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%.     

Pressurized liquid extracts from Spirulina platensis microalga. Determination of their antioxidant activity and preliminary analysis by micellar electrokinetic chromatography

In this work, different extracts from the microalga Spirulina platensis are obtained using pressurized liquid extraction (PLE) and four different solvents (hexane, light petroleum, ethanol and water). Different extraction temperatures (115 and 170 degrees C) were tested using extraction times ranging from 9 to 15 min. The antioxidant activity of the different extracts is determined by means of an in vitro assay using a free radical method. Moreover, a new and fast method is developed using micellar electrokinetic chromatography with diode array detection (MEKC-DAD) to provide a preliminary analysis on the composition of the extracts. This combined application (i.e., in vitro assays plus MEKC-DAD) allowed the fast characterization of the extracts based on their antioxidant activity and the UV-vis spectra of the different compounds found in the extracts. To our knowledge, this work shows for the first time the great possibilities of the combined use of PLE-in vitro assay-MEKC-DAD to investigate natural sources of antioxidants.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.     

Preparation and characterization of octadecyl acrylate monoliths for capillary electrochromatography by photochemical,thermal, and chemical initiation†

Monolithic stationary phases based on octadecyl acrylate for CEC using different initiating systems (UV irradiation, thermal, and chemical initiation) in the presence of lauroyl peroxide as initiator were synthesized. For each initiation mode, the influence of the porogenic solvent composition on both the morphological and electrochromatographic properties of the resulting monoliths was investigated. Under optimal conditions, excellent efficiencies for the photochemically and chemically polymerized monoliths (minimum plate heights of 6.9–10.7 and 6.5–12.6 μm, respectively) were achieved. Thermally initiated columns gave lower efficiency values, permeabilities, and longer analysis times compared to these initiating systems. The produced monolithic stationary phases were evaluated in terms of reproducibility and gave RSD values below 9.2, 10.6, and 9.8% for UV, thermally, and chemically initiated columns, respectively.     

Comparison of triple quadrupole mass spectrometry and Orbitrap high‐resolution mass spectrometry in ultrahigh performance liquid chromatography for the determination of veterinary drugs in sewage: benefits and drawbacks

This paper presents a comparison of triple quadrupole tandem mass spectrometry (MS/MS) and Orbitrap high‐resolution mass spectrometry (HRMS) combined to ultrahigh performance liquid chromatography for the determination of glucocorticoids and polyether ionophores in sewage, in order to show the major benefits and drawbacks for each mass spectrometry analyser. Overall, HRMS measurements have enhanced performance in terms of confirmatory capabilities than MS/MS measurements. Moreover, similar limits of quantification, limits of detection, linear range and repeatability for glucocorticoids with both the MS/MS and HRMS methods were compared, but in the case of polyether ionophores, slightly better limits of detection and limits of quantification were obtained with the HRMS method because of the high sensitivity obtained when diagnostic ions are used for quantification instead of selected reaction monitoring transitions for these compounds. The two methods have been applied to the analysis of several influent and effluent sewage samples from sewage treatment plants located in the Tarragona region (Catalonia, Spain), showing an excellent correlation between the two methods. Copyright © 2014 John Wiley & Sons, Ltd.