In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to bui...

This study investigated bending, buckling, and free vibration responses of hyperbolic shear deformable functionally graded (FG) higher order beams. The material properties of FG beams are varied through thickness according to power law distribution; here, the FG beam was made of aluminium/alumina, and the hyperbolic shear deformation theory was used to evaluate the effect of shear deformation i...

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

The action of Möbius transformations with real coefficients preserves the hyperbolic metric in the upper half-plane model of the hyperbolic plane. The modular group is an interesting group of hyperbolic isometries generated by two Möbius transformations, namely, an order-two element, g2 HzL = -1 ê z, and an element of infinite order, g• HzL = z + 1. Viewing the action of the group elements on a...

in exploration seismology, migration refers to a multi-channel processing step that attempts to spatially re-position events and improve focusing. before migration, seismic data is usually displayed with traces plotted at the surface location of the receivers and with a vertical time axis. this means that dipping reflections are systematically mispositioned in the lateral coordinate and the ver...

A Study of Option Pricing Models – Lognormal or Hyperbolic Levy ? By Chen Chen This paper is an investigation into two option pricing models: widely-used Black-Scholes model and one of its augmented extensions – hyperbolic Levy model. Firstly, we have a detailed discussion about the celebrated Black-Scholes model. However, clearly there are many deficiencies in Black-Scholes assumptions. In ord...

neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. in fact, they both fail to represent proper unloading slopes during cyclic loading. to overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. in this regard, various classes of plastic-damage models have...