On interpolatory divergence-free wavelets

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct compactly supported divergence-free interpolatory wavelets.

     

Extension Operators with Analytic Values

If F ? ? is a closed set such that the space of all Whitney jets on F admits an extension operator then there exists such an extension operator whose values are holomorphic in ?F if and only if ?F is compact. In the case F is a compact set, there is even an extension operatorfor which the extensions are holomorphic in (? ∪ {∞})F.     

Making equation of state models predictive: Part 2: An improved PCP-SAFT equation of state

We use the PCP-SAFT equation of state, which is of the Van der Waals type and has a sound physical basis, to predict mixture properties, such as vapor–liquid and liquid–liquid equilibria, as well as excess enthalpies. We use molecular properties, such as dipole moment, quadrupole moment, polarizability and dispersion interaction coefficients, that have been determined quantum mechanically in Part I of this publication and adjust the remaining three pure compound parameters to pure compound data. We finally present a new combination rule for the dispersion energy parameter ? that is based on the quantum mechanically determined data. The predictions based on quantum mechanically determined pure compound properties along with the new combination rule show an improved performance compared to the original PCP-SAFT combination rule.     

Sn/Ge(1 1 1) α-phase: characterization of image resonances by specular electron reflection and selective electron scattering

Image potential resonances on the Sn/Ge(1 1 1) α-phase are investigated by two closely related methods: specular electron reflection and so-called selective electron scattering. Electrons from image resonances are detected on this surface at 120 and 300 K, i.e. below and above the phase transition at about 200 K. The dispersion of the image resonances reveals at these two temperatures equivalent effective electron masses, which are characteristic for this type of electronic surface states. The results of the two methods are consistent according to the similarity of the scattering processes. Changes in the loss peak intensity with the annealing temperature are assigned to the surface quality and are reflected by characteristic photoemission intensities.     

Development and characterisation of a new interface for coupling capillary LC with collision-cell ICP–MS and its application for phosphorylation profiling of tryptic protein digests

A comparison of different nebulisers for direct hyphenation of capillary and nano liquid chromatography (Cap-LC, Nano-LC) and quadrupole-based collision cell inductively coupled plasma mass spectrometry (CC-ICP–MS) for phosphorylation profiling of tryptic protein digests is described. Helium was used as cell gas and specially tuned instrumental conditions were used to achieve background minimisation at the mass of phosphorus, because of kinetic energy discrimination of the interfering polyatomic ions. The proposed set-up is based on a modified capillary electrophoresis interface and a home-made 4 mL spray chamber. It enables the use of gradient conditions with a highly concentrated organic mobile phase as often used in protein phosphorylation analysis, without the need to apply membrane desolvation for removal of the organic phase or further background minimisation. No significant signal suppression or other negative effects caused by the organic mobile phase occur, because of the low flow rates used in Cap-LC and the robust plasma conditions of the CC-ICP–MS instrument. A tryptic digest of beta-casein was investigated as model compound to demonstrate the applicability of the proposed set-up for phosphorylation profiling in protein analysis using quadrupole based collision-cell ICP–MS as phosphorus-specific detector. Detection limits for phosphorylated peptides down to the sub picomole level were obtained. As a complementary technique, electrospray ionisation tandem mass spectrometry (ESI–MS–MS) with data base searching was used for further characterisation of the phosphorylated peptides detected.     

NONLINEAR LASERSPECTROSCOPIC INVESTIGATIONS OF THE PIGMENT-PIGMENT INTERACTION WITHIN THE LIGHT-HARVESTING COMPLEX OF PHOTOSYSTEM II

Using a pump and test beam technique in the frequency domain with pump pulses in the nanosecond time range, the nonlinear transmission properties were investigated at room temperature in photosystem (PS) II membrane fragments and isolated light-harvesting chlorophyll a/b-protein preparations (LHC II preparations). In LHC II preparations and PS II membrane fragments, respectively, pump pulses of 620 nm and 647 nm cause a transmission decrease limited to a wavelength region in the nearest vicinity of the pump pulse wavelength (full width at half maximum ' 0.24 nm). In contrast, at 670 nm neither a transmission decrease nor a narrow band feature were observed. The data obtained for PS II membrane fragments and LHC II preparations at shorter wavelengths (620 nm, 647 nm) were interpreted in terms of excited state absorption of whole pigment-protein clusters within the light-harvesting antenna of photosystem II. The interpretation of the small transmission changes as homogeneously broadened lines led to a transversal relaxation time for chlorophyll in the clusters of about 4 ps.     

Quantum transport in chains with noisy off-diagonal couplings

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.     

Exciton dissociation dynamics in model donor-acceptor polymer heterojunctions. I. Energetics and spectra

In this paper we consider the essential electronic excited states in parallel chains of semiconducting polymers that are currently being explored for photovoltaic and light-emitting diode applications. In particular, we focus upon various type II donor-acceptor heterojunctions and explore the relation between the exciton binding energy to the band offset in determining the device characteristic of a particular type II heterojunction material. As a general rule, when the exciton binding energy is greater than the band offset at the heterojunction, the exciton will remain the lowest-energy excited state and the junction will make an efficient light-emitting diode. On the other hand, if the offset is greater than the exciton binding energy, either the electron or hole can be transferred from one chain to the other. Here we use a two-band exciton to predict the vibronic absorption and emission spectra of model polymer heterojunctions. Our results underscore the role of vibrational relaxation and suggest that intersystem crossings may play some part in the formation of charge-transfer states following photoexcitation in certain cases.     

Azobridges from azines, XVII. Intra- and intermolecular [3+2] cycloaddition between nonstabilized azomethineimines and alkenes

Azo compounds 1 and 3 containing a CC-double bond in a parallel but distant position are quatemized by Me₃OBF₄ to 1,MeBF₄ and 3,MeBF₄, whereas MeI produces the cage compounds 2,HX and 4,HX. These [3+2] cycloadducts also are quantitatively formed from 1,MeBF₄ and 3,MeBF₄ with catalytic amounts of azo compounds. Intermolecular [3+2] cycloadditions occur with a mixture of DBH (5) or DBO (8), MeI and a variety of alkenes (→ HI) salts of (6, 7, 9 — 12). The intermediate azomethineimines, if stabilized by a fluorenylidene group, can be isolated (20, 22,24), but not, however, in the presence of a close parallel CC-bond (25 → 26).     

Binding the tobacco mosaic virus to inorganic surfaces

We studied the adsorption behavior and surface chemistry of the tobacco mosaic virus (TMV) on well-defined metal and insulator surfaces. TMV serves as a tubular supramolecular model system with precisely known surface termination. We show that if the surface chemistry of the substrate and the pH-dependent chemistry of the molecular surface match, for example, by hydrogen bonding, a strong adsorption occurs, and lateral movement is impeded. Due to the immobilization, the virion can be imaged by atomic force microscopy (AFM) in contact mode. We also used self-assembled monolayers with an acyl chloride group to induce covalent bonding via ester formation. Noncontact AFM proved that TMV keeps its cylindrical cross section only under weak adsorption conditions, that is, on hydrophobic surfaces, while on hydrophilic substrates a deformation occurs to maximize the number of interacting chemical groups.