Regular case

Also other closely related examples80,298 312 3171314 as well as some more regular cases.1091... 

In Figs. 3 and 4, we show numerical results for the quantum kicked rotor as in Section II. A. The system parameters are chosen to pick up a regular dynamics (Fig. 3) and a chaotic dynamics (Fig. 4), and the others are T = 400 and a = 1. The optimal field after 100 iterations for the regular case (Fig. 3a) is much simpler than that for the chaotic case (Fig. 4a). (See also Figs. 3b and 4b.) This is because more states are involved in the latter chaotic process. 

Figure 5. Time evolution of the Husimi distribution for quantum kicked rotors with H = 0.3436 under an optimal field after 100 iterations. The Zhu-Botina-Rabitz scheme was used with the penalty factor a = 1 and the target time T = 400. From left to right, quantum states immediately after the kick at t = 0, 1, 2, 10, 100, 200, 300, 398, 399, and 400 are depicted, (a) The parameters are = 1 (regular case), (0 ,/) ) = (l- j l- ) (S/jf/) = (1-0, 1-0) (b) K = 1...

Eigendistributions for ergodic systems may also be readily obtained, although they prove less useful than those obtained for the regular case. Specifically, stationary eigenfunctions that are L2 on the energy hypersurface for this case are given by... 

It should also be observed that, in the case of an infinitely ramified fractal structure fed from all the perimeter sites, an exponent 0 fairly close to 0 = 1/2 (i.e. the regular case) is obtained, 0.40 < 0 < 0.50. The small difference between the exponent 0 obtained for infinitely ramified fractals and in the regular Euclidean case makes it difficult to discriminate between the two scaling behaviors, especially if one makes use of numerical simulations on small lattices. 

Paun, G., Santean, L. Parallel communicating grammar systems the regular case. Ann. Univ. Bucharest 38, 55-63 (1989)... 

Apart from MPl and PVM, there are programming models that attempt to hide the disttibuted nature of the machine at hand fi om the user. One of these is HPF (High Performance Fortran). In this Fortran 90-like language one can specify how the data are spread out over the processors, and all communication that results fl om this is taken care of by the HPF compiler and run time system. HPF, however, can be applied only in relatively easy and very regular cases. Such applications are characterized as data parallel. Therefore, the use of HPF is fairly limited. 

If your team has a regular case discussion, ask to present people like Jenny, not just your more dramatic or worrying patients. 

Then, shift the (m-f- l)-th row to the left over k positions, so that the element rm+i,k+i becomes the first one in the line, and multiply all other entries of this row through by (-1). Since the first entry is now non-zero, one proceeds as in the regular case. Eventually, the number of roots of S(A) with positive real parts will be equal to the number of sign changes in the first column added to the sum of deficiency numbers over all irregular rows. 

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