Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)

We show that points in specific degree-2 hypersurfaces in the Grassmannian $Gr(3,n)$ correspond to generic arrangements of n hyperplanes in ${\mathbb{C}}^3$ with associated discriminantal arrangement having intersections of multiplicity three in codimension two.     

Feedback Stabilization for a Scalar Conservation Law with PID Boundary Control

This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative (PID for short) boundary control is addressed. In the proportional-integral (PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system subject to PID control is always unstable.     

Compatible blends of biorelated polyesters through catalytic transesterification in the melt

The transesterification during the melt blending of polylactide (PLA) and poly(butylene adipate-co-terephthalate) (PBAT) was investigated in presence of Ti(OBu)₄ as a catalyst. Both the effect of catalyst concentration and reaction duration was considered. The process was studied by analyzing the molecular weight of the polyesters by size exclusion chromatography (SEC). The rheological, thermal and morphological properties of the blends were investigated by melt flow rate, DSC and SEM analyses, respectively. Evidences about the formation of PBAT-PLA copolymers were obtained and discussed. The tensile properties of compression moulded films were also determined and correlated to the structure and phase morphology development of the blends. In particular, the use of Ti(OBu)₄ resulted in the improvement of compatibility. Moreover, the decrease in stiffness and the increase in elongation at break with the increase of mixing time was observed, in good agreement with the improved compatibility of the modified blend.     

Crystallographic analysis of metal-ion binding to human ubiquitin

The metal-binding ability of human ubiquitin (hUb) towards a selection of biologically relevant metal ions and complexes has been probed. Different techniques have been used to obtain crystals suitable for crystallographic analysis. In the first type of experiments, crystals of hUb have been soaked in solutions containing copper(II) acetate and two metallodrugs, Zeise salt (K[PtCl(3)(η(2)-C(2)H(4))]·H(2)O) and cisplatin (cis-[PtCl(2)(NH(3))(2)]). The Zeise salt is used in a test for hepatitis, whereas cisplatin is one of the most powerful anticancer drugs in clinical use. The Zeise salt readily reacts with hUb crystals to afford an adduct with three platinum residues per protein molecule, Pt(3)-hUb. In contrast, copper(II) acetate and cisplatin were found to be unreactive for contact times up to one hour and to cause degradation of the hUb crystals for longer times. In the second type of experiments, hUb was cocrystallized with a solution of copper(II) or zinc(II) acetate or cisplatin. Zinc(II) acetate gives, at low metal-to-protein molar ratios (8:1), crystals containing one metal ion per three molecules of protein, Zn-hUb(3) (already reported in previous work), whereas at high metal-to-protein ratios (70:1) gives crystals containing three Zn(II) ions per protein molecule, Zn(3)-hUb. In contrast, once again, copper(II) acetate and cisplatin, even at low metal-to-protein ratios, do not give crystalline material. In the soaking experiment, the Zeise anion leads to simultaneous platination of His68, Met1, and Lys6. Present and previous results of cocrystallization experiments performed with Zn(II) and other Group 12 metal ions allow a comprehensive understanding of the metal-ion binding properties of hUb with His68 as the main anchoring site, followed by Met1 and carboxylic groups of Glu16, Glu18, Glu64, Asp21, and Asp32, to be reached. In the case of platinum, Lys6 can also be a binding site. The amount of bound metal ion, with respect to that of the protein, appears to be a relevant parameter influencing crystal packing.     

Soil properties, strontium isotopic signatures and multi-element profiles to authenticate the origin of vegetables from small-scale regions: illustration with early potatoes from southern Italy

We propose a method for the authentication of the origin of vegetables grown under similar weather conditions, in sites less than 10 km distance from the sea and distributed over a rather small scale area (58651 km(2)). We studied how the strontium (Sr) isotopic signature and selected elemental concentrations ([Mn], [Cu], [Zn], [Rb], [Sr] and [Cd]) in early potatoes from three neighbouring administrative regions in the south of Italy were related to the geological substrate (alluvial sediments, volcanic substrates and carbonate rocks) and to selected soil chemical properties influencing the bioavailability of elements in soils (pH, cation exchange capacity and total carbonate content). Through multiple-step multivariate statistics (PLS-DA) we could assign 26 potatoes (including two already commercialised samples) to their respective eight sites of production, corresponding to the first two types of geological substrates. The other 12 potatoes from four sites of production had similar characteristics in terms of the geological substrate (third type) and these soil properties could be grouped together. In this case, more discriminative parameters would be required to allow the differentiation between sites. The validation of our models included external prediction tests with data of potatoes harvested the year before and a study on the robustness of the uncertainties of the measurement results. Annual variations between multi-elemental and Sr isotopic fingerprints were observed in potatoes harvested from soils overlying carbonate rocks, stressing the importance of testing long term variations in authentication studies.     

Panchromatic ruthenium sensitizer based on electron-rich heteroarylvinylene π-conjugated quaterpyridine for dye-sensitized solar cells

The first example of a heteroarylvinylene π-conjugated quaterpyridine Ru(II) sensitizer (N1044) was synthesized and used in dye-sensitized solar cells; the dye has an effective panchromatic absorption band, covering the entire visible spectrum up to the NIR region, and superior electrochemical characteristics (HOMO/LUMO and bandgap energies) with respect to previous representative Ru(II) bi- and quaterpyridine sensitizers. A record IPCE curve ranging from 360 to 920 nm has been measured with a maximum of 65% at 646 nm and still 33% efficiency at 800 nm; this leads to substantially increased photocurrent (19.2 mA cm(-2)) when compared to the prototype N719 Ru(II) sensitizer.     

Development and validation of an HPLC-MS/MS method to quantify clopidogrel acyl glucuronide, clopidogrel acid metabolite, and clopidogrel in plasma samples avoiding analyte back-conversion

A new sensitive and fast quantitative analytical method for the simultaneous determination of clopidogrel, its main metabolite clopidogrel carboxylic acid, and the newly described acyl glucuronide metabolite, in human plasma samples, is presented. The analytical procedures (plasma storage, handling, and extract storage in the autosampler) were optimized in order to avoid back-conversion; a known drawback in measurements of clopidogrel. Clopidogrel acyl glucuronide was confirmed as a major source of back-conversion to the parent drug in the presence of methanol, and thorough stability experiments were carried out to find the most appropriate conditions for an accurate analysis of clopidogrel and the two metabolites. The method was validated by assessing selectivity, sensitivity, linearity, accuracy, and precision for all three analytes, in accordance to Food and Drug Administration guidelines. Spiked quality controls in plasma as well as incurred samples were used to verify back-conversion in the selected conditions, with results meeting European Medicines Agency acceptance criteria (concentrations within 80–120% of the first reading). The method was then applied to a pharmacokinetic study, and for the first time, a pharmacokinetic curve of clopidogrel acyl glucuronide in human plasma is presented. The concentrations ranged up to 1,048.684 ng/mL, with a mean of 470.268 ng/mL, while clopidogrel had a mean C _max of 1.348 ng/mL; these orders of magnitude show how much the back-conversion of this metabolite may influence clopidogrel quantification if it is not properly controlled.     

A semi-Markov process with an inverse Gaussian distribution as sojourn time

Let X_n denote the state of a device after n repairs. We assume that the time between two repairs is the time τ taken by a Wiener process {W(t), t ? 0}, starting from w₀ and with drift μ < 0, to reach c ∈ [0, w₀). After the nth repair, the process takes on either the value X_n?1 + 1 or X_n?1 + 2. The probability that X_n = X_n?1 + j, for j = 1, 2, depends on whether τ ? t₀ (a fixed constant) or τ > t₀. The device is considered to be worn out when X_n ? k, where k ∈ {1, 2, …}. This model is based on the ones proposed by Rishel (1991) [1] and Tseng and Peng (2007) [2]. We obtain an explicit expression for the mean lifetime of the device. Numerical methods are used to illustrate the analytical findings.