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...

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.

Alas, the motivating examples of algebraically compact categories are not algebraically compact, and the enriched setting does not directly support the theory of algebraic compactness. We show that the structural setting, the same setting developed independently for models of linear logic, directly supports the theory of algebraic cocompleteness. We extend the structural setting to a bistructur...

In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In §1 we prove that Loeb spaces are compact under various assumptions, and in §2 we prove that Loeb spaces are not compact under various other assumptions. The results in §1 and §2 give a quite complete answer to a quest...

It is useful to treat real-valued functions (or complex-valued functions, or vector space-valued functions) as elements of a vector space, so that the tools from linear algebra can be applied. Given a set X one may consider the vector space R of all real-valued functions with domain X. If X is finite, say with n elements, then this is just the familiar vector space R. The more interesting examp...