Fractal wavelet dimensions and localization

In this paper we want to give a new definition of fractal dimensions as small scale behavior of theq-energy of wavelet transforms. This is a generalization of previous multi-fractal approaches. With this particular definition we will show that the 2-dimension (=correlation dimension) of the spectral measure determines the long time behavior of the time evolution generated by a bounded self-adjoint operator acting in some Hilbert space ?. It will be proved that for φ, ψ∈? we have $$\mathop {\lim \inf }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ + (2)$$ and that $$\mathop {\lim \sup }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ - (2),$$ wherek ^±(2) are the upper and lower correlation dimensions of the spectral measure associated with ψ and ?. A quantitative version of the RAGE theorem shall also be given.     

Development of a very low energy μ+ beam at PSI

At PSI we are investigating the technique of decelerating an existing very intense secondary beam of surface ⁺ (4 MeV) to an energy of 10 eV using appropriate moderators. These ⁺ can then be used as a source of a tertiary beam of low energy muons with tunable kinetic energy between 10 eV and 10 keV.With a 1000 A layer of solid Argon deposited on an Al substrate we obtain a moderation efficiency (with respect to the number of incoming surface ⁺) of the order of 10^–4.Results of our investigations and the present status of the project are presented together with future plans and possibilities.     

Development of a beam of very slow polarized muons

During the last few decades, a variety of methods has been developed which makes use of polarized positive muons as a microscopic probe of the magnetic properties of condensed matter (muon spin rotation, relaxation, resonance,SR). Until now, available beams for SR studies have delivered 100% polarized muons with energies in the MeV range, resulting in a deep penetration of the muons into the sample material under investigation. This presently limits the applications of theSR technique to the study of the bulk characteristics of matter. To be able to control the implantation depth, a very low energy beam of polarized muons is being developed at the Paul Scherrer Institute. Very slow polarized muons (kinetic energy 10 eV, polarization 90%) are obtained from the moderation of a high energy muon beam in a thin film of an appropriate condensed gas. These muons can be used as a source for a beam of tunable energy between a few tens of eV and some tens of keV. Implantation depths in the range of few to a few hundreds of nanometers can thus be achieved by varying the energy.     

Cycloaldol approach to the isobenzofuran core of eunicellin diterpenes

[reaction: see text] A novel cycloaldol approach to the isobenzofuran core common to many of the eunicellin diterpenes is described. The cycloaldol precursor was prepared by aldol addition of (S)-(+)-carvone and methacrolein followed by etherification to a glycolate ester. Chemoselective enolization of the glycolate ester led to the cycloaldol adduct in high yield and diastereoselectivity. An oxidative rearrangement-allylic diazene rearrangement sequence established the requisite cis ring fusion.     

Toward understanding the ionization of biomarkers from micrometer particles by bio-aerosol mass spectrometry

The appearance of informative signals in the mass spectra of laser-ablated bio-aerosol particles depends on the effective ionization probabilities (EIP) of individual components during the laser ionization process. This study investigates how bio-aerosol chemical composition governs the EIP values of specific components and the overall features of the spectra from the bio-aerosol mass spectrometry (BAMS). EIP values were determined for a series of amino acid, dipicolinic acid, and peptide aerosol particles to determine what chemical features aid in ionization. The spectra of individual amino acids and dipicolinic acid, as well as mixtures, were examined for extent of fragmentation and the presence of molecular ion dimers, which are indicative of ionization conditions. Standard mixtures yielded information with respect to the significance of secondary ion plume reactions on observed spectra. A greater understanding of how these parameters affect EIP and spectra characteristics of bio-aerosols will aid in the intelligent selection of viable future biomarkers for the identification of bio-terrorism agents.     

Fiber optic multi-channel protein detector for use in preparative continuous annular chromatography

On-line coupling continuous-flow liquid membrane extraction (CFLME) with HPLC, a novel automatic system was developed for the determination of sulfonylurea herbicides in water. After an automatic trace-enrichment process by CFLME, which is the combination of continuous flow liquid-liquid extraction and support liquid membrane (SLM) extraction, the target analytes were concentrated in 50 microl of 0.2 M Na2CO3-NaHCO3 (pH 10.0) buffer. The concentrated sample solutions were injected directly onto a C18 analytical column with a valve, and detected at 240 nm with a diode array detector. Metsulfuron methyl (MSM), and DPX-A 7881 were baseline separated with a mobile phase consisting of methanol and 67 mM KH2PO4-Na2HPO4 (pH 5.91) buffer (45+55, v+v) at a flow-rate of 1.0 ml min(-1). With an enrichment time of 10 min and enrichment sample volume of 20 ml, the enrichment factors and detection limits are 100 and 0.05 microg l(-1) for MSM, and 96 and 0.1 microg l(-1) for DPX-A 7881, respectively. The linear range and precision (RSD) are 0.1-50 microg l(-1) and 7.0% for MSM, and 0.2-50 microg l(-1) and 9.2% for DPX-A 7881, respectively. This proposed method was applied to determine MSM and DPX-A 7881 in seawater, tap water, and bottled mineral water with spiked recoveries in the range of 83-95% for MSM and 88-100% for DPX-A 7881, respectively.     

Proton bound homodimers and heterodimers of amides and amines in the gas phase. Equilibrium studies by Fourier transform ion cyclotron resonance spectrometry

By injection of the proton bound homodimer [DMF.H+.DMF] of N,N-dimethylformamide (DMF) generated in an external ion source into a mixture of DMF and a second base within the cell of a Fourier transform ion cyclotron resonance (FT-ICR) spectrometer the equilibria between [DMF.H+.DMF] and the other possible proton bound dimers [DMF.H+.base] and [base.H+.base] have been studied for 13 different bases. Strongly polar bases like aliphatic amides and dimethyl sulfoxide (DMSO) exchange both DMF in [DMF.H+.DMF] by a two step process, while the almost non-polar amines exchange only one DMF. If the base is a primary or secondary amine, the proton bound heterodimer [DMF.H+.amine] reacts further by the addition of one DMF to create a proton bound trimer [(DMF)2.H+.amine]. The affinity deltaG(DMFH+) of the bases towards protonated DMF relative to neutral DMF depends linearly on the difference deltaGB of the gas phase basicity of DMF and the other base, but different correlation lines are obtained for polar and non-polar ligands (deltaGDMFH+ = 0.44GB(base)-375 [kJ/mol] (r = 0.97) and deltaGDMFH+ = 0.46GB(base)-397 [kJ/mol] (r = 0.99), respectively). This different behavior is explained by a different character of the proton bridge in the heterodimers containing only polar ligands and those incorporating a non-polar ligand besides DMF. The former dimers contain a more or less symmetric proton bridge while the latter can be viewed as a protonated base solvated by DMF. The available data have been used to calculate the molecular pair gas phase basicity of DMF and the 13 bases used and to estimate the dissociation energies of the bonds of the proton bridge in various proton bound heterodimers.     

Single- and multi-channel detection for generalized quantitative analysis in cases of unresolved chromatographic peaks

Computerized quantification of components under overlapping chromatographic peaks is done by calibration of chromatograms against component mixtures. For conventional (single-channel) detectors, the limitations of earlier methods based on ordinary multiple regression, can be circumvented by data reduction with the aid of principal component analysis with the partial least-squares approach. Simulation studies show that the method can be applied even when there is severe peak overlap, unstable baseline, noisy chromatograms or non-linear detector response. Advantages in the quantification of fused peaks by means of multichannel detectors are outlined. Present limitations on the quantitative evaluation of several overlapping component peaks from a single spectro-chromatogram by means of the partial least-squares method combined with multiple regression on the pure component spectra, are discussed with respect to practical high-performance liquid chromatography.     

Synthesis of α,β-disubstituted ferrocenes via a ferrocenylepoxide intermediate. Preparation and catalytic activity of a new chiral ferrocenyloxazoline

A short synthesis of the chiral oxazoline 10 (>95% e.e.) in six steps from chloroacetylferrocene is described. The ligand can be used successfully in an asymmetric Pd(0)-catalyzed allylic alkylation reaction.     

The Monohydrate of Basic Mercuric Nitrate, [Hg(OH)](NO3)(H2O)

Colourless single crystals of [Hg(OH)](NO₃)(H₂O) were obtained by slow evaporation of an aqueous solution of Hg(NO₃)₂ and Bi(NO₃)₃. The crystal structure (orthorhombic, Pbca, Z = 8, a = 943.2(2), b = 697.6(1), c = 1349.0(2) pm, R₁(all) = 0.0780) contains [Hg(OH)] = …OH–Hg–OH–Hg… zig zag chains (O–Hg–O angle: 168°, Hg–O–Hg angle: 112°, Hg–OH distance: 212 pm) to which one water molecule is attached loosely. The [Hg(OH)](H₂O) chains are connected via bis‐monodentate‐bridging nitrate ions to corrugated layers that are stacked in the [001] direction. Hg²⁺ has an effective 2+2+2(+1) coordination.