which commute with the flow defined by (0.1) (we set τ1 = z and τ2 = τ). The important fact is that the right hand sides Pn of equations (0.2) are polynomials in v and its derivatives, i.e., differential polynomials in v. This fact allows us to treat the KdV hierarchy (0.2) in the following way. Consider the ring R = C[v]n≥0 of polynomials in the variables v (n) (we shall write v for v(0)). Let...

Concern over the nature of AI is, for the tastes many AI scientists, probably overdone. In this they are like all other scientists. Working scientists worry about experiments, data, and theories, not foundational issues such as what their work is really about or whether their discipline is methodologically healthy. However, most scientists aren’t in a field that is approximately fifty years old...

K. Sen,1,* E. Perret,1 A. Alberca,1,2 M. A. Uribe-Laverde,1 I. Marozau,1 M. Yazdi-Rizi,1 B. P. P. Mallett,1 P. Marsik,1 C. Piamonteze,2 Y. Khaydukov,3,4 M. Döbeli,5 T. Keller,3,4 N. Biškup,6,7 M. Varela,6 J. Vašátko,8 D. Munzar,8 and C. Bernhard1,† 1University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700, Fribourg, Switzerland 2Swiss Light...

We always assume k = k to be an algebraically closed field with char(k) / ∈ {2, 3}. Let E be the elliptic curve over k defined by Y 2 − X 3 − AX − B. 1 Derivations We give a quick introduction to modules of differentials. The results are simplified versions of a more general theory which is treated very well and thoroughly in [Eis94]. Your motivation for this section should be that it will be a...

We consider large-N multi-matrix models whose action closely mimics that of Yang–Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger–Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G(ξ), are quadratic equations S G = GξG in concatenation of correlations. The Schwinger–Dyson operator S i is built from the l...

We argue that space-time properties are not absolute with respect to the used frame of reference as is to be expected according to ideas of relativity of space and time properties by Berkley Leibnitz Mach Poincaré. From this point of view gravitation may manifests itself both as a field in Minkowski space-time and as space-time curvature. If the motion of test particles is described by the Thir...

T. Weber,1,2,* B. Roessli,3 C. Stock,4 T. Keller,5,2 K. Schmalzl,6 F. Bourdarot,7 R. Georgii,2 R. A. Ewings,8 R. S. Perry,8,9 and P. Böni1 1Physik-Department E21, Technische Universität München (TUM), James-Franck-Strasse 1, 85748 Garching, Germany 2Heinz-Maier-Leibnitz-Zentrum (MLZ), Technische Universität München (TUM), Lichtenbergstrasse 1, 85747 Garching, Germany 3Laboratory for Neutron Sca...

We present a survey on the results related to the theory of lexicographic differentiation. This theory ensures an efficient computation of generalized (lexicographic) derivative of a nonsmooth function belonging to a special class of lexicographically smooth functions. This class is a linear space which contains all differentiable functions, all convex functions, and which is closed with respec...

The terms “¿ macrocosm― and “¿ microcosm― have been taken by Jung from the traditions of the alchemists and the philosophy of Leibnitz for expressing his theories, but they are not often used elsewhere in psychiatry or psychology so it may be as well to define them when introducing them here.* The macrocosm is the entire universe around us, with everything in it. It is also the orderly ...

Fast Ray-Tracing for Field Strength Prediction in Cellular Mobile Network Planning Kurt Tutschku and Kenji Leibnitz Institute of Computer Science, University of W urzburg Am Hubland, D-97074 W urzburg, Germany Tel.: +49-931-8885513, Fax: +49-931-8884601 E-mail: [tutschkujleibnitz]@informatik.uni-wuerzburg.de Abstract: In this paper we present a fast ray-tracing technique with scalable approxi...