Case 2: Thermoacoustic Wave Propagation in a 2-Dimensional
It is necessary to mention that these ladder operators satisfy (6) only for a particular class of shape invariant systems and in general, the 2-dimensional
system [H.sub.s], obtained from a given master function, is not a superintegrable system.
Firstly, divide matrix A and matrix B into p x p blocks which form a 2-dimensional
grid whose size is p x p, and the number of each block is decided by its row numbers and column numbers in the 2-dimensional
The proposed method projects the fitted teaching data and each candidate region onto a 2-dimensional
plane respectively to extract texture information.
an alternative description of the 2-dimensional
subspace (36) of three-dimensional 0-balanced vectors is valid (without the 0-sequence)
For the case without rotational force, Masmoudi  proved the convergence of the weak solution of isentropic Navier-Stokes equations to the strong solution of the incompressible Euler equations in the 2-dimensional
whole space [R.sup.2] and the space case by applying the related entropy method.
Each feature point is expressed as a 2-dimensional
coordinate as follows: (x, y).
When a flat wave enters the medium along the z-axis so that at t = 0 the initial wave vector is everywhere equal to k(0) = [k.sub.0] [e.sub.z], the entire wavefront corresponds to a 2-dimensional
surface in the 6-dimensional phase space, given by the conditions
Autodesk 123D Catch software (Autodesk, Inc, San Francisco, California) was used to create 3D CADs from 2-dimensional
digital photographs using a commercially available iPhone camera (Apple Inc, Cupertino, California) and a commercially available digital single-lens reflex camera (Nikon Corporation, Tokyo, Japan).
Both brightness mode (2-dimensional
; 2D) and 3-dimensional (3D) ultrasonography were performed to identify the origin of the mass.
More teaching and learning ideas are provided by Hourigan and Leavy, who look at the identification and classification of 2-dimensional