4,729 research outputs found
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 Supersymmetric KdV-hierarchy
A detailed description is given for the construction of the deformation of
the N=2 supersymmetric 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
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