Scalar-type spectral operators and holomorphic semigroups

We show that a linear operator (possibly unbounded), A, on a reflexive Banach space, X, is a scalar-type spectral operator, with non-negative spectrum, if and only if the following conditions hold.

1. A generates a uniformly bounded holomorphic semigroup {e?^zA}_Re(z)≥0.
2. If \(F_N (s) \equiv \int_{ - N}^N {\tfrac{{\sin (sr)}}{r}} e^{irA} dr\) , then {‖F_N‖} _N=1 ^∞ is uniformly bounded on [0,∞) and, for all x in X, the sequence {F_N(s)x} _N=1 ^∞ converges pointwise on [0, ∞) to a vector-valued function of bounded variation.

The projection-valued measure, E, for A, may be constructed from the holomorphic semigroup {e^?zA}_Re(z)≥0 generated by A, as follows. $$\frac{1}{2}(E\{ s\} )x + (E[0,s)) x = \mathop {\lim }\limits_{N \to \infty } \int_{ - N}^N {\frac{{\sin (sr)}}{r}} e^{irA} x\frac{{dr}}{\pi }$$ for any x in X.     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.     

Particle shape in thixotropic aluminium and thorium molybdates gels

Summary Electron microscope examination of thixotropic aluminium and thorium molybdate gels shows that one hour after formation they are constituted by short fibrils of small axial ratio. The fibrils of the aluminium molybdate gels, with ageing at room temperature or with boiling, increase in diameter and length; the fibrous shape of the particles is maintained after two and a half years of ageing; all fibrils are crystalline by electron diffraction. The fibrils of the thorium molybdate gels, except in the gels containing hydrochloric acid, change with ageing at room temperature or with boiling, into plates of hexagonal, elliptical or rectangular profile; the fibrils and plates are crystalline and have the same electron diffraction pattern as the fibrils.This work was aided, in part, by grants from Conselho Nacional de Pesquisas and the Rockefeller Foundation.     

Time-resolved enzymatic determination of glucose using a fluorescent europium probe for hydrogen peroxide

An enzymatic assay for glucose based on the use of the fluorescent probe for hydrogen peroxide, europium(III) tetracycline (EuTc), is described. The weakly fluorescent EuTc and enzymatically generated H₂O₂ form a strongly fluorescent complex (EuTc–H₂O₂) whose fluorescence decay profile is significantly different. Since the decay time of EuTc–H₂O₂ is in the microseconds time domain, fluorescence can be detected in the time-resolved mode, thus enabling substantial reduction of background fluorescence. The scheme represents the first H₂O₂-based time-resolved fluorescence assay for glucose not requiring the presence of a peroxidase. The time-resolved assay (with a delay time of 60 s and using endpoint detection) enables glucose to be determined at levels as low as 2.2 mol L^–1, with a dynamic range of 2.2–100 mol L^–1. The method also was adapted to a kinetic assay in order to cover higher glucose levels (mmol L^–1 range). The latter was validated by analyzing spiked serum samples and gave a good linear relationship for glucose levels from 2.5 to 55.5 mmol L^–1. Noteworthy features of the assay include easy accessibility of the probe, large Stokes shift, a line-like fluorescence peaking at 616 nm, stability towards oxygen, a working pH of approximately 7, and its suitability for both kinetic and endpoint determination.     

Mössbauer studies on one-dimensional iron phthalocyanines

Summary Magnetic moments and⁵⁷Fe Mössbauer spectra at room temperature and at liquid nitrogen temperature of polynuclear ligand-bridged iron phthalocyanines, FePcL (L = pyrazine and 4,4-bipyridyl), are reported. The experimental data are in agreement with a pseudo-octahedral environment around the iron(II) cation. Partially oxidized derivatives, FePc(pz)I_0.26 and FePc(bipy)I_1.06 have been synthesized and their⁵⁷Fe Mössbauer spectra and magnetic moments within the same temperature range obtained. Oxidation is shown to be metal centred and the iodine is found to be in I^– form for FePc(pz)_0.26 and as both I^– and I ₃ ^– species for FePc(bipy)I_1.06. While the magnetic moment of FePc(pz) increases upon oxidation, the opposite occurs for FePc(bipy).     

Accurate intermolecular ground state potential of the Ar-N2 van der Waals complex

After carrying out a systematic basis set convergence study, we evaluate several ground state potential energy surfaces of the Ar-N(2) van der Waals complex at the coupled cluster singles and doubles model including connected triples corrections. We use the aug-cc-pVXZ (X=5,Q,D) and the daug-cc-pVQZ basis sets augmented with a set of 3s3p2d1f1g (denoted 33211) and 3s3p2d2f1g (denoted 33221) midbond functions, respectively. aug-cc-pVTZ-33211 results were available in the literature. The aug-cc-pV5Z-33211 (daug-cc-pVQZ-33221) surface is characterized by a T-shaped minimum at R(e)=3.709 (3.701) A and of 99.01 (102.50) cm(-1), and a linear saddle point at 4.260 (4.257) A and D(e)=75.28 (79.73) cm(-1). These results are compared with the values provided by the semiempirical potentials available, and those of previous theoretical studies. The basis set convergence of the intermolecular potentials is also analyzed. From the potentials the rovibronic spectroscopic properties are determined. We study the basis set convergence of the rotational frequencies. The binding parameters that characterized the aug-cc-pVTZ-33211 surface are reasonable, but the surface is not good enough to evaluate the microwave spectra. The aug-cc-pVQZ-33211 basis set results considerably improve the triple zeta and are close to the aug-cc-pV5Z-33211. Considering the small differences between the quadruple and the quintuple zeta surfaces, the latter results can be expected to be close to convergence. At this level the differences with respect to the accurate experimental frequencies are in the order of 0.7%. In the case of the daug-cc-pVXZ-33211,33221 (X=5,Q,T,D) series, the convergence of the interaction energies with respect to basis set improvement is not so smooth. The errors in the frequencies obtained with the daug-cc-pVQZ-33221 basis set with respect to experiment are in the order of 0.4%.     

Prosthetic heme modification during halide ion oxidation. Demonstration of chloride oxidation by horseradish peroxidase

Myeloperoxidase (MPO), eosinophil peroxidase (EPO), and chloroperoxidase can oxidize iodide, bromide, and chloride, but most peroxidases, including the prototypical horseradish peroxidase (HRP), reportedly only oxidize iodide and, in some cases, bromide. We report here that incubation of HRP with Br(-) and H(2)O(2) at acidic pH results in both bromination of monochlorodimedone and modification of the heme group. Mass spectrometry indicates that the heme 2- and 4-vinyl groups are modified by either replacement of a vinyl hydrogen by a bromide or addition of HOBr to give a bromohydrin. These reactions do not occur if protein-free heme and Br(-) are co-incubated with H(2)O(2) or if the HRP reaction is carried out at pH 7. Surprisingly, similar prosthetic heme modifications occur in incubations of HRP with H(2)O(2) and Cl(-). A mechanism is proposed involving oxidation of Br(-) or Cl(-) to give HOBr or HOCl, respectively, followed by addition to a vinyl group. In the reaction with Cl(-), a meso-chloro heme adduct is also formed. This first demonstration of Cl(-) oxidation by HRP, and the finding that prosthetic heme modification occurs when Br(-) or Cl(-) is oxidized in the absence of a cosubstrate, show that only modest tuning is required to achieve the unique chloride oxidation activity of MPO and EPO. The results raise the question of how the prosthetic hemes of MPO and EPO, whose function is to produce oxidized halide species, escape modification.     

Theoretical study of alkyl-pi and aryl-pi interactions. Reconciling theory and experiment

Quantum mechanical and quantum mechanical/molecular mechanical calculations in conjunction with continuum solvation models have been used to analyze CH-pi interactions in model systems of aryl- and alkyl-aromatic interactions, as well as in a model folding system designed to study those interactions. High level calculations reproduced accurately the interaction of CH-pi interactions in both alkyl- and aryl-based model systems. Dispersion effects dominate the interaction, but the electrostatics term is also relevant for aryl CH-pi interactions. Theoretical calculations were also used to examine the influence of CH-pi interactions in determining the conformational flexibility of folding models. Finally, a critical comparison of the results obtained from high level calculations on model systems and the experimental data derived for folding models in apolar solvents was carried out, which allowed us to reconcile the apparent discrepancy found between both data.