Exact solutions of semilinear radial wave equations in n dimensions

Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system of group-invariant variables given by group foliations of the wave equation, using the one-dimensional admitted point symmetry groups. (These groups comprise scalings and time translations, admitted for any nonlinearity power, in addition to space-time inversions admitted for a particular conformal nonlinearity power). This is shown to yield not only group-invariant solutions as derived by standard symmetry reduction, but also other exact solutions of a more general form. In particular, solutions with interesting analytical behavior connected with blow ups as well as static monopoles are obtained.Comment: 29 pages, 1 figure. Published version with minor correction

Structural Completeness of a Multi-channel Linear System with Dependent Parameters

It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of a multi-channel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multi-channel linear system is said to be "structurally complete" if it has no fixed spectrum for almost all parameter values. Necessary and sufficient algebraic conditions are presented for a multi-channel linear system with dependent parameters to be structurally complete. An equivalent graphical condition is also given for a certain type of parameterization

A normative approach to multi-agent systems for intelligent buildings

Building Management Systems (BMS) are widely adopted in modern buildings around the world in order to provide high-quality building services, and reduce the running cost of the building. However, most BMS are functionality-oriented and do not consider user personalization. The aim of this research is to capture and represent building management rules using organizational semiotics methods. We implement Semantic Analysis, which determines semantic units in building management and their relationship patterns of behaviour, and Norm Analysis, which extracts and specifies the norms that establish how and when these management actions occur. Finally, we propose a multi-agent framework for norm based building management. This framework contributes to the design domain of intelligent building management system by defining a set of behaviour patterns, and the norms that govern the real-time behaviour in a building