Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative

Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior DerivativeComment: Key Words: Korn's inequality, theory of generalized Maxwell equations, Helmholtz decomposition, Poincare/Friedrichs-type estimates, incompatible tensor

A NOTE ON THE CLIFFORD FOURIER-STIELTJES TRANSFORM

The purpose of this article is to provide an overview of the real Clifford Fourier- Stieltjes transform (CFST) and of its important properties. Additionally, we introduce the definition of convolution of Clifford functions of bounded variation

ORTHOGONAL DECOMPOSITIONS AND THEIR APPLICATIONS

It is well known that complex quaternion analysis plays an important role in the study of higher order boundary value problems of mathematical physics. Following the ideas given for real quaternion analysis, the paper deals with certain orthogonal decompositions of the complex quaternion Hilbert space into its subspaces of null solutions of Dirac type operator with an arbitrary complex potential. We then apply them to consider related boundary value problems, and to prove the existence and uniqueness as well as the explicit representation formulae of the underlying solutions

APPLICATIONS OF QUATERNIONIC ANALYSIS IN ENGINEERING

The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular symmetric finite and infinite cylinders as particular subcases. In this talk we want to give an overview over the recent developments in this direction

Entwicklung einer offenen Softwareplattform für Visual Servoing

Ziel dieser Diplomarbeit ist es, eine flexibel zu verwendende Plattform für Visual Servoing-Aufgaben zu Erstellen, mit der eine Vielzahl von verschiedenen Anwendungsfällen abgedeckt werden kann. Kernaufgabe der Arbeit ist es dabei, verschiedene Verfahren der Gesichtserkennung (face detection) am Beispiel der Haar-Kaskade und -wiedererkennung (face recognition) am Beispiel von Eigenfaces und Fisherfaces zu betrachten und an ausführlichen Beispielen vorzustellen. Dabei sollen allgemeine Grundbegriffe der Bildverarbeitung und bereits bekannte Verfahren vorgestellt und ihre Implementierung im Detail dargestellt werden. Aus den dadurch gewonnen Erkenntnissen und dem sich ergebenden Anforderungsprofil an die zu entwickelnde Plattform leitet sich anschließend die Realisierung als eigenständige Anwendung ab. Hierbei ist weiterhin zu untersuchen, wie die neu zu entwickelnde Software zukunftssicher und in Hinblick auf einen möglichen Einsatz in Praktika einfach zu verwenden realisiert werden kann. Sämtliche während der Arbeit entstandenen Programme und Quellcodes werden auf einem separaten Datenträger zur Verfügung gestellt. Eine komplett funktionsfähige Entwicklungsumgebung wird als virtuelle Maschine beigelegt

Defining the baseline for river restoration: comparing carabid beetle diversity of natural and human-impacted riparian habitats

Near-natural rivers and riparian ecosystems can represent biodiversity hotspots harbouring many highly specialised, rare and endangered species. During the past centuries, these habitats have been heavily degraded by anthropogenic use, and therefore river restoration is one of the most striking fields of action that is legally defined by the European Union Water Framework Directive. Successful restoration depends on realistic and specified targets that should be defined beforehand and founded on status quo surveys. We present a comparison of carabid beetle communities in riparian habitats of natural and managed river sites of the Mulde River in the Biosphere Reserve Middle Elbe. This endeavour is part of a unique multi-level revitalisation project. Pitfall trapping in 2016 and 2017 yielded 111 carabid species with many species of conservation concern in natural and managed habitats. However, Simpson diversity and functional diversity were lower in the latter. Both habitats harboured specific species assemblages with characteristic indicator species. Additionally, the trap location on slip-off slopes or cut banks was a significant driver of species composition. Our results indicate high ecological development potentials for the Mulde River, but restoration should consider differences between slip-off slopes and cut-off banks. We postulate that future restoration will foster population increases as well as a wider distribution of rare and endangered riparian habitat specialists.TU Berlin, Open-Access-Mittel – 202