Fractional integrals and derivatives: mapping properties

This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known, the fractional integrals defined in this or other forms improve in some sense the properties of the functions, at least locally, while fractional derivatives to the contrary worsen them. With the development of functional analysis this simple fact led to a number of important results on the mapping properties of fractional integrals in various function spaces.In the one-dimensional case we consider both Riemann-Liouville and Liouville forms of fractional integrals and derivatives. In the multidimensional case we consider in particular mixed Liouville fractional integrals, Riesz fractional integrals of elliptic and hyperbolic type and hypersingular integrals. Among the function spaces considered in this survey, the reader can find Holder spaces, Lebesgue spaces, Morrey spaces, Grand spaces and also weighted and/or variable exponent versions

Supporting social innovation through visualisations of community interactions

Online communities that form through the introduction of sociotechnical platforms require significant effort to cultivate and sustain. Providing open, transparent information on community behaviour can motivate participation from community members themselves, while also providing platform administrators with detailed interaction dynamics. However, challenges arise in both understanding what information is conducive to engagement and sustainability, and then how best to represent this information to platform stakeholders. Towards a better understanding of these challenges, we present the design, implementation, and evaluation of a set of simple visualisations integrated into a Collective Awareness Platform for Social Innovation platform titled commonfare.net. We discuss the promise and challenge of bringing social innovation into the digital age, in terms of supporting sustained platform use and collective action, and how the introduction of community visualisations has been directed towards achieving this goal

Initiating organizational memories using ontology network analysis

One of the important problems in organizational memories is their initial set-up. It is difficult to choose the right information to include in an organizational memory, and the right information is also a prerequisite for maximizing the uptake and relevance of the memory content. To tackle this problem, most developers adopt heavy-weight solutions and rely on a faithful continuous interaction with users to create and improve its content. In this paper, we explore the use of an automatic, light-weight solution, drawn from the underlying ingredients of an organizational memory: ontologies. We have developed an ontology-based network analysis method which we applied to tackle the problem of identifying communities of practice in an organization. We use ontology-based network analysis as a means to provide content automatically for the initial set up of an organizational memory

Grid service discovery with rough sets

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The computational grid is evolving as a service-oriented computing infrastructure that facilitates resource sharing and large-scale problem solving over the Internet. Service discovery becomes an issue of vital importance in utilising grid facilities. This paper presents ROSSE, a Rough sets based search engine for grid service discovery. Building on Rough sets theory, ROSSE is novel in its capability to deal with uncertainty of properties when matching services. In this way, ROSSE can discover the services that are most relevant to a service query from a functional point of view. Since functionally matched services may have distinct non-functional properties related to Quality of Service (QoS), ROSSE introduces a QoS model to further filter matched services with their QoS values to maximise user satisfaction in service discovery. ROSSE is evaluated in terms of its accuracy and efficiency in discovery of computing services