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.

Kinetic analysis of the cleavage of human protease-activated receptor-1/2/3 and 4 using quenched-fluorescent peptide substrates

Protease-activated receptors [PARs] are a family of G-protein-coupled seven-transmembrane domain receptors that are activated by proteolytic cleavage of their amino-terminal exodomain. To characterize the cleavage rate of human PAR-1 / 2 / 3 and 4 by trypsin and thrombin, four synthetic quenched-fluorescent peptide substrates have been synthesized. Each substrate consisted of a ten-residue peptide spanning the receptor activation cleavage site and using progress-curve kinetics, k(cat)/K-m values were determined.

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.

Extraction of electrode kinetic parameters from microdisc voltammetric data measured under transport conditions intermediate between steady-state convergent and transient linear diffusion as typically applies to room temperature ionic liquids

The extraction of electrode kinetic parameters for electrochemical couples in room-temperature ionic liquids (RTILs) is currently an area of considerable interest. Electrochemists typically measure electrode kinetics in the limits of either transient planar or steady-state convergent diffusion for which the voltammetic response is well understood. In this paper we develop a general method allowing the extraction of this kinetic data in the region where the diffusion is intermediate between the planar and convergent limits, such as is often encountered in RTILs using microelectrode voltammetry. A general working surface is derived, allowing the inference of Butler-Volmer standard electrochemical rate constants for the peak-to-peak potential separation in a cyclic voltammogram as a function of voltage scan rate. The method is applied to the case of the ferrocene/ferrocenium couple in [C(2)mim][N(Tf)(2)] and [C(4)mim][N(Tf)(2)].

Oxidation of several p-phenylenediamines in room temperature ionic liquids: Estimation of transport and electrode kinetic parameters

The electrochemical oxidation of N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) has been studied by cyclic voltammetry and potential step chronoamperometry at 303 K in five ionic liquids, namely [C(2)mim] [NTf2], [C(4)mim] [NTf2] [C(4)mpyrr] [NTf2] [C(4)mim] [BF4], and [C(4)mim] [PF6] (where [C(n)mim](+) = 1-alkyl-3-methylimidazolium, [C(4)mpyrr](+) = N-butyl-N-methylpyrrolidinium, [NTf2](-) = bis(trifluoromethylsulfonyl)imide, [BF4](-) = tetrafluoroborate, and [PF6](-) = hexafluorophosphate). Diffusion coefficients, D, of 4.87, 3.32, 2.05, 1.74, and 1.34 x 10(-11) m(2) s(-1) and heterogeneous electron-transfer rate constants, k(0), of 0.0109, 0.0103, 0.0079, 0.0066, and 0.0059 cm s(-1) were calculated for TMPD in [C(2)mim] [NTf2], [C(4)mim] [NTf2], [C(4)mpyrr] [NTf2], [C(4)mim] [BF4], and [C(4)mim] [PF6], respectively, at 303 K. The oxidation of TMPD in [C4mim][PF6] was also carried out at increasing temperatures from 303 to 343 K, with an activation energy for diffusion of 32.3 kJ mol(-1). k(0) was found to increase systematically with increasing temperature, and an activation energy of 31.4 kJ mol(-1) was calculated. The study was extended to six other p-phenylenediamines with alkyl/phenyl group substitutions. D and k(0) values were calculated for these compounds in [C(2)mim] [NTf2], and it was found that k(0) showed no obvious relationship with the hydrodynamic radius, r.

Kinetic analysis of the reaction between electrogenerated superoxide and carbon dioxide in the room temperature ionic liquids 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and hexyltriethylammonium bis(trifluoromethylsulfonyl)imide

The reduction of oxygen in the presence of carbon dioxide has been investigated by cyclic voltammetry at a gold microdisk electrode in the two room-temperature ionic liquids 1-ethyl-3-methylimidazolium bis-(trifluoromethylsulfonyl)imide ([EMIM][N(Tf)(2)]) and hexyltriethylammonium bis(trifluoromethylsulfonyl)imide ([N-6222] [N(Tf)(2)]). With increasing levels of CO2, cyclic voltammetry shows an increase in the reductive wave and diminishing of the oxidative wave, indicating that the generated superoxide readily reacts with carbon dioxide. The kinetics of this reaction are investigated in both ionic liquids. The reaction was found to proceed via a DISP1 type mechanism in [EMIM][N(Tf)(2)] with an overall second-order rate constant of 1.4 +/- 0.4 x 10(3) M-1 s(-1). An ECE or DISP1 mechanism was determined to be the most likely pathway for the reaction in [N-6222][N(Tf)(2)], with an overall second-order rate constant of 1.72 +/- 0.45 x 10(3) m(-1) s(-1).

Trends in C-O and C-N bond formations over transition metal surfaces: An insight into kinetic sensitivity in catalytic reactions

Transition metal catalyzed bond formation is a fundamental process in catalysis and is of general interest throughout chemistry. To date, however, the knowledge of association reactions is rather limited, relative to what is known about dissociative processes. For example, surprisingly little is known about how the bond-forming ability of a metal, in general, varies across the Periodic Table. In particular, the effect of reactant valency on such trends is poorly understood. Herein, the authors examine these key issues by using density functional theory calculations to study CO and CN formations over the 4d metals. The calculations reveal that the chemistries differ in a fundamental way. In the case of CO formation, the reaction enthalpies span a much greater range than those of CN formation. Moreover, CO formation is found to be kinetically sensitive to the metal; here the reaction barriers (E-a) are found to be influenced by the reaction enthalpy. CN formation, conversely, is found to be relatively kinetically insensitive to the metal, and there is no correlation found between the reaction barriers and the reaction enthalpy. Analysis has shown that at the final adsorbed state, the interaction between N and the surface is relatively greater than that of O. Furthermore, in comparison with O, relatively less bonding between the surface and N is observed to be lost during transition state formation. These greater interactions between N and the surface, which can be related to the larger valency of N, are found to be responsible for the relatively smaller enthalpy range and limited variation in E-a for CN formation. (C) 2007 American Institute of Physics.

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.

Isolation and characterisation of bacterial strains containing enantioselective DMSO reductase activity: application to the kinetic resolution of racemic sulfoxides

The kinetic resolution of racemic sulfoxides by dimethyl sulfoxide (DMSO) reductases was investigated with a range of microorganisms. Three bacterial isolates (provisionally identified as Citrobacter braakii, Klebsiella sp. and Serratia sp.) expressing DMSO reductase activity were isolated from environmental samples by anaerobic enrichment with DMSO as terminal electron acceptor. The organisms reduced a diverse range of racemic sulfoxides to yield either residual enantiomer depending upon the strain used. C. braakii DMSO-11 exhibited wide substrate specificity that included dialkyl, diaryl and alkylaryl sulfoxides, and was unique in its ability to reduce the thiosulfinate 1,4-dihydrobenzo-2, 3-dithian-2-oxide. DMSO reductase was purified from the periplasmic fraction of C. braakii DMSO-11 and was used to demonstrate unequivocally that the DMSO reductase was responsible for enantiospecific reductive resolution of racemic sulfoxides.

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.