A computation of Poisson kernels for some standard weighted biharmonic operators in the unit disc

We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and suggest similar formulas for these Poisson kernels to hold true in more generality. Computations have been carried out using the open source computer algebra package Maxima

Hele-Shaw flow on weakly hyperbolic surfaces

We consider the Hele-Shaw flow that arises from injection of two-dimensional fluid into a point of a curved surface. The resulting fluid domains have and are more or less determined implicitly by a mean value property for harmonic functions. We improve on the results of Hedenmalm and Shimorin \cite{HS} and obtain essentially the same conclusions while imposing a weaker curvature condition on the surface. Incidentally, the curvature condition is the same as the one that appears in a recent paper of Hedenmalm and Perdomo, where the problem of finding smooth area minimizing surfaces for a given curvature form under a natural normalizing condition was considered. Probably there are deep reasons behind this coincidence.Comment: 16 page

A Convex Approach to Path Tracking with Obstacle Avoidance for Pseudo-Omnidirectional Vehicles

This report addresses the related problems of trajectory generation and time-optimal path tracking with online obstacle avoidance. We consider the class of four-wheeled vehicles with independent steering and driving on each wheel, also referred to as pseudo-omnidirectional vehicles. Appropriate approximations of the dynamic model enable a convex reformulation of the path-tracking problem. Using the precomputed trajectories together with model predictive control that utilizes feedback from the estimated global pose, provides robustness to model uncertainty and disturbances. The considered approach also incorporates avoidance of a priori unknown moving obstacles by local online replanning. We verify the approach by successful execution on a pseudo-omnidirectional mobile robot, and compare it to an existing algorithm. The result is a significant decrease in the time for completing the desired path. In addition, the method allows a smooth velocity trajectory while avoiding intermittent stops in the path execution

A Pyrrhic Victory: Harold Wilson, Helmut Schmidt, and the British Renegotiation of EC Membership, 1974–5

Britain’s renegotiation of EC membership in 1974-5 has commonly been praised by historians as a tactical masterpiece by Prime Minister Harold Wilson in holding a divided country and party together while also keeping Britain inside the European Community. By contrast, this article focuses on the detrimental effect the episode had on Britain’s standing inside the EC. Using the prism of high-level diplomacy between Wilson and the German Chancellor Helmut Schmidt, it reconstructs precisely the changes in German perceptions of British positions, showing how initial goodwill towards Britain’s demands soon gave way to widespread scepticism over British motives and ultimate intentions. While highlighting the strong domestic pressures driving Britain and Germany apart, the article ultimately argues that these differences were unnecessarily exacerbated by Wilson’s failure at personal diplomacy on the highest level. A different handling of Schmidt may not have resulted in a radically different outcome of the renegotiations; but it may well have avoided the profound sense of distrust and suspicion over Britain’s future role in Europe that the episode stimulated among the Germans. The article is based on recently declassified sources from three countries, as well as on rare materials from Schmidt’s private archive in Hamburg.This is the author accepted manuscript. The final version is available from Taylor & Francis via http://dx.doi.org/10.1080/07075332.2014.98533

Optimal Tracking and Identification of Paths for Industrial Robots

This paper presents results from time-optimal path tracking for industrial robots. More specifically, three subproblems are studied and experimentally evaluated. The first is a contact-force control approach for determining the geometric robot motion, such that the tool centre point of the robot is moved according to the specification. The second problem is off-line solution of the optimisation problem describing the time-optimal path tracking problem, by using software which allows highlevel implementation and solution of optimisation problems. The third problem is robust control of the robot during real-time path tracking based on the optimisation results determined off-line. An earlier developed control structure for robust control is implemented and tested in a robot system. This paper discusses the theory behind time-optimal path tracking and presents experimental results. Both contact-force controlled path identification and real-time path tracking of the identified path are evaluated on a 6-DOF industrial robot of type IRB140 from ABB

Urine is an important nitrogen source for plants irrespective of vegetation composition in an Arctic tundra:insights from a 15N-enriched urea tracer experiment

1. Mammalian herbivores can strongly influence nitrogen (N) cycling and herbivore urine could be a central component of the N cycle in grazed ecosystems. Despite its potential role for ecosystem productivity and functioning, the fate of N derived from urine has rarely been investigated in grazed ecosystems. 2. This study explored the fate of 15N-enriched urea in tundra sites that have been either lightly or intensively grazed by reindeer for more than 50 years. We followed the fate of the 15N applied to the plant canopy, at 2 weeks and 1 year after tracer addition, in the different ecosystem N pools. 3. 15N-urea was rapidly incorporated in cryptogams and in aboveground parts of vascular plants, while the soil microbial pool and plant roots sequestered only a marginal proportion. Further, the litter layer constituted a large sink for the 15N-urea, at least in the short term, indicating a high biological activity in the litter layer and high immobilization in the first phases of organic matter decomposition. 4. Mosses and lichens still constituted the largest sink for the 15N-urea 1 year after tracer addition at both levels of grazing intensity demonstrating their large ability to capture and retain N from urine. Despite large fundamental differences in their traits, deciduous and evergreen shrubs were just as efficient as graminoids in taking up the 15N-urea. The total recovery of 15N-urea was lower in the intensively grazed sites, suggesting that reindeer reduce ecosystem N retention. 5. Synthesis The rapid incorporation of the applied 15N-urea indicates that arctic plants can take advantage of a pulse of incoming N from urine. In addition, δ 15N values of all taxa in the heavily grazed sites converged towards the δ 15N values for urine, bringing further evidence that urine is an important N source for plants in grazed tundra ecosystems

Adaptive Internal Model Control for Mid-Ranging of Closed-Loop Systems with Internal Saturation

This paper considers the problem of performing mid-ranging control of two closed-loop controlled systems that have internal saturations. The problem originates from previous work in machining with industrial robots, where an external compensation mechanism is used to compensate for position errors. Because of the limited workspace and the considerably higher bandwidth of the compensator, a mid-ranging control approach is proposed. An adaptive, model-based solution is presented, which is verified through simulations and experiments, where a close correspondence of the obtained results is achieved. Comparing the IAE of experiments using the proposed controller to previously established methods, a performance increase of up to 56 % is obtained