A fast direct solver for the integral equations of scattering theory on planar curves with corners

We describe an approach to the numerical solution of the integral equations of scattering theory on planar curves with corners. It is rather comprehensive in that it applies to a wide variety of boundary value problems; here, we treat the Neumann and Dirichlet problems as well as the boundary value problem arising from acoustic scattering at the interface of two fluids. It achieves high accuracy, is applicable to large-scale problems and, perhaps most importantly, does not require asymptotic estimates for solutions. Instead, the singularities of solutions are resolved numerically. The approach is efficient, however, only in the low- and mid-frequency regimes. Once the scatterer becomes more than several hundred wavelengths in size, the performance of the algorithm of this paper deteriorates significantly. We illustrate our method with several numerical experiments, including the solution of a Neumann problem for the Helmholtz equation given on a domain with nearly 10000 corner points.     

On the Suitability of Different Online Gait Generation Methods for Pre-Defined Footsteps

Detailed dynamical modeling is the basis for simulation and model based control. In this contribution the Projection Equation is used for the modeling of a biped walking machine, resulting in the equations of motion which are needed for gait generation and verification of its stability. For biped robots one main issue is the generation of stable trajectories for the center of mass (CoM). Several different approaches based on the Zero Moment Point (ZMP) scheme have been presented in the past. Due to the complex dynamic structure of bipedal robots most of the considered algorithms use a linear inverted pendulum as a simplified model. This results in a decoupling of the ZMP equations in lateral and forward direction, but limits the trajectories to a constant height of the CoM. An extension of the well known LQR theory by future reference values has been proposed. This model based approach seems to perform quite well, but does not allow the consideration of constraints on the position of the ZMP. This limitation is removed by the use of Model Predictive Control (MPC) with inequality constraints. By extending this approach to a time invariant one the restriction to a constant height of the CoM is no longer necessary. Both methods as well as the time invariant approach for variable CoM heights have been evaluated in simulations and will be experimentally verified on a real robot soon. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adsorption of enterobactin to metal oxides and the role of siderophores in bacterial adhesion to metals

The potential contribution of chemical bonds formed between bacterial cells and metal surfaces during biofilm initiation has received little attention. Previous work has suggested that bacterial siderophores may play a role in bacterial adhesion to metals. It has now been shown using in situ ATR-IR spectroscopy that enterobactin, a catecholate siderophore secreted by Escherichia coli, forms covalent bonds with particle films of titanium dioxide, boehmite (AlOOH), and chromium oxide-hydroxide which model the surfaces of metals of significance in medical and industrial settings. Adsorption of enterobactin to the metal oxides occurred through the 2,3-dihydroxybenzoyl moieties, with the trilactone macrocycle having little involvement. Vibrational modes of the 2,3-dihydroxybenzoyl moiety of enterobactin, adsorbed to TiO(2), were assigned by comparing the observed IR spectra with those calculated by the density functional method. Comparison of the observed adsorbate IR spectrum with the calculated spectra of catecholate-type [H(2)NCOC(6)H(3)O(2)Ti(OH)(4)](2-) and salicylate-type [H(2)NCOC(6)H(3)O(2)HTi(OH)(4)](2-) surface complexes indicated that the catecholate type is dominant. Analysis of the spectra for enterobactin in solution and that adsorbed to TiO(2) revealed that the amide of the 2,3-dihydroxybenzoylserine group reorientates during coordination to surface Ti(IV) ions. Investigation into the pH dependence of enterobactin adsorption to TiO(2) surfaces showed that all 2,3-dihydroxybenzoyl groups are involved. Infrared absorption bands attributed to adsorbed enterobactin were also strongly evident for E. coli cells attached to TiO(2) particle films. These studies give evidence of enterobactin-metal bond formation and further suggest the generality of siderophore involvement in bacterial biofilm initiation on metal surfaces.     

Varieties of Finitism

We consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either on temporal readings of infinity (or infinite series) or on anti-realistic background assumptions. Both these motivations may be considered problematic. The approaches centering on the indefinitely large and the use of schemata would provide a work-around to circumvent usage of actual infinities if we had a clear understanding of how schemata work and where to draw the conceptual line between the indefinitely large and the infinite. Neither of this seems to be clear enough. Versions of strict finitism in contrast provide a clear picture of a (realistic) finite number theory. One can recapture standard arithmetic without being committed to actual infinities. The major problem of them is their usage of a paraconsistent logic with an accompanying theory of inconsistent objects. If we are, however, already using a paraconsistent approach for other reasons (in semantics, epistemology or set theory), we get finitism for free. This strengthens the case for paraconsistency.     

Ueber das Drehungsverm?gen der Aepfels?ure

Ohne Zusammenfassung     

Der Einfluss inactiver K?rper auf das Drehungsverm?gen activer Substanzen

Ohne Zusammenfassung