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.     

Optimized spacer layer thickness for plasmonic-induced enhancement of photocurrent in a-Si:H

Journal of Nanoparticle Research - Plasmonic interfaces consisting of silver nanoparticles of different sizes (50–100&;nbsp;nm) have been processed by the self-assembled dewetting...     

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.     

Interactions of the mitochondrial membrane rat liver D-3-hydroxybutyrate dehydrogenase with glass beads during adsorption chromatography. Relationships with the activation of the enzyme by phospholipids

D-3-Hydroxybutyrate dehydrogenase (BDH) is an NAD(+)-dependent dehydrogenase of the mitochondrial inner membrane involved in the energetic balance between the liver and peripheral organs in mammals. It allows the conversion of ketone bodies (acetoacetate and D-3-hydroxybutyrate) and it is one of the best documented lipid-requiring enzymes with a dependence on lecithins. After release of proteins from the membrane by phospholipase A2 treatment of salt-treated mitochondria, the rat liver enzyme is absorbed on controlled-pore glass beads. After batch washing, the enzyme, devoid of lipids (apoBDH), is specifically eluted at pH 8.05-8.15 with a 0.1 M Tris-1 M LiBr buffer under reducing conditions (5 mM dithiothreitol). It appears that during BDH absorption, the glass beads mimic the phospholipid surface of biomembranes.     

Complex polymer architectures through dimethoxymethyl 1,1‐diphenylethylene derivatives

The reactions of polystyryllithium and potassium on dimethoxymethyl 1,1‐diphenylethylene derivatives were studied in different solvents. In a polar medium, A₃ and A₆ star types were formed according to the stoichiometry, whereas in a nonpolar medium, hyperbranched structures were synthesized. Extensions of an already proposed mechanism in polar and nonpolar media were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3329–3335, 2003     

Oxidative Coupling of Thiols to Disulfides with Ti(IV) in the Presence of NaI under Air Atmosphere

Ti(IV) as TiCl₃(O₃SCF₃) and TiO(O₂CCF₃)₂ are used as efficient catalysts for oxidative coupling of aliphatic, aromatic and heteroaromatic thiols to their disulfides in the presence of NaI under air atmosphere.     

Effect of temperature on IR-absorption of diphenyl

In this work, the temperature dependence of the intensities of the IR absorption bands corresponding to the fundamental vibrations, overtones and combination frequencies of diphenyl is presented. A thorough discussion of the interpretation of the fundamental modes of vibration has been made on the basis of the temperature dependence of the intensities of these absorption bands.The structure of the diphenyl molecule has been the subject of numerous investigations. Despite a considerable amount of work on the Raman(1), IR(3,4,5) and ultraviolet (2) spectra, the assignment of the fundamental frequencies has not yet been established with certainty, Some assistance can be obtained from the temperature dependence of the IR spectrum of this material.     

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.     

Synthesis of N-1-(Indanyloxymethyl) and N-1-(4-Hydroxybut-2-enyloxymethyl) Analogues of the HIV Drugs Emivirine and GCA-186

A series of Emivirine and GCA-186 analogues substituted at N-1 with indan-1-yloxymethyl (6a–6c) and indan-2-yloxymethyl (6d–6f) were synthesized by reaction of the corresponding bis(indanyloxy)methans with uracils having 5-ethyl or 5-isopropyl and 6-benzyl or 6-(3,5-dimethylbenzyl) substituents. A route to the corresponding N-1 substituted 4-hydroxybut-2-enyloxymethyl analogue was also devised. All newly synthesized compounds showed potent activity against wild-type HIV-1, the most active compound being 5-ethyl-1-(indan-1-yloxymethyl)-6-(3,5-dimethylbenzyl)uracil (6b), which was 50-fold more active than Emivirine.