Equivariant maps and bimodule projections

We construct a counterexample to Solel's [B. Solel, Contractive projections onto bimodules of von Neumann algebras, J. London Math. Soc. 45 (2) (1992) 169–179] conjecture that the range of any contractive, idempotent, MASA bimodule map on is necessarily a ternary subalgebra. Our construction reduces this problem to an analogous problem about the ranges of idempotent maps that are equivariant with respect to a group action. Such maps are important to understand Hamana's theory [M. Hamana, Injective envelopes of C^*-dynamical systems, Tohoku Math. J. 37 (1985) 463–487] of G-injective operator spaces and G-injective envelopes.     

Excited state dynamics in recombinant water-soluble chlorophyll proteins (WSCP) from cauliflower investigated by transient fluorescence spectroscopy

The present study describes the fluorescence emission properties of recombinant water-soluble chlorophyll (Chl) protein (WSCP) complexes reconstituted with either Chl a or Chl b alone (Chl a only or Chl b only WSCP, respectively) or mixtures of both pigments at different stoichiometrical ratios. Detailed investigations were performed with time and space correlated ps fluorescence spectroscopy within the temperature range from 10 to 295 K. The following points were found: (a) The emission spectra at room temperature (295 K) are well characterized by bands with a dominating Lorentzian profile broadened due to phonon scattering and peak positions located at 677, 684 and 693 nm in the case of Chl a only WSCP and at 665, 675 and 689 nm for Chl b only WSCP. In addition, all spectra contain minor bands in the longer wavelength region. (b) The emission spectra at 10 K of samples suspended in buffer containing 50% glycerol are dominated by bands peaking at 668 nm for Chl b only WSCP and at 685 nm for Chl a only WSCP and samples reconstituted with mixtures of Chl a and Chl b. (c) At 10 K and in buffer with 50% glycerol the decay kinetics of WSCP samples with Chl a only are dominated by a component with a time constant of 6.2 (+/-0.2) ns at 685 nm while those of WSCP containing mixtures of Chl a and Chl b are characterized by a slightly shorter value of 6.0 (+/-0.2) ns. WSCP containing Chl b only exhibits a distinctly longer value of 7.0 (+/-0.3) ns at an emission wavelength of 668 nm. (d) The decay associated emission spectra at 10 K of all samples exhibit at least 3 decay components with time constants of 80-120 ps, 2-4 ns and 6-7 ns in 50% glycerol. These results are consistently described within the framework of our previously presented model (J. Phys. Chem. B 2007, 111, No. 46, 13325; J. Phys. Chem. B 2007, 111, No. 35, 10487) , for the structural motifs of chlorophyll binding to the tetrameric protein matrix of WSCP. It is shown that formation of strongly coupled open sandwich dimers does not lead to quenching of 1Chl a* or 1Chl b*.     

Unconventional methyl galactan synthesized via the thexyldimethylsilyl intermediate: preparation, characterization, and properties

Reaction of a beta-(1 --> 4) linked galactan with TDMS chloride followed by methylation and desilylation yields methyl galactans with unconventional functionalization patterns. The products were characterized via FTIR and NMR of the intact polymer and by CE after controlled depolymerization. A TDMS-derivatized methyl galactan contains differently methylated secondary hydroxyl groups. SEC and analytical ultracentrifugation showed a consistent decrease in the molecular weight after the consecutive reaction steps. Biological studies revealed that the methyl galactans are less active in complement fixation assays as compared with a 3-O-methyl galactan-enriched polysaccharide fraction isolated from Acanthus ebracteatus.     

Closed form equilibrium evaluation of interest rate caps and related derivatives in a real business cycle setting

The objective of this study is to provide closed form solutions to financial derivatives on mean-reverting cash flows. The general equilibrium real business cycle specification implies that underlying prices follow geometric mean reversion processes. Option-pricing formulas are derived, in terms of macroeconomic parameters or observable market prices, both for consumption goods and interest rates. The framework offers a rich specification of the economy’s yield curve and caplet volatility surface, which seems to fit well with criteria suggested by the empirical literature. The methodology may be useful for studying the effects of real economy changes on financial markets.     

Analysis of 'ARN' naphthenic acids by high temperature gas chromatography and high performance liquid chromatography

Examination by high temperature GC (HTGC) of the methyl esters of the so-called 'ARN' naphthenic acids from crude oils of North Sea UK, Norwegian Sea and West African oilfields revealed the distributions of resolved 4-8 ring C80 tetra acids and trace amounts of other acids. Whilst all three oils contained apparently the same major acids, the proportions of each differed, possibly reflecting the growth temperatures of the archaebacteria from which the acids are assumed to have originated. The structures of the 4, 5, 7 and 8 ring acids are tentatively assigned by comparison with the known 6 ring acid and related natural products and an HPLC method for the isolation of the individual acids is described. ESI-MS of individual acids isolated by preparative HPLC established the elution order of the 4-8 ring acids on the HPLC and HTGC systems and revealed the presence of previously unreported acids tentatively identified as C81 and C82 7 and 8 ring analogues.     

Estimate of the vibrational contribution to the entropy change associated with the spin transition in the d4 systems [MnIII(pyrol)3tren] and [CrII(depe)2I2

The vibrational contribution to DeltaS of the low-spin ((3)T(1)) to high-spin ((5)E) spin transition in two 3d(4) octahedral systems [Mn(III)(pyrol)(3)tren] and [Cr(depe)(2)I(2)] have been estimated by means of DFT calculations (B3LYP/CEP-31G) of the vibrational normal-modes frequencies. The obtained value at the transition temperature for the Mn(iii) complex is DeltaS(vib)(44 K) = 6.3 J K(-1) mol(-1), which is comparable with the proposed Jahn-Teller contribution of R ln3 = 9.1 J K(-1) mol(-1) and which is approximately half of the experimentally determined 13.8 J K(-1) mol(-1). The corresponding value for the Cr(ii) complex is DeltaS(vib)(171.45 K) = 46.5 J K(-1) mol(-1), as compared to the experimental value of 39.45 J K(-1) mol(-1). The analysis of the vibrational normal modes reveals that for the d(4) systems under study, contrary to Fe(ii) d(6) systems, not all metal-ligand stretching vibrations make a contribution. For the Mn(iii) complex, the only vibration that contributes to DeltaS(vib) involve the nitrogens occupying the Jahn-Teller axis, while in the case of Cr(ii) the contributing vibrations involve the Cr-I bonds. Low-frequency modes due to ring vibrations, metal-ligand bending and movement of the molecule as a whole also contribute to the vibrational entropy associated with the spin transition.     

Pigment-pigment and pigment-protein interactions in recombinant water-soluble chlorophyll proteins (WSCP) from cauliflower

Plants contain water-soluble chlorophyll-binding proteins (WSCPs) that function neither as antennas nor as components of light-induced electron transfer of photosynthesis but are likely constituents of regulatory protective pathways in particular under stress conditions. This study presents results on the spectroscopic properties of recombinant WSCP from cauliflower reconstituted with chlorophyll b (Chl b) alone or with mixtures of Chl a and Chl b. Two types of experiments were performed: (a) measurements of stationary absorption spectra at 77 and 298 K and CD spectra at 298 K and (b) monitoring of laser flash-induced transient absorption changes with a resolution of 200 fs in the time domain of up to 100 ps. On the basis of a theoretical analysis outlined by Renger et al. (J. Phys. Chem. B 2007, 111, 10487) the data obtained in part (a) are interpreted within a model where tetrameric WSCP binds predominantly two Chl molecules in the form of an excitonically coupled "open sandwich" dimer with a tilt angle of about 30 degrees between the chlorin planes. The time-resolved measurements on Chl a/Chl b heterodimers are described by two exponential kinetics with time constants of 400 fs and 7 ps. These kinetics are assumed to reflect a heterogeneous population of WSCPs with Chl dimers either in excitonic coupled "open sandwich" or weakly coupled geometric arrays. The 400 fs component is assigned to excited-state relaxations from the upper to the lower excitonic level of the strongly coupled "open sandwich" dimer, while the 7-8 ps component probably indicates excitation energy transfer from 1Chl b* to Chl a in a dimer array with weak coupling due to significantly longer mutual distances between the chlorin rings.     

Synthesis of Isotope Enriched (CN3H6)2[57Fe(CN)5NO] starting from 57Fe

A high‐yield, mmolar‐scale synthesis of pure guanidinium nitroprusside, (CN₃H₆)₂[⁽⁵⁷⁾Fe(CN)₅NO] (GNP) from iron metal is described. The iron metal contained pieces of 95.3% ⁵⁷Fe together with normal iron so that an isotope enrichment in ⁵⁷Fe of 25% was achieved. Single‐crystals of GNP could be grown in cubic shape and dimensions of about 3 × 4 × 4 mm³. The purity of the GNP product and the intermediates K₄[⁽⁵⁷⁾Fe(CN)₆] · 3 H₂O and Na₂[⁽⁵⁷⁾Fe(CN)₅NO] · 2 H₂O was ascertained by ⁵⁷Fe Mössbauer spectroscopy as well as ¹³C, ¹⁴N and ⁵⁷Fe NMR spectroscopy. The ⁵⁷Fe NMR chemical shift for [⁽⁵⁷⁾Fe(CN)₅NO]^2– in GNP was detected at +2004.0 ppm [vs Fe(CO)₅].     

A range of spin-crossover temperature T1/2>300 K results from out-of-sphere anion exchange in a series of ferrous materials based on the 4-(4-imidazolylmethyl)-2-(2-imidazolylmethyl)imidazole (trim) ligand, [Fe(trim)2]X2 (X=F, Cl, Br, I): comparison of experimental results with those derived from density functional theory calculations

The synthesis and characterization of [FeII(trim)2]Cl2 (2), [FeII(trim)2]Br2MeOH (3), and [FeII(trim)2]I2MeOH (4), including the X-ray crystal structure determinations of 2 (50 and 293 K) and 4 (293 K), have been performed and their properties have been examined. In agreement with the magnetic susceptibility results, the M?ssbauer data show the presence of high-spin (HS) to low-spin (LS) crossover with a range of T1/2 larger than 300 K (from approximately 20 K for [FeII(trim)2]F2 (1) to approximately 380 K for 4). All complexes in this series include the same [Fe(trim)2]2+ complex cation: the ligand field comprises a constant contribution from the trim ligands and a variable one originating from the out-of-sphere anions, which is transmitted to the metal center by the connecting imidazole rings and hydrogen bonds. The impressive variation in the intrinsic characteristics of the spin-crossover (SCO) phenomenon in this series is then interpreted as an inductive effect of the anions transmitted to the nitrogen donors through the hydrogen bonds. Based on this qualitative analysis, an increased inductive effect of the out-of-sphere anion corresponds to a decreased SCO temperature T1/2, in agreement with the experimental results. Electronic structure calculations with periodic boundary conditions have been performed that show the importance of intermolecular effects in tuning the ligand field, and thus in determining the transition temperature. Starting with the geometries obtained from the X-ray studies, the [FeII(trim)2]X2 complex molecules 1-4 have been investigated both for the single molecules and the crystal lattices with the local density approximation of density functional theory. The bulk geometries of the complex cations deduced from the X-ray studies and those calculated are in fair agreement for both approaches. However, the trend observed for the transition temperatures of 1-4 disagrees with the trend for the spin-state splittings ES (difference EHS-ELS between the energy of the HS and LS isomers) calculated for the isolated molecules, whereas it agrees with the trend for ES calculated with periodic boundary conditions. The latter calculations predict the strongest stabilization of the HS state for the fluoride complex, which actually is essentially HS above T=50 K, while the most pronounced stabilization of the LS state is predicted for 4, in line with the experimental results.