We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial ...

Hot deformation behavior of a medium Cr/Mn Al6061 aluminum alloy was studied by isothermal compression test at temperatures range of 320 to 480 °C and strain rates range of 0.001 to 0.1 s −1. The true stresstrue strain curves were analyzed to characterize the flow stress of Al6061. Plastic behavior, as a function of both temperature and strain rate for Al6061, was also modeled using a hyperboli...

The dynamic performance of structures under traveling loads should be exactly analyzed to have a safe and reasonable structural design. Different higher-order shear deformation theories are proposed in this paper to analyze the dynamic stability of thick elastic plates carrying a moving mass. The displacement fields of different theories are chosen based upon variations along the thickness as c...

Radial lines, suitably parameterized, are geodesics, but notice that the distance from the origin to the (Euclidean) unit sphere is infinite. This model makes it intuitively clear that the boundary at infinity of hyperbolic space is Sn−1. Hyperbolic space together with its boundary at infinity has the topology of a closed ball, and isometries of hyperbolic space extend uniquely to a homeomorphi...

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives rise to a complex valued geometry consistent with both the hyperbolic and de Sitter space. Such a construction shed a light and inspires a new insight for the ...

Spatial information processing has been a focus of research in the past decade. In spatial databases, data are associated with spatial coordinates and extents, and are retrieved based on spatial proximity. A formidable number of spatial indexes have been proposed to facilitate spatial data retrieval. In this paper, we propose a new scalable, reliable and consistent architecture for spatial data...