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...

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.

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

andApplied AnalysisHindawi Publishing Corporationhttp://www.hindawi.comVolume 2013 ISRNAppliedMathematicsHindawi Publishing Corporationhttp://www.hindawi.comVolume 2013Hindawi Publishing Corporationhttp://www.hindawi.comVolume 2013International Journal ofCombinatorics Hindawi Publishing Corporationhttp://www.hindawi.comVolume 2013<...

This chapter explores the philosophical notion of The Virtual in response to the writings of Gilles Deleuze and unfolds this thinking through its interdisciplinary and transformative effects upon contemporary fine art. The Virtual is discussed in relation to forms of contemporary painting, yet the chapter provides a model for thinking through interdisciplinarity within, and from, other media. T...

The international research network, Gender in the European Town, funded by the Danish Research council, has brought together new and established scholars from twelve countries to explore the place of gender in three interrelated areas that shaped the development of the earlymodern town: the economy, politics and civic identity, and real and imagined space. This workshop will draw upon the exten...