The ergodic problem for some subelliptic operators with unbounded coefficients

We study existence and uniqueness of the invariant measure for stochastic processes with degenerate diffusion, whose infinitesimal generators are linear subelliptic operators in the whole space \({{\mathbb{R}}^N}\) with possibly unbounded coefficients. Such a measure together with a Liouville-type theorem will play a crucial role in two applications: the ergodic problem studied through stationary problems with vanishing discount and the long time behavior of the solution to a parabolic Cauchy problem. In both cases, the constants will be characterized in terms of the invariant measure.     

Isometric actions on spheres with an orbifold quotient

Mathematische Annalen - We classify representations of compact connected Lie groups whose induced action on the unit sphere has the orbit space isometric to a Riemannian orbifold.     

Synthesis and electrochemical investigation of <Emphasis Type="Italic">beta</Emphasis>-substituted thiophene-based donor–acceptor copolymers with 3,4-ethylenedioxythiophene (EDOT)

The present work reports the synthesis of four electron-acceptor beta-substituted thiophenes that were studied as monomers for electrochemical polymerization with 3,4-ethylenedioxythiophene (EDOT), an electron-donating monomer, aiming the combination of electron-acceptor and donor monomer thiophene to a simpler and convenient build up of novel donor–acceptor copolymeric materials via electrochemical polymerization. Four novel copolymers poly(EDOT-co-3-thiophene phenylacetate), (PEDOT-co-PPhTAc-2a), poly(EDOT-co-3-thiophene(4-nitrophenyl)acetate) (PEDOT-co-PPhTAc-2b), poly(EDOT-co-3-thiophenephenylcarboxylate) (PEDOT-co-PPhTCb), and poly(EDOT-co-3-(phenoxymethyl)thiophene) (PEDOT-co-PPhOMT) were electrochemically polymerized. The monomers were characterized by spectrometric techniques (FTIR, ¹H NMR, and ¹³C NMR), and the copolymers were identified by electrochemical analyses and FT-IR. Although the corresponding homopolymers could not be obtained, in the presence of EDOT, the copolymers were formed in a quasi-reversible electrochemical kinetics. The infrared spectra of the copolymers as well the electrochemical profile corroborates their obtaining. The mass variation during the electrosynthesis was analyzed using a quartz crystal microbalance. The film’s morphologies were investigated by SEM. Interestingly, the combination of electron-rich monomer thiophene (EDOT) and these electron-deficient carboxy-substituted thiophenes might be a convenient building block couple to increase the performance control of physic-chemical properties of mixed polythiophenes with innovative applications and they also showed a possible applicability as charge storage device.     

UVA self-photosensitized oxygenation of beta-ionone

The steady-state UVA (350 nm) photolysis of ( E )-β-ionone ( 1 ) in aerated toluene solutions was studied by ¹H NMR spectroscopy. The formation of the 1,2,4-trioxane ( 2 ) and 5,8-endoperoxide ( 5 ) derivatives in the ratio of 4:1 was observed. Time-resolved laser induced experiments at 355 nm, such as laser-flash photolysis, photoacoustic and singlet oxygen ¹O₂ phosphorescence detection, confirmed the formation of the excited triplet state of 1 with a quantum yield Φ _T = 0.50 as the precursor for the generation of singlet oxygen ¹O₂ ( Φ _Δ = 0.16) and the isomeric α-pyran derivative ( 3 ), which was a reaction intermediate detected by NMR. In turn, the reaction of ¹O₂ with 1 and 3 occurred with rate constants of 1.0 × 10⁶ and 2.5 × 10⁸  m ⁻¹s⁻¹ to yield the oxygenated products 5 and 2 , respectively, indicating the relevance of the fixed s-cis configuration in the α-pyran ring in the concerted [2+4] cycloaddition of ¹O₂.     

An evaluation of british columbian beetle-killed hybrid spruce for bioethanol production

The development of bioconversion technologies for production of fuels, chemicals, and power from renewable resources is currently a high priority for developed nations such as the United States, Canada, and the European Union as a way to improve national energy security and reduce greenhouse gas emissions. The widespread implementation of such technologies will require a sustainable supply of biomass from forestry and agriculture. Forests are a major source of feedstocks for biofuels production in Canada. Woody biomass includes residues from logging and forest thinning, and from wood processing and pulp production. More recently, damaged wood caused by beetle infestations has become available on a large scale in Western Canada. This study evaluates beetle-killed British Columbian hybrid spruce (HS) (Picea glauca x P. engelmannii) as a feedstock for the production of bioethanol. In the past 30 yr, attack by the beetle Dendroctonus rufipennis and associated fungi has resulted in estimated losses of more than three billion board feet in British Columbia alone. Here we describe the chemical and some physical characteristics of both healthy (HHS) and beetle-killed (BKHS) British Columbian HS and evaluate the technical feasibility of using these feedstocks as a source of biomass for bioethanol production. Untreated HHS and BKHS did not differ significantly in chemical composition except for the moisture content, which was significantly lower in BKHS (approx 10%) compared with HHS (approx 18%). However, the yields of carbohydrates in hydrolyzable and fermentable forms were higher at mild pretreatment conditions (H-Factor <1000) for BKHS compared with HHS. At medium (H-Factor 1000-2000) and severe (H-Factor >2000) pretreatment conditions HHS and BKHS behaved similarly. Organosolv pretreated HHS and BKHS demonstrated good ethanol theoretical yields, approx 70 and 80%, respectively.     

Unraveling solvent-driven equilibria between alpha- and 3(10)-helices through an integrated spin labeling and computational approach

In this work we present an effective and flexible computational approach, which is the result of an ongoing development in our groups, allowing the complete a priori simulation of the ESR spectra of complex systems in solution. The usefulness and reliability of the method are demonstrated on the very demanding playground represented by the tuning of the equilibrium between 3(10)- and alpha-helices of polypeptides by different solvents. The starting point is the good agreement between computed and X-ray diffraction structures for the 3(10)-helix adopted by the double spin-labelled heptapeptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe. Next, density functional computations, including dispersion interactions and bulk solvent effects, suggest another energy minimum corresponding to an alpha-helix in polar solvents, which, eventually, becomes the most stable structure. Computation of magnetic and diffusion tensors provides the basic ingredients for the building of complete spectra by methods rooted in the Stochastic Liouville Equation (SLE). The remarkable agreement between computed and experimental spectra at different temperatures allowed us to identify helical structures in the various solvents. The generality of the computational strategy and its implementation in effective and user-friendly computer codes pave the route toward systematic applications in the field of biomolecules and other complex systems.     

Exploring the subtleties of drug-receptor interactions: the case of matrix metalloproteinases

By solving high-resolution crystal structures of a large number (14 in this case) of adducts of matrix metalloproteinase 12 (MMP12) with strong, nanomolar, inhibitors all derived from a single ligand scaffold, it is shown that the energetics of the ligand-protein interactions can be accounted for directly from the structures to a level of detail that allows us to rationalize for the differential binding affinity between pairs of closely related ligands. In each case, variations in binding affinities can be traced back to slight improvements or worsening of specific interactions with the protein of one or more ligand atoms. Isothermal calorimetry measurements show that the binding of this class of MMP inhibitors is largely enthalpy driven, but a favorable entropic contribution is always present. The binding enthalpy of acetohydroxamic acid (AHA), the prototype zinc-binding group in MMP drug discovery, has been also accurately measured. In principle, this research permits the planning of either improved inhibitors, or inhibitors with improved selectivity for one or another MMP. The present analysis is applicable to any drug target for which structural information on adducts with a series of homologous ligands can be obtained, while structural information obtained from in silico docking is probably not accurate enough for this type of study.     

Paramagnetism-based NMR restraints provide maximum allowed probabilities for the different conformations of partially independent protein domains

An innovative analytical/computational approach is presented to provide maximum allowed probabilities (MAPs) of conformations in protein domains not rigidly connected. The approach is applied to calmodulin and to its adduct with alpha-synuclein. Calmodulin is a protein constituted by two rigid domains, each of them composed by two calcium-binding EF-hand motifs, which in solution are largely free to move with respect to one another. We used the N60D mutant of calmodulin, which had been engineered to selectively bind a paramagnetic lanthanide ion to only one of its four calcium binding sites, specifically in the second EF-hand motif of the N-terminal domain. In this way, pseudocontact shifts (pcs's) and self-orientation residual dipolar couplings (rdc's) measured on the C-terminal domain provide information on its relative mobility with respect to the domain hosting the paramagnetic center. Available NMR data for terbium(III) and thulium(III) calmodulin were supplemented with additional data for dysprosium(III), analogous data were generated for the alpha-synuclein adduct, and the conformations with the largest MAPs were obtained for both systems. The MAP analysis for calmodulin provides further information on the variety of conformations experienced by the system. Such variety is somewhat reduced in the calmodulin-alpha-synuclein adduct, which however still retains high flexibility. The flexibility of the calmodulin-alpha-synuclein adduct is an unexpected result of this research.     

Measurements of lower carbonyls and hydrocarbons at Ny-Alesund, Svalbard

Measurements of gaseous organic compounds were carried out near Ny-Alesund, in the Norwegian Arctic, during September 2004. Twenty alkanes, alkenes and aromatic hydrocarbons from ethane to toluene and six aldehydes and ketones from formaldehyde to butanal, were identified and quantified in air samples. Hydrocarbons showed a quite uniform distribution, with ethane being by far the most abundant component (> 1 ppb), followed by propane (> 0.4 ppb) and butanes (> 0.3 ppb), while for unsaturated homologues, except ethene, concentrations never exceeding 0.05 ppb were observed. This distribution confirmed that hydrocarbon depletion during the transport time from Europe into the Arctic was depending upon their atmospheric lifetimes, calculated relatively to the OH reactivity scale. The presence of short lived hydrocarbons could be associated to local sources of anthropogenic and/or biogenic origin. Although the local air photochemistry played a primary role in the production of lower aldehydes in late summer, the observed mixing ratios of formaldehyde (in the 0.25 - 0.50 ppb range) could not be fully explained by known gas-phase chemistry. In this case additional sources, such as fluxes of formaldehyde from snow pack to the atmosphere and/or local anthropogenic activities, were to be taken into consideration. The possible influences of these sources on HCHO mixing ratios were analysed by means of a backward-trajectory circulation model.