English in England

The intention of the present volume is to unite the research of a range of scholars who have been working on features of non-standard, vernacular English which show an areal distribution, i.e. which cluster geographically across the world. Features common to an area can be due to (i) shared dialect input, (ii) common but separate innovations after settlement, or (iii) area-internal diffusion from one variety to another and/or others. The relative weighting of these factors is an important topic in the book and is a key focus in the 17 chapters. The book is divided into two large blocks, the first one consisting of case studies (8 chapters) and the second with features complexes (9 chapters). The former look at major anglophone locations from an areal perspective while the latter examine linguistic categories and features with a view to determine whether these could be areally based or not.

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Evaluation of a new six degrees of freedom couch for radiation therapy

Purpose: The aim of this work is to evaluate the geometric accuracy of a prerelease version of a new six degrees of freedom (6DoF) couch. Additionally, a quality assurance method for 6DoF couches is proposed. Methods: The main principle of the performance tests was to request a known shift for the 6DoF couch and to compare this requested shift with the actually applied shift by independently measuring the applied shift using different methods (graph paper, laser, inclinometer, and imaging system). The performance of each of the six axes was tested separately as well as in combination with the other axes. Functional cases as well as realistic clinical cases were analyzed. The tests were performed without a couch load and with a couch load of up to 200 kg and shifts in the range between −4 and +4 cm for the translational axes and between −3° and +3° for the rotational axes were applied. The quality assurance method of the new 6DoF couch was performed using a simple cube phantom and the imaging system. Results: The deviations (mean ± one standard deviation) accumulated over all performance tests between the requested shifts and the measurements of the applied shifts were −0.01 ± 0.02, 0.01 ± 0.02, and 0.01 ± 0.02 cm for the longitudinal, lateral, and vertical axes, respectively. The corresponding values for the three rotational axes couch rotation, pitch, and roll were 0.03° ± 0.06°, −0.04° ± 0.12°, and −0.01° ± 0.08°, respectively. There was no difference found between the tests with and without a couch load of up to 200 kg. Conclusions: The new 6DoF couch is able to apply requested shifts with high accuracy. It has the potential to be used for treatment techniques with the highest demands in patient setup accuracy such as those needed in stereotactic treatments. Shifts can be applied efficiently and automatically. Daily quality assurance of the 6DoF couch can be performed in an easy and efficient way. Long-term stability has to be evaluated in further tests.

Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.