Search results for "510 Mathematik"

Parallelisierte Faktorisierung mit dem Quadratischen Sieb

2018

Observable radizielle Untergruppen von halbeinfachen algebraischen Gruppen

1979

Sei G eine affine algebraische Gruppe, definiert tiber einem algebraisch abgeschlossenen K6rper k von beliebiger Charakteristik. Die observablen Untergruppen von G sind die Untergruppen, die als Stabilisatoren bei rationalen Darstellungen von G auftreten. Sie wurden in [2] und [5] ausfiihrlich diskutiert. Dabei zeigte sich, dab es im allgemeinen wohl sehr schwierig ist zu entscheiden, ob eine Untergruppe observabel ist. Daher ist es sinnvoll, Kriterien zu finden. In [9] gab Sukhanov ftir Charakteristik 0 ein notwendiges und hinreichendes Kriterium daftir an, dab eine radizielle Untergruppe einer halbeinfachen algebraischen Gruppe observabel ist; dabei will ich unter einer radiziellen Unterg…

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…

Computing Euclidean Steiner trees over segments

2020

In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…

Soldner, Einstein, gravitational light deflection and factors of two

2021

Einstein's Washington Manuscript on Unified Field Theory

2020

In this note, we point attention to and briefly discuss a curious manuscript of Einstein, composed in 1938 and entitled "Unified Field Theory," the only such writing, published or unpublished, carrying this title without any further specification. Apparently never intended for publication, the manuscript sheds light both on Einstein's modus operandi as well as on the public role of Einstein's later work on a unified field theory of gravitation and electromagnetism.

Fixpunktmengen von halbeinfachen Automorphismen in halbeinfachen Lie-Algebren

1976

Let g be a semisimple Lie algebra over an algebraically closed field of characteristic 0. The set of fixed points of a semisimple inner automorphism of g is a regular reductive subalgebra of maximal rank [1], so it is defined by a subsystem of the root system Φ of g relative to a suitable Cartan subalgebra. The main theorem of the article characterizes the corresponding subsystems of Φ. The second part of the article shows how to compute the fixed point algebras of semisimple outer automorphisms of g. A complete list of all fixed point algebras is then easily obtainable. The results are applied to bounded symmetric domains. References

A sampling method for detecting buried objects using electromagnetic scattering

2005

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scat…