DFT studies of long-chain FAMEs: theoretical justification for determining chain length and unsaturation from experimental Raman spectra

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of a series of long-chain, saturated fatty acid methyl esters (FAMEs) with the formula CH2nO2 (n = 5-21) and two series of unsaturated FAMEs. The calculations showed that the lowest energy conformer within the saturated FAMEs is the simple (all-trans) structure and, in general, it was possible to reproduce experimental data using calculations on only the all-trans conformer. The only exception was C6H12O2, where a second low-lying conformer had to be included in order to correctly simulate the experimental Raman spectrum. The objective of the work was to provide theoretical justification for the methods that are commonly used to determine the properties of the fats and oils, such as chain length and degree of unsaturation, from experimental Raman data. Here it is shown that the calculations reproduce the trends and calibration curves that are found experimentally and also allow the reasons for the failure of what would appear to be rational measurements to be understood. This work shows that although the assumption that each FAME can simply be treated as a collection of functional groups can be justified in some cases, many of the vibrational modes are complex motions of large sections of the molecules and thus would not be expected to show simple linear trends with changes in structure, such as increasing chain length and/or unsaturation. Simple linear trends obtained from experimental data may thus arise from cancellation of opposing effects, rather than reflecting an underlying simplicity.

Dissociation of H2+ from a short, intense, infrared laser pulse: proton emission spectra and pulse calibration

The proton energy spectrum from photodissociation of the hydrogen molecular ion by short intense pulses of infrared light is calculated. The time-dependent Schrödinger equation is discretized and integrated. For few-cycle pulses one can resolve vibrational structure, arising from the experimental preparation of the molecular ion. We calculate the corresponding energy spectrum and analyse the dependence on the pulse time delay, pulse length and intensity of the laser for ? ~ 790 nm. We conclude that the proton spectrum is a sensitive probe of both the vibrational populations and phases, and allows us to distinguish between adiabatic and nonadiabatic dissociation. Furthermore, the sensitivity of the proton spectrum from H2+ is a practical means of calibrating the pulse. Our results are compared with recent measurements of the proton spectrum for 65 fs pulses using a Ti:Sapphire laser (? ~ 790 nm) including molecular orientation and focal-volume averaging. Integrating over the laser focal volume, for the intensity I ~ 3 × 1015 W cm-2, we find our results are in excellent agreement with these experiments.

Iron abundances from optical FeIII absorption lines in B-type stellar spectra

The role of optical FeIII absorption lines in B-type stars as iron abundance diagnostics is considered. To date, ultraviolet Fe lines have been widely used in B-type stars, although line blending can severely hinder their diagnostic power. Using optical spectra, covering a wavelength range ~3560-9200Å, a sample of Galactic B-type main-sequence and supergiant stars of spectral types B0.5 to B7 are investigated. A comparison of the observed FeIII spectra of supergiants, and those predicted from the model atmosphere codes TLUSTY [plane-parallel, non-local thermodynamic equilibrium (LTE)], with spectra generated using SYNSPEC (LTE), and CMFGEN (spherical, non-LTE), reveal that non-LTE effects appear small. In addition, a sample of main-sequence and supergiant objects, observed with the Fiber-fed Extended Range Optical Spectrograph (FEROS), reveal LTE abundance estimates consistent with the Galactic environment and previous optical studies. Based on the present study, we list a number of FeIII transitions which we recommend for estimating the iron abundance from early B-type stellar spectra.

Numerical analysis of surface and fossil pollen spectra from northern Fennoscandia

Aim Determination of the main directions of variance in an extensive data base of annual pollen deposition, and the relationship between pollen data from modified Tauber traps and palaeoecological data. Location Northern Finland and Norway. Methods Pollen analysis of annual samples from pollen traps and contiguous high-resolution samples from a peat sequence. Numerical analysis (principal components analysis) of the resulting data. Results The main direction of variation in the trap data is due to the vegetation region in which each trap is located. A secondary direction of variation is due to the annual variability of pollen production of some of the tree taxa, especially Betula and Pinus. This annual variability is more conspicuous in ‘absolute’ data than it is in percentage data which, at this annual resolution, becomes more random. There are systematic differences, with respect to peat-forming taxa, between pollen data from traps and pollen data from a peat profile collected over the same period of time. Main conclusions Annual variability in pollen production is rarely visible in fossil pollen samples because these cannot be sampled at precisely a 12-month resolution. At near-annual resolution sampling, it results in erratic percentage values which do not reflect changes in vegetation. Profiles sampled at near annual resolution are better analysed in terms of pollen accumulation rates with the realization that even these do not record changes in plant abundance but changes in pollen abundance. However, at the coarser temporal resolution common in most fossil samples it does not mask the origin of the pollen in terms of its vegetation region. Climate change may not be recognizable from pollen assemblages until the change has persisted in the same direction sufficiently long enough to alter the flowering (pollen production) pattern of the dominant trees.

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.