Concave measures and the fuzzy core of exchange economies with heterogeneous divisible commodities

Cataloged from PDF version of article.The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of individuals are given by nonadditive utility functions defined on a sigma-algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many individuals. Applying the Yosida-Hewitt decomposition theorem, we also demonstrate that partitions in the fuzzy core are supportable by prices in L-1. (c) 2012 Elsevier B.V. All rights reserved

Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility function of each individual is uniformly continuous and strictly monotonic with respect to set inclusion, and if the partition matrix range of the utility functions is closed, a Pareto optimal envy-free partition exists. This result follows from the existence of Pareto optimal envy-free allocations in an extended version of the original allocation problem. © 2013 Springer-Verlag Berlin Heidelberg

The three- and four-nucleon systems from chiral effective field theory

Recently developed chiral nucleon-nucleon (NN) forces at next-to-leading order (NLO) that describe NN phase shifts up to about 100 MeV fairly well have been applied to 3N and 4N systems. Faddeev-Yakubovsky equations have been solved rigorously. The chiral NLO forces depend on a momentum cut-off \Lambda lying between 540-600 MeV/c. The resulting 3N and 4N binding energies are in the same range as found using standard NN potentials. In additon, low-energy 3N scattering observables are very well reproduced like for standard NN forces. Surprisingly, the long standing A_y-puzzle is resolved at NLO. The cut-off dependence of the scattering observables is rather mild.Comment: 4 pp, revtex, 3 figure

proton-deuteron elastic scattering above the deuteron breakup

The complex Kohn variational principle and the (correlated) hyperspherical harmonics method are applied to study the proton-deuteron elastic scattering at energies above the deuteron breakup threshold. Results for the elastic cross section and various elastic polarization observables have been obtained by fully taking into account the long-range effect of the Coulomb interaction and using a realistic nucleon-nucleon interaction model. Detailed comparison between the theoretical predictions and the accurate and abundant proton-deuteron experimental data can now be performed.Comment: 6 pages, 2 figure

Faddeev Calculations of Proton-Deuteron Radiative Capture with Exchange Currents

pd capture processes at various energies have been analyzed based on solutions of 3N-Faddeev equations and using modern NN forces. The application of the Siegert theorem is compared to the explicit use of $\pi$- and $\rho$-like exchange currents connected to the AV18 NN interaction. Overall good agreement with cross sections and spin observables has been obtained but leaving room for improvement in some cases. Feasibility studies for 3NF's consistently included in the 3N continuum and the 3N bound state have been performed as well.Comment: Minor changes in notation, ps files for figure