Search results for "Mathematik"

A conspectus of Tephroseris (Asteraceae: Senecioneae) in Europe outside Russia and notes on the decline of the genus

2021

Tephroseris is generally considered a difficult genus. Based on the examination of extensive herbarium material and considering the existing literature, we recognize seven species in Europe outside Russia. These are T. palustris, T. integrifolia with subsp. integrifolia, subsp. aurantiaca, subsp. capitata, subsp. maritima, subsp. serpentini and subsp. “tundricola”, T. balbisiana, T. crispa, T. helenitis, T. longifolia and T. papposa. Phylogenetic analysis of ITS and ETS sequences showed that these species fall into three lineages. These are: (1) T. palustris, clearly related to Arctic species of the genus; (2) T. integrifolia; and (3) the remaining species. Molecular dating of the T. integr…

The 2020 magnetism roadmap

2020

Following the success and relevance of the 2014 and 2017 Magnetism Roadmap articles, this 2020 Magnetism Roadmap edition takes yet another timely look at newly relevant and highly active areas in magnetism research. The overall layout of this article is unchanged, given that it has proved the most appropriate way to convey the most relevant aspects of today's magnetism research in a wide variety of sub-fields to a broad readership. A different group of experts has again been selected for this article, representing both the breadth of new research areas, and the desire to incorporate different voices and viewpoints. The latter is especially relevant for thistype of article, in which one's fi…

Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

2003

Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space, ramified over a hypersurface of degree d. Iterating this construction, one obtains M(d,n;r). We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack M(d,n;2) deforms. We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r), and we construct a 4-dimensional family of quintic hypersurfaces, and a dense set of points in the base, where the fibres ha…

A posteriori estimates for the stationary Stokes problem in exterior domains

2020

This paper is concerned with the analysis of the inf-sup condition arising in the stationary Stokes problem in exterior domains and applications to the derivation of computable bounds for the distance between the exact solution of the exterior Stokes problem and a certain approximation (which may be of a rather general form). In the first part, guaranteed bounds are deduced for the constant in the stability lemma associated with the exterior domain. These bounds depend only on known constants and the stability constant related to bounded domains that arise after suitable truncations of the unbounded domains. The lemma in question implies computable estimates of the distance to the set of di…

Invarianten unipotenter Gruppen

1981

Sampling methods for low-frequency electromagnetic imaging

2007

For the detection of hidden objects by low-frequency electromagnetic imaging the linear sampling method works remarkably well despite the fact that the rigorous mathematical justification is still incomplete. In this work, we give an explanation for this good performance by showing that in the low-frequency limit the measurement operator fulfils the assumptions for the fully justified variant of the linear sampling method, the so-called factorization method. We also show how the method has to be modified in the physically relevant case of electromagnetic imaging with divergence-free currents. We present numerical results to illustrate our findings, and to show that similar performance can b…

The factorization method for real elliptic problems

2006

The Factorization Method localizes inclusions inside a body from mea- surements on its surface. Without a priori knowing the physical parameters inside the inclusions, the points belonging to them can be characterized using the range of an auxiliary operator. The method relies on a range characterization that relates the range of the auxiliary operator to the measurements and is only known for very particular applications. In this work we develop a general framework for the method by considering sym- metric and coercive operators between abstract Hilbert spaces. We show that the important range characterization holds if the difference between the inclusions and the background medium satisfi…

Our Friend and Mathematician Karl Strambach

2020

This paper is dedicated to Karl Strambach on the occasion of his 80th birthday. Here we want to describe our work with Prof. Karl Strambach.

Supramolecular polymerization of sulfated dendritic peptide amphiphiles into multivalent L-selectin binders

2021

The synthesis of a sulfate-modified dendritic peptide amphiphile and its self-assembly into one-dimensional rod-like architectures in aqueous medium is reported. The influence of the ionic strength on the supramolecular polymerization was probed via circular dichroism spectroscopy and cryogenic transmission electron microscopy. Physiological salt concentrations efficiently screen the charges of the dendritic building block equipped with eight sulfate groups and trigger the formation of rigid supramolecular polymers. Since multivalent sulfated supramolecular structures mimic naturally occurring L-selectin ligands, the corresponding affinity was evaluated using a competitive SPR binding assay…

Construction de Triplets Spectraux à Partir de Modules de Fredholm

1998

Soit (A, H, F) un module de Fredholm p-sommable, où l'algèbre A = CT est engendrée par un groupe discret Gamma d'éléments unitaires de L(H) qui est de croissance polynomiale r. On construit alors un triplet spectral (A, H, D) sommabilité q pour tout q > p + r + 1 avec F = signD. Dans le cas où (A, H, F) est (p, infini)-sommable on obtient la (q, infini)-sommabilité de (A, H, D)pour tout q > p + r + 1. Let (A, H, F) be a p-summable Fredholm module where the algebra A = CT is generated by a discrete group of unitaries in L(H) which is of polynomial growth r. Then we construct a spectral triple (A, H, D) with F = signD which is q-summable for each q > p + r + 1. In case (A, H, F) is (p, infini…