On the quiver-theoretical quantum Yang–Baxter equation

Quivers over a fixed base set form a monoidal category with tensor product given by pullback. The quantum Yang–Baxter equation, or more properly the braid equation, is investigated in this setting. A solution of the braid equation in this category is called a “solution” for short. Results of Etingof–Schedler–Soloviev, Lu–Yan–Zhu and Takeuchi on the set-theoretical quantum Yang–Baxter equation are generalized to the context of quivers, with groupoids playing the role of groups. The notion of “braided groupoid” is introduced. Braided groupoids are solutions and are characterized in terms of bijective 1-cocycles. The structure groupoid of a non-degenerate solution is defined; it is shown that it is a braided groupoid. The reduced structure groupoid of a non-degenerate solution is also defined. Non-degenerate solutions are classified in terms of representations of matched pairs of groupoids. By linearization we construct star-triangular face models and realize them as modules over quasitriangular quantum groupoids introduced in papers by M. Aguiar, S. Natale and the author.     

Central Limit Theorems for the Shrinking Target Problem

Suppose B _i :=B(p,r _i ) are nested balls of radius r _i about a point p in a dynamical system (T,X,μ). The question of whether T ⁱ x∈B _i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if $E_{n}:=\sum_{i=1}^{n} \mu(B_{i})$ diverges then there is a quantitative rate of entry and $\lim_{n\to\infty} \frac{1}{E_{n}} \sum_{j=1}^{n} 1_{B_{i}} (T^{i} x) \to1$ for μ a.e. x∈X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form $\lim_{ n\to\infty} \frac{1}{a_{n}} \sum_{i=1}^{n} [1_{B_{i}} (T^{i} x)-\mu(B_{i})] \to N(0,1)$ (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are $a^{2}_{n} \sim E [\sum_{i=1}^{n} 1_{B_{i}} (T^{i} x)-\mu(B_{i})]^{2}$ . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.     

“Surface-enhanced Raman spectroscopy studies of the passive layer formation in gold leaching from thiosulfate solutions in the presence of cupric ion”

Complementary electrochemical and spectroscopic techniques were used to characterize the behavior and composition of the passive layer formed at the gold surface in a thiosulfate electrolyte in the presence of cupric ions. Raman studies of three different cationic (calcium, ammonium, and sodium) thiosulfate leaching solutions revealed that the concentrations of thiosulfate, trithionate, sulfate, and tetrathionate remained constant in the bulk solution over a 3-h time period. The initial leaching current densities of these three systems were identical; however, significant differences in the open circuit potentials of these systems were observed. To provide additional information about the nature of the passive layer, gold nanorod array electrodes were fabricated and employed as substrates for studying the species present at the gold–thiosulfate interface using surface-enhanced Raman spectroscopy (SERS). The composition and behavior of the passive layer at the gold–thiosulfate interface greatly differed from those of the bulk solutions. The passive layer consisted primarily of elemental sulfur and sulfide-like species, with thiosulfate and its oxidation products, such as tri- and tetrathionates, as minority components. The nature of the cation (calcium, sodium, or ammonium) of the thiosulfate salt showed no significant effect on the composition of the passive layer at leaching times longer than 100 min. In addition, the presence of cupric ions also had no significant effect on the formation of the passive layer. However, copper is a much better oxidant than oxygen in gold–thiosulfate leaching reactions.     

Molecular structure of cyanidin metal complexes: Al(III) versus Mg(II)

Metal complexation by anthocyanins is a very efficient mechanism for protecting plants. While Mg is an essential metal for life, typically found bound to anthocyanins, Al interferes with the metabolism of the former. Density functional theory and the polarizable continuum model are used to study cyanin (the simplest anthocyanin bearing a catechol unit) complexes with Mg(II) and Al(III), considering different metal ligand stoichiometries. Results obtained for metal-binding energies indicate that Al(III) complexes are always more stable than those of Mg(II). Furthermore, reaction energies for the metal exchange process show that free Al(III) (hexaaquo complex) is always able to displace Mg(II). This displacement is more favored when the metal ligand ratio decreases. Thus, anthocyanins are implied in suppressing Al(III) toxicity by enabling its accumulation and reducing its migration to ecosystems. The characteristics of Al(III)?Ccyanidin and Mg(II)?Ccyanidin bonds are investigated using the quantum theory of atoms in molecules. We find these complexes are more stabilized by ion?Cdipole electrostatic interactions than by electron pair sharing, as predicted by the Hard and Soft Acids Theory. Globally, two factors increase the covalent character: replacement of Mg(II) by Al(III) and replacement of water by cyanidin ligands.     

A Zn(II) luminescent complex with a Schiff base ligand: solution,computational and solid state studies

Abstract

A new mononuclear complex of zinc(II), [Zn(HL)₂]?2DMF (H₂L = (E)-N′-((E)-(hydroxyimino)butan-2-ylidene)salicyloylhydrazide, DMF = N,N-dimethylformamide), was prepared and characterized. Single-crystal X-ray crystallography revealed a six-coordinate zinc(II) surrounded by nitrogen of the oxime function and oxygen and distal nitrogens of the acylhydrazone group. This entity also exists in solution as demonstrated by ¹H-NMR and potentiometric titrations. The computational analysis showed that the molecular orbitals involved in the main electronic transitions of the complex species in solution are centered on the ligand with negligible contribution of the metal ion. The photophysical properties of the complex were evaluated in solution and in the solid state. Luminescence studies showed that the solid has a strong emission at 550 nm with a large Stokes shift with respect to absorption. The solid state fluorescence emission is ascribed to ligand-centered and/or ligand-to-ligand charge transfer transitions, following the DFT results in solution. A comparison with a previously reported mononuclear [Zn(HL)₂] allowed the investigation of the influence of DMF molecules in the structural packing and the luminescence properties.     

Monoparameter sensors for the determination of the antioxidants butylated hydroxyanisole and n-propyl gallate in foods and cosmetics by flow injection spectrophotometry.

A flow-through optosensor with solid phase UV spectroscopic detection is proposed for the direct determination of single antioxidants, namely butylated hydroxyanisole (BHA) and n-propyl gallate (n-PG), without previous derivatization. The methods are based on the transient retention behaviour of these compounds in a flow-through cell packed with C-18 silica using ethanol-water mixtures as a carrier, and on the intrinsic absorbance monitored at 290 and 283 nm, respectively. After recording the analytical signal, the antioxidants were easily and quickly desorbed from the solid support by the same carrier. For BHA, calibration graphs were linear over the range 1.0-300.0 mg L-1 using area as the analytical parameter. The relative standard deviation (RSD) was between 0.5 and 1.6%. For n-PG, calibration graphs were linear over the range 1.0-300.0 mg L-1 in area and the RSD was between 1.4 and 1.5%. The methods were applied to the determination of these antioxidants in several food and cosmetics samples, and were validated using the standard additions method and an HPLC reference method.     

Poly‐l‐Lactic Acid Nanofiber–Polyamidoamine Hydrogel Composites: Preparation,Properties, and Preliminary Evaluation as Scaffolds for Human Pluripotent Stem Cell Culturing

Electrospun poly‐l ‐lactic acid (PLLA) nanofiber mats carrying surface amine groups, previously introduced by nitrogen atmospheric pressure nonequilibrium plasma, are embedded into aqueous solutions of oligomeric acrylamide‐end capped AGMA1, a biocompatible polyamidoamine with arg‐gly‐asp (RGD)‐reminiscent repeating units. The resultant mixture is finally cured giving PLLA‐AGMA1 hydrogel composites that absorb large amounts of water and, in the swollen state, are translucent, soft, and pliable, yet as strong as the parent PLLA mat. They do not split apart from each other when swollen in water and remain highly flexible and resistant, since the hydrogel portion is covalently grafted onto the PLLA nanofibers via the addition reaction of the surface amine groups to a part of the terminal acrylic double bonds of AGMA1 oligomers. Preliminary tested as scaffolds, the composites prove capable of maintaining short‐term undifferentiated cultures of human pluripotent stem cells in feeder‐free conditions.

     

Tandem mass spectrometric study of 1,3,5-trinitrobenzene molecular ion: an unusual ortho effect involving a hydrogen atom from the aromatic ring

Unimolecular (metastable) and collision-induced dissociation of 1,3, 5-trinitrobenzene molecular ion was studied using linked scans and mass-analyzed ion kinetic energy spectrometry on a hybrid instrument of EBEqQ geometry. An unusual ortho effect leading to the loss of OH radical from the parent molecular ion is observed as a unimolecular dissociation process only in the first-field free region between the ion source and the electric sector, although corresponding dissociation in the ion source is of negligible abundance (<0.1%). This unimolecular process is taken over by other dissociation pathways when the parent ion is collisionally activated, suggesting that this dissociation process occurs only in a very narrow energy window with a rate constant of the order of 2 x 10(5) s(-1). Copyright 2000 John Wiley & Sons, Ltd.     

Electrochemistry and Spin-Crossover Behavior of Fluorinated Terpyridine-Based Co(II) and Fe(II) Complexes

Due to their ability to form stable molecular complexes that have tailor-made properties, terpyridine ligands are of great interest in chemistry and material science. In this regard, we prepared two terpyridine ligands with two different fluorinated phenyl rings on the backbone. The corresponding Co^II and Fe^II complexes were synthesized and characterized by single-crystal X-ray structural analysis, electrochemistry and temperature-dependent SQUID magnetometry. Single crystal X-ray diffraction analyses at 100 K of these complexes revealed Co−N and Fe−N bond lengths that are typical of low spin Co^II and Fe^II centers. The metal centers are coordinated in an octahedral fashion and the fluorinated phenyl rings on the backbone are twisted out of the plane of the terpyridine unit. The complexes were investigated with cyclic voltammetry and UV/Vis-NIR spectroelectrochemistry. All complexes show a reversible oxidation and several reduction processes. Temperature dependent SQUID magnetometry revealed a gradual thermal SCO behavior in two of the complexes, while EPR spectroscopy provided further insights on the electronic structure of the metal complexes, as well as site of reduction.