Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

Simultaneous determination of quinolone antibacterials in bovine milk by liquid chromatography-mass spectrometry

A new liquid chromatography-mass spectrometry (LC-MS) method has been developed and validated for the simultaneous determination of eight quinolone antibacterials for veterinary use in processed bovine milk samples. The quinolones studied included marbofloxacin, ciprofloxacin, danofloxacin, enrofloxacin, sarafloxacin, difloxacin, oxolinic acid and flumequine. Also, a new sample-treatment procedure was used for extraction and preconcentration of these compounds. It involved defatting by centrifugation, protein precipitation by adding a mixture of glacial acetic acid-acetonitrile and removing acetonitrile with dichloromethane; finally, the acidified aqueous layer was evaporated to dryness in a speed vac system, resuspended in the mobile phase and filtered prior to LC injection. The mobile phase was composed of a formic acid aqueous solution 0.1% (v/v) and acetonitrile, with an initial composition of water-acetonitrile 95: 5 (v/v) and using linear gradient elution. Norfloxacin was used as internal standard. The limits of quantification found (2-7 ng g(-1)) were in all cases lower than the maximum residue limits tolerated by the European Union for these compounds in milk.     

Simulations of gas transport in membranes based on polynorbornenes functionalized with substituted imide side groups

This paper studies the diffusive and sorption steps of several gases across membranes cast from poly(N-phenyl-exo,endo-norbornene-5,6-dicarboximide) chloroform solutions. Chains packing effects on gas transport was investigated by conducting a parallel study on the permeation characteristics of membranes cast from hydrogenated poly(N-phenyl-exo,endo-norbornene-5,6-dicarboximide) chloroform solutions. The permeability coefficients of several gases in the two membranes were measured finding that hydrogenation of the norbornene moieties decreases gas permeability. The transition states approach was used to determine the trajectories of the gases in the two types of membranes from which the diffusion coefficients were obtained. Monte Carlo techniques based on the Widom method were used to simulate gas sorption process as a function of pressure. The values of the solubility coefficients thus obtained undergo a relatively sharp drop at low pressures approaching to a constant value as pressure increases. With the exception of carbon dioxide, pretty good agreement between the experimental and simulated values of the permeability coefficient is found for the gases studied.     

Aharonov–Bohm Effect and High-Momenta Inverse Scattering for the Klein–Gordon Equation

We analyze spin-0 relativistic scattering of charged particles propagating in the exterior, \({\Lambda \subset \mathbb{R}^3}\), of a compact obstacle \({K \subset \mathbb{R}^3}\). The connected components of the obstacle are handlebodies. The particles interact with an electromagnetic field in Λ and an inaccessible magnetic field localized in the interior of the obstacle (through the Aharonov–Bohm effect). We obtain high-momenta estimates, with error bounds, for the scattering operator that we use to recover physical information: we give a reconstruction method for the electric potential and the exterior magnetic field and prove that, if the electric potential vanishes, circulations of the magnetic potential around handles (or equivalently, by Stokes’ theorem, magnetic fluxes over transverse sections of handles) of the obstacle can be recovered, modulo 2π. We additionally give a simple formula for the high momenta limit of the scattering operator in terms of certain magnetic fluxes, in the absence of electric potential. If the electric potential does not vanish, the magnetic fluxes on the handles above referred can be only recovered modulo π and the simple expression of the high-momenta limit of the scattering operator does not hold true.     

Synthesis and characterization of nanostructured iron compounds prepared from the decomposition of iron pentacarbonyl dispersed into carbon materials with varying porosities

This work describes the production and characterization of carbon-iron nanocomposites obtained from the decomposition of iron pentacarbonyl (Fe(CO)₅) mixed with different carbon materials: a high surface area activated carbon (AC), powdered graphite (G), milled graphite (MG), and carbon black (CB). The nanocomposites were prepared either under argon or in ambient atmosphere, with a fixed ratio of Fe(CO)₅ (4.0 mL) to carbon precursor (2.0 g). The images of scanning electron microscopy and the analysis of textural properties indicated the presence of nanostructured Fe compounds homogeneously dispersed into the different classes of pores of the carbon matrices. The elemental Fe content was always larger for samples prepared in ambient atmosphere, reaching values in the range of 20–32 wt%. On the other hand, samples prepared under argon showed reduced Fe content, with values in the range 5–10 wt% for samples prepared from precursors with low surface area (G, MG, and CB) and a much higher value (~19 wt%) for samples prepared from the precursor of high surface area (AC). Mössbauer spectroscopy and X-ray diffractometry showed that the nanoparticles were mostly composed of iron oxides in the case of the samples prepared in oxygen-rich ambient atmosphere and also for the AC-derived nanocomposite prepared under argon, which is consistent with the large oxygen content of this precursor. For the other precursors, with reduced or no oxygen content, metallic iron and iron carbides were found to be the dominant phases in samples prepared under oxygen-free atmosphere. The samples prepared in ambient atmosphere and the AC-derived sample prepared under argon exhibited superparamagnetic behavior at room temperature, as revealed by temperature-dependent magnetization curves and Mössbauer spectroscopy.     

Secondary and primary relaxations in hyperbranched polyglycerol: a comparative study in the frequency and time domains

The non-Debye relaxation behavior of hyperbranched polyglycerol was investigated by broadband dielectric spectroscopy. A thorough study of the relaxations was carried out paying special attention to truncation effects on deconvolutions of overlapping processes. Hyperbranched polyglycerol exhibits two relaxations in the glassy state named in increasing order of frequency beta and gamma processes. The study of the evolution of these two fast processes with temperature in the time retardation spectra shows that the beta absorption is swallowed by the alpha in the glass-liquid transition, the gamma absorption being the only relaxation that remains operative in the liquid state. In heating, a temperature is reached at which the alpha absorption vanishes appearing the alphagamma relaxation. Two characteristics of alpha absorptions, decrease of the dielectric strength with increasing temperature and rather high activation energy, are displayed by the alphagamma process. Williams' ansatz seems to hold for these topologically complex macromolecules.     

Comparison of the sensitivities of seven N-nitrosamines in pre-screened waters using an automated preconcentration system and gas chromatography with different detectors

A simple, expeditious procedure for confirming the presence of N-nitrosamines in previously screened positive water samples was proposed. Water samples were continuously aspirated into a photometric flow system for screening. Positive samples were then confirmed and N-nitrosamines were identified by gas chromatography using different detectors (mass spectrometry, flame ionization and nitrogen-phosphorus). The system for the screening purpose was based on the preconcentration of the analytes onto a sorbent column, elution, and derivatization to form nitrite, then formation of a coloured product (Griess reaction) and photometric detection. The detection limits of the gas chromatographic method for 100 ml of sample were 2.0-3.5 microg/l, 20-80 and 3-13 ng/l for flame ionization, nitrogen-phosphorus and mass spectrometric detectors, respectively. The precision as RSD was similar for all detectors (3.0-6.5%). The screening of different types of water showed that wastewaters contain levels of N-nitrosamines that can be detected only using MS as a detector.     

On-line precipitation/dissolution system for the preconcentration and determination of manganese traces by atomic absorption spectrometry

Flame atomic absorption spectrometry was used for the determination of Mn in biological material following preconcentration by precipitation. The proposed preconcentration method is based on the continuous precipitation of Mn(II) as hydrated Mn(IV) oxide in ammonia buffer and dissolution of the precipitate with hydrogen oxalate or dilute nitric acid. The sensitivity of the Mn determination is increased by the presence of hydrogen peroxide, which raises the rate of oxidation of Mn(II) to Mn(IV). By using a time-based technique (at a sample loading rate of 4 ml min⁻¹) a concentration factor of up to 55 was obtained using 24 ml of sample. The effect of concurrent cations was investigated; the most adverse effect was exerted by Fe(III), which interfered at concentrations 50 times higher than that of Mn(II).     

Pseudohexagonal crystallinity and thermal and tensile properties of ethene–propene copolymers

Structural (X‐ray diffraction), melting (differential scanning calorimetry), as well as mechanical (tensile tests) characterizations on uncrosslinked ethene–propene copolymer samples, obtained using a metallocene‐based catalytic system and having an ethene content in the range 80–50% by mol, are reported. Samples with an ethene content in the range 80–60% by mol present a disordered pseudohexagonal crystalline phase, whose melting moves from ≈ 40°C down to ≈ −20°C as the ethene content is reduced. The dramatic influence of the crystalline phase on tensile properties of uncrosslinked ethene–propene copolymers is shown. In particular, highest elongation at break values are obtained for samples being essentially amorphous in the unstretched state and partially crystallizing under stretching. On the other hand, lowest tension set values (most elastic behavior) are observed for samples presenting, already in the unstretched state, microcrystalline domains acting as physical crosslinks in a prevailing amorphous phase. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1095–1103, 1999