13,212 research outputs found
A counterexample for Improved Sobolev Inequalities over the 2-adic group
On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality
where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov
space B(-1,\infty,\infty) norm. We first show, using the special topological
properties of the p-adic groups, that the set of functions of bounded
variations BV can be identified to the Besov space B(1,\infty,1). This
identification lead us to the construction of a counterexample to the improved
Sobolev inequality.Comment: 10
A remark on Besov spaces interpolation over the 2-adic group
Motivated by a recent result which identifies in the special setting of the
2-adic group the Besov space with
, the space of function of bounded variation, we study in
this article some functional relationships between Besov spaces.Comment: 6 page
Non-local diffusion equations with L\'evy-type operators and divergence free drift
We are interested in some properties related to the solutions of non-local
diffusion equations with divergence free drift. Existence, maximum principle
and a positivity principle are proved. In order to study Holder regularity, we
apply a method that relies in the Holder-Hardy spaces duality and in the
molecular characterisation of local Hardy spaces. In these equations, the
diffusion is given by L\'evy-type operators with an associated L\'evy measure
satisfying some upper and lower bounds.Comment: arXiv admin note: substantial text overlap with arXiv:1007.391
A molecular method applied to a non-local PDE in stratified Lie groups
In this article we study a transport-diffusion equation in the framework of
the stratified Lie groups. For this equation we will study the existence of the
solutions, a maximum principle, a positivity principle and H\"older regularity.Comment: 26 pages. arXiv admin note: substantial text overlap with
arXiv:1205.2834, arXiv:1007.391
Improved Sobolev Inequalities and Muckenhoupt weights on stratified Lie groups
We study in this article the Improved Sobolev inequalities with Muckenhoupt
weights within the framework of stratified Lie groups. This family of
inequalities estimate the Lq norm of a function by the geometric mean of two
norms corresponding to Sobolev spaces W(s;p) and Besov spaces B(-b, infty,
infty). When the value p which characterizes Sobolev space is strictly larger
than 1, the required result is well known in R^n and is classically obtained by
a Littlewood-Paley dyadic blocks manipulation. For these inequalities we will
develop here another totally different technique. When p = 1, these two
techniques are not available anymore and following M. Ledoux in R^n, we will
treat here the critical case p = 1 for general stratified Lie groups in a
weighted functional space setting. Finally, we will go a step further with a
new generalization of Improved Sobolev inequalities using weak-type Sobolev
spaces.Comment: 17 page
Gap solitons and symmetry breaking in parity-time symmetric microring CROWs
The propagation properties of optical fields in linear and nonlinear
parity-time symmetric microring coupled resonator optical waveguides are
studied. The effects described include the existence of symmetry breaking
thresholds, the propagation of gap solitons in nonlinear transmission lines and
the existence of quasi stable propagation regimes outside the broken symmetry
regions.Comment: Final Versio
A complementary view to the bonding pattern in the N5 +cation an electron localization function and local temperature analysis
Indexación: ScieloThe electron localization function (ELF), a local measure of the Pauli repulsion effect,
and the local Kohn-Sham temperature analysis, which is defined within the framework of a local
thermodynamics description of density functional theory, have been used to explore the bonding
characteristics in the open chain N5+ cation. It is found that both the ELF and local temperature maps depict
uniquely the regions of pair localizations, yielding a description of bonding which agrees and
complements previous techniques of analysis. Particularly, the three-center four-electron interaction in
the NNN terminal atoms of N5+ and the contribution of terminal triple bonds to the bonding nature of
the cation have been characterized in detail from the electron fluctuation among ELF basins
populations. The features of bonding in terms of the local kinetic energy analysis have been visualized
directly from the analysis of local temperature map.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072003000400010&lang=p
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