10,304 research outputs found
Nonabelian KP hierarchy with Moyal algebraic coefficients
A higher dimensional analogue of the KP hierarchy is presented. Fundamental
constituents of the theory are pseudo-differential operators with Moyal
algebraic coefficients. The new hierarchy can be interpreted as large- limit
of multi-component (\gl(N) symmetric) KP hierarchies. Actually, two different
hierarchies are constructed. The first hierarchy consists of commuting flows
and may be thought of as a straightforward extension of the ordinary and
multi-component KP hierarchies. The second one is a hierarchy of noncommuting
flows, and related to Moyal algebraic deformations of selfdual gravity. Both
hierarchies turn out to possess quasi-classical limit, replacing Moyal
algebraic structures by Poisson algebraic structures. The language of
W-infinity algebras provides a unified point of view to these results.Comment: 37 pages, Kyoto University KUCP-0062/9
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
Comparing hierarchies of total functionals
In this paper we consider two hierarchies of hereditarily total and
continuous functionals over the reals based on one extensional and one
intensional representation of real numbers, and we discuss under which
asumptions these hierarchies coincide. This coincidense problem is equivalent
to a statement about the topology of the Kleene-Kreisel continuous functionals.
As a tool of independent interest, we show that the Kleene-Kreisel functionals
may be embedded into both these hierarchies.Comment: 28 page
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