1,209 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
Algebraic theories of brackets and related (co)homologies
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets
in the category of modules over a commutative algebra is described. Some
related structures and (co)homology invariants are discussed, as well as
applications to geometry.Comment: 14 pages; v2: minor correction
Generalized Lenard Chains, Separation of Variables and Superintegrability
We show that the notion of generalized Lenard chains naturally allows
formulation of the theory of multi-separable and superintegrable systems in the
context of bi-Hamiltonian geometry. We prove that the existence of generalized
Lenard chains generated by a Hamiltonian function defined on a four-dimensional
\omega N manifold guarantees the separation of variables. As an application, we
construct such chains for the H\'enon-Heiles systems and for the classical
Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler
potential are found.Comment: 14 pages Revte
Lie Superalgebra Stability and Branes
The algebra of the generators of translations in superspace is unstable, in
the sense that infinitesimal perturbations of its structure constants lead to
non-isomorphic algebras. We show how superspace extensions remedy this
situation (after arguing that remedy is indeed needed) and review the benefits
reaped in the description of branes of all kinds in the presence of the extra
dimensions.Comment: Talk given at the conference ``Brane New World and Non-commutative
Geometry'', held in Torino, October 2000. To appear in the proceedings by
World Scientific. 10 pages, 1 figur
Periodically driven Taylor-Couette turbulence
We study periodically driven Taylor-Couette turbulence, i.e. the flow
confined between two concentric, independently rotating cylinders. Here, the
inner cylinder is driven sinusoidally while the outer cylinder is kept at rest
(time-averaged Reynolds number is ). Using particle image
velocimetry (PIV), we measure the velocity over a wide range of modulation
periods, corresponding to a change in Womersley number in the range . To understand how the flow responds to a given modulation, we
calculate the phase delay and amplitude response of the azimuthal velocity.
In agreement with earlier theoretical and numerical work, we find that for
large modulation periods the system follows the given modulation of the
driving, i.e. the system behaves quasi-stationary. For smaller modulation
periods, the flow cannot follow the modulation, and the flow velocity responds
with a phase delay and a smaller amplitude response to the given modulation. If
we compare our results with numerical and theoretical results for the laminar
case, we find that the scalings of the phase delay and the amplitude response
are similar. However, the local response in the bulk of the flow is independent
of the distance to the modulated boundary. Apparently, the turbulent mixing is
strong enough to prevent the flow from having radius-dependent responses to the
given modulation.Comment: 12 pages, 6 figure
Exterior Differentials in Superspace and Poisson Brackets
It is shown that two definitions for an exterior differential in superspace,
giving the same exterior calculus, yet lead to different results when applied
to the Poisson bracket. A prescription for the transition with the help of
these exterior differentials from the given Poisson bracket of definite
Grassmann parity to another bracket is introduced. It is also indicated that
the resulting bracket leads to generalization of the Schouten-Nijenhuis bracket
for the cases of superspace and brackets of diverse Grassmann parities. It is
shown that in the case of the Grassmann-odd exterior differential the resulting
bracket is the bracket given on exterior forms. The above-mentioned transition
with the use of the odd exterior differential applied to the linear even/odd
Poisson brackets, that correspond to semi-simple Lie groups, results,
respectively, in also linear odd/even brackets which are naturally connected
with the Lie superalgebra. The latter contains the BRST and anti-BRST charges
and can be used for calculation of the BRST operator cohomology.Comment: 12 pages, LATEX 2e, JHEP format. Correction of misprints. The titles
for some references are adde
Kodaira-Spencer formality of products of complex manifolds
We shall say that a complex manifold is emph{Kodaira-Spencer formal} if its Kodaira-Spencer differential graded Lie algebra
is formal; if this happen, then the deformation theory of
is completely determined by the graded Lie algebra and the base space of the semiuniversal deformation is a quadratic singularity..
Determine when a complex manifold is Kodaira-Spencer formal is generally difficult and
we actually know only a limited class of cases where this happen. Among such examples we have
Riemann surfaces, projective spaces, holomorphic Poisson manifolds with surjective anchor map
and every compact K"{a}hler manifold with trivial or torsion canonical
bundle.
In this short note we investigate the behavior of this property under finite products. Let be compact complex manifolds; we prove that whenever and are
K"{a}hler, then is Kodaira-Spencer formal if and only if the same
holds for and . A revisit of a classical example by Douady shows that the above result fails if the K"{a}hler assumption is droppe
Training modalities in robot-mediated upper limb rehabilitation in stroke : A framework for classification based on a systematic review
© 2014 Basteris et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The work described in this manuscript was partially funded by the European project ‘SCRIPT’ Grant agreement no: 288698 (http://scriptproject.eu). SN has been hosted at University of Hertfordshire in a short-term scientific mission funded by the COST Action TD1006 European Network on Robotics for NeuroRehabilitationRobot-mediated post-stroke therapy for the upper-extremity dates back to the 1990s. Since then, a number of robotic devices have become commercially available. There is clear evidence that robotic interventions improve upper limb motor scores and strength, but these improvements are often not transferred to performance of activities of daily living. We wish to better understand why. Our systematic review of 74 papers focuses on the targeted stage of recovery, the part of the limb trained, the different modalities used, and the effectiveness of each. The review shows that most of the studies so far focus on training of the proximal arm for chronic stroke patients. About the training modalities, studies typically refer to active, active-assisted and passive interaction. Robot-therapy in active assisted mode was associated with consistent improvements in arm function. More specifically, the use of HRI features stressing active contribution by the patient, such as EMG-modulated forces or a pushing force in combination with spring-damper guidance, may be beneficial.Our work also highlights that current literature frequently lacks information regarding the mechanism about the physical human-robot interaction (HRI). It is often unclear how the different modalities are implemented by different research groups (using different robots and platforms). In order to have a better and more reliable evidence of usefulness for these technologies, it is recommended that the HRI is better described and documented so that work of various teams can be considered in the same group and categories, allowing to infer for more suitable approaches. We propose a framework for categorisation of HRI modalities and features that will allow comparing their therapeutic benefits.Peer reviewedFinal Published versio
Do Killing-Yano tensors form a Lie Algebra?
Killing-Yano tensors are natural generalizations of Killing vectors. We
investigate whether Killing-Yano tensors form a graded Lie algebra with respect
to the Schouten-Nijenhuis bracket. We find that this proposition does not hold
in general, but that it does hold for constant curvature spacetimes. We also
show that Minkowski and (anti)-deSitter spacetimes have the maximal number of
Killing-Yano tensors of each rank and that the algebras of these tensors under
the SN bracket are relatively simple extensions of the Poincare and (A)dS
symmetry algebras.Comment: 17 page
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