25,852 research outputs found
Maharam's problem
We construct an exhaustive submeasure that is not equivalent to a measure.
This solves problems of J. von Neumann (1937) and D. Maharam (1947)
Gamow Shell-Model Description of Weakly Bound and Unbound Nuclear States
Recently, the shell model in the complex k-plane (the so-called Gamow Shell
Model) has been formulated using a complex Berggren ensemble representing bound
single-particle states, single-particle resonances, and non-resonant continuum
states. In this framework, we shall discuss binding energies and energy spectra
of neutron-rich helium and lithium isotopes. The single-particle basis used is
that of the Hartree-Fock potential generated self-consistently by the
finite-range residual interaction.Comment: 13 pages, 2 figures, presented by N. Michel at the XXVII Symposium On
Nuclear Physics, Taxco, Guerrero, Mexico, January 5-8 200
The Fr\"olicher-Nijenhuis bracket for derivation based non commutative differential forms
In commutative differential geometry the Fr\"olicher-Nijenhuis bracket
computes all kinds of curvatures and obstructions to integrability. In \cit!{3}
the Fr\"olicher-Nijenhuis bracket was developped for universal differential
forms of non-commutative algebras, and several applications were given. In this
paper this bracket and the Fr\"olicher-Nijenhuis calculus will be developped
for several kinds of differential graded algebras based on derivations, which
were indroduced by \cit!{6}.Comment: AmSTeX, 28 pages, ESI Preprint 13
Isospin mixing and the continuum coupling in weakly bound nuclei
The isospin breaking effects due to the Coulomb interaction in weakly-bound
nuclei are studied using the Gamow Shell Model, a complex-energy configuration
interaction approach which simultaneously takes into account many-body
correlations between valence nucleons and continuum effects. We investigate the
near-threshold behavior of one-nucleon spectroscopic factors and the structure
of wave functions along an isomultiplet. Illustrative calculations are carried
out for the T=1 isobaric triplet. By using a shell-model Hamiltonian consisting
of an isoscalar nuclear interaction and the Coulomb term, we demonstrate that
for weakly bound or unbound systems the structure of isobaric analog states
varies within the isotriplet and impacts the energy dependence of spectroscopic
factors. We discuss the partial dynamical isospin symmetry present in
isospin-stretched systems, in spite of the Coulomb interaction that gives rise
to large mirror symmetry breaking effects.Comment: 10 pages, 5 figures ; published versio
Incremental Magnetoelastic Deformations, with Application to Surface Instability
In this paper the equations governing the deformations of infinitesimal
(incremental) disturbances superimposed on finite static deformation fields
involving magnetic and elastic interactions are presented. The coupling between
the equations of mechanical equilibrium and Maxwell's equations complicates the
incremental formulation and particular attention is therefore paid to the
derivation of the incremental equations, of the tensors of magnetoelastic
moduli and of the incremental boundary conditions at a magnetoelastic/vacuum
interface. The problem of surface stability for a solid half-space under plane
strain with a magnetic field normal to its surface is used to illustrate the
general results. The analysis involved leads to the simultaneous resolution of
a bicubic and vanishing of a 7x7 determinant. In order to provide specific
demonstration of the effect of the magnetic field, the material model is
specialized to that of a "magnetoelastic Mooney-Rivlin solid". Depending on the
magnitudes of the magnetic field and the magnetoelastic coupling parameters,
this shows that the half-space may become either more stable or less stable
than in the absence of a magnetic field.Comment: 24 page
Deterministic Approximation of Stochastic Evolution in Games
This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The deterministic approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the stochastic process, for large populations, and its deterministic approximation. In particular, we show that if the deterministic solution through the initial state of the stochastic process at some point in time enters a basin of attraction, then the stochastic process will enter any given neighborhood of that attractor within a finite and deterministic time with a probability that exponentially approaches one as the population size goes to infinity. The process will remain in this neighborhood for a random time that almost surely exceeds an exponential function of the population size. During this time interval, the process spends almost all time at a certain subset of the attractor, its so-called Birkhoff center. We sharpen this result in the special case of ergodic processes. Game Theory; Evolution; Approximation
Smale Strategies for Network Prisoner's Dilemma Games
Smale's approach \cite{Smale80} to the classical two-players repeated
Prisoner's Dilemma game is revisited here for -players and Network games in
the framework of Blackwell's approachability, stochastic approximations and
differential inclusions
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