In a setting where agents have quasi-linear utilities over social alternatives and a transferable commodity, we consider three properties that a social choice function may possess: truthful implementation (in dominant strategies); monotonicity in differences; lexicographic affine maximization. We introduce the notion of a flexible domain of preferences that allows elevation of pairs and study w...

We study the Lyaponov exponent y A (E) of (h u) (n) = u(n + 1) + u(n-l) + A V (n) u (n) in the limit as A +a where V is a suitable random potential. We prove that yA(E)-ln A as A +CO uniformly as E/A runs through compact sets. We also describe a formal expansion (to order A-*) for random and almost periodic potentials. In this note, we study one-dimensional tight binding Hamiltonians h = ho + A...

Ayache has recently proved that if R is an integrally closed domain such that each overring of R is treed, then R is a locally pseudo-valuation domain. We investigate the extent to which the analogue (in which one concludes that R is a locally pseudo-valuation ring) holds if R is generalized to a commutative ring. A positive result is obtained if R is an idealization D(+)K where D is an integra...

We recall that a ring R is called near pseudo-valuation ring if every minimal prime ideal is a strongly prime ideal. Let R be a commutative ring, σ an automorphism of R. Recall that a prime ideal P of R is σ-divided if it is comparable (under inclusion) to every σ-stable ideal I of R. A ring R is called a σ-divided ring if every prime ideal of R is σ-divided. Also a ring R is almost σ-divided r...