27 research outputs found
The modular class of a Poisson map
We introduce the modular class of a Poisson map. We look at several examples
and we use the modular classes of Poisson maps to study the behavior of the
modular class of a Poisson manifold under different kinds of reduction. We also
discuss their symplectic groupoid version, which lives in groupoid cohomology.Comment: Final version accepted for publication in Annales de l'Institut
Fourier. Several changes made to the manuscript, based on referees' remark
A note on modular classes of Lie algebroids
We introduce the modular class of a twisted Jacobi structure on a Lie
algebroid and establish a relation between this modular class and the modular class
of the underlying Lie algebroid
A note on modular classes of Lie algebroids
We introduce the modular class of a twisted Jacobi structure on a Lie
algebroid and establish a relation between this modular class and the modular class
of the underlying Lie algebroid
Inversion of a mapping associated with the Aomoto-Forrester system
This article is devoted to the study of a general class of Hamiltonian
systems which extends the Calogero systems with external quadratic potential
associated to any root system. The interest for such a class comes from a
previous article of Aomoto and Forrester. We consider first the one-degree of
freedom case and compute the Birkhoff series defined near each of its
stationary points. In general, the analysis of the system motivates finding
some expression for the inverses of a rational map introduced by Aomoto and
Forrester. We derive here some diagrammatic expansion series for these
inverses
On Poisson quasi-Nijenhuis Lie algebroids
We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a
natural generalization of Poisson quasi-Nijenhuis manifolds and show that any
such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an
associated Courant algebroid is obtained. We introduce the notion of a morphism
of quasi-Lie bialgebroids and of the induced Courant algebroids morphism and
provide some examples of Courant algebroid morphisms. Finally, we use paired
operators to deform doubles of Lie and quasi-Lie bialgebroids and find an
application to generalized complex geometry.Comment: 12 page
SÃntese de calix[4]pirróis sulfonados e complexação com aniões
Mestrado em QuÃmica Orgânica e Produtos NaturaisO trabalho apresentado ao longo desta dissertação teve
como objetivo a sÃntese de novos calix[4]pirróis contendo
grupos sulfonamida de modo a torná-los mais seletivos na
complexação com aniões. Esta dissertação está dividida
em três capÃtulos essenciais. O primeiro apresenta uma
breve introdução focando as caracterÃsticas, métodos de
sÃntese e funcionalização bem como as aplicações dos
calix[4]pirróis. No capÃtulo que se segue encontra-se
descrito o trabalho de sÃntese, purificação e
caracterização de novos compostos, tais como
dipirrometano, calix[4]pirróis e calix[4]firinas. A
caracterização dos compostos obtidos foi realizada
recorrendo a espectroscopia de ressonância magnética
nuclear e espectrometria de massa. Nesta parte também
são descritos e apresentados os estudos onde se verifica
a capacidade dos calix[4]pirróis e dos dipirrometanos
sintetizados atuarem como sensores de aniões. Esta
deteção é feita recorrendo à leitura da absorvância das
soluções na zona do visÃvel e utilizando o método indireto.
No último capÃtulo descreve-se, pormenorizadamente, os
métodos de sÃntese e de purificação e caracterização
estrutural dos compostos sintetizados.The work presented in this dissertation lays on the synthesis
of new calix[4]pyrroles with sulfonamide groups aiming to
obtain novel selective sensors for anion binding applications.
This dissertation is the combination of three essential
chapters. The first one introducing the subjects of
characterization, synthetic routes and functionalization, as
well as the applications of calix[4]pyrroles. The following
chapter describes the synthesis implemented for the proposed
work, purification and characterization of the new compounds,
such as dipyrromethanes, calix[4]pyrroles and
calix[4]phyrines. The compounds were characterized by
nuclear magnetic resonance (1H NMR, 13C NMR, and
bidimensional techniques when required) and mass
spectrometry techniques. It is also presented the anion
binding tests using compounds 31, 35a, 35b, 37a and 37b.
The ability of such compounds to act as anion sensor was
followed by UV-Vis spectroscopy using the indirect method.
The last chapter describes the experimental procedures and
the structural characterization of synthesized compounds
On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms
We propose a definition of Jacobi quasi-Nijenhuis algebroid and show that any
such Jacobi algebroid has an associated quasi-Jacobi bialgebroid. Therefore,
also an associated Courant-Jacobi algebroid is obtained. We introduce the
notions of quasi-Jacobi bialgebroid morphism and Courant-Jacobi algebroid
morphism providing also some examples of Courant-Jacobi algebroid morphisms.Comment: 14 pages, to appear in Journal of Geometry and Physic
Modular classes of Poisson-Nijenhuis Lie algebroids
The modular vector field of a Poisson-Nijenhuis Lie algebroid is defined
and we prove that, in case of non-degeneracy, this vector field defines a
hierarchy of bi-Hamiltonian -vector fields. This hierarchy covers an
integrable hierarchy on the base manifold, which may not have a
Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic
Jacobi-Nijenhuis algebroids and their modular classes
Jacobi-Nijenhuis algebroids are defined as a natural generalization of
Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis
operator on a Jacobi algebroid which is compatible with it. We study modular
classes of Jacobi and Jacobi-Nijenhuis algebroids