Search

The AKNS system, an integrable system of partial differential equations (PDEs), has been introduced in 1974 by and named after Mark J. Ablowitz, David J. Kaup, Alan C. Newell and Harvey Segur. Following the scheme developed for these systems, the integrable initial value problem on the line can be rewritten as a compatibility condition, or as a zero curvature condition, of two linear ordinary differential equations. Important examples falling into this category are the nonlinear Schrödinger (NLS) equation and the sine-Gordon (sG) equation. A particular class of internal boundary conditions, the defect conditions, have been investigated for which in some cases it can be verified that integrability is preserved. Further, the combination of such a defect condition with a boundary condition has in specific cases proven instructive in the derivation of integrable initial-boundary value problems regarding the mentioned PDEs on the half-line. Particularly, the new boundary conditions for the NLS equation on the half-line have been constructed through this approach. However, even though integrability of these models has been treated by several authors in the field, the construction of actual solutions is a subject which has been barely worked on. One approach in the direction of solution construction has been developed based on the ideas of the unified transform method combined with the Dressing method, which is commonly known as dressing the boundary. In this thesis, we develop this method further and apply it to all models mentioned thereby constructing explicit soliton solutions therein.

This work studies the complete kinematic reconstruction of top quark pairs through their decay products under the constraint that one top-quark decays semileptonically into one myon and the other top-quark decays hadronically. Monte-Carlo data are used so one has access to the generator information. The developed algorithm is then applied to the SUSY models LM0 and LM1, and it is shown how possible supersymmetric particles can be separated from the top background.

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

The top-physicist Felicitas Pauss applies for the post of the general manager of CERN. (2 pages)

Die Freie Energie der anisotropen Heisenberg-Kette kann im thermodynamischen Limes durch den führenden Eigenwert einer Quantentransfermatrix dargestellt werden. Diese ist eine spezielle Darstellung der Yang-Baxter-Algebra zur R-Matrix der XXZ-Kette und ist mit dem algebraischen Bethe-Ansatz diagonalisierbar. Am Beispiel einer erzeugenden Funktion der zz-Korrelation soll gezeigt werden, dass der zugeordnete Eigenvektor zum führenden Eigenwert alle statischen Korrelationen umfasst: Die Erzeugende wird durch Bildung von Skalarprodukten im Sinne des algebraischen Bethe-Ansatzes mit dem führenden Eigenvektor bestimmt und in einer Vielfachintegraldarstellung angegeben. Die Ergebnisse sind gültig für endliche Temperaturen und endliche, longitudinale Magnetfelder. The free energy of the anisotropic Heisenberg chain can be represented by the leading eigenvalue of some quantum transfer matrix if the thermodynamic limit is assumed. The quantum transfer matrix is a special representation of the Yang-Baxter algebra and can be diagonalized by means of the algebraic Bethe-ansatz. Considering the example of a generating function of the zz-correlation, it will be shown that the eigenvector corresponding to the leading eigenvalue contains all information about static correlations: The generating function is determined by calculating scalar products in the sense of the algebraic Bethe-ansatz, involving the leading eigenvector. The results are given in a multiple integral representation, valid for finite temperatures and finite, longitudinal magnetic fields.

hrsg. von Andreas Gordon

zsgest. von W. Bang Kaup

John Trenchard, Thomas Gordon, Verfasser gemäss Vorrede, Übersetzer laut dessen Vorbericht, Aus dem Vorbesitz von Johann Jakob Bodmer gemäss handschriftlicher Liste seiner Bibliothek Ms Bodmer 38a

von Joh[ann] Christian Schneider, Öffentliche Bibliothek der Universität Basel, Deutsch, Verzeichnung=Description=Inventaire April 2016 HAN-Katalogisierungsregeln Vollständige Rekatalogisierung nach Standortverzeichnis und Briefkatalog

von Alexander Gordon