Multiplicative spectra of Banach spaces

The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.

Structure of spectra of linear operators in Banach spaces

Descriptive characterizations of the point, the continuous, and the residual spectra of operators in Banach spaces are put forward. In particular, necessary and sufficient conditions for three disjoint subsets of the complex plane to be the point spectrum, the continuous spectrum, and the residual spectrum of a linear continuous operator in a separable Banach space are obtained.

Line intensity enhancements in stellar coronal X-ray spectra due to opacity effects

Context. The I(15.01 Å)/I(16.78 Å) emission line intensity ratio in Fe xvii has been reported to deviate from its theoretical value
in solar and stellar X-ray spectra. This is attributed to opacity in the 15.01 Å line, leading to a reduction in its intensity, and was
interpreted in terms of a geometry in which the emitters and absorbers are spatially distinct.
Aims. We study the I(15.01 Å)/I(16.78 Å) intensity ratio for the active cool dwarf EV Lac, in both flare and quiescent spectra.
Methods. The observations were obtained with the Reflection Grating Spectrometer on the XMM-Newton satellite. The emission
measure distribution versus temperature reconstruction technique is used for our analysis.
Results. We find that the 15.01 Å line exhibits a significant enhancement in intensity over the optically thin value. To our knowledge,
this is the first time that such an enhancement has been detected on such a sound statistical basis. We interpret this enhancement
in terms of a geometry in which the emitters and absorbers are not spatially distinct, and where the geometry is such that resonant
pumping of the upper level has a greater effect on the observed line intensity than resonant absorption in the line-of-sight.

An investigation of Fe XVI emission lines in solar and stellar extreme-ultraviolet and soft X-ray spectra

New fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe XVI are used to determine theoretical emission-line ratios applicable to the 251-361 and 32-77 angstrom portions of the extreme-ultraviolet (EUV) and soft X-ray spectral regions, respectively. A comparison of the EUV results with observations from the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS) reveals excellent agreement between theory and experiment. However, for emission lines in the 32-49 angstrom portion of the soft X-ray spectral region, there are large discrepancies between theory and measurement for both a solar flare spectrum obtained with the X-Ray Spectrometer/Spectrograph Telescope (XSST) and for observations of Capella from the Low- Energy Transmission Grating Spectrometer (LETGS) on the Chandra X-ray Observatory. These are probably due to blending in the solar flare and Capella data from both first-order lines and from shorter wavelength transitions detected in second and third order. By contrast, there is very good agreement between our theoretical results and the XSST and LETGS observations in the 50-77 angstrom wavelength range, contrary to previous results. In particular, there is no evidence that the Fe XVI emission from the XSST flare arises from plasma at a much higher temperature than that expected for Fe XVI in ionization equilibrium, as suggested by earlier work.

Quantitative studies of the optical and UV spectra of Galactic early B supergiants - I. Fundamental parameters

Aims. We undertake an optical and ultraviolet spectroscopic analysis of a sample of 20 Galactic B0-B5 supergiants of luminosity classes Ia, Ib, Iab, and II. Fundamental stellar parameters are obtained from optical diagnostics and a critical comparison of the model predictions to observed UV spectral features is made.

Determination of absolute configuration of conformationally flexible cis-dihydrodiol metabolites: Effect of diene substitution pattern on the circular dichroism spectra and optical rotations

Absolute configurations of a number of cis-dihydrodiols (cis-1,2-dihydroxy-3,5-cyclohexadienes), synthetically useful products of TDO-catalyzed dihydroxylations of 1,2- and 1,3-disubstituted benzene derivatives, have been determined by a comparison of calculated and experimental CD spectra and optical rotations and by methods involving X-ray crystallography, H-1 NMR spectra of diastereoisomeric derivatives, and by stereochemical correlations. The computations disclosed a significant effect of the substituents on conformational equilibria of cis-dihydrodiols and chiroptical properties of individual conformers. The assigned absolute configurations of cis-dihydrodiols have allowed the validity of a simple predictive model for TDO-catalyzed arene dihydroxylations to be extended.

Absolute configuration of conformationally flexible cis-dihydrodiol metabolites by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations

We have determined the absolute configurations of conformationally flexible cis-dihydrodiol metabolites (cis-1,2-dihydroxy-3,5-cyclohexadienes), bearing different substituents (e.g., Br, F, CF3, CN, Me) in 3- and 5-positions, by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations. Convergent results were obtained by both methods in eight out of ten cases. For the difficult cases, where either conformer population and/or chiroptical properties (calculated rotational strengths of the long-wavelength Cotton effect or optical rotations) of contributing conformers remain inconclusive, the absolute configuration could still be correctly assigned based on one of the biased properties (either ECD or optical rotation). This approach appears well-suited for a broad spectrum of conformationally flexible chiral molecules.

Analysis procedure for calculation of electron energy distribution functions from incoherent Thomson scattering spectra

Incoherent Thomson scattering (ITS) provides a nonintrusive diagnostic for the determination of one-dimensional (1D) electron velocity distribution in plasmas. When the ITS spectrum is Gaussian its interpretation as a three-dimensional (3D) Maxwellian velocity distribution is straightforward. For more complex ITS line shapes derivation of the corresponding 3D velocity distribution and electron energy probability distribution function is more difficult. This article reviews current techniques and proposes an approach to making the transformation between a 1D velocity distribution and the corresponding 3D energy distribution. Previous approaches have either transformed the ITS spectra directly from a 1D distribution to a 3D or fitted two Gaussians assuming a Maxwellian or bi-Maxwellian distribution. Here, the measured ITS spectrum transformed into a 1D velocity distribution and the probability of finding a particle with speed within 0 and given value v is calculated. The differentiation of this probability function is shown to be the normalized electron velocity distribution function. (C) 2003 American Institute of Physics.

Emission lines of Fe X in active region spectra obtained with the Solar Extreme-ultraviolet Research Telescope and Spectrograph

Fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe X are used to derive theoretical emission-line ratios involving transitions in the 174-366 angstrom wavelength range. A comparison of these with solar active region observations obtained during the 1989 and 1995 flights of the Solar Extreme-ultraviolet Research Telescope and Spectrograph (SERTS) reveals generally very good agreement between theory and experiment. Several Fe X emission features are detected for the first time in SERTS spectra, while the 3s(2)3p(5) P-2(3/2)-3s(2)3p(4)(S-1)3d D-2(3/2) transition at 195.32 angstrom is identified for the first time (to our knowledge) in an astronomical source. The most useful Fe X electron density (N-e) diagnostic line ratios are assessed to be 175.27/174.53 and 175.27/177.24, which both involve lines close in wavelength and free from blends, vary by factors of 13 between N-e = 10(8) and 10(11) cm(-3), and yet show little temperature sensitivity. Should these lines not be available, then the 257.25/345.74 ratio may be employed to determine N-e, although this requires an accurate evaluation of the instrument intensity calibration over a relatively large wavelength range. However, if the weak 324.73 angstrom line of Fe X is reliably detected, the use of 324.73/345.74 or 257.25/324.73 is recommended over 257.25/345.74. Electron densities deduced from 175.27/174.53 and 175.27/177.24 for the stars Procyon and alpha Cen, using observations from the Extreme-Ultraviolet Explorer (EUVE) satellite, are found to be consistent and in agreement with the values of N-e determined from other diagnostic ratios in the EUVE spectra. A comparison of several theoretical extreme-ultraviolet Fe X line ratios with experimental values for a theta-pinch, for which the plasma parameters have been independently determined, reveals reasonable agreement between theory and observation, providing some independent support for the accuracy of the adopted atomic data.

A novel application of ratio spectra derivative spectroscopy for the determination of amphotericin in highly icteric plasma.

Derivative spectroscopy has been utilised for the determination of amphotericin in various biological matrices including plasma, serum, urine and brain tissue. Whilst these methods have all been shown to be suitable for the determination of the drug in these matrices it has been reported that the application fails in the case of highly icteric plasma, this being due to the presence of high concentrations (>50 mu M) of bilirubin. This paper details the application of ratio spectra derivative spectroscopy to overcome the interference of bilirubin with amphotericin in such situations.

Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems

In this paper, we present a random iterative graph based hyper-heuristic to produce a collection of heuristic sequences to construct solutions of different quality. These heuristic sequences can be seen as dynamic hybridisations of different graph colouring heuristics that construct solutions step by step. Based on these sequences, we statistically analyse the way in which graph colouring heuristics are automatically hybridised. This, to our knowledge, represents a new direction in hyper-heuristic research. It is observed that spending the search effort on hybridising Largest Weighted Degree with Saturation Degree at the early stage of solution construction tends to generate high quality solutions. Based on these observations, an iterative hybrid approach is developed to adaptively hybridise these two graph colouring heuristics at different stages of solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme on developing computer methods to design and adapt heuristics automatically. Experimental results on benchmark exam timetabling and graph colouring problems demonstrate the effectiveness and generality of this adaptive hybrid approach compared with previous methods on automatically generating and adapting heuristics. Indeed, we also show that the approach is competitive with the state of the art human produced methods.

Preliminary investigations on the effects of ageing and cooking on the Raman spectra of porcine longissimus dorsi

The influence of ageing and cooking on the Raman spectrum of porcine longissimus dorsi was investigated. The rich information contained in the Raman spectrum was highlighted, with numerous changes attributed to changes in the environment and conformations of the myofibrillar proteins.