites thus formed have been characterized using X‐ray diffraction (XRD), scanning and transmission electron microscopies (SEM, TEM) combined with energy dispersive X‐ray (EDX) microanalysis, Rh3d X‐ray photoelectron (XPS), and IR spectroscopies. This has made it possible to find out that metallic Rh nanoparticles, mainly of sizes below 10 nm, have been present in the composites. Agglomerates, with sizes up to 0.7 µm, have been formed in the systems containing higher amounts of Rh. PPy serving as the matrix in the composites has been doped. However, its doping level has been lower than that of the starting PPyCl. This has been explained by partial reduction of the polymer occurring during preparation of the composites. Catalytic properties of the PPy–Rh systems have been investigated using isopropyl alcohol conversion as a test reaction. It has been established that the composites are active redox catalysts. This makes them promising materials for applications as catalysts of various redox processes. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterization of grape seed procyanidins by comprehensive two-dimensional hydrophilic interaction × reversed phase liquid chromatography coupled to diode array detection and tandem mass spectrometry

In this work, the development and optimization of a new methodology to analyze grape seed procyanidins based on the application of two-dimensional comprehensive LC is presented. This two-dimensional method involves the use of a microbore column containing a diol stationary phase in the first dimension coupled to either a C₁₈ partially porous short column or a C₁₈ monolithic column in the second dimension. The orthogonal hydrophilic interaction?×?reversed phase liquid chromatography (HILIC×RP-LC) system is interfaced through a ten-port two-position switching valve. The optimized HILIC×RP-LC separation followed by diode array and tandem mass spectrometry detection (HILIC×RP-LC-DAD-MS/MS) made possible the direct analysis of a complex grape seed extract and allowed the tentative identification of 43 flavan-3-ols, including monomers and procyanidin oligomers till a polymerization degree of 7 units with different galloylation degrees. To the best of our knowledge, this is the first time that this powerful analytical technique is employed to characterize complex procyanidin samples. This work successfully demonstrates the great capabilities of the HILIC×RP-LC-DAD-MS/MS coupling for the direct analysis of very complex natural samples like grape seeds.

Defect structures in the brannerite-type vanadates: VI. Preparation and study of Co1−x∅xV2−2xMo2xO6 and phase diagram of the ternary CoO-V2O5-MoO3 system

The phase diagram of the ternary CoO-V₂O₅-MoO₃ system and in particular its T-CoV₂O₆-MoO₃ slice have been determined with DTA and X-ray phase analysis. CoV₂O₆ crystallizes in two modifications: a low-temperature γ-form of unknown structure and a high-temperature α-form of brannerite-type structure. The transition temperature is 660-665°C. The γ ? α transformations are very slow and the α-polymorph may be easily frozen. On doping with MoO₃, a solid solution is formed that is described by the formula Co_1?x?_xV_2?2xMo_2xO₆. Above x = 0.02 the α-type structure is stabilized. The x_max equals 0.22 at the eutectic temperature of 620°C and 0.20 at room temperature. Other features of the phase diagram, including its division into the natural subdiagrams and three ternary eutectics, are described in detail. X-Ray data are listed for α-CoV₂O₆ and for the solid solution having x = 0.20. On doping with MoO₃ the monoclinic lattice dilates primarily in the direction of the b-axis.     

Morphology of the f ? f intensity parameters

The structure of the intensity parameters understood within the framework of ab initio