Biliaison Classes of Rank Two Reflexive Sheaves on P3

A biliaison theory for rank two reflexive sheaves on projective 3 - space is established, In analogy with the existing theory for curves and, more generally, for 2 - codimensional subschemes of projective n - space. By definition two such sheaves are in the same biliaison class if their first cohomology modules are isomorphic. A parametrization of these classes is given. It is then shown that any class not corresponding to the zero module has a structure described by the Lazarsfeld - Rao property. In particular, it is shown that vector bundles are precisely the minimal elements (in the of the LR - property) in their biliaison classes.     

Kabuli and Apulian black Chickpea Milling By-Products as Innovative Ingredients to Provide High Levels of Dietary Fibre and Bioactive Compounds in Gluten-Free Fresh Pasta

Gluten-free (GF) products, including pasta, are often characterised by nutritional deficiencies, such as scarce dietary fibre and excess of calories. Chickpea flour is increasingly being used by the food industries. Hulls, rich in dietary fibre and bioactive compounds, are discarded after milling. The aim of this work was to evaluate the quality features of short-cut GF fresh pasta added of hull (8% w/w) derived from kabuli (KH) or Apulian black (ABH) chickpeas, in comparison with control GF pasta prepared without hull. The enriched pasta, which could be labelled as “high fibre”, was characterised by a higher level of bioactive compounds and antioxidant activity than the control. ABH-enriched pasta showed the highest anthocyanins (33.37 ± 1.20 and 20.59 ± 0.11 mg/kg of cyanidin-3-O-glucoside on dry matter in raw and cooked pasta, respectively). Hull addition increased colour intensity and structural quality of GF pasta: ABH-enriched pasta had the lowest cooking loss and the highest water absorption capacity; KH-enriched pasta showed the highest firmness. No significant differences in sensory liking were found among the samples, except for “aftertaste”. Chickpea hull can be used as an innovative ingredient to produce potentially functional GF pasta, meeting the dietary needs of consumers without affecting quality.     

Condensation of β‐Diester Titanium Enolates with Carbonyl Substrates: A Combined DFT and Experimental Investigation

The condensation of dialkyl β‐diesters with various aldehydes promoted by TiCl₄ has been studied by DFT approaches and experimental methods, including NMR, IR and UV/Vis spectroscopy. Various possible reaction pathways have been investigated and their energy profiles evaluated to find out a plausible mechanism of the reaction. Theoretical results and experimental evidence point to a three‐step mechanism: 1) Ti‐induced formation of the enolate ion; 2) aldol reaction between the enolate ion and the aldehyde, both coordinated to titanium; and 3) intramolecular elimination that leads to a titanyl complex. The presented mechanistic hypothesis allows one to better understand the pivotal role of titanium(IV) in the reaction.     

Solid‐phase extraction and HPLC determination of fluoroquinolones in surface waters

An investigation on filtration procedures and SPE sorbents used for the determination of traces of the most common veterinary fluoroquinolones (FQs), marbofloxacin (MAR) and enrofloxacin (ENR) used as antibacterial agents in cattle and swine farms in the province of Pavia (Italy), was performed in natural waters. The filter composition and the sorbent used in the SPE strongly influence the correct recovery, both in terms of total and dissolved FQs concentration. An accurate comparison among different filters and SPE sorbents showed that a full determination of analytes was possible on nylon filters followed by anionic (WAX) and hydrophilic–lipophilic balance (HLB) resins as SPE. Quantitative analysis was done by chromatography with fluorescence detection (HPLC‐FD). Fluoroquinolones recovery was between 90 and 116% with RSD not greater than 10% (sample volume 250 mL). The developed method allowed to determine both dissolved and NOM‐absorbed fractions of FQs, therefore a full determination of the analytes was possible. Limits of detection (LOD) and quantification (LOQ) were, respectively, 0.7 and 2.2 ng/L for ENR and 2 and 6 ng/L for MAR. The kinetics of degradation under solar light was explored.     

Generalized polar coordinates on Lie groups and numerical integrators

Motivated by developments in numerical Lie group integrators, we introduce a family of local coordinates on Lie groups denoted generalized polar coordinates. Fast algorithms are derived for the computation of the coordinate maps, their tangent maps and the inverse tangent maps. In particular we discuss algorithms for all the classical matrix Lie groups and optimal complexity integrators for n-spheres.     

Prescribing valuations of the order of a point in the reductions of abelian varieties and tori

Let G be the product of an abelian variety and a torus defined over a number field K. Let R be a K-rational point on G of infinite order. Call nR the number of connected components of the smallest algebraic K-subgroup of G to which R belongs. We prove that nR is the greatest positive integer which divides the order of for all but finitely many primes p of K. Furthermore, let m>0 be a multiple of nR and let S be a finite set of rational primes. Then there exists a positive Dirichlet density of primes p of K such that for every ? in S the ?-adic valuation of the order of equals v?(m).     

Two variants of the support problem for products of abelian varieties and tori

Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of divides the order of . Then there exist a K-endomorphism ? of G and a non-zero integer c such that ?(P)=cQ. Furthermore, we are able to prove the above result with weaker assumptions: instead of comparing the order of the points we only compare the radical of the order (radical support problem) or the ?-adic valuation of the order for some fixed rational prime ? (?-adic support problem).