Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its f...

To improve the application and transfer of troubleshooting skills when diagnosing faults in complex automated production units, we developed and implemented an “anchored instruction” learning module in the context of a computer based simulation environment. The effects of the instructional module were evaluated in a quasi-experimental evaluation study. During the study 42 mechatronic apprentice...

In this paper we investigate the conditions under which a given ring is a sub-ring of a semi-simple ring. For convenience, we say that a ring A is an extension of a ring B, if B is a sub-ring of A. It is found that the existence of a semi-simple extension is equivalent to the vanishing of the extension radical, a two-sided ideal defined analogously to the ordinary radical. In Theorem II we give...

In modern road surveys, hanging power cables are among the most commonly-found geometric features. These cables are catenary curves that are conventionally modelled with three parameters in 2D Cartesian space. With the advent and popularity of the mobile mapping system (MMS), the 3D point clouds of hanging power cables can be captured within a short period of time. These point clouds, similarly...

Recently, the coupled dynamical simulation of pantograph and catenary in high speed trains has found much interest. The equations of motion form a partial diierential-algebraic equation (PDAE) that combines a partial diierential equation (PDE) for the catenary and a diierential-algebraic equation (DAE) for the pantograph. In the present paper we discuss the relation of this PDAE model to curren...

In this paper a user-friendly environment for the representation of the dynamic results on the pantograph-catenary interactions is presented. This environment consists of an interactive interface for the representation of graphics and another for the representation of video. By means of the first interface for the representation of graphics, the user can interact with the different graphic repr...