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...

urban green spaces and parks are important land use of cities which promote quality of life by providing facilities for leisure and also play a crucial role in social cohesion and participation due to their socio-economic and environmental functions. hence the distribution of such spaces is very important in cities. however the zone of 3 in tehran has a relative appropriate green space per capi...

Opportunistic use of White Spaces (WS) has opened up a whole new paradigm in research on cognitive radio (CR). One of the issues addressed by the QoSMOS project is the design of a flexible and efficient physical layer (PHY) for CR systems. To this aim, different modulation techniques are being investigated and are presented in this paper. They fulfil the low out of band leakage and spectral eff...

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.

A wide range of evidence suggests that contact with safe, green spaces can improve a number of aspects of mental and physical health and wellbeing as well as various social and environmental indicators. For example: • Contact with green spaces and natural environments can reduce symptoms of poor mental health and stress, and can improve mental wellbeing across all age groups. • Access to green ...

Information spaces have emerged as a powerful concept for providing managed exchange of information between members of communities of interest (COIs), including information brokering and dissemination by publish-subscribequery middleware. To support COIs with real-time or critical information exchange requirements, information spaces require quality of service (QoS) management algorithms that c...