Normal Multi-scale Transforms for Curves

Extending upon Daubechies et al. (Constr. Approx. 20:399–463, 2004) and Runborg (Multiscale Methods in Science and Engineering, pp. 205–224, 2005), we provide the theoretical analysis of normal multi-scale transforms for curves with general linear predictor S, and a more flexible choice of normal directions. The main parameters influencing the asymptotic properties (convergence, decay estimates for detail coefficients, smoothness of normal re-parametrization) of this transform are the smoothness of the curve, the smoothness of S, and its order of exact polynomial reproduction. Our results give another indication why approximating S may not be the first choice in compression applications of normal multi-scale transforms.     

Spectroscopy of the hyperfine structure of antiprotonic 4He and 3He

The spin magnetic moment $\mu^{\overline{p}}_{s}$ of the antiproton can be determined by comparing the measured transition frequencies in $\overline{p}^4$ He^?+? with three-body QED calculations. A comparison between the proton and antiproton can then be used as a test of CPT invariance. The highest measurement precision of the difference between the proton and the antiproton spin magnetic moments to date is 0.3%. A new experimental value of the spin magnetic moment of the antiproton was obtained as $\mu^{\overline{p}}_{s} = -2.7862(83)\mu_{N}$ , slightly better than the previously best measurement. This agrees with $\mu^{p}_{s}$ within 0.24%. In 2009, a new measurement with antiprotonic ³He has been started. A comparison between the theoretical calculations and experimental results would lead to a stronger test of the theory and address systematic errors therein. A measurement of this state will be the first HF measurement on $\overline{p}^3$ He^?+?. We report here on the new experimental setup and the first tests.     

A branch-and-bound algorithm for the coupled task problem

The coupled task problem is to schedule jobs on a single machine where each job consists of two subtasks and where the second subtask has to be started after a given time interval with respect to the first one. The problem has several applications and is NP-hard. In this paper we present a branch-and-bound algorithm for this problem and compare its performance with four integer programming models.     

Crystallizability of ethylene homopolymers by crystallization analysis fractionation

The effect of molecular weight and long‐chain branching on the crystallization analysis fractionation (CRYSTAF) of ethylene homopolymers was investigated. Several ethylene homopolymers were prepared with different molecular weights and levels of long‐chain branching to isolate these effects from the dominant effect of comonomer content on crystallizability measured by CRYSTAF. Molecular weight effects might be significant for samples with number‐average molecular weights below 5000, but this effect can be corrected if terminal methyl groups are taken into account. Long‐chain branching has only a very small effect on the CRYSTAF profile of the samples investigated in this study. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1616–1628, 2001     

Factor analysis and XPS-data preprocessing for non-conducting samples

The use of factor analysis for automatic interpretation of electron spectra needs in some cases a special data preprocessing. It was shown for x-ray photoelectron spectroscopy that in the case of non-conducting samples in addition to experimental methods (low energy electron flooding) a shift of the measured spectra with respect to a reference peak was useful. Thus, the residual energy shift due to sample charging, especially if the surface conductivity changes during measurement, could be removed. Several shift methods and the influence of different reference peaks were discussed.     

Planar waveguide lasers and structures created by laser ablation — an overview

The parameters of planar and channel waveguide lasers fabricated by different techniques are reviewed. Materials and properties of thin films used for creation of planar waveguide lasers are summarized. The parameters of active and passive planar waveguides created by the method of pulsed laser deposition and problems of laser deposition are described. The aspects of laser generation of planar waveguide lasers, resonators and channel waveguides are presented. The results of our experiments of laser deposition of thin Ti:sapphire layers and thin layers of Nd:YAG and Nd:YAP are briefly discussed. This work was supported by the grant of Czech Grant Agency No. 102/96/0429.     

Nonconforming P1 elements on distorted triangulations: Lower bounds for the discrete energy norm error

Compared to conforming P1 finite elements, nonconforming P1 finite element discretizations are thought to be less sensitive to the appearance of distorted triangulations. E.g., optimal-order discrete H¹ norm best approximation error estimates for H² functions hold for arbitrary triangulations. However, the constants in similar estimates for the error of the Galerkin projection for second-order elliptic problems show a dependence on the maximum angle of all triangles in the triangulation. We demonstrate on an example of a special family of distorted triangulations that this dependence is essential, and due to the deterioration of the consistency error. We also provide examples of sequences of triangulations such that the nonconforming P1 Galerkin projections for a Poisson problem with polynomial solution do not converge or converge at arbitrarily low speed. The results complement analogous findings for conforming P1 finite elements.     

Simple one-step process for immobilization of biomolecules on polymer substrates based on surface-attached polymer networks

For the miniaturization of biological assays, especially for the fabrication of microarrays, immobilization of biomolecules at the surfaces of the chips is the decisive factor. Accordingly, a variety of binding techniques have been developed over the years to immobilize DNA or proteins onto such substrates. Most of them require rather complex fabrication processes and sophisticated surface chemistry. Here, a comparatively simple immobilization technique is presented, which is based on the local generation of small spots of surface attached polymer networks. Immobilization is achieved in a one-step procedure: probe molecules are mixed with a photoactive copolymer in aqueous buffer, spotted onto a solid support, and cross-linked as well as bound to the substrate during brief flood exposure to UV light. The described procedure permits spatially confined surface functionalization and allows reliable binding of biological species to conventional substrates such as glass microscope slides as well as various types of plastic substrates with comparable performance. The latter also permits immobilization on structured, thermoformed substrates resulting in an all-plastic biochip platform, which is simple and cheap and seems to be promising for a variety of microdiagnostic applications.