Every completely polynomially bounded operator is similar to a contraction

It is proved that a bounded operator on a Hilbert space is similar to a contraction if and only if it is completely polynomially bounded. This gives a partial answer to Problem 6 of Halmos (Bull. Amer. Math. Soc.76 (1970). 877–933). The set of completely bounded maps between C¹-algebras is studied to obtain some structure, representation, and extension theorems for this class of maps. These allow a characterization of the completely bounded representations, on a Hilbert space, of any subalgebra of a C¹-algebra to be obtained. The result in the title follows by applying this characterization to the disk algebra.     

A coulometric method for determining substances that interfere with the measurement of water in oils and other chemicals by the Karl Fischer method

In order to fulfill a need to measure water in crude oils containing materials that interfere with the measurement of water by the Karl Fischer method, by reacting with iodine or iodide, a coulometric method has been developed and validated using 0.1 mol L(-1) Sodium thiosulfate as a calibrant. These interfering substances were measured in water-mass-equivalents, which were expressed as the mass of water that reacts with an equal mass of iodine in the Karl Fischer method. The SO(2)-free reagent that has been modified reacts quantitatively with sodium thiosulfate, cysteine and ascorbic acid but does not react with vinyl acetate. The level of interfering substances was measured in five transformer oils (including Reference Materials RM 8506 and RM 8507), a high and a low sulfur crude oil (Standard Reference Materials SRM 2721 and SRM 2722 respectively), a white oil, a high-vacuum oil and a high-viscosity base-stock oil. One oil contained less than 10 mg kg(-1) (water-mass-equivalents of interfering substances in oil) and two oils (RM 8507 and Drakeol 35) contained no measurable amount of interfering material (<0.2 mg kg(-1)). SRM 2271, a sour crude oil contained 834 mg kg(-1) (standard deviation (SD)=25 mg kg(-1)) (water-mass-equivalents of interfering substances in oil). Approximately 20% of this material was volatile and an additional 20% appeared to undergo some degradation (possibly oxidation) once the oil was exposed to air. These results indicate that this is a general method for measuring substances in oils that react with iodine and that it is capable of measuring in a variety of oils, using commercial instrumentation, interfering substances that inflate water measurements.     

Metastable isonitrosyl structure of the nitroprusside anion confirmed by nuclear inelastic scattering

Nuclear inelastic scattering (NIS) measurements were performed on a guanidium nitroprusside ((CN(3)H(6))(2)[Fe(CN)(5)NO], GNP) monocrystal at 77 K after the sample was illuminated with blue light (450 nm) at 50 K to populate the two metastable states, MS(1) and MS(2), of the nitroprusside anion. A second measurement was performed at 77 K after warming up the illuminated crystal to 250 K where the metastable states decay to the groundstate. The measured spectra were compared with simulated NIS spectra that were calculated by using density functional methods. Comparison of measured and simulated spectra provides strong evidence for the isonitrosyl structure of the metastable MS(1) state proposed by Carducci et al. (Carducci, M. D.; Pressprich, M. R.; Coppens, P. J. Am. Chem. Soc. 1997, 119, 2669-2678).     

Single-ion versus dipolar origin of the magnetic anisotropy in iron(III)-oxo clusters: a case study

A multitechnique approach has allowed the first experimental determination of single-ion anisotropies in a large iron(III)-oxo cluster, namely [NaFe6(OCH3)12(pmdbm)6ClO4 (1) in which Hpmdbm = 1,3-bis(4-methoxyphenyl)-1,3-propanedione. High-frequency EPR (HF-EPR). bulk susceptibility measurements, and high-field cantilever torque magnetometry (HF-CTM) have been applied to iron-doped samples of an isomorphous hexagallium(III) cluster [NaGa6(OCH3)12-(pmdbm)6]ClO4, whose synthesis and X-ray structure are also presented. HF-EPR at 240 GHz and susceptibility data have shown that the iron(III) ions have a hard-axis type anisotropy with DFe = 0.43(1) cm(-1) and EFe = 0.066(3) cm(-1) in the zero-field splitting (ZFS) Hamiltonian H = DFe[S2(z) - S(S + 1)/3] + Fe[S2(x) - S2(y)]. HF-CTM at 0.4 K has then been used to establish the orientation of the ZFS tensors with respect to the unique molecular axis of the cluster, Z. The hard magnetic axes of the iron(III) ions are found to be almost perpendicular to Z, so that the anisotropic components projected onto Z are negative, DFe(ZZ)= -0.164(4) cm(-1). Due to the dominant antiferromagnetic coupling, a negative DFe(ZZ) value determines a hard-axis molecular anisotropy in 1, as experimentally observed. By adding point-dipolar interactions between iron(III) spins, the calculated ZFS parameter of the triplet state, D1 = 4.70(9) cm(-1), is in excellent agreement with that determined by inelastic neutron scattering experiments at 2 K, D1 = 4.57(2) cm(-1). Iron-doped samples of a structurally related compound, the dimer [Ga2(OCH3)2(dbm)4] (Hdbm = dibenzoylmethane), have also been investigated by HF-EPR at 525 GHz. The single-ion anisotropy is of the hard-axis type as well, but the DFe parameter is significantly larger [DFe = 0.770(3) cm(-1). EFe = 0.090(3) cm(-1)]. We conclude that, although the ZFS tensors depend very unpredictably on the coordination environment of the metal ions, single-ion terms can contribute significantly to the magnetic anisotropy of iron(III)-oxo clusters, which are currently investigated as single-molecule magnets.     

Characterization of O-glycosylation sites in MUC2 glycopeptides by nanoelectrospray QTOF mass spectrometry

Sequencing of eight O-glycosylated peptides by nanoESI-QTOF-MS/MS was carried out to provide a sensitive general characterization method for determination of glycosylation site(s) and of the type of the attached carbohydrate moiety in a single experiment. The glycopeptide structures were chosen to demonstrate the feasibility of this sensitive and accurate approach, where isobaric peptide structures either (i) with the same number of attachment sites in different position in the peptide backbone, and (ii) with the same number of sugar moieties distributed on different attachment sites in the peptide backbone, can be clearly distinguished. Beside the B-type carbohydrate sequence ions of high abundance, it is possible to register diagnostic b- and y-type glycosylated peptide ions of lower abundance due to high dynamic range of the QTOF analyser. The applicability of this approach for detailed analysis of highly clustered O-glycan structures as found in biological mucin samples is discussed.     

Some remarks on C1-convexity

Recently the study of completely positive maps has become important to the results of Brown, Douglas, and Fillmore on Ext(

),

a C¹-algebra. Attempts to solve questions related to Ext have often turned into questions about the matrix algebras M_n. In this paper we wish to discuss a notion of C¹-convexity related to completely positive linear maps, to state some facts about C¹-convexity, and to ask some questions about C¹-convexity. To a large degree, the tone of this paper is expository.     

Stably isomorphic dual operator algebras

We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Δ-equivalent (Eleftherakis in J Pure Appl Algebra, ArXiv:math. OA/0607489v4, 2007), if and only if they have completely isometric normal representations α,β on Hilbert spaces H, K respectively and there exists a ternary ring of operators such that and This project is cofunded by European Social Fund and National Resources—(EPEAEK II) “Pyhtagoras II” grant No. 70/3/7997.     

Chemical Bonds and Spin State Splittings in Spin Crossover Complexes. A DFT and QTAIM Analysis

Summary. Density functional theory (DFT) calculations have been performed for the high-spin (HS) and low-spin (LS) isomers of a series of iron(II) spin crossover complexes with nitrogen ligands. The calculated charge densities have been analyzed in the framework of the quantum theory of atoms in molecules (QTAIM). For a number of iron(II) complexes with substituted tris(pyrazolyl) ligands the energy difference between HS and LS isomers, the spin state splitting, has been decomposed into atomic contributions in order to rationalize changes of the spin state splitting due to substituent effects.     

Darstellung von (s) -2,5-dimethyl-2-isopropyl-2,3-dihydrofuran,einem der beiden enantiomeren des sexuallockstoffs des werftkäfers hylecoetus dermestoides L.

The optical pure title compound II is synthesized by conversion of the branched chain sugar methyl-2-C-acetyl-4,6-O-benzylidene-3-deoxy-α-d-ribo-hexopyranose (I) which is available from d-glucose. 2,5-Di-methyl-2-isopropyl-2,3-dihydrofuran is found for the first time as a natural product and represents a new type of insect pheromones.