9,538 research outputs found
Uniformly bounded components of normality
Suppose that is a transcendental entire function and that the Fatou
set . Set and
where the supremum is taken over all components of
. If or , then we say is strongly
uniformly bounded or uniformly bounded respectively. In this article, we will
show that, under some conditions, is (strongly) uniformly bounded.Comment: 17 pages, a revised version, to appear in Mathematical Proceedings
Cambridge Philosophical Societ
Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data
The aim of this note is to adapt the strategy in [4][See,B.Dodson, J.Murphy,
a new proof of scattering below the ground state for the 3D radial focusing
cubic NLS, arXiv:1611.04195 ] to prove the scattering of radial solutions below
sharp threshold for certain focusing fractional NLS with cubic nonlinearity.
The main ingredient is to apply the fractional virial identity proved in
[11][See,T.Boulenger, D.Himmelsbach,E.Lenzmann, Blow up for fractional
NLS,J.Func.Anal,271(2016),2569-2603] to exclude the concentration of mass near
the origin.Comment: This version is an extension of the last version by the first and
fourth author, where the dimensional case is treate
Competing electronic orders on Kagome lattices at van Hove filling
The electronic orders in Hubbard models on a Kagome lattice at van Hove
filling are of intense current interest and debate. We study this issue using
the singular-mode functional renormalization group theory. We discover a rich
variety of electronic instabilities under short range interactions. With
increasing on-site repulsion , the system develops successively
ferromagnetism, intra unit-cell antiferromagnetism, and charge bond order. With
nearest-neighbor Coulomb interaction alone (U=0), the system develops
intra-unit-cell charge density wave order for small , s-wave
superconductivity for moderate , and the charge density wave order appears
again for even larger . With both and , we also find spin bond order
and chiral superconductivity in some particular
regimes of the phase diagram. We find that the s-wave superconductivity is a
result of charge density wave fluctuations and the squared logarithmic
divergence in the pairing susceptibility. On the other hand, the d-wave
superconductivity follows from bond order fluctuations that avoid the matrix
element effect. The phase diagram is vastly different from that in honeycomb
lattices because of the geometrical frustration in the Kagome lattice.Comment: 8 pages with 9 color figure
- …