The N=2 supersymmetric unconstrained matrix GNLS hierarchies

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.Comment: 11 pages, LaTex, misprints correcte

On symmetries and cohomological invariants of equations possessing flat representations

We study the equation E_fc of flat connections in a fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitrary PDE and prove that flat representations of an equation E are in 1-1 correspondence with morphisms f: E\to E_fc, where E and E_fc are treated as submanifolds of infinite jet spaces. We show that flat representations include several known types of zero-curvature formulations of PDE. In particular, the Lax pairs of the self-dual Yang-Mills equations and their reductions are of this type. With each flat representation we associate a complex C_f of vector-valued differential forms such that its first cohomology describes infinitesimal deformations of the flat structure, which are responsible, in particular, for parameters in Backlund transformations. In addition, each higher infinitesimal symmetry S of E defines a 1-cocycle c_S of C_f. Symmetries with exact c_S form a subalgebra reflecting some geometric properties of E and f. We show that the complex corresponding to E_fc itself is 0-acyclic and 1-acyclic (independently of the bundle topology), which means that higher symmetries of E_fc are exhausted by generalized gauge ones, and compute the bracket on 0-cochains induced by commutation of symmetries.Comment: 30 page

On Waylen's regular axisymmetric similarity solutions

We review the similarity solutions proposed by Waylen for a regular time-dependent axisymmetric vacuum space-time, and show that the key equation introduced to solve the invariant surface conditions is related by a Baecklund transform to a restriction on the similarity variables. We further show that the vacuum space-times produced via this path automatically possess a (possibly homothetic) Killing vector, which may be time-like.Comment: 8 pages, LaTeX2

Development of a Detector Control System for the ATLAS Pixel Detector

The innermost part of the ATLAS experiment will be a pixel detector containing around 1750 individual detector modules. A detector control system (DCS) is required to handle thousands of I/O channels with varying characteristics. The main building blocks of the pixel DCS are the cooling system, the power supplies and the thermal interlock system, responsible for the ultimate safety of the pixel sensors. The ATLAS Embedded Local Monitor Board (ELMB), a multi purpose front end I/O system with a CAN interface, is foreseen for several monitoring and control tasks. The Supervisory, Control And Data Acquisition (SCADA) system will use PVSS, a commercial software product chosen for the CERN LHC experiments. We report on the status of the different building blocks of the ATLAS pixel DCS.Comment: 3 pages, 2 figures, ICALEPCS 200

Deformation and Recursion for the N=2 α=1\alpha=1 Supersymmetric KdV-hierarchy

A detailed description is given for the construction of the deformation of the N=2 supersymmetric $\alpha=1$ KdV-equation, leading to the recursion operator for symmetries and the zero-th Hamiltonian structure; the solution to a longstanding problem

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page