Linnik's problems and maximal entropy methods

We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas and follow techniques presented by Einsiedler, Lindenstrauss, Michel and Venkatesh in 2011

Derivation of a time dependent Schr\"odinger equation as quantum mechanical Landau-Lifshitz-Bloch equation

The derivation of the time dependent Schr\"odinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schr\"odinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schr\"odinger equation

Current and field driven domain wall motion under influence of the Dzyaloshinsky-Moriya interaction

A complete analytical description of the dynamics of current and field driven transverse domain walls under the influence of the Dzyaloshinsky-Moriya interaction using the $\phi - q$ model will be given. Five different scenarios will be observed where the Dzyaloshinsky-Moriya vector is either parallel or perpendicular to the easy axis anisotropy of the system and a direct reversal respectively precessional motion will be assumed.Comment: 9 pages, 7 figures, 1 tabl

Positioning in time and space: cost-effective exterior orientation for airborne archaeological photographs

Since manned, airborne aerial reconnaissance for archaeological purposes is often characterised by more-or-less random photographing of archaeological features on the Earth, the exact position and orientation of the camera during image acquisition becomes very important in an effective inventorying and interpretation workflow of these aerial photographs. Although the positioning is generally achieved by simultaneously logging the flight path or directly recording the camera's position with a GNSS receiver, this approach does not allow to record the necessary roll, pitch and yaw angles of the camera. The latter are essential elements for the complete exterior orientation of the camera, which allows – together with the inner orientation of the camera – to accurately define the portion of the Earth recorded in the photograph. This paper proposes a cost-effective, accurate and precise GNSS/IMU solution (image position: 2.5 m and orientation: 2°, both at 1σ) to record all essential exterior orientation parameters for the direct georeferencing of the images. After the introduction of the utilised hardware, this paper presents the developed software that allows recording and estimating these parameters. Furthermore, this direct georeferencing information can be embedded into the image's metadata. Subsequently, the first results of the estimation of the mounting calibration (i.e. the misalignment between the camera and GNSS/IMU coordinate frame) are provided. Furthermore, a comparison with a dedicated commercial photographic GNSS/IMU solution will prove the superiority of the introduced solution. Finally, an outlook on future tests and improvements finalises this article

Pattern Avoidance in Task-Precedence Posets

We have extended classical pattern avoidance to a new structure: multiple task-precedence posets whose Hasse diagrams have three levels, which we will call diamonds. The vertices of each diamond are assigned labels which are compatible with the poset. A corresponding permutation is formed by reading these labels by increasing levels, and then from left to right. We used Sage to form enumerative conjectures for the associated permutations avoiding collections of patterns of length three, which we then proved. We have discovered a bijection between diamonds avoiding 132 and certain generalized Dyck paths. We have also found the generating function for descents, and therefore the number of avoiders, in these permutations for the majority of collections of patterns of length three. An interesting application of this work (and the motivating example) can be found when task-precedence posets represent warehouse package fulfillment by robots, in which case avoidance of both 231 and 321 ensures we never stack two heavier packages on top of a lighter package.Comment: 17 page