Algebras of Convolution Type Operators with Piecewise Slowly Oscillating Data. I: Local and Structural Study

Let ${\mathcal{B}_{p,w}}$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space ${L^{p}(\mathbb{R}, w)}$ , where ${p \in (1, \infty)}$ and w is a Muckenhoupt weight. We study the Banach subalgebra ${\mathfrak{A}_{p,w}}$ of ${\mathcal{B}_{p,w}}$ generated by all multiplication operators aI ( ${a \in PSO^{\diamond}}$ ) and all convolution operators W ⁰(b) ( ${b \in PSO_{p,w}^{\diamond}}$ ), where ${PSO^{\diamond} \subset L^{\infty}(\mathbb{R})}$ and ${PSO_{p,w}^{\diamond} \subset M_{p,w}}$ are algebras of piecewise slowly oscillating functions that admit piecewise slowly oscillating discontinuities at arbitrary points of ${\mathbb{R} \cup \{\infty\}}$ , and M _p,w is the Banach algebra of Fourier multipliers on ${L^{p}(\mathbb{R}, w)}$ . Under some conditions on the Muckenhoupt weight w, we construct a Fredholm symbol calculus for the Banach algebra ${\mathfrak{A}_{p,w}}$ and establish a Fredholm criterion for the operators ${A \in \mathfrak{A}_{p,w}}$ in terms of their Fredholm symbols. To study the Banach algebra ${\mathfrak{A}_{p,w}}$ we apply the theory of Mellin pseudodifferential operators, the Allan–Douglas local principle, the two idempotents theorem and the method of limit operators. The paper is divided in two parts. The first part deals with the local study of ${\mathfrak{A}_{p,w}}$ and necessary tools for studying local algebras.     

Determination of abamectin in citrus fruits by liquid chromatography-electrospray ionization mass spectrometry

Liquid chromatography coupled to electrospray mass spectrometry (LC-ES-MS) with positive ion detection was used to determine abamectin in oranges. MS conditions were optimized to achieve maximum sensitivity. The main ion for abamectin was [M+Na]+ at a fragmentor voltage of 180 V. Abundant structural information can be obtained at different fragmentor voltages. The detection limit for the standard solution was 12 pg injected, and good linearity and reproducibility were observed. Abamectin residues were extracted using matrix solid-phase dispersion. Orange samples were homogenized with C18 bonded silica placed onto a glass column and eluted with dichloromethane. Recoveries of the abamectin from oranges fortified with approximately 0.01-10 mg/kg ranged from 94 to 99% with an overall average recovery of 96%. The quantification limit is 0.0025 mg/kg, which means detection limit for this analyte could be set at a few hundred picograms per gram of fruit. The presence in the electrosprayed solution of numerous citrus constituents did not interfere significantly with the ionization process of abamectin. The assay procedure provides a simple, rapid, and sensitive method for monitoring residues in oranges. The method was applied to field treatment orange samples.     

N-Amination of 3-amino-1,2,4-triazole with hydroxylamine-O-sulfonic acid: Synthesis of 1,5-diamino-1,2,4-triazole

N-Amination of the 3(5)-amino-1,2,4-triazolide anion with hydroxylamine-O-sulfonic acid is studied. This method provided an access to the previously unknown 1,5-diamino-1,2,4-triazole.     

Consistent predictable patterns in the hydrogen and oxygen stable isotope ratios of animal proteins consumed by modern humans in the USA

Published datasets of proteinaceous animal tissues suggest that co‐variation between amino acid hydrogen (δ²H) and oxygen (δ¹⁸O) isotope ratios is a common feature in systems where isotopic variation is driven by geographic or temporal variation in the δ²H and δ¹⁸O values of environmental water. This has led to the development of models relating tissue δ²H and δ¹⁸O values to those of water, with potential application in a number of fields. However, the strength and ubiquity of the influence of environmental water on protein isotope ratios across taxonomic groups, and thus the relevance of predictive models, is an open question. Here we report strong co‐variation of δ²H and δ¹⁸O values across a suite of terrestrial and aquatic animal meats purchased in American food markets, including beef, poultry (chicken and turkey), chicken eggs, pork, lamb, freshwater fish, and marine fish. Significant isotope co‐variation was not found for small collections of marine bivalves and crustaceans. These results imply that isotopic signals from environmental water were propagated similarly through most of the diverse natural and human‐managed foodwebs represented by our samples. Freshwater fish had the largest variation in δ²H and δ¹⁸O values, with ranges of 121 ‰ and 19.2 ‰, respectively, reflecting the large isotopic variation in environmental freshwaters. In contrast marine animals had the smallest variation for both δ²H (7 ‰ range, crustaceans) and δ¹⁸O (3.0 ‰ range, bivalves) values. Known‐origin beef samples demonstrated direct relationships between the variance of environmental water isotope ratios and that of collected meats. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization of magnetic materials by low-field microwave absorption techniques

A low-field non-resonant microwave absorption has recently been observed in a variety of magnetically ordered materials at low DC fields (−1000 Oe H_DC+1000 Oe), which is known as low-field microwave absorption (LFA). It has been shown that LFA is essentially similar to giant magnetoimpedance (GMI), and clearly different from ferromagnetic resonance (FMR). LFA strongly depends on the anisotropy field of the sample. In contrast with FMR (which can be described as the homogeneous precession of spins in the saturated state), LFA can be thought as a spin rotation process occurring during the magnetic saturation. In this work, we present a detailed study of the basic features of LFA in several types of materials: ferrites and amorphous microwires and ribbons; in particular the effects sample shape, temperature up to the Curie transition, the influence of easy axis and the effects of annealings. These examples show that once LFA is fully understood, it can become a powerful characterization tool.     

Effects of torsion stress on the domain wall unpinning AC field in amorphous FeCoBSi wires

The unpinning or propagation field, h_p, where domain walls are unpinned and start their displacement under the AC magnetic field of as-cast amorphous wires of nominal composition (Co₉₄Fe₆)_72.5B₁₅Si_12.5, was determined for each torsion angle between –90° (counterclockwise) and +150° (clockwise) at a constant frequency of 1 kHz. A plot of h_p as a function of torsion angle showed a sharp minimum at a torsion angle of +120. The results are interpreted in terms of the counterbalance effect of the torsion against the intrinsic helical anisotropy induced during the wire fabrication.     

Phenomenological description of the two energy scales in underdoped cuprate superconductors

Raman and angle-resolved photoemission spectroscopy experiments have demonstrated that in superconducting underdoped cuprates nodal and antinodal regions are characterized by two energy scales instead of the one expected in BCS theory. The nodal scale decreases with underdoping while the antinodal one increases. Contrary to the behavior expected for an increasing energy scale, the antinodal Raman intensity decreases with decreasing doping. Using the Yang-Rice-Zhang model, we show that these features are a consequence of the nonconventional nature of the superconducting state in which superconductivity and pseudogap correlations are both present and compete for the phase space.     

Simultaneous Differential Pulse Adsorptive Stripping Determination of Imipramine and Its Metabolite Desipramine by the PLS‐1 Multivariate Method

A method, using stripping differential pulse voltammetry, for the simultaneous determination of Imipramine and its metabolite Desipramine is reported. Both compounds produce, at glassy carbon electrode, an electrochemical signal due to an adsorptive‐oxidative process. The voltammograms show a very high overlap degree between IM and DE peaks. The multivariate calibration method PLS‐1 was employed for the simultaneous determination of both compounds. An experimental design together with the response surface methodology has been used to find the optimum experimental conditions. The developed procedure has been utilized in the analysis of fortified human serum samples with good recovery values for each analyte.     

A Cyclic and Polymeric Phosphazene as Solid State Template for the Formation of RuO<Subscript>2</Subscript> Nanoparticles

Pyrolysis of the organometallic polymer: {{[N=P(R₁)]_0.8[N=P(OC₆H₄CH₂CN[Ru])₂]_0.15[N=P((OC₆H₅)(OC₆H₄CH₂CN[Ru]]_0.05}{Cl}_0.31} _n , [Ru]=CpRu(PPh₃)₂, R₁ = O₂C₁₂H₈ (1) as well of the cyclic specie {N₃P₃ (OC₆H₅)₅(OC₆H₄CH₂CN[Ru])}{PF₆} (2) under a flow of air at 800°C affords nanostructured RuO₂. Nanoparticles near to 10 nm were observed. The differences in the use of cyclic or polymeric phosphazenes, as solid state template, influence strongly the morphology and slightly the composition of the pyrolytic product. Temperature variable (SQUID) measurements in the range of 5–300 K of the material obtained from the polymer, indicate an antiferromagnetic interaction between the Ru atoms, although lower than that found for the crystalline ruthenium oxide, probably due to some amorphous product present in the pyrolytic material. The possible formation mechanism is discussed and the differences in using the cyclic or the polymeric compound as precursor is analyzed in terms of the relative content of Ru to P, N. A general formation method of nanostructured metal oxides is proposed.