Gauge techniques in time and frequency domain TLM

Typical features of the Transmission Line Matrix (TLM) algorithm in connection with stub loading techniques and prone to be hidden in common frequency domain formulations are elucidated within the propagator approach to TLM. In particular, the latter reflects properly the perturbative character of the TLM scheme and its relation to gauge field models. Internal 'gauge' degrees of freedom are made explicit in the frequency domain by introducing the complex nodal S-matrix as a function of operators that act on external or internal fields or virtually couple the two. As a main benefit, many techniques and results gained in the time domain thus generalize straight away. The recently developed deflection method for algorithm synthesis, which is extended in this paper, or the non-orthogonal node approximating Maxwell's equations, for instance, become so at once available in the frequency domain. In view of applications in computational plasma physics, the TLM model of a relativistic charged particle current coupled to the Maxwell field is treated as a prototype.Comment: 20 pages; Keywords: Gauge techniques, perturbative schemes, TLM method, propagator approach, plasma physic

Civil Justice Systems in Europe and the United States

Professor Dr. Hein D. Kötz - dean of Bucerius Law School in Hamburg, Germany, and a leading scholar in comparative law - presents the inaugural Herbert L. Bernstein Memorial Lecture titled, Civil Justice Systems in Europe and the United States

Restriction of stable rank two vector bundles in arbitrary characteristic

Let $X$ be a smooth variety defined over an algebraically closed field of arbitrary characteristic and \O_X(H) be a very ample line bundle on $X$. We show that for a semistable $X$-bundle $E$ of rank two, there exists an integer $m$ depending only on $\Delta(E).H^{\dim(X)-2}$ and $H^{\dim(X)}$ such that the restriction of $E$ to a general divisor in $|mH|$ is again semistable. As corollaries we obtain boundedness results, and weak versions of Bogomolov's theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic.Comment: LaTeX document, 16 pages, no figure

Civil Justice Systems in Europe and the United States

Professor Kötz delivered the inaugural Herbert L. Bernstein Memorial Lecture in Comparative Law in 2002 and this article is based on his remarks. The article is included in the inaugural volume of CICLOPs that collects the first six Bernstein lectures. In order to highlight the similarities and differences in legal regimes between Europe and the United States, Professor Hein Kötz analyzes the German and American civil legal systems and, to a minor extent, the British civil legal system. Specifically, Kötz focuses on one of the distinguishing features of the American legal system, the civil jury, and its impact on the structure and flow of the civil court case. By targeting this feature of the American system, he highlights the differences in values held by each society, the impact these differing values have in altering fairly similar legal objectives, and the mechanisms that are created to fulfill these objectives, as well as the consequences of such mechanisms. Kötz shows how the American preference for a jury over a judge as the trier of fact for a civil trial greatly impacts a number of aspects of the trial, including discovery, the role of the judge, and the approach governing the introduction of expert testimony. This comparison puts into relief not only the differences between the two systems, but also the benefits and drawbacks of each. These differences are highlighted particularly well through the use of examples of solutions found within the legal systems to deal with unique problems – such as the American class-action suit