On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients

Regular polynomials with quaternionic coefficients admit only isolated zeroes and spherical zeroes. In this paper we prove a factorization theorem for such polynomials. Specifically, we show that every regular polynomial can be written as a product of degree one binomials and special second degree polynomials with real coefficients. The degree one binomials are determined (but not uniquely) by the knowledge of the isolated zeroes of the original polynomial, while the second degree factors are uniquely determined by the spherical zeroes. We also show that the number of zeroes of a polynomial, counted with their multiplicity as defined in this paper, equals the degree of the polynomial. While some of these results are known in the general setting of an arbitrary division ring, our proofs are based on the theory of regular functions of a quaternionic variable, and as such they are elementary in nature and offer explicit constructions in the quaternionic setting. Partially supported by G.N.S.A.G.A.of the I.N.D.A.M. and by M.I.U.R.. Lecture held by G. Gentili in the Seminario Matematico e Fisico on February 12, 2007. Received: August 2008     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

Targeting Bacterial Membranes: NMR Spectroscopy Characterization of Substrate Recognition and Binding Requirements of D‐Arabinose‐5‐Phosphate Isomerase

Lipopolysaccharide (LPS) is an essential component of the outer membrane of Gram‐negative bacteria and consists of three elements: lipid A, the core oligosaccharide, and the O‐antigen. The inner‐core region is highly conserved and contains at least one residue of 3‐deoxy‐D ‐manno‐octulosonate (Kdo). Arabinose‐5‐phosphate isomerase (API) is an aldo–keto isomerase catalyzing the reversible isomerization of D ‐ribulose‐5‐phosphate (Ru5P) to D ‐arabinose‐5‐phosphate (A5P), the first step of Kdo biosynthesis. By exploiting saturation transfer difference (STD) NMR spectroscopy, the structural requirements necessary for API substrate recognition and binding were identified, with the aim of designing new API inhibitors. In addition, simple experimental conditions for the STD experiments to perform a fast, robust, and efficient screening of small libraries of potential API inhibitors, allowing the identification of new potential leads, were set up. Due to the essential role of API enzymes in LPS biosynthesis and Gram‐negative bacteria survival, by exploiting these data, a new generation of potent antibacterial drugs could be developed.     

The O-neophyl rearrangement of 1,1-diarylalkoxyl radicals. Experimental evidence for the formation of an intermediate 1-oxaspiro[2,5]octadienyl radical

A product study on the reactivity of a 1,1-diarylalkoxyl radical bearing 2,2-diphenylcyclopropyl groups in the para-positions has been carried out. The exclusive formation of a product deriving from cyclopropyl ring-opening has been observed, indicating that 1,1-diarylalkoxyl radicals exist in equilibrium with a bridged 1-oxaspiro[2,5]octadienyl radical. This represents the first experimental evidence in support of the stepwise nature of the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals.     

UV‐Dissipation Mechanisms in the Eumelanin Building Block DHICA

The UV‐dissipative mechanisms of the eumelanin building block 5,6‐dihydroxyindole‐2‐carboxylic acid (DHICA) and the 4,7‐dideutero derivative (DHICA‐d₂) in buffered H₂O or D₂O have been characterized by using ultrafast time‐resolved fluorescence spectroscopy. Excitation of the carboxylate anion form, the dominating state at neutral pH, leads to dual fluorescence. The band peaking at λ=378 nm is caused by emission from the excited initial geometry. The second band around λ=450 nm is owed to a complex formed between the mono‐anion and specific buffer components. In the absence of complex formation, the mono‐anion solely decays non‐radiatively or by emission with a lifetime of about 2.1 ns. Excitation of the neutral carboxylic acid state, which dominates at acidic pH, leads to a weak emission around λ=427 nm with a short lifetime of 240 ps. This emission originates from the zwitterionic state, formed upon excitation of the neutral state by sub‐ps excited‐state intramolecular proton transfer (ESIPT) between the carboxylic acid group and the indole nitrogen. Future studies will unravel whether this also occurs in larger building blocks and ESIPT is a built‐in photoprotective mechanism in epidermal eumelanin.     

Determination of different recreational drugs in hair by HS-SPME and GC/MS

A simple procedure combining headspace solid-phase microextraction (HS-SPME) and gas chromatography–mass spectrometry (GC/MS) to detect and quantify amphetamines, ketamine, methadone, cocaine, cocaethylene and ∆⁹-tetrahydrocannabinol (THC) in hair is described. This procedure allows, in a single sample, even scant, analysis of drugs requiring different analytical conditions. A hair sample (10 mg) is washed and subjected to acidic hydrolysis. Then the HS-SPME is carried out (10 min at 90 °C) for amphetamines, ketamine, methadone, cocaine and cocaethylene. For derivatization of analytes, the fibre is introduced into the headspace of another closed vial containing acetic anhydride. After a chromatographic run, an alkaline hydrolysis for THC analysis is carried out in the same vial containing the hair sample previously used. For adsorption, the solid-phase microextraction needle is inserted into the headspace of the vial and the fibre is exposed for 30 min at 150 °C. For derivatization of analytes, the fibre is introduced into the headspace of another closed vial containing N-methyl-N-(trimethylsilyl)trifluoroacetamide. The GC/MS parameters were the same for both chromatographic runs. The linearity was proved to be between 0.01 and 10.00 ng/mg. The repeatability (intra- and interday precision) was below 10% as the coefficient of variation for all compounds. The accuracy, as the relative recovery, was 96.2–103.5% (spiked samples) and 88.6–101.7% (quality control sample). The limit of detection ranged from 0.01 to 0.12 ng/mg, and the limit of quantification ranged from 0.02 to 0.37 ng/mg. Application of the procedure to real hair samples is described. To the best of our knowledge, the proposed procedure combining HS-SPME and GC/MS is the first one be to successfully applied to the simultaneous determination of most of the common recreational drugs, including THC, in a single hair sample.     

Global QSAR models of skin sensitisers for regulatory purposes

Background

The new European Regulation on chemical safety, REACH, (Registration, Evaluation, Authorisation and Restriction of CHemical substances), is in the process of being implemented. Many chemicals used in industry require additional testing to comply with the REACH regulations. At the same time EU member states are attempting to reduce the number of animals used in experiments under the 3 Rs policy, (refining, reducing, and replacing the use of animals in laboratory procedures). Computational techniques such as QSAR have the potential to offer an alternative for generating REACH data. The FP6 project CAESAR was aimed at developing QSAR models for 5 key toxicological endpoints of which skin sensitisation was one.

Results

This paper reports the development of two global QSAR models using two different computational approaches, which contribute to the hybrid model freely available online.

Conclusions

The QSAR models for assessing skin sensitisation have been developed and tested under stringent quality criteria to fulfil the principles laid down by the OECD. The final models, accessible from CAESAR website, offer a robust and reliable method of assessing skin sensitisation for regulatory use.

     

Combined analysis by GC (RI), GC-MS and 13C NMR of the supercritical fluid extract of Abies alba twigs

Two samples (leaves and twigs) of Abies alba Miller from Corsica were extracted using supercritical CO2 and their chemical compositions were compared with those of the essential oils obtained from the same batch of plant material. In total 45 components were identified using combined analysis by GC (RI), GC-MS and 13C NMR. It was observed that the contents of monoterpenes (mainly represented by limonene, alpha-pinene and camphene) were significantly lower in the supercritical fluid extract (SFE) than in the essential oil (EO). Conversely, the proportions of sesquiterpenes were much higher in CO2 extracts than in essential oils (around 30% vs 4%). Cis-abienol, a diterpene alcohol, was identified only in SFE, and the proportions of this constituent (7.5% and 17.3%) were determined using quantitative 13C NMR since it was under estimated using the standard conditions of GC.     

Hydrogen abstraction from H‐donor substrates by the 6‐CF3‐benzotriazol‐N‐oxyl radical (TFNO)

The aminoxyl radical 6‐trifluoromethyl‐benzotriazol‐N‐oxyl (TFNO) has been generated from the parent hydroxylamine 6‐CF₃‐1‐hydroxy‐benzotriazole (TFBT) by one‐electron oxidation with a Ce^IV salt and characterized by spectrophotometry and cyclic voltammetry (CV). Rate constants of H‐abstraction (k_H) by TFNO from a number of H‐donor benzylic substrates have been determined spectrophotometrically in MeCN solution at 25 °C. A radical H‐atom transfer (HAT) route of oxidation is substantiated for TFNO by several pieces of evidence. The kinetic data also testify the relevance of stereoelectronic effects upon the HAT reactivity of TFNO. Copyright © 2010 John Wiley & Sons, Ltd.