Dealing with dynamics is a vital problem in Artificial Intelligence (AI). An intelligent system should be able to perceive and interact its environment perform tasks satisfactorily. To do so, it must sense external actions that might interfere tasks, demanding the agent self-adapt dynamics. In AI, field studies how rational change knowledge order respond new piece of information known as...

1 Contents Applications of Hamilton's Compactness Theorem for Ricci flow Peter Topping 1 Applications of Hamilton's Compactness Theorem for Ricci flow 3 Overview 3 Background reading 4 Lecture 1. Ricci flow basics – existence and singularities 5 1.1. Initial PDE remarks 5 1.2. Basic Ricci flow theory 6 Lecture 2. Cheeger-Gromov convergence and Hamilton's compactness theorem 9 2.1. Convergence a...

Let S = {x ∈ R | g1(x) ≥ 0, . . . , gm(x) ≥ 0} be a basic closed semialgebraic set defined by real polynomials gi. Putinar’s Positivstellensatz says that, under a certain condition stronger than compactness of S, every real polynomial f positive on S posesses a representation f = P m i=0 σigi where g0 := 1 and each σi is a sum of squares of polynomials. Such a representation is a certificate fo...

We discuss compactness of the ∂-Neumann operator in the setting of weighted Lspaces on Cn. For this purpose we use a description of relatively compact subsets of Lspaces. We also point out how to use this method to show that property (P) implies compactness for the ∂-Neumann operator on a smoothly bounded pseudoconvex domain and mention an abstract functional analysis characterization of compac...

A generalized fuzzy topological space called countable fuzzy topological space has already been introduced by the authors. The generalization has been performed by relaxing the criterion of preservation of arbitrary supremum of fuzzy topology to countable supremum. In this paper the notion of fuzzy compactness called c-compactness has been initiated and various properties are studied. Other rel...

In this note, we establish some results which suggest a possible solution to the problem of finding the right constructive notion of compactness in the context of a not–necessarily–uniform apartness space.