We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the butterfly decomposition we obtain a oneto-one correspondence between doubly rooted plane trees and free Dyck paths, which implies a simple derivation of a relation between the Catalan numbers and the central binomial...

Published data on unconfined plane-wall jets and plane-free jets were reviewed and used to assess the accuracy of numerical simulations, A plane-free jet was numerically simulated using the standard k-e model and four nonuniform grid patterns (70 x32,100 x52,120 x 60, and 120 x 74), The solution for a plane-free jet with adequate grid resolution was in good agreement with the published data, A ...

Abstrct The detection of ground plane and free space remains challenging for non-flat plane, especially with the varying latitudinal and longitudinal slope or in the case of multi-ground plane. In this paper, we propose a framework of the ground plane detection with stereo vision. The main contribution of this paper is a newly proposed descriptor which is implemented in the disparity image to o...

In this paper a variationally consistent trigonometric shear deformation theory is presented for the free vibration of thick isotropic square and rectangular plate. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in tr...