We recognize the Gromoll-Meyer sphere Σ as the geodesic join of a simple closed geodesic and a minimal subsphere Σ ⊂ Σ, which can be equivariantly identified with the Brieskorn sphere W 5 3 . As applications we in particular determine the full isometry group of Σ, classify all closed subgroups which act freely, determine the homotopy types of the corresponding orbit spaces, identify the Hirsch-...

The Gaia ubiquitous computing platform currently supports mobile devices through a thin client proxy architecture. Mobile devices run a lightweight proxy client written in J2ME to join an active space. While this approach allows a wide variety of devices to interact with active spaces, it lacks the ability to use device specific functionality. This problem is addressed by combining the J2ME cli...

We establish a boundary connected sum theorem for asymptotically hyperbolic Einstein metrics, and also show that if the two metrics have scalar positive conformal infinities, then the same is true for this boundary join. This construction is also extended to spaces with a finite number of interior conic singularities, and as a result we show that any 3-manifold which is a finite connected sum o...

This paper extends earlier research on hash-join algorithms to a multiprocessor architecture. Implementations of a number of centralized join algorithms are described and measured. Evaluation of these algorithms served to verify earlier analytical results. In addition, they demonstrate that bit vector filtering provides dramatic improvement in the performance of all algorithms including the sor...

Adaptive query processors make decisions as to the most effective evaluation strategy for a query based on feedback received while the query is being evaluated. In essence, any of the decisions made by the optimizer (e.g., on operator order or on which operators to use) may be revisited in an adaptive query processor. This paper focuses on changes to physical operators (e.g., the specific join ...

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Using notions of Minkowski geometry (i.e., of the geometry of finite dimensional Banach spaces) we find new characterizations of centrally symmetric convex bodies, equiframed curves, bodies of constant width and certain convex bodies with modified constant width property. In particular, we show that straightforward extensions of some properties of bodies of constant Euclidean width are also val...

A bottle up hyperbox granular computing (HBGrC) is developed based on distance measure. Firstly, hyperbox granule is represented by the beginning point and the end point. Secondly, the distance measure between two hyperbox granules is defined by the beginning points and the end points. Thirdly, operations between two hyperbox granules are designed to the transformation between two hyperbox gran...

This work is a contribution to a recent field, Directed Algebraic Topology. Categories which appear as fundamental categories of ‘directed structures’, e.g. ordered topological spaces, have to be studied up to appropriate notions of directed homotopy equivalence, which are more general than ordinary equivalence of categories. Here we introduce past and future equivalences of categories—sort of ...