Dilation equation transforms

Equation (6a) implies that the scale (dilation) parameter, m, is required to vary from - ac to + =. In practice, though, a process variable is measured at a finite resolution (sampling time), and only a finite number of distinct scales are of interest for the solution of engineering problems. Let m = 0 signify the finest temporal scale (i.e., the sampling interval at which a variable is measured) and m = Lbe coarsest desired scale. To capture the information contained at scales m > L, we define a scaling function, (r), whose Fourier transform is related to that of the wavelet, tf/(t), by... 

Equation (2.13.8) is called the Lorentz-FitzGerald94 contraction of space Eq. (2.13.11) is the Einstein time dilatation A clock advances more slowly in a system moving at a high speed V. When V Lorentz transformation reduces to the Galilean transformation. 

Analogous to the previous treatments /69/ the Fourier transformed equation of motion of the dilated electron propagator may now be written as... 

Wavelet transforms use a single function t/f Z.2(R) (wavelet) and its dilated and shifted versions to analyze data. Wavelets are associated with scaling functions 0eZ2(M). The scaling function usually serve to represent a smooth part of data and it is obtained as a solution of scaling equation... 

The parameters Cq, C, Ce, and are model constants and need to be specified [30,31]. The same goes for the pressure dilatation term lid [31,32]. The transport equations for all of the SGS moments are readily obtained by integration of this Fokker-Planck equation. This provides a complete statistical description of turbulence. The idea is to find methods that could take advantage of quantum resources in order to speed up these calculations, at least polyno-mially in the number of variables. Because of the size of the problem typically considered, such a speedup could transform the way these problems are treated in engineering providing solutions to problems many orders of magnitude faster than are possible with classical computers. 

---