Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Ultracold, radiative charge transfer in hybrid Yb ion – Rb atom traps

Ultracold hybrid ion–atom traps offer the possibility of microscopic manipulation of quantum coherences in the gas using the ion as a probe. However, inelastic processes, particularly charge transfer can be a significant process of ion loss and has been measured experimentally for the ${\rm Y}{{{\rm b}}^{+}}$ ion immersed in a Rb vapour. We use first-principles quantum chemistry codes to obtain the potential energy curves and dipole moments for the lowest-lying energy states of this complex. Calculations for the radiative decay processes cross sections and rate coefficients are presented for the total decay processes; ${\rm Y}{{{\rm b}}^{+}}(6{\rm s}{{\;}^{2}}{\rm S})+{\rm Rb}(5{\rm s}{{\;}^{2}}{\rm S})\to {\rm Yb}(6{{{\rm s}}^{2}}{{\;}^{1}}{\rm S})+{\rm R}{{{\rm b}}^{+}}(4{{{\rm p}}^{6}}{{\;}^{1}}{\rm S})+h\nu $ and ${\rm Y}{{{\rm b}}^{+}}(6{\rm s}{{\;}^{2}}{\rm S})+{\rm Rb}(5{\rm s}{{\;}^{2}}{\rm S})\to {\rm YbR}{{{\rm b}}^{+}}({{X}^{1}}{{\Sigma }^{+}})+h\nu $. Comparing the semi-classical Langevin approximation with the quantum approach, we find it provides a very good estimate of the background at higher energies. The results demonstrate that radiative decay mechanisms are important over the energy and temperature region considered. In fact, the Langevin process of ion–atom collisions dominates cold ion–atom collisions. For spin-dependent processes [1] the anisotropic magnetic dipole–dipole interaction and the second-order spin–orbit coupling can play important roles, inducing coupling between the spin and the orbital motion. They measured the spin-relaxing collision rate to be approximately five orders of magnitude higher than the charge-exchange collision rate [1]. Regarding the measured radiative charge transfer collision rate, we find that our calculation is in very good agreement with experiment and with previous calculations. Nonetheless, we find no broad resonances features that might underly a strong isotope effect. In conclusion, we find, in agreement with previous theory that the isotope anomaly observed in experiment remains an open question.

Towards An Acoustic Model-Based Poroelastic Imaging Method: I. Theoretical Foundation

The ultrasonic measurement and imaging of tissue elasticity is currently under wide investigation and development as a clinical tool for the assessment of a broad range of diseases, but little account in this field has yet been taken of the fact that soft tissue is porous and contains mobile fluid. The ability to squeeze fluid out of tissue may have implications for conventional elasticity imaging, and may present opportunities for new investigative tools. When a homogeneous, isotropic, fluid-saturated poroelastic material with a linearly elastic solid phase and incompressible solid and fluid constituents is subjected to stress, the behaviour of the induced internal strain field is influenced by three material constants: the Young's modulus (E(s)) and Poisson's ratio (nu(s)) of the solid matrix and the permeability (k) of the solid matrix to the pore fluid. New analytical expressions were derived and used to model the time-dependent behaviour of the strain field inside simulated homogeneous cylindrical samples of such a poroelastic material undergoing sustained unconfined compression. A model-based reconstruction technique was developed to produce images of parameters related to the poroelastic material constants (E(s), nu(s), k) from a comparison of the measured and predicted time-dependent spatially varying radial strain. Tests of the method using simulated noisy strain data showed that it is capable of producing three unique parametric images: an image of the Poisson's ratio of the solid matrix, an image of the axial strain (which was not time-dependent subsequent to the application of the compression) and an image representing the product of the aggregate modulus E(s)(1-nu(s))/(1+nu(s))(1-2nu(s)) of the solid matrix and the permeability of the solid matrix to the pore fluid. The analytical expressions were further used to numerically validate a finite element model and to clarify previous work on poroelastography.

Restricted rotation dynamics and far-infrared spectra of liquid water governed by elastic interactions

A semi-phenomenological model describing wideband dielectric and far-infrared spectra of liquid water was proposed recently by the same authors [J. Mol. Struct. 606 (2002) 9], where a small dipole-moment component changing harmonically with time determines a weak absorption band (termed here the R-band) centred at the wavenumber v similar to 200 cm(-1). In the present work, a rough molecular theory of the R-band based on the concept of elastic interactions is given. Stretching and bending of hydrogen bonds cause restricted rotation (RR) of a polar water molecule in terms of a dimer comprising the H- bonded molecules. Analytical expression for the RR frequency nu(str) is derived as a function of the RR amplitude, geometrical parameters and force constants. The density g(nu(str)) of frequency distribution is shown to be centred in the R-band. The spectrum of the dipolar auto-correlation function calculated for this structural-dynamical model is found. A composite model comprising two intermolecular potentials is proposed, which yields for water a good description of the experimental wideband (from 0 to 1000 cm(- 1)) spectra of complex permittivity and of absorption coefficient. The presented interpretation of these spectra is based on a concept that water presents a two-component solution, with components differing by the types of molecular rotation. (C) 2003 Elsevier B.V. All rights reserved.

Analytical calculation of far infrared spectra of ice in terms of a molecular model

Wideband far infrared (FIR) spectra of complex permittivity e(p) of ice are calculated in terms of a simple analytical theory based on the method of dipolar autocorrelation functions. The molecular model represents a revision of the model recently presented for liquid water in Adv. Chem. Phys. 127 (2003) 65. A composite two-fractional model is proposed. The model is characterised by three phenomenological potential wells corresponding to the three FIR bands observed in ice. The first fraction comprises dipoles reorienting in a rather narrow and deep hat-like well; these dipoles generate the librational band centred at the frequency approximate to 880 cm(-1). The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cm(-1). For description of one of these bands the harmonic oscillator (HO) model is used, in which translational oscillations of two charged molecules along the H-bond are considered. The other band is produced by the H-bond stretch, which governs hindered rotation of a rigid dipole. Such a motion and its dielectric response are described in terms of a new cut parabolic (CP) model applicable for any vibration amplitude. The composite hat-HO-CP model results in a smooth epsilon(nu) ice spectrum, which does not resemble the noise-like spectra of ice met in the known literature. The proposed theory satisfactorily agrees with the experimental ice spectrum measured at - 7 degrees C. The calculated longitudinal optic-transverse optic (LO-TO) splitting occurring at approximate to 250 cm(-1) qualitatively agrees with the measured data. (c) 2004 Elsevier B.V. All rights reserved.

A critical evaluation of Raman spectroscopy for the analysis of lipids: fatty acid methyl esters.

The work presented here is aimed at determining the potential and limitations of Raman spectroscopy for fat analysis by carrying out a systematic investigation of C-4-C-24 FAME. These provide a simple, well-characterized set of compounds in which the effect of making incremental changes can be studied over a wide range of chain lengths and degrees of unsaturation. The effect of temperature on the spectra was investigated over much larger ranges than would normally be encountered in real analytical measurements. It was found that for liquid FAME the best internal standard band was the carbonyl stretching vibration nu(C = O), whose position is affected by changes in sample chain length and physical state; in the samples studied here, it was found to lie between 1729 and 1748 cm(-1). Further, molar unsaturation could be correlated with the ratio of the nu(C = O) to either nu(C = C) or delta(H-C = ) with R-2 > 0.995. Chain length was correlated with the delta(CH2)(tw)/nu(C = O) ratio, (where "tw" indicates twisting) but separate plots for odd- and even-numbered carbon chains were necessary to obtain R-2 > 0.99 for liquid samples. Combining the odd- ani even-numbered carbon chain data in a single plot reduced the correlation to R-2 = 0.94-0.96, depending on the band ratios used. For molal unsaturation the band ratio that correlated linearly with unsaturation (R-2 > 0.99) was nu(C = C)/delta(CH2)(SC) (where "sc" indicates scissoring). Other band ratios show much more complex behavior with changes in chemical and physical structure. This complex behavior results from the fact that the bands do not arise from simple vibrations of small, discrete regions of the molecules but are due to complex motions of large sections of the FAME so that making incremental changes in structure does not necessarily lead to simple incremental changes in spectra.

Bright Multi-keV Harmonic Generation from Relativistically Oscillating Plasma Surfaces

The first evidence of x-ray harmonic radiation extending to 3.3 A, 3.8 keV (order n > 3200) from petawatt class laser-solid interactions is presented, exhibiting relativistic limit efficiency scaling (eta similar to n(-2.5)-n(-3)) at multi-keV energies. This scaling holds up to a maximum order, n(RO)similar to 8(1/2)gamma(3), where gamma is the relativistic Lorentz factor, above which the first evidence of an intensity dependent efficiency rollover is observed. The coherent nature of the generated harmonics is demonstrated by the highly directional beamed emission, which for photon energy h nu > 1 keV is found to be into a cone angle similar to 4 degrees, significantly less than that of the incident laser cone (20 degrees).

Alternative transcription factor sigma(B) is involved in regulation of biofilm expression in a Staphylococcus aureus mucosal isolate.

Rachid S, Ohlsen K, Wallner U, Hacker J, Hecker M, Ziebuhr W. Institut für Molekulare Infektionsbiologie, D-97070 Würzburg, Germany. Osmotic stress was found to induce biofilm formation in a Staphylococcus aureus mucosal isolate. Inactivation of a global regulator of the bacterial stress response, the alternative transcription factor sigma(B), resulted in a biofilm-negative phenotype and loss of salt-induced biofilm production. Complementation of the mutant strain with an expression plasmid encoding sigma(B) completely restored the wild-type phenotype. The combined data suggest a critical role of sigma(B) in S. aureus biofilm regulation under environmental stress conditions.

The VLT-FLAMES Survey of massive stars: Rotation and nitrogen enrichment as the key to understanding massive star evolution

Rotation has become an important element in evolutionary models of massive stars, specifically via the prediction of rotational mixing. Here we study a sample of stars, including rapid rotators, to constrain such models and use nitrogen enrichments as a probe of the mixing process. Chemical compositions (C, N, O, Mg, and Si) have been estimated for 135 early B-type stars in the Large Magellanic Cloud with projected rotational velocities up to similar to 300 km s(-1) using a non-LTE TLUSTY model atmosphere grid. Evolutionary models, including rotational mixing, have been generated attempting to reproduce these observations by adjusting the overshooting and rotational mixing parameters and produce reasonable agreement with 60% of our core hydrogen burning sample. We find (excluding known binaries) a significant population of highly nitrogen-enriched intrinsic slow rotators (nu sin i less than or similar to 50 km s(-1)) incompatible with our models (similar to 20% of the sample). Furthermore, while we find fast rotators with enrichments in agreement with the models, the observation of evolved (dex) fast rotators (log g < 3.7 dex) that are relatively unenriched (a further similar to 20% of the sample) challenges the concept of rotational mixing. We also find that 70% of our blue supergiant sample cannot have evolved directly from the hydrogen-burning main sequence. We are left with a picture where invoking binarity and perhaps fossil magnetic fields is required to understand the surface properties of a population of massive main- sequence stars.

The alternative sigma factor sigma B of Staphylococcus aureus modulates virulence in experimental central venous catheter-related infections.

The impact of the alternative sigma factor sigma B (SigB) on pathogenesis of Staphylococcus aureus is not conclusively clarified. In this study, a central venous catheter (CVC) related model of multiorgan infection was used to investigate the role of SigB for the pathogenesis of S. aureus infections and biofilm formation in vivo. Analysis of two SigB-positive wild-type strains and their isogenic mutants revealed uniformly that the wild-type was significantly more virulent than the SigB-deficient mutant. The observed difference in virulence was apparently not linked to the capability of the strains to form biofilms in vivo since wild-type and mutant strains were able to produce biofilm layers inside of the catheter. The data strongly indicate that the alternative sigma factor SigB plays a role in CVC-associated infections caused by S. aureus.

Surface properties of Rosetta's targets (21) Lutetia and (2867) Steins from ESO observations

Aims. The aim of this work is to constrain the size, composition and surface properties of asteroids (2867) Steins and (21) Lutetia, targets of the Rosetta mission. Rosetta is en route to rendezvous with comet 67P/Churyumov-Gerasimenko.

Methods. Thermal-Infrared N-band observations for Lutetia and Steins were obtained using, respectively, TIMMI2 on the ESO 3.6-m telescope at La Silla and VISIR at the UT3 VLT telescope on Cerro Paranal; visible light curves for Steins were obtained using NTT+SUSI2, while R-band photometry for Lutetia was obtained with the 2.0-m Faulkes Telescope North on Haleakala. For Steins, the NEATM model was used to constrain its visible geometric albedo and beaming parameter. A detailed thermophysical model was implemented and used to analyze our set of observations of Lutetia as well as previous reported measurements.

Results. The visible photometry of Steins was used along with data from the literature to yield a slope parameter of G=0.32(-0.11)(+0.14). Problems during the observations led to the loss of measurements on two of the three N-band filters requested for Steins. Using the remaining data and the polarimetric albedo recently published, we were able to constrain the thermal beaming parameter as eta > 1.2, which is more similar to near-Earth asteroids and suggests either high thermal inertia or a very rough surface. For Lutetia, the best fit visible geometric albedo obtained with our model and the reported observation is p(nu)=0.129, significantly lower than that obtained if one applies the same model to previously reported measurements. The discrepancy cannot be explained solely by assuming inhomogeneities in the surface properties and we suggest that the most plausible explanation is the presence of one or more large craters on the northern hemisphere. For both sets of measurements, the implied single scattering albedo of Lutetia is compatible with laboratory measurements of carbonaceous chondrite meteorites.

Resonance Raman and DFT studies of tetra-tert-butyl porphine: Assignment of strongly enhanced distortion modes in a ruffled porphyrin

The free-base form of tetra-tert-butyl porphine (TtBP), which has extremely bulky meso substituents, is severely distorted from planarity, with a ruffling angle of 65.5degrees. The resonance Raman spectrum of TtBP (lambda(ex) = 457.9 nm) and its d(2), d(8), and d(10) isotopomers have been recorded, and while the spectra show high-frequency bands similar to those observed for planar meso-substituted porphyrins, there are several additional intense bands in the low-frequency region. Density functional calculations at the B3-LYP/6-31G(d) level were carried out for all four isotopomers, and calculated frequencies were scaled using a single factor of 0.98. The single factor scaling approach was validated on free base porphine where the RMS error was found to be 14.9 cm(-1). All the assigned bands in the high-frequency (> 1000 cm(-1)) region of TtBP were found to be due to vibrations similar in character to the in-plane skeletal modes of conventional planar porphyrins. In the low-frequency region, two of the bands, assigned as nu(8) (ca. 330 cm(-1)) and nu(16) (ca. 540 cm(-1)), are also found in planar porphyrins such as tetra-phenyl porphine (TPP) and tetra-iso-propyl porphine (IPP). Of the remaining three very strong bands, the lowest frequency band was assigned as gamma(12) (pyr swivel, obsd 415 cm(-1), calcd 407 cm(-1) in do). The next band, observed at 589 cm-1 in the do compound (calcd 583 cm(-1)), was assigned as a mode whose composition is a mixture of modes that were previously labeled gamma(13) (gamma(CmCaHmCa)) andy gamma(11) (pyr fold(asym)) in NiOEP. The final strong band, observed at 744 cm(-1) (calcd 746 cm(-1)), was assigned to a mode whose composition is again a mixture of gamma(11) and gamma(13), although here it is gamma(11) rather than gamma(13) which predominates. These bands have characters and positions similar to those of three of the four porphyrin ring-based, weak bands that have previously been observed for NiTPP. In addition there are several weaker bands in the TtBP spectra that are also