Fishburn (1970) showed that in an infinite society Arrow’s axioms for a preference aggregation rule do not necessarily imply a dictator. Kirman and Sondermann (1972) showed that, in this case, nondictatorial rules imply an invisible dictator that, whenever the agent set is an atomless finite measure space, can be viewed as the limit of coalitions of arbitrarily small size. We show first that, w...

Tetration F as the analytic solution of equations F (z − 1) = ln(F (z)), F (0) = 1 is considered. The representation is suggested through the integral equation for values of F at the imaginary axis. Numerical analysis of this equation is described. The straightforward iteration converges within tens of cycles; with double precision arithmetics, the residual of order of 1.e14 is achieved. The nu...

Abstract This article focuses on understandings of fog capture as an alternative water supply system in Lima. In neighbourhoods where state infrastructure is missing, catchers promise to alleviate residents’ dependency private suppliers. However, the utility these micro-infrastructures not self-evident. I show how a local NGO attempted bring about commitment among prospective beneficiaries by f...

We show that minimizers of elastic-plastic energies dependent on jump integrals are smooth provided a smallness condition is fulfilled by the load. We examine also the structure of extremals when this smallness condition is violated.

The paper is mainly concerned with an approximate three-ball inequality for solutions in elliptic periodic homogenization. We consider a family of second order operators $\mathcal{L}_\epsilon$ divergence form rapidly oscillating and coefficients. It the first time such homogenization theory obtained. implies quantitative propagation smallness. proof relies on representation solution by Poisson ...