The Poincaré series of a local Gorenstein ring of multiplicity up to 10 is rational

Let R be a local, Gorenstein ring with algebraically closed residue field k of characteristic 0 and let P _R (z):= Σ _p=0^∞ dim _k (Tor _p ^R (k, k))z ^p be its Poincaré series. We compute P _R when R belongs to a particular class defined in the Introduction, proving its rationality. As a by-product we prove the rationality of P _R for all local, Gorenstein rings of multiplicity at most 10.     

Hybrid polyoxotungstates as second-generation POM-based catalysts for microwave-assisted H2O2 activation

[structure: see text] Organic-inorganic hybrids synthesized from lacunary polyoxotungstates (POMs) have been screened as oxidation catalysts with H2O2 under MW irradiation. Yields up to 99% have been obtained in 25-50 min depending both on the POM structure and on the organic moiety. The reaction scope, optimized with the best performing catalyst [gamma-SiW10O36(PhPO)2]4-, includes epoxidation of terminal and internal double bonds, alcohol oxidation, and sulfoxidation, as well as oxygen transfer to electron-deficient substrates as chalcone, ketones, and sulfoxides.     

Bonding trends and dimensionality crossover of gold nanoclusters on metal-supported MgO thin films

Bonding of gold clusters, , 16, and 20, on MgO(100) and on thin MgO films supported on Mo(100) is investigated using first-principles density-functional theory. Enhanced adhesive bonding is found for clusters deposited on metal-supported MgO films of thickness up to about 1 nm, or 4 to 5 MgO layers, originating from electrostatic interaction between the underlying metal and metal-induced excess electronic charge accumulated at the cluster interface with the oxide film. The increased wetting propensity is accompanied by a dimensionality crossover from three-dimensional optimal cluster geometries on MgO(100) to energetically favored two-dimensional structures on the metal-supported films.     

Peptide folding dynamics: a time-resolved study from the nanosecond to the microsecond time regime

Time-resolved spectroscopies, spanning from the nanosecond to the microsecond time regime, coupled with molecular mechanics calculations, allowed us to assess the most populated conformations in solution of a series of analogues of trichogin GA IV, a natural undecapeptide showing significant antimicrobial activity. This peptide is characterized by a high content of the conformationally constrained alpha-aminoisobutyric acid and by a glycine-glycine motif in the central part of the sequence. Nanosecond time-resolved fluorescence experiments were performed to determine the conformational properties of the peptide analogues in solution, while transient absorption measurements allowed us to study the peptide dynamics on the microsecond time scale. Because the peptides examined were functionalized by a fluorescent probe at the N-terminus and a nitroxide quencher placed along the backbone at three different positions, the distance-dependent fluorophore-quencher interaction was exploited to obtain a deeper insight into their three-dimensional structural and dynamical properties. Further information on the conformational and dynamical features was obtained by photophysical experiments as a function of the viscosity and polarity of the medium. Taken together, the results revealed a transition from an elongated, helical conformation to a family of compact, folded structures mimicking a helix-turn-helix motif, which may represent a model of the early steps of the protein hydrophobic collapse.     

α-chymotrypsin superactivity in cetyltrialkylammonium bromide-rich media

α-Chymotrypsin (α-CT) activity was tested with N-glutaryl-l-phenylalanine p-nitroanilide in buffered media with added cationic surfactants. The effect of the commercial cetyltrimethylammonium bromide (CTABr) was compared with that of three other surfactants with ethyl (CTEABr), propyl (CTPABr), and butyl (CTBABr) head groups. These were synthesized and purified in this laboratory. Surfactant head groups provided distinct environments that largely modulated the catalytic performance. Larger alkyl head group hydrophobicity led to a marked enhancement of α-CT activity. CTBABr-rich media induced the highest superactivity. Kinetic measurements were performed in Tris-HCl buffer at a surfactant concentration either below or above CMC, and α-CT superactivity occurred in both media. Positive interactions between the enzyme and surfactants happened independently of thesupramolecular organization of the medium. The reaction followed the Michaelis-Menten kinetics. The substrate to micelle aggregates binding constant was used to calculate the substrate concentration available for catalysis. The k _cat to k _m ratio was in CTBABr-rich media always higher than in pure buffer and depended on the surfactant concentration. α-CT superactivity depended on the pH value of buffer solution. Enzyme inactivation followed a single-step mechanism in pure buffer and a series mechanism in the presence of a surfactant. The rate of activity decay obeyed a first-order kinetics.     

Molecular orbital cluster model study of bonding and vibrations of CO adsorbed on MgO surface

The interaction of CO with the MgO(100) surface has been investigated by means of all electron cluster model calculations. The CO molecule is bound on the Mg²⁺ site of MgO with a chemisorption energy of about 0.2 eV. The binding mechanism is electrostatic in nature and arises almost entirely from the interaction of the weak electric field generated by the ionic surface and the CO charge distribution, with negligible contributions from chemical effects as the CO σ donation. When CO is bound through carbon, its vibrational frequency increases with respect to the gas-phase value. This shift, Δ, has been analyzed and decomposed into the sum of different contributions. It is found that the positive Δω does not arise entirely from the field–dipole interaction but is due, in part, to the increase in Pauli repulsion occurring when the C? O molecule vibrates in the presence of the surface “wall.” A stronger electrostatic interaction, bringing the CO adsorbate closer to the surface, increases this wall effect and results in a more pronounced positive ω shift. It is also found that the two CO orientations exhibit opposite shifts in ω_e, thus, the two orientations can be distinguished, in principle, by IR spectroscopy. The analysis of our ab initio cluster wave functions gives a very different picture than the standard view of the metal–CO bond as arising from σ donation and π back donation.