In this treatise the convergence of iterative algorithms for the solution of non-linear operator equations in complex linear topological spaces are studied from the point of view of fixed-point theorems in such spaces... It was felt that the concept of the Gâteaux differential is a more natural one to use in connection with linear topological spaces. The beauty of the developed technique we mentioned earlier is essentially due to the fact that we are considering spaces over the complex number field. The resulting convergence theorems have also the added advantage of imposing no conditions on the second or higher order differentials of the operator T, as would be the case in an obvious extension ( which was not written down) of Kantorovich's work to such real linear topological spaces. [...]

The purpose of this paper is two fold. Firstly, to introduce and study the Silov Boundary of a Banach algebra of continuous complex valued functions defined on a compact Hausdorff space X. Secondly, to apply the definition of Silov Boundary to more general families of functions, namely, to linear spaces and semi-groups of functions. It will be seen that in these latter cases, existence of the Silov Boundary depends on certain restricting assumptions about the linear space or semi-group. [...]

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Advances in smart technologies, wireless networking, and increased interest in contextual services have led to the emergence of ubiquitous and pervasive computing as one of the most promising areas of computing in recent years. Smart Spaces, in particular, have gained significant interest within the research community. Currently, most Smart Spaces rely on physical components, such as sensors, to acquire information about the real-world environment. Although current sensor networks can acquire some useful contextual information from the physical environment, their information resources are often limited, and the data acquired is often unreliable. We argue that by introducing social network information into such systems, smarter and more adaptive spaces can be created. Social networks have recently become extremely popular, and are now an integral part of millions of people’s daily lives. Through social networks, users create profiles, build relationships, and join groups, forming intermingled sets and communities. Social Networks contain a wealth of information, which, if exploited properly, can lead to a whole new level of smart contextual services. A mechanism is therefore needed to extract data from heterogeneous social networks, to link profiles across different networks, and to aggregate the data obtained. We therefore propose the design and implementation of a Smart Spaces framework that utilizes the social context. In order to manage services and sessions, we integrate our system with the IP Multimedia Subsystem. Our system, which we call SocioSpace, includes full design and implementation of all components, including the central server, the location management system, the social network interfacing system, the service delivery platform, and user agents. We have built a prototype for proof of concept and carried out exhaustive performance analysis; the results show that SocioSpace is scalable, extensible, and fault-tolerant. It is capable of creating Smart Spaces that can truly deliver adaptive services that enhance the users’ overall experience, increase their satisfaction, and make the surroundings more beneficial and interesting to them. / Thesis (Ph.D, Computing) -- Queen's University, 2012-04-30 11:14:29.054