81 research outputs found
[Bespreking van: T.H. von der Dunk (2007) Een Hollands heiligdom: de moeizame architectonische eenwording van Nederland]
National museums and national identity, seen from an international and comparative perspective, c. 1760-1918: an assesment
Old and New Fields on Super Riemann Surfaces
The ``new fields" or ``superconformal functions" on super Riemann
surfaces introduced recently by Rogers and Langer are shown to coincide with
the Abelian differentials (plus constants), viewed as a subset of the functions
on the associated super Riemann surface. We confirm that, as originally
defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new
reference
Tzitz\'eica transformation is a dressing action
We classify the simplest rational elements in a twisted loop group, and prove
that dressing actions of them on proper indefinite affine spheres give the
classical Tzitz\'eica transformation and its dual. We also give the group point
of view of the Permutability Theorem, construct complex Tzitz\'eica
transformations, and discuss the group structure for these transformations
Applications of Temperley-Lieb algebras to Lorentz lattice gases
Motived by the study of motion in a random environment we introduce and
investigate a variant of the Temperley-Lieb algebra. This algebra is very rich,
providing us three classes of solutions of the Yang-Baxter equation. This
allows us to establish a theoretical framework to study the diffusive behaviour
of a Lorentz Lattice gas. Exact results for the geometrical scaling behaviour
of closed paths are also presented.Comment: 10 pages, latex file, one figure(by request
The multicomponent 2D Toda hierarchy: Discrete flows and string equations
The multicomponent 2D Toda hierarchy is analyzed through a factorization
problem associated to an infinite-dimensional group. A new set of discrete
flows is considered and the corresponding Lax and Zakharov--Shabat equations
are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix
types are proposed and studied. Orlov--Schulman operators, string equations and
additional symmetries (discrete and continuous) are considered. The
continuous-discrete Lax equations are shown to be equivalent to a factorization
problem as well as to a set of string equations. A congruence method to derive
site independent equations is presented and used to derive equations in the
discrete multicomponent KP sector (and also for its modification) of the theory
as well as dispersive Whitham equations.Comment: 27 pages. In the revised paper we improved the presentatio
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local
reductions of Hamiltonian flows generated by monodromy invariants on the dual
of a loop algebra. Following earlier work of De Groot et al, reductions based
upon graded regular elements of arbitrary Heisenberg subalgebras are
considered. We show that, in the case of the nontwisted loop algebra
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case considered by DS. The methods of DS are
utilized throughout the analysis, but formulating the reduction entirely within
the Hamiltonian framework provided by the classical r-matrix approach leads to
some simplifications even for .Comment: 43 page
Hamiltonian structure of real Monge-Amp\`ere equations
The real homogeneous Monge-Amp\`{e}re equation in one space and one time
dimensions admits infinitely many Hamiltonian operators and is completely
integrable by Magri's theorem. This remarkable property holds in arbitrary
number of dimensions as well, so that among all integrable nonlinear evolution
equations the real homogeneous Monge-Amp\`{e}re equation is distinguished as
one that retains its character as an integrable system in multi-dimensions.
This property can be traced back to the appearance of arbitrary functions in
the Lagrangian formulation of the real homogeneous Monge-Amp\`ere equation
which is degenerate and requires use of Dirac's theory of constraints for its
Hamiltonian formulation. As in the case of most completely integrable systems
the constraints are second class and Dirac brackets directly yield the
Hamiltonian operators. The simplest Hamiltonian operator results in the
Kac-Moody algebra of vector fields and functions on the unit circle.Comment: published in J. Phys. A 29 (1996) 325
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