Extremal Betti numbers of graded ideals

The possible extremal Betti numbers of graded ideals in the polynomial ring K[x₁,…,x_n] in n variables with coefficients in a field K are studied, completing our results in [7]. In case char(K) = 0 we determine, given any integers r < n, the conditions under which there exists a graded ideal I ? K[x₁,…, x_n] with extremal Betti numbers $\beta_{k_{i}k_{i}+\ell_{i}}\ {\rm for}\ i=1,\cdots,r$ . We also treat a similar problem for squarefree lexsegment ideals.     

Aromatization of aliphatic compounds—II: On the aromatization of some alkyl substituted cyclohexenones

2,3,5-Trimethyl-4-oxo-cyclohex-2-en acetic acid 5 treated with PyHCl aromatizes to the corresponding 2,3,5-trimethyl-benzene acetic acid 9 through a mechanism different from that leading to arylacetic acids from 2-oxo-cyclohex-3-en acetic acids 3. 2,3,4,6-Tetrakyl cyclohexenone 11, lacking the 2-carboxymethyl group, also aromatizes to tetralkyl benzene 13.     

On the Asymptotic Behavior of Dilution Parameters for Gaussian and Hole–Gaussian Log-Conductivity Covariance Functions

Using a Lagrangian approach, the authors have previously shown that the kinetics of concentration variance and dilution of passive solutes in heterogeneous aquifers depend on the ratio between two- and one-particle covariances. Extending this approach, it is here demonstrated that, for point injections, the two-particle covariance coincides with the variance of the centroid location. Then, based on an Eulerian formulation, analytical first-order approximations are obtained for the two-particle covariance, for two types of log-conductivity covariance. For Gaussian covariance functions, whereas the transverse moments are asymptotically constant, the longitudinal moment tends to increase logarithmically over time. For hole–Gaussian covariances, both transverse and longitudinal moments tend to constant values. In both cases, the longitudinal two-particle correlation, which plays a crucial role in determining the dynamics of the concentration fluctuations, is controlled by the magnitude of the local dispersivity. The theoretical predictions are compared to the data collected at the Cape Cod site in terms of time derivative of the longitudinal two-particle moment, for Gaussian log-conductivity covariance and resorting to maximum likelihood estimates. Generally, good agreement is there, between experimental data and analytical expressions.     

Adsorption of formic acid on Si(111)7 × 7 at room temperature: a valence band photoemission and Si2p photodesorption study

Formic acid is the simplest of the carboxylic acids and a model adsorption system for several surfaces. In spite of the simple structure, formic acid reactivity and photoreactivity may be quite complex. In this paper, a study is presented on the deuterated formic acid adsorption on Si(111)7 × 7 at room temperature. The study is performed both by valence band photoemission and by photon‐stimulated desorption as a function of time and of photon energy in the 90–120 eV range. A primarily adsorption on rest atoms is found. This is verified by monitoring rest atoms and adatom intensity as a function of formic acid exposure. Further checks were made to control that surface adatoms were still free to react after the adsorption of formic acid. The photon stimulated desorption produces 5 single positively charged fragments: D⁺, O⁺, OD⁺ CO⁺ and CDO⁺. Possible fragmentation mechanisms are discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Validation according to European Commission Decision 2002/657/EC of a confirmatory method for aflatoxin M1 in milk based on immunoaffinity columns and high performance liquid chromatography with fluorescence detection

A high performance liquid chromatographic method with fluorimetric detection for the determination of aflatoxin M₁ (AFM₁) in milk has been optimized and validated according to Commission Decision 2002/657/EC by using the conventional validation approach. The procedure for determining selectivity, recovery, precision, decision limit (CC_α), detection capability (CC_β) and ruggedness of the method has been reported. The results of the validation process demonstrate the agreement of the method with the provisions of Commission Regulation 401/2006/EC. The mean recovery calculated at three levels of fortification (0.5, 1.0, and 1.5-fold the MRL) was 91% and the maximum relative standard deviation value for the within-laboratory reproducibility was 15%. Limit of detection (LOD) and limit of quantitation (LOQ) values were 0.006 μg kg⁻¹ and 0.015 μg kg⁻¹ while the CC_α and CC_β values were 0.058 μg kg⁻¹ and 0.065 μg kg⁻¹, respectively. The relative expanded measurement uncertainty of the method was 7%. The method was not affected by slight variations of some critical factors (ruggedness minor changes) as pre-treatment and clean-up of milk samples, thermal treatment and different storage conditions, as well as by major changes valued in terms of milk produced by different species (buffalo, goat and sheep). The method allowed accurate confirmation analyses of milk samples, resulted positive by the screening method. In fact, the Z-score values attained in a proficiency test round were well below the reference value of 1, proving the excellent laboratory performances.     

Spin coupling in the supramolecular structure of a new tetra(quinoline-TEMPO)yttrium(III) complex

The newly synthesized tetra(quinoline-TEMPO)yttrium(III) potassium salt shows interesting structural features at the molecular and supramolecular levels, revealed by the analysis of the X-ray diffraction data. The magnetic susceptibility and EPR data corroborated with structural considerations showed that the exchange and dipolar spin coupling interactions are taking place at the nodes assembling the supramolecular 2D structure. The Y(III) center shows antiprismatic octacoordination, close to the idealized D2 symmetry. The diamagnetic transition metal plays no role in mediating the radical interactions since the TEMPO-type fragments are remote from the chelating moieties of the ligand. In turn, significant interaction occurs on the nodes consisting in the quasi-rectangular coordination of potassium counterions by the spin-bearing TEMPO groups coming from four distinct complex units. The antiferromagnetic susceptibility was consistently modeled by a spin Hamiltonian based on the rectangle topology of four spins S = 1/2. The fitted exchange parameters are Ja = -5.1 cm-1 and Jb = -3.4 cm-1 for the edges, imposing Jd = 0 for the diagonal. These values are in excellent agreement with the ab initio results Ja = -4.83 cm-1, Jb = -3.44 cm-1, Jd = -0.07 cm-1 obtained in a CASSCF(12,8) calculation. Based on the reliability of the ab initio results we were able to select the presented J parameters among several versions of multiple solutions with acceptable goodness of the fit. A methodological caveat about the artifacts of the automatic use of best fit parameters, in the absence of supplementary criteria, in the context of relative blindness of magnetic susceptibility modeling, is raised. The details of the EPR spectrum at 10 K are also consistent, in the frame of dipolar approximation, with the model of four interacting spins at the nodes of the supramolecular assembling.     

Comparison of comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry and gas chromatography-mass spectrometry for the qualitative characterisation of roasted barley by solid-phase microextraction

Volatile compounds of roasted barley used in the production of barley coffee, the most common coffee substitute, were analysed by using solid-phase microextraction (SPME) followed by GC-MS and comprehensive GC x GC-TOF-MS, respectively. The optimised SPME extraction conditions in terms of selection of the fibre coating, extraction time and extraction temperature allowed to obtain the highest GC response, thus enhancing the identification capabilities of the developed method. As for the SPME-GC x GC-TOF-MS analysis, 64 compounds with similarity, reverse and probability values above 800, 900 and 6000, respectively, were identified, by using a polar x apolar column set combination; in contrast, GC-MS was able to identify a lower number of compounds, i.e. 40 volatiles.     

An Empirical Correction Term to Density Functional Theory for the Description of the TiCl4-Lewis Base Complexes

Calorimetric and computational investigation on the interaction of TiCl₄ with some Lewis bases (esters and ethers) is presented. The bases were chosen for their relevance in heterogeneous Ziegler-Natta polymerization of propene. Comparison of the theoretical data with the calorimetric data indicates that calculations consistently underestimate the experimental binding energies. In light of this consistency, we propose that an empirical correction term added to the theoretical binding energies could represent an empirical solution for the prediction of the TiCl₄/donor binding energies with reasonable accuracy.     

Recent Advances in the Synthesis of Inorganic Materials Using Environmentally Friendly Media

Deep Eutectic Solvents have gained a lot of attention in the last few years because of their vast applicability in a large number of technological processes, the simplicity of their preparation and their high biocompatibility and harmlessness. One of the fields where DES prove to be particularly valuable is the synthesis and modification of inorganic materials—in particular, nanoparticles. In this field, the inherent structural inhomogeneity of DES results in a marked templating effect, which has led to an increasing number of studies focusing on exploiting these new reaction media to prepare nanomaterials. This review aims to provide a summary of the numerous and most recent achievements made in this area, reporting several examples of the newest mixtures obtained by mixing molecules originating from natural feedstocks, as well as linking them to the more consolidated methods that use “classical” DES, such as reline.