Random walks on quasisymmetric functions

Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations. Spectral results are also obtained. Several important random walks are now realized this way: Stanley's QS-distribution results from endomorphisms given by evaluation maps, a-shuffles result from the ath convolution power of the universal character, and the Tchebyshev operator of the second kind introduced recently by Ehrenborg and Readdy yields traditional riffle shuffles. A conjecture of Ehrenborg regarding the spectra for a family of random walks on ab-words is proven. A theorem of Stembridge from the theory of enriched P-partitions is also recovered as a special case.     

Synthesis and characterisation of the anion-ordered tellurides MGeTe (M = Co,Rh)

The synthesis and structural characterisation, carried out using a combination of single-crystal and powder X-ray diffraction, of the materials MGeTe (M = Co, Rh) are described. These phases adopt an ordered α-NiAs₂ structure, which can be considered intermediate between those of pyrite and marcasite. Electrical resistivity and Seebeck coefficient measurements, carried out over the temperature range 77 ≤ T/K ≤ 325, indicate that these materials are n-type semiconductors.     

Reaction chemistry of tricarbonyl-η-pentadienylmanganese: Straightforward synthesis of stable manganese carbonyl terminal thiolates and a dinuclear bis(ethylenediaminyl) complex

Tricarbonyl-η⁵-pentadienylmanganese reacts with mercaptans RSH, R = Ph, C₆F₅, m-NH₂C₆H₄, p-NH₂C₆H₄, and HSCH₂CH₂ in the presence of ECH₂CH₂E, E = -PPh₂ or -NH₂ to give novel stable terminal thiolate mononuclear complexes fac-Mn(CO)₃(SR)(Ph₂PCH₂CH₂PPh₂-κ²-P,P′) for R = Ph, C₆F₅, m-NH₂C₆H₄, p-NH₂C₆H₄, and HSCH₂CH₂ and fac-Mn(CO)₃(SR)(H₂NCH₂CH₂NH₂-κ²-N,N′) for R = Ph and C₆F₅. Upon reaction of tricarbonyl-η⁵-pentadienylmanganese with ethylenediamine a dinuclear complex [fac-Mn(CO)₃(μ-H₂NCH₂CH₂NH-κ²-N,N′)]₂ was formed wherein the diaminyl ligand functions in the capacity of chelating and bridging ligand.     

Synthesis of non-cytotoxic poly(ester-amine) dendrimers as potential solubility enhancers for drugs: methotrexate as a case study

This study describes the synthesis of two new families of dendrimers based on the esterification of N-alkylated 3-amine-1-propanol with two different cores, adipic acid (1st and 2nd generations) and ethylenediamine (generation 1.5), both with carboxylic acid end groups, offering a wide variety of further modifications at the periphery. According to the cytotoxic evaluation of the dendrimers and their possible degradation products within cell lines, these materials could be considered as innocuous. In preliminary studies, the synthesized dendrimers proved to be potential enhancers of solubility of highly hydrophobic drugs, like methotrexate, widely used in chemotherapy.     

Polycyclic aromatic hydrocarbons (PAHs) in a coal tar standard reference material—SRM 1597a updated

SRM 1597 Complex Mixture of Polycyclic Aromatic Hydrocarbons from Coal Tar, originally issued in 1987, was recently reanalyzed and reissued as SRM 1597a with 34 certified, 46 reference, and 12 information concentrations (as mass fractions) for polycyclic aromatic hydrocarbons (PAHs) and polycyclic aromatic sulfur heterocycles (PASHs) including methyl-substituted PAHs and PASHs. The certified and reference concentrations (as mass fractions) were based on results of analyses of the coal tar material using multiple analytical techniques including gas chromatography/mass spectrometry on four different stationary phases and reversed-phase liquid chromatography. SRM 1597a is currently the most extensively characterized SRM for PAHs and PASHs.     

The preparation of certified calibration solutions for azaspiracid-1, -2, and -3, potent marine biotoxins found in shellfish

The production and certification of a series of azaspiracid (AZA) calibration solution reference materials is described. Azaspiracids were isolated from contaminated mussels, purified by preparative liquid chromatography and dried under vacuum to the anhydrous form. The purity was assessed by liquid chromatography–mass spectrometry and nuclear magnetic resonance spectroscopy. The final concentration of each AZA in a CD₃OH stock solution was determined by quantitative NMR spectroscopy. This solution was then diluted very accurately in degassed, high purity methanol to a concentration of 1.47?±?0.08 μmol/L for CRM-AZA1, 1.52?±?0.05 μmol/L for CRM-AZA2, and 1.37?±?0.13 μmol/L for CRM-AZA3. Aliquots were dispensed into argon-filled glass ampoules, which were immediately flame-sealed. The calibration solutions are suitable for method development, method validation, calibration of liquid chromatography or mass spectrometry instrumentation and quality control of shellfish monitoring programs.     

Error estimates for discrete spline interpolation: Quintic and biquintic splines

In this paper we shall develop a class of discrete spline interpolates in one and two independent variables. Further, explicit error bounds in _?∞${?}_{\infty }$ norm are derived for the quintic and biquintic discrete spline interpolates. We also present some numerical examples to illustrate the results obtained.     

Comparative study of different methods for the preparation of tetraamidato- and tetracarboxylatodiruthenium compounds. Structural and magnetic characterization

Solvothermal and microwave assisted synthesis were used as green and very useful alternative methods to obtain new chloridotetraamidatodiruthenium compounds, [Ru(2)Cl(μ-NHOCR)(4)](n) [R = Me-o-C(6)H(4) (1), Me-m-C(6)H(4) (2), Me-p-C(6)H(4) (3)]. The analogous tetracarboxylato complexes [Ru(2)Cl(μ-O(2)CR)(4)](n) [R = Me-o-C(6)H(4) (4), Me-m-C(6)H(4) (5), Me-p-C(6)H(4) (6)] have also been obtained. These synthetic methods allow the use of greener solvents like water or ethanol. Moreover, solvothermal synthesis permits the direct crystallization of the desired complexes, which are extremely insoluble in common solvents, during the synthetic process. Therefore, the crystal structure of all of them has been established using single crystal X-ray diffraction. Complex 1 shows a Ru-Cl-Ru angle of 180° and constitutes the first example of a chloridotetraamidatodiruthenium derivative displaying linear chains in the solid state. In contrast, complexes 2·0.5EtOH, and 3-6 show polymeric arrangements with the diruthenium units linked by chloride ligands, forming zigzag chains with Ru-Cl-Ru angles ranging between 117.03(6) and 121.45(3)°. All of the complexes show magnetic moments at room temperature corresponding to three unpaired electrons in agreement with the σ(2)π(4)δ(2)(π*δ*)(3) ground-state configuration, which indicates a similar magnetic behaviour in amidato and carboxylato derivatives. In the linear arrangement of complex 1 there is a better magnetic communication between diruthenium units (antiferromagnetic coupling, zJ = -10.5 or -8.7 cm(-1)) than the one observed in the zigzag 2-6 complexes (zJ = -1.23 to -5.75 cm(-1)).