Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Investigation on Ochratoxin A stability using different extraction techniques

The stability of Ochratoxin A during its extraction using different extraction techniques has been evaluated. Microwave-assisted extraction and pressurised liquid extraction, in addition to two other reference methods of extraction, i.e. ultrasound-assisted and magnetic stirring-assisted extraction, were evaluated. The effect of extraction temperature using the cited techniques was checked.The results show that Ochratoxin A can be extracted using microwave-assisted extraction at temperatures up to 150 °C without degradation. Pressurised liquid extraction can be used at temperatures up to 100 °C, for extraction times of less than 30 min. Further, both ultrasound-assisted extraction and magnetic stirring extraction can be applied at temperatures up to 65 °C.High-performance liquid chromatography combined with fluorescence detection using a Chromolith RP-18e column at a flow rate of 5 mL min⁻¹ was used to quantify the Ochratoxin A. The retention time for the Ochratoxin A was 1.3 min. The limits of detection (LOD) and of quantification (LOQ) were 0.03 and 0.10 μg L⁻¹, respectively.     

Optimization of a New Extraction Technique for Analysis of Verbenone and cis-Verbenol in Pine Seeds

Results from a systematic study of the factors affecting extraction of cis-verbenol and verbenone from pine seeds are presented. Five extraction conditions were investigated: extraction solvent, method of extraction, extraction temperature, volume of solvent, and the ratio of the mass of sample to the amount of extraction solvent. The resulting optimized method uses magnetic-stirring-assisted extraction of pine seeds (5 g) with ethyl acetate (75 mL) for 20 min, at room temperature. RSDs were less than 5% for both compounds. GC–FID was used for quantification of cis-verbenol and verbenone in the extracts.     

Polarographic behaviour of salicylaldehyde-2-pyridylhydrazone and its copper(II) complex

The polarographic behaviour of salicylaldehyde-2-pyridylhydrazone (SAPH) has been studied in aqueous buffer solution containing 40% ethanol using DC and DP polarographic methods. In the pH range 1.8–7.5 the observed single irreversible reduction wave is assigned to the splitting of the N-N bond and reduction of C=N centre. In alkaline medium, a second wave appears at a more negative potential due to the reduction of the salicylaldehyde which is formed by hydrolytic decomposition of the SAPH molecule. The effect of pH on the limiting current andE _1/2 as well as the reduction mechanism are discussed and compared with similar compounds. The kinetic parameters of the electrode reaction have been calculated.The analytical properties of the copper(II)-SAPH system is described. The complex gave rise to a single irreversible well-defined wave (E _1/2=–0.58 V at pH=5.2). The reaction process is diffusion controlled. A method is suggested for the determination of Cu(II) in presence of different metal ions as the difference in theirE _1/2 values is sufficient for the purpose.This work is taken partly from the M. Sc. Thesis of Jamal S. Shalabi     

Simultaneous determination of carbaryl and azinphos-methyl in water by first-derivative synchronous spectrofluorimetry

A method is proposed for the simultaneous determination of the pesticides carbaryl (CBL) and azinphos-methyl (AZM) in water by first-derivative synchronous spectrofluorimetry. It is based on the alkaline hydrolysis of both pesticides to their metabolites 1-naphthol (from CBL) and anthranilic acid (from AZM). The constant wavelength difference chosen to optimize the determination is Δλ=λ_em?λ_ex=103 nm. CBL is measured at 302/405 nm and AZM at 333/436 nm. The calibration graphs are linear between 2.0 and 500.0 ng/ml for CBL and between 1.2 and 500.0 ng/ml for AZM with detection limits of 0.62 ng/ml and 0.35 ng/ml, respectively. The precision of the method (RSD) is 2.4% at the 80.0 ng/ml level for CBL and 2.5% at the 80.0 ng/ml level for AZM. The method is applied to the determination of both analytes in samples of natural waters.     

Some spectroscopic aspects of electron transfer in ruthenium(II) polypyridyl complexes

The metal-to-ligand charge transfer (MLCT) absorption and emission properties of several ruthenium(II)-bipyridine am(m)ine complexes are compared. The Gaussian deconvolution of the spectra indicates that: (a) the emission MLCT bandwidths are smaller than the absorption bandwidths for the first components of the apparent vibronic progressions; (b) the emission bands decrease in energy and width when a polypyridyl is replaced by an am(m)ine. The observations can be interpreted in terms of a two state model and the perturbation theory-based treatment of the attenuation of the effective reorganizational energy, λ_r =^~ λ_r ^o(1- 4α² _DA), where λ_r ^o is the reorganizational energy corresponding to no mixing between the two electron transfer states and α_DA = (H_DA/E_DA) is the mixing coefficient. Both the solvent and molecular contributions to λ_r are attenuated. The MLCT excited state lifetimes also decrease with am(m)ine substitution, and the non-radiative decay rate constant at 77 K is roughly proportional to the number of am(m)ine moieties coordinated to the ruthenium center.     

Proton and antiproton impact ionization of atomic hydrogen and helium

Single ionization of helium and atomic hydrogen by the impact of protons and antiprotons is considered. Using a multiple scattering model, first proposed by Garibotti and Miraglia [1], angular and energy distributions of the ejected electrons are calculated. Structures arising in the cross section, especially the Coulomb density of states effect (CDS), are analysed. The contributions of various scattering amplitudes to the cross section are studied. It is concluded that multiple scattering together with the CDS-effect play an important role in determining the transition amplitude. Differences between particle and antiparticle impact are examined. In addition to the different behaviour of the CDS-effect, the interference of two scattering amplitudes turns out to be decisive in ionization by particle and antiparticle impact.     

Adsorption of phenanthrene on organoclays from distilled and saline water

Isotherms of phenanthrene adsorption on different organoclay complexes were obtained using the HPLC technique to understand the adsorption behavior and to characterize the effect of sodium chloride (NaCl) on the adsorption. The adsorbed amounts of phenanthrene on montmorillonite exchanged by organic cations such as tetraheptylammonium, benzyltrimethylammonium, hexadecyltrimethylammonium, or tetraphenylphosphonium were several times higher than those obtained using montmorillonite clay without surface modification. At the same equilibrium concentration, the adsorbed amount of phenanthrene is higher on clay modified with benzyltrimethylammonium than on clay modified with hexadecyltrimethylammonium or other cations. Adsorption of phenanthrene on clay modified with benzyltrimethylammonium increased dramatically as the concentration of NaCl increased up to 150 g/l in the aqueous solution. The shape of the curves obtained can be classified as S-type. The adsorption data obtained from salinity experiments support a mathematical model that links the Langmuir constant with the salinity constant. This model may be useful to predict the equilibrium concentration of a contaminant in saline solution. FTIR studies showed strong interactions between the aromatic rings of phenanthrene and the preadsorbed benzyltrimethylammonium on clay surfaces.