We present a geometric interpretation of a product form stationary distribution for a d-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The d-dimensional SRBM data can be equivalently specified by d + 1 geometric objects: an ellipse and d rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing p...

The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for sym...

investigations are carried out to evaluate the performance of a low heat rejection (lhr) diesel engine consisting of air gap insulated piston with 3-mm air gap, with superni (an alloy of nickel) crown and air gap insulated liner with superni insert with different operating conditions of crude jatropha oil with varied injection timing and injection pressure.  performance parameters of brake ther...

Geometric metaphors have been used in fraud theory for more than 60 years. The most commonly of these is the triangle. triangle has criticized severely its scope, substitutability elements, perceptuality, individuality and one-sidedness. Different models developed afterwards tried to cover shortcomings with additions modifications, but none them became as popular In this study, by moving away f...

We consider a simple model of d families of scalar field interacting with geometry in two dimensions. The geometry is locally flat and has only global degrees of freedom. When d < 0 the universe is locally two dimensional but for d > 0 it collapses to a one dimensional manifold. The model has some, but not all, of the characteristics believed to be features of the full theory of conformal matte...

This paper applies a recently developed geometric PID controller to stabilize a three-link planar bipedal hybrid dynamic walking model. The three links represent the robot torso and two kneeless legs, with an independent control torque available at each hip joint. The geometric PID controller is derived for fully actuated mechanical systems, however in the swing phase the three-link biped robot...

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transf...

Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density λ c for d-dimensional Poisson random geometric graphs in continuum percolation theory. In two-dimensional space with the Euclidean norm, simulation studies show λ c ≈ 1.44, while the best theoretical bounds obtained thus far...