Expansion formulas. II. Variations on a theme

Escherichia coli ST131: variations on a theme of clonal expansion.

The worldwide emergence and spread of the antimicrobialresistant Escherichia coli clonal group ST131 represents a pandemic.1 Since ST131 was first identified in 2008 it has disseminated rapidly and has contributed, in large part, to the rising prevalence of antimicrobial-resistant E. coli throughout the world.2,3 The ST131 clonal group is associated with serotype O25b:H4, contains numerous viru...

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 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...

Variations on a Theme by James Stirling