Thue equations and torsion groups of elliptic curves

A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.     

Analysis of underivatized oligosaccharides by liquid chromatography/electrospray ionization tandem mass spectrometry with post‐column addition of formic acid

Underivatized oligosaccharides were analyzed by electrospray ionization (ESI) using a linear ion trap mass spectrometer in the negative ion mode with post‐column addition of an aqueous solution of formic acid. Under these conditions all oligosaccharides showed the presence of the corresponding formate adduct [M + HCOO]^? with high intensity and easy subsequent low‐energy collision‐induced dissociation (CID) fragmentation using successive MSⁿ experiments. A careful examination of the mass spectra obtained from these MSⁿ experiments pointed out some significant differences useful to identify and quantify the single components in mixtures of coeluted disaccharides. This new sensitive and rapid method was successfully applied to the quantification of oligosaccharides in some juices minimizing sample handling. Copyright © 2009 John Wiley & Sons, Ltd.     

The Challenges of Machine Learning and Their Economic Implications

The deployment of machine learning models is expected to bring several benefits. Nevertheless, as a result of the complexity of the ecosystem in which models are generally trained and deployed, this technology also raises concerns regarding its (1) interpretability, (2) fairness, (3) safety, and (4) privacy. These issues can have substantial economic implications because they may hinder the development and mass adoption of machine learning. In light of this, the purpose of this paper was to determine, from a positive economics point of view, whether the free use of machine learning models maximizes aggregate social welfare or, alternatively, regulations are required. In cases in which restrictions should be enacted, policies are proposed. The adaptation of current tort and anti-discrimination laws is found to guarantee an optimal level of interpretability and fairness. Additionally, existing market solutions appear to incentivize machine learning operators to equip models with a degree of security and privacy that maximizes aggregate social welfare. These findings are expected to be valuable to inform the design of efficient public policies.     

Sorting out the value of spectroscopic tools to assess the Colletotrichum acutatum impact in olive cultivars with different susceptibilities

The olive tree (Olea europaea L.) can be affected by Colletotrichum acutatum, causing a loss of yield and quality of the final products, whilst the incidence of this fungal infection depends on several factors, including cultivar susceptibility. Thus, the effect of C. acutatum infection in cultivars displaying different susceptibilities to this fungal disease (‘Galega Vulgar’ ‐ susceptible, ‘Cobrançosa’ ‐ moderately susceptible, ‘Picual’ ‐ tolerant) has been assessed through spectrophotometric methods and HPLC, while the FTIR spectra of the cuticles have been concomitantly registered, resorting to the ATR accessory. With the support of multivariate analysis, these spectra allowed to discriminate olives with distinct infection times, besides retrieving evidences concerning the different susceptibility of each cultivar, while these observations were reinforced by the spectrophotometric and chromatographic methods. Furthermore, the assessment of the phenolic profile evidenced individual compounds in the distinct cultivars, so as their variations in response to the fungal infection.     

Enhanced Electrocatalytic Oxygen Evolution in Au–Fe Nanoalloys

Oxygen evolution reaction (OER) is the most critical step in water splitting, still limiting the development of efficient alkaline water electrolyzers. Here we investigate the OER activity of Au–Fe nanoalloys obtained by laser-ablation synthesis in solution. This method allows a high amount of iron (up to 11 at %) to be incorporated into the gold lattice, which is not possible in Au–Fe alloys synthesized by other routes, due to thermodynamic constraints. The Au_0.89Fe_0.11 nanoalloys exhibit strongly enhanced OER in comparison to the individual pure metal nanoparticles, lowering the onset of OER and increasing up to 20 times the current density in alkaline aqueous solutions. Such a remarkable electrocatalytic activity is associated to nanoalloying, as demonstrated by comparative examples with physical mixtures of gold and iron nanoparticles. These results open attractive scenarios to the use of kinetically stable nanoalloys for catalysis and energy conversion.     

On a Volume‐Constrained Variational Problem

. Existence of minimizers for a volume-constrained energy $ E(u) := \int_{\Omega} W(\nabla u)\, dx Existence of minimizers for a volume-constrained energy E(u) : = ò_W W(?u) dx E(u) := \int_{\Omega} W(\nabla u)\, dx where L^N({u = z_i}) = a_i, i = 1, ?, P, {\cal L}^N(\{u = z_i\}) = \alpha_i, i = 1, \ldots, P, is proved for the case in which z_iz_i are extremal points of a compact, convex set in \Bbb R^d\Bbb R^d and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1d=1, P=2P=2, W(x)=|x|²W(\xi)=|\xi|^2, and the &-limit as the sum of the measures of the 2 phases tends to \L(W)\L(\Omega) is identified. Minimizers are fully characterized when N=1N=1, and candidates for solutions are studied for the circle and the square in the plane.     

Enantioselective synthesis of 3(S)-hydroxy polygodial derivatives and evaluation of their vanilloid activity

The enantioselective synthesis of 3(S)-hydroxy polygodial and its acetyl derivative is described. The construction of the 3-hydroxy drimane skeleton was based on the titanium-catalyzed radical cyclization of (10S)-10, 11-epoxy-farnesyl acetate. Only underivatized 3(S)-hydroxy polygodial showed activity in assays on VR1 vanilloid receptor in HEK cells transfected with the human VR1.     

Metal-organic chains constructed from pre-organized N2S2 donor ligands

Three new N₂S₂ donor ligands 1,1′-((2-(2-(phenylthio)phenylthio)phenyl)methylene)bis(3,5-R-1H-pyrazole), R = H (L^H), R = Me (L^Me), R = i-Pr (L^i-Pr) have been prepared and characterized. These bifunctional ligands incorporate two distinct chelate donor systems, by virtue of the presence of bispyrazole and bisthioether functions. The preferred conformation of these ligands is such that the N₂ and S₂ donor moieties may be oriented in opposite directions, thus favoring the formation of molecular chains when treated with AgBF₄. The X-ray structures of Ag(I) complexes show that, depending on the steric hindrance present on the pyrazole rings, these ligands behave as κ⁴-SSNN-μ bridging tetradentate (when R = H), or κ³-SNN-μ bridging tridentate (when R = Me, i-Pr). Interestingly, [Ag(L^H)]BF₄ crystallizes in the chiral space group P4₁, with the molecular chain that is folded around the 4₁ screw axis.     

Hydrophilic interaction liquid chromatography/positive ion electrospray ionization mass spectrometry method for the quantification of perindopril and its main metabolite in human plasma

A validated method based on liquid chromatography/positive ion electrospray–mass spectrometry (LC-ESI/MS) is described for the quantification of perindopril and its active metabolite, perindoprilat, in human plasma. The assay was based on 500-μL plasma samples, following solid-phase extraction using Oasis HLB cartridges. All analytes and the internal standard (trandolapril) were separated by hydrophilic interaction liquid chromatography using a SeQuant Zic-HILIC analytical column (150.0?×?2.1 mm i.d., particle size 3.5 μm, 200 Å) with isocratic elution. The mobile phase consisted of 10% 5.0 mM ammonium acetate water solution in a binary mixture of acetonitrile/methanol (60:40, v/v) and pumped at a flow rate of 0.10 mL min^?1. Quantitation of the analytes was performed with selected ion monitoring (SIM) in positive ionization mode using electrospray ionization interface. The assay was found to be linear in the concentration range of 5.0–500.0 ng mL^?1 for perindopril and perindoprilat. Intermediate precision were found less than 3.5% over the tested concentration ranges. A run time of less than 6.0 min for each sample made it possible to analyze a large number of human plasma samples per day. The method is the first reported application of HILIC in the analysis of angiotensin-converting enzyme inhibitors and can be used to quantify perindopril and perindoprilat in human plasma covering a variety of pharmacokinetic or bioequivalence studies.     

Dynamic covalent hydrazine chemistry as a selective extraction and cleanup technique for the quantification of the Fusarium mycotoxin zearalenone in edible oils

A novel, cost-efficient method for the analytical extraction of the Fusarium mycotoxin zearalenone (ZON) from edible oils by dynamic covalent hydrazine chemistry (DCHC) was developed and validated for its application with high performance liquid chromatography-fluorescence detection (HPLC-FLD). ZON is extracted from the edible oil by hydrazone formation on a polymer resin functionalised with hydrazine groups and subsequently released by hydrolysis. Specifity and precision of this approach are superior to liquid partitioning or gel permeation chromatography (GPC). DCHC also extracts zearalanone (ZAN) but not α-/β-zearalenol or -zearalanol. The hydrodynamic properties of ZON, which were estimated using molecular simulation data, indicate that the compound is unaffected by nanofiltration through the resin pores and thus selectively extracted. The method's levels of detection and quantification are 10 and 30 μg/kg, using 0.2 g of sample. Linearity is given in the range of 10–20,000 μg/kg, the average recovery being 89%. Bias and relative standard deviations do not exceed 7%. In a sample survey of 44 commercial edible oils based on various agricultural commodities (maize, olives, nuts, seeds, etc.) ZON was detected in four maize oil samples, the average content in the positive samples being 99 μg/kg. The HPLC-FLD results were confirmed by HPLC–tandem mass spectrometry and compared to those obtained by a liquid partitioning based sample preparation procedure.