Variations on the theme of quantum Lefschetz

Variations on a theme.

A ring satisfying x = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x = x implies commutativity.

Variations on a Theme

Variations on the Theme of Caching

This thesis is concerned with caching algorithms. We investigate three variations of the caching problem: web caching in the Torng framework, relative competitiveness and caching with request reordering. In the first variation we define different cost models involving page sizes and page costs. We also present the Torng cost framework introduced by Torng in [29]. We analyze the competitive rati...

Variations on a Montagovian theme

What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than ofte...

The Klein Bottle: Variations on a Theme

It is a well-known fact that K is a genus 2 nonorientable closed surface with Euler characteristic χ = 0, which is topologically equivalent to a couple of Möbius bands glued together along the border, and that it is nonembeddable in R. It is possible, however, to immerse it in R, that is, to map it into R obtaining an image with no singular points. To give an immersion of K in R, it suffices to...