Invariant connections, Lie algebra actions, and foundations of numerical integration on manifolds

Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant connections on algebroids. This has fundamental consequences for the theory of numerical integrators, giving a characterization of the spaces on which Butcher and Lie-Butcher series methods, which generalize Runge-Kutta methods, may be applied.Comment: 18 page

Critical Reflections on Self-Management Support in Chronic Disease: The Value of Occupational Therapy in Health Promotion

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Systematically creating coincidental product evolution:case studies of the application of the Systematic Inventive Thinking® (SIT) method in the chemical industry

The article shows the need for an unconventional innovation methodology within the field of new product development (NPD). Systematic Inventive Thinking (SIT) is such a method which has been applied successfully in the chemical industry. An overview of the method, together with case studies from the industry, demonstrates the value of this departure from traditional thinking and other, more widespread, innovation methods

PseudoSkyrmion Effects on Tunneling Conductivity in Coherent Bilayer Quantum Hall States at ν=1\nu =1

We present a mechamism why interlayer tunneling conductivity in coherent bilayer quantum Hall states at $\nu=1$ is anomalously large, but finite in the recent experiment. According to the mechanism, pseudoSkyrmions causes the finite conductivity, although there exists an expectation that dissipationless tunneling current arises in the state. PseudoSkyrmions have an intrinsic polarization field perpendicular to the layers, which causes the dissipation. Using the mechanism we show that the large peak in the conductivity remains for weak parallel magnetic field, but decay rapidly after its strength is beyond a critical one, $\sim 0.1$ Tesla.Comment: 6 pages, no figure

Spatially resolved spectroscopy of the globular cluster RZ 2109 and the nature of its black hole

We present optical HST/STIS spectroscopy of RZ 2109, a globular cluster in the elliptical galaxy NGC 4472. This globular cluster is notable for hosting an ultraluminous X-ray source as well as associated strong and broad [OIII] 4959, 5007 emission. We show that the HST/STIS spectroscopy spatially resolves the [OIII] emission in RZ 2109. While we are unable to make a precise determination of the morphology of the emission line nebula, the best fitting models all require that the [OIII] 5007 emission has a half light radius in the range 3-7 pc. The extended nature of the [OIII] 5007 emission is inconsistent with published models that invoke an intermediate mass black hole origin. It is also inconsistent with the ionization of ejecta from a nova in the cluster. The spatial scale of the nebula could be produced via the photoionization of a strong wind driven from a stellar mass black hole accreting at roughly its Eddington rate.Comment: 7 pages, 4 figures - accepted for publication in Ap