1,039 research outputs found
Symmetric vortices for two-component Ginzburg-Landau systems
We study Ginzburg--Landau equations for a complex vector order parameter
Psi=(psi_+,psi_-). We consider symmetric (equivariant) vortex solutions in the
plane R^2 with given degrees n_\pm, and prove existence, uniqueness, and
asymptotic behavior of solutions for large r. We also consider the monotonicity
properties of solutions, and exhibit parameter ranges in which both vortex
profiles |psi_+|, |psi_i| are monotone, as well as parameter regimes where one
component is non-monotone. The qualitative results are obtained by means of a
sub- and supersolution construction and a comparison theorem for elliptic
systems.Comment: 32 page
Complete independence of an axiom system for central translations
A recently proposed axiom system for Andr\'e's central translation structures
is improved upon. First, one of its axioms turns out to be dependent (derivable
from the other axioms). Without this axiom, the axiom system is indeed
independent. Second, whereas most of the original independence models were
infinite, finite independence models are available. Moreover, the independence
proof for one of the axioms employed proof-theoretic techniques rather than
independence models; for this axiom, too, a finite independence model exists.
For every axiom, then, there is a finite independence model. Finally, the axiom
system (without its single dependent axiom) is not only independent, but
completely independent.Comment: 10 pages. Submitted to Note di Matematic
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