1 Preface In these three chapters I treat a variety of issues that surround the current state of set theory. Through an analysis of the relationships between set theory and other branches of mathematics, I try to paint a truer picture of the nature of the theory of sets than what seems to be the prevalent characterization of the subject. This same analysis directs my approach to questions about...

ions The description of the meaning of expressions just given above is vague and intuitive It took about years for logicians Dana Scott in fact to make it rigorous in a useful way We shall not be going into details of this Example x x denotes the identity function x x E E Example x f f x denotes the function which when applied to E yields f f x E x i e f f E This is the function which when appl...

ASD (Abstract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambda-calculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family...

The role of the web user is under transformation from merely being an information consumer to also being a content provider, “from information age to participation age”, in the words of Sun CEO Scott McNealy. This increase in participation is most obviously manifested by the growth of online communities, weblogs (blogs), and various forms of cooperative and participatory publication of informat...

This paper presents two new MATLAB-based tools for tuning fixed-structure linear control systems in the frequency domain: HINFSTRUCT and LOOPTUNE. These tools can directly tune control architectures with multiple feedback loops and multiple fixed-order, fixed-structure control elements. The controller parameters are tuned using nonsmooth H∞ optimization but little a-priori knowledge of the H∞ t...

A new mixed  halo chromate  nanoparticle compound was synthesised and characterized. Triphenylphosphonium trifluoroiodochromate (III)[P(C6H5)3H]+[CrF3I]- nanoparticle was synthesized by using triphenylphosphonium  iodide reaction with CrF3, in the presence of  3-mercaptopropionic acid. This method is a simple and direc...