Nash multiplicities and isolated points of maximum multiplicity

Let X be an algebraic variety defined over a field of characteristic zero, and let $\xi \in \underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$ be a point in the closed subset of maximum multiplicity of X. We provide a criterion, given in terms of arcs, to determine whether ξ is isolated in $\underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$. More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in $\underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$.     

Dual catalytic performance of arene-ruthenium amine complexes for norbornene ring-opening metathesis and methyl methacrylate atom-transfer radical polymerizations

Arene ruthenium(II) complexes bearing the cyclic amines RuCl₂(η⁶-p-cymene)(pyrrolidine)] ( 1 ), [RuCl₂(η⁶-p-cymene)(piperidine)] ( 2 ), and [RuCl₂(η⁶-p-cymene)(peridroazepine)] ( 3 ) were successfully synthesized. Complexes 1 – 3 were fully characterized by means of Fourier transform infrared, UV–visible, and NMR spectroscopy, elemental analysis, cyclic voltammetry, computational methods, and one of the complexes was further studied by single crystal X-ray crystallography. These compounds were evaluated as catalytic precursors for ring-opening metathesis polymerization (ROMP) of norbornene (NBE) and atom-transfer radical polymerization (ATRP) of methyl methacrylate (MMA). NBE polymerization via ROMP was evaluated using complexes 1 – 3 as precatalysts in the presence of ethyl diazoacetate (EDA) under different [NBE]/[EDA]/[Ru] ratios, temperatures (25 and 50°C), and reaction times (5–60 min). The highest yields of polyNBE were obtained with [NBE]/[EDA]/[Ru] = 5000/28/1 for 60 min at 50°C. MMA polymerization via ATRP was conducted using 1 – 3 as catalysts in the presence of ethyl-α-bromoisobutyrate (EBiB) as initiator. The catalytic tests were evaluated as a function of the reaction time using the initial molar ratio of [MMA]/[EBiB]/[Ru] = 1000/2/1 at 95°C. The increase in molecular weight as function of time indicates that complexes 1–3 were able to mediate the MMA polymerization with an acceptable rate and some level of control. Differences in the rate of polymerization were observed in the order 3 > 2 > 1 for the ROMP and ATRP.     

On the Structure and Chiral Aggregation of Liquid Crystalline Star-Shaped Triazines H-Bonded to Benzoic Acids

The ability of a star-shaped tris(triazolyl)triazine derivative to hierarchically build supramolecular chiral columnar organizations through the formation of H-bonded complexes with benzoic acids was studied from a theoretical and experimental point of view. The combined study has been done at three different levels including the study of the structure of the triazine core, the association with benzoic acids in stoichiometry 1:3, and the assembly of 1:3 complexes in helical aggregates. Although the star-shaped triazine core crystallizes in a non-C₃ conformation, the C₃-symmetric conformation is theoretically predicted to be more stable and gives rise to a favorable C₃ supramolecular 1:3 complex upon the interaction with three benzoic acids in their voids. In addition, calculations at different levels (DFT, PM7, and MM3) for the 1:3 host-guest complex predict the formation of large stable columnar helical aggregates stabilized by the compact packing of the interstitial acids by π–π and CH⋅⋅⋅π interactions. The acids restrict the movement of the the star-shaped triazine cores along the stacking axis causing a template effect in the self-assembly of the complex. Theoretical predictions correlate with experimental results, since the interaction with achiral or chiral 3,4,5-(4-alkoxybenzyloxy)benzoic acids gives rise to supramolecular complexes that organize in bulk hexagonal columnar mesophases stable at room temperature with intracolumnar order. The existence of supramolecular chirality in the mesophase was determined for complexes formed by acids derived from (S)-2-octanol. Chiral aggregation was also evidenced for complexes formed in dodecane.     

Asymptotically stable periodic orbits of a coupled electromechanical system

In this paper an electromechanical system is analyzed. The existence and asymptotic stability of a periodic orbit are obtained in a mathematically rigorous way as well as an expansion of the period by using an adequate small parameter. For the analytical results the main tool used is the regular perturbation theory. Some results, such as the growing of the period according to some powers of the parameters and the relation 2:1 between the period of the cart, which is a part of the electromechanical system, and the period of the current, are compatible with earlier numerical findings.     

XANES speciation of mercury in three mining districts – Almadén,Asturias (Spain), Idria (Slovenia)

The mobility, bioavailability and toxicity of mercury in the environment strongly depend on the chemical species in which it is present in soil, sediments, water or air. In mining districts, differences in mobility and bioavailability of mercury mainly arise from the different type of mineralization and ore processing. In this work, synchrotron‐based X‐ray absorption near‐edge spectroscopy (XANES) has been taken advantage of to study the speciation of mercury in geological samples from three of the largest European mercury mining districts: Almadén (Spain), Idria (Slovenia) and Asturias (Spain). XANES has been complemented with a single extraction protocol for the determination of Hg mobility. Ore, calcines, dump material, soil, sediment and suspended particles from the three sites have been considered in the study. In the three sites, rather insoluble sulfide compounds (cinnabar and metacinnabar) were found to predominate. Minor amounts of more soluble mercury compounds (chlorides and sulfates) were also identified in some samples. Single extraction procedures have put forward a strong dependence of the mobility with the concentration of chlorides and sulfates. Differences in efficiency of roasting furnaces from the three sites have been found.     

Gold internal standard correction for elemental imaging of soft tissue sections by LA-ICP-MS: element distribution in eye microstructures

Laser ablation coupled to inductively coupled plasma mass spectrometry has been developed for the elemental imaging of Mg, Fe and Cu distribution in histological tissue sections of fixed eyes, embedded in paraffin, from human donors (cadavers). This work presents the development of a novel internal standard correction methodology based on the deposition of a homogeneous thin gold film on the tissue surface and the use of the ¹⁹⁷Au⁺ signal as internal standard. Sample preparation (tissue section thickness) and laser conditions were carefully optimized, and internal normalisation using ¹⁹⁷Au⁺ was compared with ¹³C⁺ correction for imaging applications. ²⁴Mg⁺, ⁵⁶Fe⁺ and ⁶³Cu⁺ distributions were investigated in histological sections of the anterior segment of the eye (including the iris, ciliary body, cornea and trabecular meshwork) and were shown to be heterogeneously distributed along those tissue structures. Reproducibility was assessed by imaging different human eye sections from the same donor and from ten different eyes from adult normal donors, which showed that similar spatial maps were obtained and therefore demonstrate the analytical potential of using ¹⁹⁷Au⁺ as internal standard. The proposed analytical approach could offer a robust tool with great practical interest for clinical studies, e.g. to investigate trace element distribution of metals and their alterations in ocular diseases.

Critical evaluation of the potential of radiofrequency pulsed glow discharge–time-of-flight mass spectrometry for depth-profile analysis of innovative materials

The combination of radiofrequency pulsed glow discharge (RF-PGD) analytical plasmas with time-of-flight mass spectrometry (TOFMS) has promoted the applicability of this ion source to direct analysis of innovative materials. In this sense, this emerging technique enables multi-elemental depth profiling with high depth resolution and sensitivity, and simultaneous production of elemental, structural, and molecular information. The analytical potential and trends of this technique are critically presented, including comparison with other complementary and well-established techniques (e.g. SIMS, GD–OES, etc.). An overview of recent applications of RF-PGD–TOFMS is given, including analysis of nano-structured materials, coated-glasses, photovoltaic materials, and polymer coatings     

Gas chromatography–triple-quadrupole mass spectrometry for analysis of selected polyhalogenated pollutants in plants. Comparison of extraction methods

Different extraction methods, followed by gas chromatography coupled to triple quadrupole mass spectrometry, were evaluated for simultaneous extraction of seven polychlorinated biphenyls (PCBs) and six polybrominated diphenyl ethers (PBDEs) from common weeds. Pressurized liquid extraction (PLE) with in-cell clean-up, ultrasound-assisted extraction (UAE) with in-column clean-up, and UAE with dispersive solid-phase extraction (dSPE) clean-up were evaluated and compared. In-cell clean-up with 4 g Florisil and 0.5 g graphitized carbon black (GCB) and two extraction cycles of 10 min with n-hexane–ethyl acetate 80:20 (v/v) at 60 °C were used for the PLE procedure. UAE with in-column clean-up was conducted under conditions similar to those reported for the PLE method whereas in UAE with dSPE clean-up purification of the extract was performed after extraction using primary and secondary amine sorbent (PSA) and GCB. Recovery from 82 to 104 % was obtained for all the compounds by PLE whereas, in general, lower extraction efficiency was obtained by UAE with in-column clean-up (especially for BDE-17 and BDE-183, for which recovery was 70 and 41 %, respectively) and by UAE with dSPE clean-up, for which the main drawback is that BDE-183 cannot be extracted. Finally, PLE was used for analysis of PCBs and PBDEs in different plants (Lolium rigidum, Lactuca serriola, Malva sylvestris, and Verbascum thapsus) collected from residential and/or rural areas of Madrid (Spain). Several of the analyzed compounds were detected at low levels in these plants, but only PCB-153 could be quantified.