Abstract-We present our ongoing work building a Raspberry Pi cluster consisting of 300 nodes. The unique characteristics of this single board computer pose several challenges, but also offer a number of interesting opportunities. On the one hand, a single Raspberry Pi can be purchased cheaply and has a low power consumption, which makes it possible to create an affordable and energy-efficient cluster. On the other hand, it lacks in computing power, which makes it difficult to run computationally intensive software on it. Nevertheless, by combining a large number of Raspberries into a cluster, this drawback can be (partially) offset. Here we report on the first important steps of creating our cluster: how to set up and configure the hardware and the system software, and how to monitor and maintain the system. We also discuss potential use cases for our cluster, the two most important being an inexpensive and green testbed for cloud computing research and a robust and mobile data center for operating in adverse environments.
The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the symmetry group of Lie sphere contact transformations from the point of view of the deformation theory of submanifolds in homogeneous spaces. Necessary and sufficient conditions are provided for a Legendre surface to admit non-trivial deformations and the corresponding existence problem is discussed.2000 Mathematics Subject Classification. Primary 53A40, 53C24.
A theorem of I. M. Singer [9] states that a Riemannian mnanifold is locally homogeneous if and only if the Riemannian curvature tensor and its covariant derivatives are the same at each point up to some order kM + 1.In the present paper we reprove this theorem by a more direct approach. By using the same approach we also prove, in addition, that a homogeneous Riemannian manifold is completely determined by the curvature and its covariant derivatives at some point up to order kM + 2. Moreover, we show how to reconstruct a homogeneous Riemannian manifold only from these curvature data. Finally, we formulate precisely and prove a statement which was announced without proof by Singer in [9].
Abstract. We consider the variational problem defined by the functionaldA on immersed surfaces in Euclidean space. Using the invariance of the functional under the group of Laguerre transformations, we study the extremal surfaces by the method of moving frames.
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