In this paper, we introduce a family of Lagrange functions on the plane rotation group and verify that Euler-Lagrange and Hamilton equations associated to each of these functions must coincide with the Lie equations in the Lie transformation group.
According to the contour distribution of the objective function on the plane, it is easy to decide the optimal point or region on the plane.
The classical form of Iversen's theorem asserts that if is an entire holomorphic function of the plane, then there exists a curve tending to infinity such that (6.4).
Companies should be allowed to integrate the functions of the airport, plane, security, weather planning and flight control.
The displacement field is approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z.
Both the displacement and transverse stress fields are approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z.
The displacement field is approximated as a sum of separated functions of the in-plane coordinates x,y, the transverse coordinate z and the orientation of each ply θi.
The amplitude A Ω at the point P(2θ) (Fig. 4 ▶ a) for a beam incident at an angle Ω to a crystal plane is found by deriving the phase difference for different possible paths, which can be represented by a sinc function: The shape of this profile is a function of the scattering plane lateral dimension in the plane of the incident-beam direction, L x.
In this method, a plate is treated as a three-dimensional elastic body and the displacement field is approximated by a set of admissible trial functions in the plane of the plate.
First, we calculated the HiLo images corresponding to each axial plane and then used these images as the first prior for the object function of the corresponding plane λ ^ (1 ) (x, y, z ).
