Existence, uniqueness and graph representation of weighted minimal hypersurfaces

By means of a weight matrix, we introduce the class of weighted minimal hypersurfaces which yield a natural generalisation of minimal surfaces. Generalising a classical result of Radó, we prove existence, uniqueness and graph representation for weighted minimal hypersurfaces in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} with prescribed boundary manifold.     

Conversational Implicatures and Cancellability

In this paper I argue against a criticism by Matthew Weiner to Grice’s thesis that cancellability is a necessary condition for conversational implicature. I argue that the purported counterexamples fail because the supposed failed cancellation in the cases Weiner presents is not meant as a cancellation but as a reinforcement of the implicature. I moreover point out that there are special situations in which the supposed cancellation may really work as a cancellation.

Composite dipolar recoupling: anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments.     

Dimensions of triangulated categories via Koszul objects

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin algebras.     

Modeling and numerical simulations of rate and temperature-dependent damage and fracture in aluminum alloys

The paper deals with a continuum damage model and corresponding numerical simulations of the inelastic deformation and failure behavior of aluminum alloys. The focus is on generalized plasticity, damage and fracture approaches taking into account different tiaxialities as well as rate and temperature-dependence. Furthermore, the special intent of the present work are dynamic applications. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of Time-Dependent Structural Responses with Recurrent Neural Networks

A concept for the mapping of fuzzy structural action processes onto fuzzy structural response processes is presented. Recurrent neural networks for fuzzy data are developed for this mapping. The presented method can be applied to the model-free numerical prediction of time-dependent structural responses. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model reduction via quasistatic approximations

Stiff terms in second-order differential equations may cause long computation time due to high frequencies. Quasi-static approximations eliminate these high frequency solution components by neglecting inertia forces. In this interpretation, the equations of motion of systems with small masses correspond to a singularly perturbed problem. Results from singular perturbation theory will be extended to problems with perturbations of more than two different orders of magnitude. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the combinatorics of Galois numbers

We define interval decompositions of the lattice of subspaces of a finite-dimensional vector space. We show that such a decomposition exists if and only if there exists a family of linear forms with certain properties. As applications we prove that all finite-dimensional real vector spaces admit an interval decomposition, while GF(2)ⁿ has an interval decomposition if and only if n≤4. On the other hand, we present an interval decomposition of GF(3)⁵. This partially answers a question of Faigle and Kruse (2004) [1] and [4].     

Capillary electrophoresis‐based enzyme assays for β‐lactamase enzymes

Generic in‐capillary as well as offline CE‐based enzyme assays were developed for serine‐β‐lactamases and metallo‐β‐lactamases. The hydrolysis of benzylpenicillin to benzylpenicilloic acid was analyzed using 100 mM sodium phosphate solution, pH 6.0, as a background electrolyte. In‐capillary assays employed an uncoated as well as a polyethylene oxide‐coated capillary, while the offline assays employing long end and short end injection were performed in an uncoated capillary. Using procaine hydrochloride or 4‐hydroxybenzoic acid as internal standard, the respective assays were validated with regard to linearity, LOD and LOQ, repeatability, precision, and accuracy. The assays were applied to the determination of the Michaelis‐Menten parameters K_m and V_max of Bacillus cereus penicillinase as well as New Delhi metallo‐β‐lactamase 1 and Verona integrin‐encoded metallo‐β‐lactamase 2. Furthermore, the inhibition of the enzymes by irreversible and competitive inhibitors was evaluated. Comparable data were obtained with all assays. The use of a simple substrate ensured broad applicability to the various types of β‐lactamases.