Eigenvectors and cyclic vectors of bilateral weighted shifts. II: Simply invariant subspaces

Let T be an injective bilateral weighted shift onl ² thought as "multiplication by λ" on a space of formal Laurent series L²(β). (a) If L²(β) is contained in a space of quasi-analytic class of functions, then the point spectrum σ_p(T^?) of T^? contains a circle and the cyclic invariant subspaceM _f of T generated by f is simply invariant (i.e., ∩{(T^k M _f)^?: k ≥ 0}= {0}) for each f in L²(β); (b) If L²(β) contains a non-quasi-analytic class of functions (defined on a circle г) of a certain type related with the weight sequence of T, then there exists f in L²(ß) such thatM _f is a non-trivial doubly invariant subspace (i.e., (TM _f)^? =M _f); furthermore, if г ? σ_p(T^*), then σ_p (T^*) = г and f can be chosen so that σ_p([T∣M _f]^*) = г?{α}, for some α ε г. Several examples show that the gap between operators satisfying (a) and operators satisfying (b) is rather small.     

Optimisation of a flow injection system with electrochemical detection using the desirability function: Application to the determination of hydroquinone in cosmetics

A procedure is proposed in which the determination of hydroquinone using a flow injection system with electrochemical detection is described. Size and coefficient of variation of the signal are optimised by a desirability function and a central composite design. The robustness of the optimum reached in the optimisation step is evaluated by means a Plackett-Burman design. The optimised FIA system is able to determine hydroquinone with a minimum detectable net concentration of 10 μg l⁻¹ with a false positive probability of 0.05 and a false negative probability less than 0.05. In samples of bleaching cream, the proposed procedure has a recovery of 102.2% with standard deviation of 4.4% and a relative error of 6.2%.     

Determination of organophosphorus and triazine pesticides in olive oil by on-line coupling reversed-phase liquid chromatography/gas chromatography with nitrogen-phosphorus detection and an automated through-oven transfer adsorption-desorption interface

A method is described for the simultaneous determination of organophosphorus and triazine pesticides in olive oil, whereby reversed-phase liquid chromatography (LC) is coupled to gas chromatography by means of an automated through-oven transfer adsorption-desorption (TOTAD) interface. The olive oil needs to be filtered only before it is loaded into the liquid chromatograph, where preseparation of the pesticide residues from the other olive oil components is carried out by using methanol-water as the eluant. The LC fraction containing the pesticides is automatically transferred to the gas chromatograph by using the TOTAD interface, which almost totally eliminates the solvent, so that water-sensitive detectors such as the nitrogen-phosphorus detector can be used. Detection limits range from 0.07 to 0.38 microg/L for organophosphorus pesticides and from 6.0 to 7.0 microg/L for triazines. The results were compared with those obtained by flame ionization detection.     

Studies on the chemistry of 2-(2-oxo-3-phenylpropyl)-benzaldehydes: novel total synthesis of 3-phenylnaphthalen-2-ols and 2-hydroxy-3-phenyl-1,4-naphthoquinones

We describe the first studies on the chemistry of 2-(2-oxo-3-phenylpropyl)benzaldehydes, which were converted into 3-benzylisochromen-1-ones via the corresponding 2-(2-oxo-3-phenylpropyl)benzoic acid. The 2-(2-oxo-3-phenylpropyl)benzaldehydes proved to be convenient starting materials for the synthesis of 3-phenyl-2-naphthols. Oxidation of the latter compounds resulted in a novel, efficient synthesis of 3-phenyl-1,2-naphthoquinones, which were efficiently transformed into 2-hydroxy-3-phenyl-1,4-naphthoquinones.     

Separation of proteins with a molecular mass difference of 2 kDa utilizing preparative double-inverted gradient polyacrylamide gel electrophoresis under nonreducing conditions: application to the isolation of 24 kDa human growth hormone

A method for separating proteins with a molecular mass difference of 2 kDa using SDS-PAGE under nonreducing conditions is presented. A sample mixture containing several human growth hormone (hGH) isoforms was initially separated on a weak anion-exchange column. Fractions rich in 24 kDa hGH as determined by analytical SDS-PAGE were pooled and further separated by cation-exchange chromatography. The fractions pooled from the cation-exchange chromatography contained two hGH isoforms with a 2 kDa molecular mass difference according to SDS-PAGE analysis, 22 and 24 kDa hGH. The 22 and 24 kDa hGH were separated using continuous-elution preparative double-inverted gradient PAGE (PDG-PAGE) under nonreducing conditions. The preparative electrophoresis gel was composed of three stacked tubular polyacrylamide matrices, a 4% stacking gel, a 13-18% linear gradient gel, and a 15-10% linear inverted gradient gel. Fractions containing purified 24 kDa hGH were pooled and Western blot analysis displayed immunoreactivity to antihGH antibodies. PDG-PAGE provides researchers with an electrophoretic technique to preparatively purify proteins under nonreducing conditions with molecular mass differences of 2 kDa.     

Stereoselective syntheses of 1,4-dideoxy-1,4-imino-octitols and novel tetrahydroxyindolizidines

A new route for the preparation of four new indolizidines, (1R,2S,6S,7S,8aS)- and (1R,2S,6R,7R,8aS)-1,2,6,7-tetrahydroxyindolizidine (30 and 32) and (1S,2R,7S,8S,8aR)- and (1S,2R,7R,8R,8aR)-1,2,7,8-tetrahydroxyindolizidine (44 and 46), is reported. The synthesis is based on Knoevenagel homologation of the readily available enantiomerically pure pyrrolidin-carbaldehydes 13 and 37followed by asymmetric dihydroxylation of the subsequent alkenyl pyrrolidines and cyclization of the corresponding imino-octitols. The new indolizidines and their precursors (imino-octitols 20, 25, 26) and indolizidinones 28a and 28b have been tested for inhibitory activities toward 26 glycosidases. The enzymatic inhibition of trans-7-hydroxy-d-(-)-swainsonine (44) toward alpha-mannosidases is similar to that described for trans-7-hydroxy-l-(+)-swainsonine (11b) toward naringinase (alpha-l-rhamnosidase from Penicillium decumbens).     

Copper-assisted oxidation of catechols into quinone derivatives

Catechols are ubiquitous substances often acting as antioxidants, thus of importance in a variety of biological processes. The Fenton and Haber–Weiss processes are thought to transform these molecules into aggressive reactive oxygen species (ROS), a source of oxidative stress and possibly inducing degenerative diseases. Here, using model conditions (ultrahigh vacuum and single crystals), we unveil another process capable of converting catechols into ROSs, namely an intramolecular redox reaction catalysed by a Cu surface. We focus on a tri-catechol, the hexahydroxytriphenylene molecule, and show that this antioxidant is thereby transformed into a semiquinone, as an intermediate product, and then into an even stronger oxidant, a quinone, as final product. We argue that the transformations occur via two intramolecular redox reactions: since the Cu surface cannot oxidise the molecules, the starting catechol and the semiquinone forms each are, at the same time, self-oxidised and self-reduced. Thanks to these reactions, the quinone and semiquinone are able to interact with the substrate by readily accepting electrons donated by the substrate. Our combined experimental surface science and ab initio analysis highlights the key role played by metal nanoparticles in the development of degenerative diseases.

An antioxidant catechol transforms following intramolecular redox reactions into highly reactive oxygen species, a semiquinone and a quinone, on copper.     

Anaerobic reduction of a sulfonated azo dye, Congo Red, by sulfate-reducing bacteria

The capacity for anaerobic decolorization of a sulfonated azo dye, Congo Red, by a strain of a sulfate-reducing bacterium was evaluated. After optimizing the growth rate of the bacteria on a simple carbon source and terminal electron acceptor pair, lactate and sulfate, respectively, the effect of the dye concentration on their growth rate was analyzed. The decolorization rate was affected by the dye concentration in the growth medium. The azo-bond cleavage mechanism of reductive decolorization with the formation of benzidine was consistent with the results, as this metabolite was identified by high-performance liquid chromatography. Several fractions of the culture medium, including lysed cell extracts, were examined for the capacity to reduce the azo dye. This reduction capacity was found in the culture medium in which the cells had previously grown. The results showed that the mechanism of reductive decolorization of this sulfonated azo dye was extracellular and nonenzymatic, consistent with the production of sulfide anion by the microorganisms while growing on lactate and sulfate. The sulfide anions were the cause of the reduction leading to the disappearance of color in the medium. To increase the rate of decolorization, the presence of ferrous ion was also necessary together with the lactate and sulfate substrates.     

Early-late heterobimetallic alkoxides as model systems for late-transition-metal catalysts supported on titania

Titanium complexes with chelating alkoxide ligands [TiCp*(O(2)Bz)(OBzOH)] (1) and [TiCp*(Me)((OCH(2))(2)Py)] (2) were synthesised by reaction of [TiCp*Me(3)] (Cp*=eta(5)-C(5)Me(5)) with 2-hydroxybenzyl alcohol ((HO)(2)Bz) and 2,6-pyridinedimethanol ((HOCH(2))(2)Py), respectively. Complex 1 reacts with [(M(mu-OH)(cod))(2)] (M=Rh, Ir) to yield the early-late heterobimetallic complexes [TiCp*(O(2)Bz)(2)M(cod)] [M=Rh (3), Ir (4)]. Carbon monoxide readily replaces the COD ligand in 3 to give the rhodium dicarbonyl derivative [TiCp*(O(2)Bz)(2)Rh(CO)(2)] (5). Compound 2 reacts with [(M(mu-OH)(cod))(2)] (M=Rh, Ir) with protonolysis of a Tibond;Me bond to give [TiCp*((OCH(2))(2)Py)(mu-O)M(cod)] [M=Rh (6), Ir (7)]. The molecular structures of complexes 3, 5 and 7 were established by single-crystal X-ray diffraction studies.     

Convergent stereocontrolled synthesis of substituted exo-glycals by Stille cross-coupling of halo-exo-glycals and stannanes

(Z)-exo-Glycals can be conveniently prepared in a convergent manner by Stille cross-coupling of (Z)-halo(Br,I)-exo-glycals and aryl or alkenyl stannanes, the latter are readily obtained by addition of tributylstannyl radicals to terminal alkynes.