778 research outputs found
Linear Form of 3-scale Relativity Algebra and the Relevance of Stability
We show that the algebra of the recently proposed Triply Special Relativity
can be brought to a linear (ie, Lie) form by a correct identification of its
generators. The resulting Lie algebra is the stable form proposed by Vilela
Mendes a decade ago, itself a reapparition of Yang's algebra, dating from 1947.
As a corollary we assure that, within the Lie algebra framework, there is no
Quadruply Special Relativity.Comment: 5 page
Alternative linear structures for classical and quantum systems
The possibility of deforming the (associative or Lie) product to obtain
alternative descriptions for a given classical or quantum system has been
considered in many papers. Here we discuss the possibility of obtaining some
novel alternative descriptions by changing the linear structure instead. In
particular we show how it is possible to construct alternative linear
structures on the tangent bundle TQ of some classical configuration space Q
that can be considered as "adapted" to the given dynamical system. This fact
opens the possibility to use the Weyl scheme to quantize the system in
different non equivalent ways, "evading", so to speak, the von Neumann
uniqueness theorem.Comment: 32 pages, two figures, to be published in IJMP
Upper semi-continuity of the Royden-Kobayashi pseudo-norm, a counterexample for H\"olderian almost complex structures
If is an almost complex manifold, with an almost complex structure of
class \CC^\alpha, for some , for every point and every
tangent vector at , there exists a germ of -holomorphic disc through
with this prescribed tangent vector. This existence result goes back to
Nijenhuis-Woolf. All the holomorphic curves are of class \CC^{1,\alpha}
in this case.
Then, exactly as for complex manifolds one can define the Royden-Kobayashi
pseudo-norm of tangent vectors. The question arises whether this pseudo-norm is
an upper semi-continuous function on the tangent bundle. For complex manifolds
it is the crucial point in Royden's proof of the equivalence of the two
standard definitions of the Kobayashi pseudo-metric. The upper semi-continuity
of the Royden-Kobayashi pseudo-norm has been established by Kruglikov for
structures that are smooth enough. In [I-R], it is shown that \CC^{1,\alpha}
regularity of is enough.
Here we show the following:
Theorem. There exists an almost complex structure of class \CC^{1\over
2} on the unit bidisc \D^2\subset \C^2, such that the Royden-Kobayashi
seudo-norm is not an upper semi-continuous function on the tangent bundle.Comment: 5 page
Citrullinated proteins in arthritis: presence in joints and effects on immunogenicity
Contains fulltext :
60098.pdf (publisher's version ) (Open Access
Extensions, expansions, Lie algebra cohomology and enlarged superspaces
After briefly reviewing the methods that allow us to derive consistently new
Lie (super)algebras from given ones, we consider enlarged superspaces and
superalgebras, their relevance and some possible applications.Comment: 9 pages. Invited talk delivered at the EU RTN Workshop, Copenhagen,
Sep. 15-19 and at the Argonne Workshop on Branes and Generalized Dynamics,
Oct. 20-24, 2003. Only change: wrong number of a reference correcte
Equivalence problem for the orthogonal webs on the sphere
We solve the equivalence problem for the orthogonally separable webs on the
three-sphere under the action of the isometry group. This continues a classical
project initiated by Olevsky in which he solved the corresponding canonical
forms problem. The solution to the equivalence problem together with the
results by Olevsky forms a complete solution to the problem of orthogonal
separation of variables to the Hamilton-Jacobi equation defined on the
three-sphere via orthogonal separation of variables. It is based on invariant
properties of the characteristic Killing two-tensors in addition to properties
of the corresponding algebraic curvature tensor and the associated Ricci
tensor. The result is illustrated by a non-trivial application to a natural
Hamiltonian defined on the three-sphere.Comment: 32 page
Jacobi structures revisited
Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra
associated with a vector bundle which satisfy a property similar to that of the
Jacobi brackets, are introduced. They turn out to be equivalent to generalized
Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as
odd Jacobi brackets on the supermanifolds associated with the vector bundles.
Jacobi bialgebroids are defined in the same manner. A lifting procedure of
elements of this Grassmann algebra to multivector fields on the total space of
the vector bundle which preserves the corresponding brackets is developed. This
gives the possibility of associating canonically a Lie algebroid with any local
Lie algebra in the sense of Kirillov.Comment: 20 page
Кон'юнктурний аналіз розвитку ринку рекреаційних послуг АР Крим
Метою дослідження є кон’юнктурний аналіз розвитку ринку рекреаційних послуг АР Крим та порівняльна оцінка функціонування конкурентоспроможних рекреаційних районів
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