A great variety of languages can be designed by different people for different purposes to operate resource spaces. Two fundamental issues are: can we design more operations in addition to existing operations? and, how many operations are sufficient or necessary? This paper solves these problems by investigating the theoretical basis for determining how complete a selection capability is provid...

For every α < ω1 we establish the existence of a separable Banach space whose Szlenk index is ω and which is universal for all separable Banach spaces whose Szlenkindex does not exceed ω. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates.

Conceptual spaces were originally introduced by Gärdenfors as a bridge between symbolic and connectionist models of information representation. In our opinion, a cognitive agent, besides being able to work within his (current) conceptual space, must also be able to ‘produce a new space’ by means of ‘global’ operations. These are operations which, acting on a conceptual space taken as a whole, g...

The notion of Common Information Spaces (CIS) is extensively used as a framework to analyse cooperative work. Drawing on recent contributions to the discourse on CIS, this paper develops a perspective on how information is shared in heterogeneous contexts. We study the introduction of an electronic nursing plan in the psychogeriatric ward at the University Hospital of North Norway. The plan was...

We verify the following three basic results on the free loop space LM . (1) We show that the set of all points, where the fundamental form on LM is nondegenerate, is an open subset. (2) The connections of a Fréchet bundle over LM can be extended to S1-central extensions and, in particular, there exist natural connections on the string structures. (3) The notion of Christoffel symbols and the cu...

If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential...

We introduce a new knowledge operator called ``knowing whether.'' Knowing whether an event occurred means either knowing that it occurred or knowing that it did not occur. We demonstrate the following difference between ``knowing whether'' and ``knowing that.'' In a multiple agent model, a sequence of events generated by successively applying ``knowing that'' operators, or their negations, may ...

4 Sobolev-Spaces 23 4.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2 Poisson’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3 Abstract Eigenvalue Problem . . . . . . . . . . . . . . . . . . 30 4.4 Sobolev Spaces for Periodic Functions . . . . . . . . . . . . . . 32 4.5 Fractional Sobolev Spaces for Periodic Functions . . . . . . . . 32 4.6 Trace T...

in this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.