Preliminary notes on audiences in Africa

Preliminary Notes on Galois Theory

Definition 1.1. Let E be a field. An automorphism of E is a (ring) isomorphism from E to itself. The set of all automorphisms of E forms a group under function composition, which we denote by AutE. Let E be a finite extension of a field F . Define the Galois group Gal(E/F ) to be the subset of AutE consisting of all automorphisms σ : E → E such that σ(a) = a for all a ∈ F . We write this last c...

Preliminary Notes on Interpretability Logic

Preliminary Notes

Bombesin and eledoisin are both biologically active peptides derived from amphibian skin. They have been established to affect a variety of centrally mediated physiological processes in mammals (e.g. DeCaro, Micossi , Venturi, Brancati and Scarnati, 1974; Rivier and Brown, 1978), and may therefore be similar to or identical with endogenous mammalian neuropeptides. One prominent class of peptide...

Preliminary Notes on Decentralized Auctions of Complements

This note was motivated by a feature of decentralized markets: usually there is no central coordination on the selling mechanisms of items owned by different individuals. Specifically, I analyze separate auctions of several items possibly followed by resale among bidders. These items are complements for some bidders and are initially owned by different individuals. Without central coordination,...

Preliminary Exam Notes

ly one can define a Lie group as a smooth manifold which is also a group such that inversion and multiplication are smooth maps. A special case we focus on is any (topologically) closed subgroup of any SL(`,R). The major examples of “classical” Lie groups are SL(n,R), SO(m,n) (with g Im,ng = Im,n), SU(m,n) (same as SO but with conjugate transpose and complex elements), and Sp(2m,R) (similar to ...