Linear Convergence of Iterative Soft-Thresholding

In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized gradient methods and present a new convergence analysis. As main result we show that the algorithm converges with linear rate as soon as the underlying operator satisfies the so-called finite basis injectivity property or the minimizer possesses a so-called strict sparsity pattern. Moreover it is shown that the constants can be calculated explicitly in special cases (i.e. for compact operators). Furthermore, the techniques also can be used to establish linear convergence for related methods such as the iterative thresholding algorithm for joint sparsity and the accelerated gradient projection method.     

Synthesis of carbohydrate‐segmented polydimethylsiloxanes by hydrosilylation

Carbohydrate‐modified polysiloxanes have been presented several times within the last decade. In this work, a new route to carbohydrate‐segmented polysiloxanes is presented. A series of allyl‐group‐containing bifunctional carbohydrate derivatives was synthesized and reacted with hydrodimethylsilyl‐terminated polysiloxane in hydrosilylation reactions with Speier's catalyst. The carbohydrate monomers and the resulting materials were fully characterized with ¹H and ¹³C NMR spectroscopy. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3814–3822, 2005     

Labeling of macrophages using bacterial magnetosomes and their characterization by magnetic resonance imaging

This work investigated macrophages labeled with magnetosomes for the possible detection of inflammations by MR molecular imaging. Pure magnetosomes and macrophages containing magnetosomes were analyzed using a clinical 1.5 T MR-scanner. Relaxivities of magnetosomes and relaxation rates of cells containing magnetosomes were determined. Peritonitis was induced in two mice. T₁, T₂ and T₂* weighted images were acquired following injection of the probes. Pure magnetosomes and labeled cells showed slight effects on T₁, but strong effects on T₂ and T₂* images. Labeled macrophages were located with magnetic resonance imaging (MRI) in the colon area, thus demonstrating the feasibility of the proposed approach.     

A radial analogue of Poisson’s summation formula with applications to powder diffraction and pinwheel patterns

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction.     

Structural and mechanical properties of spark plasma sintered n‐ and p‐type bismuth telluride alloys

Spark Plasma Sintering (SPS) is used for the fabrication of wafers of n‐ and p‐type thermoelectric V₂VI₃ materials. The SPS process did not change the overall chemical composition. X‐ray diffraction analysis and the electron backscattered selected area diffraction prove the preferential orientation after the SPS procedure expecting anisotropic thermoelectric prop‐ erties. The mechanical properties of the SPS material are enormously enhanced, so that the fabrication of thin wafers with only 100 µm thickness suitable for the development of Peltier devices with high cooling power density will be possible. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solvent Electrostatic and Covalent Effects on Complexation Thermodynamics

A new method is suggested for estimating the electrostatic and covalent contributions to the standard Gibbs energy, enthalpy and entropy of complexation reactions upon transfer from water (W) to non-aqueous and mixed aqueous organic solvents (S). The equations derived for calculation of the electrostatic (temperature dependent) contributions are based on the temperature dependences of thermodynamic parameters of complexation in aqueous solution and the temperature dependence of the dielectric constant of water. These contributions correspond to the transfer process in water from T₁ = 298.15 K to a higher temperature (T₂) at which water has the same dielectric constant as does the solvent S at 298.15 K (εW(T₂) = εS(T₁)). The covalent (temperature independent) contributions are calculated at isodielectric conditions (transfer from water at T₂ to S at T₁) using the corresponding thermodynamic cycle. Application of the model to an analysis of solvent effects is demonstrated and discussed with an example given of a typical complexation reaction between K⁺ and 18-crown-6 in pure non-aqueous and water-acetonitrile mixed solvents.