Market equilibria and money

By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system.Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only.Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.

W1,p versus C1: The nonsmooth case involving critical growth

In this paper, we study a class of generalized and not necessarily differentiable functionals of the form [Formula: see text] with functions [Formula: see text], [Formula: see text] that are only locally Lipschitz in the second argument and involving critical growth for the elements of their generalized gradients [Formula: see text] even on the boundary [Formula: see text]. We generalize the famous result of Brezis and Nirenberg [[Formula: see text] versus [Formula: see text] local minimizers, C. R. Acad. Sci. Paris Sér. I Math. 317(5) (1993) 465–472] to a more general class of functionals and extend all the other generalizations of this result which has been published in the last decades.

First-Principles Study of Electronic Structure, Optical Properties and LO-TO Splitting of GaP

The electronic structure and optical properties of GaP were calculated using generalized gradients in density functional theory. The Bonn effective charge, optical frequency dielectric constant and the LO-TO splitting value were calculated by density functional theory perturbation method.