Spaces of Tilings, Finite Telescopic Approximations and Gap-Labeling

The continuous Hull of a repetitive tiling T in ℝ^d with the Finite Pattern Condition (FPC) inherits a minimal ℝ^d-lamination structure with flat leaves and a transversal which is a Cantor set. This class of tiling includes the Penrose & the Amman Benkker ones in 2D, as well as the icosahedral tilings in 3D. We show that the continuous Hull, with its canonical ℝ^d-action, can be seen as the projective limit of a suitable sequence of branched, oriented and flat compact d-manifolds. As a consequence, the longitudinal cohomology and the K-theory of the corresponding C*-algebra are obtained as direct limits of cohomology and K-theory of ordinary manifolds. Moreover, the space of invariant finite positive measures can be identified with a cone in the d^th homology group canonically associated with the orientation of ℝ^d. At last, the gap labeling theorem holds: given an invariant ergodic probability measure μ on the Hull the corresponding Integrated Density of States (IDS) of any selfadjoint operators affiliated to takes on values on spectral gaps in the ℤ-module generated by the occurrence probabilities of finite patches in the tiling. Accepted in Revised Form: 7 May 2005     

The unexpected reactivity of Zeise's anion in strong basic medium discloses new substitution patterns at the platinum centre

Zeise's anion in strongly basic hydroxylated solvents undergoes unprecedented nucleophilic addition of OR- (R = H, Me, Et) to the eta2-ethene giving trans-[PtCl2(eta1-C2H4OR)(OR)]2- which readily reacts with bidentate nitrogen donors N-N to give Cl- and OR- substitution and formation of [PtCl(CH2CH2OR)(N-N)]. Protonolysis of this stable organometallic species offers a versatile route to cationic [PtCl(eta2-C2H4)(N-N)]+ complexes.     

Regularity of line configurations

We show that in arithmetically-Gorenstein line arrangements with only planar singularities, each line intersects the same number of other lines. This number has an algebraic interpretation: it is the Castelnuovo–Mumford regularity of the coordinate ring of the arrangement.We also prove that every $(d?1)$-dimensional simplicial complex whose 0-th and 1-st homologies are trivial is the nerve complex of a suitable d-dimensional standard graded algebra of depth ≥3. This provides the converse of a recent result by Katzman, Lyubeznik and Zhang.     

The experimental design approach to the optimization of a simple quick easy cheap effective rugged and safe method for the analysis of phytoestrogens in complex soy‐based food

The present paper deals with the multivariate optimization of an extraction‐purification strategy for the determination of phytoestrogens (daidzein, genistein, coumestrol, formononetin, and biochanin A) in soy‐based meat substitutes by high performance liquid chromatography with tandem mass spectrometry. For a reliable quantitation of these new concerning compounds in such a complex matrix, recovery and matrix effect must be carefully evaluated. Therefore, two sequential experimental designs were used to optimize the sample‐pretreatment of soy‐based burgers: the chosen technique was the quick, easy, cheap, effective, rugged and safe methodology, which does not require any particular facility or instrumentation. Thanks to the first screening design (Plackett‐Burman), the significant factors influencing the studied responses were identified and further investigated through a response surface design (Box‐Behnken). The optimal values of the variables (volume of extraction solvent mix/sample mass ratio and two clean‐up sorbents) led to quantitative recoveries (97–104%) and low ion suppression (matrix effect 60–93%) for all analytes. This optimized method was characterized by low detection limits (0.2–1.5 ng/g) and excellent intraday precision (RSD 2–4%). It was applied to the determination of the considered compounds in several soy‐burgers from the Italian market, detecting low ng/g levels (up to 40 ng/g) of coumestrol, formononetin, and biochanin A, and high concentrations (7.9–78 µg/g) of genistein and daidzein.     

Application of ray-path geometry modification to the design of a collimating structure for LEDs

We investigate a system that is able to trace the ray path we decided previously, in particular, we would like to change a cylindrical raypath into a plane one after a given coordinate of the propagation axis. The technique we used is completely general, so we can calculate every kind of system to move some rays path in another one we want.     

Three‐Dimensional Branched and Faceted Gold–Ruthenium Nanoparticles: Using Nanostructure to Improve Stability in Oxygen Evolution Electrocatalysis

Achieving stability with highly active Ru nanoparticles for electrocatalysis is a major challenge for the oxygen evolution reaction. As improved stability of Ru catalysts has been shown for bulk surfaces with low‐index facets, there is an opportunity to incorporate these stable facets into Ru nanoparticles. Now, a new solution synthesis is presented in which hexagonal close‐packed structured Ru is grown on Au to form nanoparticles with 3D branches. Exposing low‐index facets on these 3D branches creates stable reaction kinetics to achieve high activity and the highest stability observed for Ru nanoparticle oxygen evolution reaction catalysts. These design principles provide a synthetic strategy to achieve stable and active electrocatalysts.     

Electrostatic layer-by-layer deposition and electrochemical characterization of thin films composed of MnO2 nanoparticles in a room-temperature ionic liquid

Thin films of MnO(2) nanoparticles were grown using the layer-by-layer method with poly(diallyldimetylammonium) as the intercalated layer. The film growth was followed by UV-vis, electrochemical quartz crystal microbalance (EQCM), and atomic force microscopy. Linear growth due to electrostatic immobilization of layers was observed up to 30 bilayers, but electrical connectivity was maintained only for 12 MnO(2)/PPDA bilayers. The electrochemical characterization of this film in 1-butyl-2,3-dimethyl-imidazolium (BMMI) bis(trifluoromethanesulfonyl)imide (TFSI) (BMMITFSI) with and without addition of a lithium salt indicated a higher electrochemical response of the nanostructured electrode in the lithium-containing electrolyte. On the basis of EQCM experiments, it was possible to confirm that the charge compensation process is achieved mainly by the TFSI anion at short times (<2 s) and by BMMI and lithium cations at longer times. The fact that large ions like TFSI and BMMI participate in the electroneutrality is attributed to the redox reaction that occurs at the superficial sites and to the high concentration of these species compared to that of lithium cations.     

The first pure LambdaHT rotamer of a complex with a cis-[metal(nucleotide)2] unit: a cis-[Pt(amine)2(nucleotide)2] LambdaHT rotamer with unique molecular structural features

cis-[PtA2(nucleotide)2] complexes (A2 stands for two amines or a diamine) have been extensively investigated as model compounds for key cisplatin-DNA adducts. All cis-[metal(nucleotide/nucleoside)2] complexes with guanine and related purines characterized in the solid state thus far have the DeltaHT conformation (head-to-tail orientation of the two bases and right-handed chirality). In sharp contrast, the LambdaHT conformation (left-handed chirality) dominates in acidic and neutral aqueous solutions of cis-[PtA2(5'-GMP)2] complexes. Molecular models and solution experiments indicate that the LambdaHT conformer is stabilized by 5'-phosphate/N1H hydrogen-bond interactions between cis nucleotides with the normal anti conformation. However, this evidence, while compelling, is indirect. At last, conditions have been defined to allow crystallization of this elusive conformer. The structure obtained reveals three unique features not present in all other cis-[PtA2(nucleotide)2] solid-state structures: a LambdaHT conformation, very strong hydrogen-bond interactions between the phosphate and N1H of cis nucleotides, and a very small dihedral angle between the planes of the two guanines lying nearly perpendicular to the coordination plane. These new results indicate that, because there are no local base-base repulsions precluding the LambdaHT conformer, global forces rather than local interactions account for the predominance of the DeltaHT conformer over the LambdaHT conformer in the solid state and in both inter- and intrastrand HT crosslinks of oligonucleotides and DNA.