26,858 research outputs found
Coadjoint Orbits of the Generalised Sl(2) Sl(3) Kdv Hierarchies
In this paper we develop two coadjoint orbit constructions for the phase
spaces of the generalised and KdV hierachies. This involves the
construction of two group actions in terms of Yang Baxter operators, and an
Hamiltonian reduction of the coadjoint orbits. The Poisson brackets are
reproduced by the Kirillov construction. From this construction we obtain a
`natural' gauge fixing proceedure for the generalised hierarchies.Comment: 37 page
Integrability, quantization and moduli spaces of curves
This paper has the purpose of presenting in an organic way a new approach to
integrable (1+1)-dimensional field systems and their systematic quantization
emerging from intersection theory of the moduli space of stable algebraic
curves and, in particular, cohomological field theories, Hodge classes and
double ramification cycles. This methods are alternative to the traditional
Witten-Kontsevich framework and its generalizations by Dubrovin and Zhang and,
among other advantages, have the merit of encompassing quantum integrable
systems. Most of this material originates from an ongoing collaboration with A.
Buryak, B. Dubrovin and J. Gu\'er\'e
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MultiView : a methodology for supporting multiple view schemata in object-oriented databases
It has been widely recognized that object-oriented database (OODB) technology needs to be extended to provide a mechanism similar to views in relational database systems. We define an object-oriented view to be an arbitrarily complex virtual schema graph with possibly restructured generalization and decomposition hierarchies - rather than just one virtual class as has been proposed in the literature. In this paper, we propose a methodology, called MultiView, for supporting multiple such view schemata. MultiView breaks the schema design task into the following independent and well-defined subtasks: (1) the customization of type descriptions and object sets of existing classes by deriving virtual classes, (2) the integration of all derived classes into one consistent global schema graph, and (3) the definition of arbitrarily complex view schemata on this augmented global schema. For the first task of MultiView, we define a set of object algebra operators that can be used by the view definer for class customization. For the second task of MultiView, we propose an algorithm that automatically integrates these newly derived virtual classes into the global schema. We solve the third task of MultiView by first letting the view definer explicitly select the desired view classes from the global schema using a view definition language and then by automatically generating a view class hierarchy for these selected classes. In addition, we present algorithms that verify the closure property of a view and, if found to be incomplete, transform it into a closed, yet minimal, view. In this paper, we introduce the fundamental concept of view independence and show MultiView to be view independent. We also outline implementation techniques for realizing MultiView with existing OODB technology
Tau-Functions and Generalized Integrable Hierarchies
The tau-function formalism for a class of generalized ``zero-curvature''
integrable hierarchies of partial differential equations, is constructed. The
class includes the Drinfel'd-Sokolov hierarchies. A direct relation between the
variables of the zero-curvature formalism and the tau-functions is established.
The formalism also clarifies the connection between the zero-curvature
hierarchies and the Hirota-type hierarchies of Kac and Wakimoto.Comment: 23 page
Pattern tree-based XOLAP rollup operator for XML complex hierarchies
With the rise of XML as a standard for representing business data, XML data
warehousing appears as a suitable solution for decision-support applications.
In this context, it is necessary to allow OLAP analyses on XML data cubes.
Thus, XQuery extensions are needed. To define a formal framework and allow
much-needed performance optimizations on analytical queries expressed in
XQuery, defining an algebra is desirable. However, XML-OLAP (XOLAP) algebras
from the literature still largely rely on the relational model. Hence, we
propose in this paper a rollup operator based on a pattern tree in order to
handle multidimensional XML data expressed within complex hierarchies
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