10,304 research outputs found

    Algebraic representation of language hierarchies

    Get PDF

    Nonabelian KP hierarchy with Moyal algebraic coefficients

    Full text link
    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-NN 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

    Full text link
    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

    Full text link
    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
    • …
    corecore