### Table 5. Characteristic roots, damping periods, periods of cyde France Germany Italy Japan

"... In PAGE 29: ... In what follows we discuss the results of the stability and sensitivity analysis for the five country models considering each national case as, once, again national differences are of some relevance. Table5 presents the characteristic roots, damping periods and periods of cycle 43 for the five country cases. Tables 6-10 present sensitivity results for selected parameters (i.... ..."

### Table 1: Termination with critical damping

"... In PAGE 4: ... 7.1 ClockTree Construction The characteristic parameters of the clock-trees con- structed using our approach are presented in Table1 , cor- responding to termination condition #10 =1:0. These clock- trees have a driver at the root and no additional bu#0Bers inserted.... ..."

### Table 2 Load powers at some characteristic small signal stability points 1st minimum 2nd minimum Bus damping point damping point Bifurcation point

### Table 1, and the damping factor is increasing with larger domains. However, several cycles damp the residual. Let us briefly try to explain this behavior of the damping for the two grid method with h 1 =2h 0 . The evolution of the initial Dirac measure residual yields, after one V-cycle, a small part R 2 of the residual error with L 1 -norm

"... In PAGE 4: ...1) in the computational domain #0A = #280; 1#29 #02 #280; 1#29, with #0F = h 0 and homogeneous Dirichlet boundary conditions. For a description of the parameters used in the multigrid cycle see Table1 , Experiment A in Section 7. Experiments I (upper figure #02) and II (lower figure #02) start with an initial Dirac-like algebraic residual with L 1 -norm equal to 1.... In PAGE 25: ... This replacement indicates that the multigrid method, based on Jacobi smoothing steps, could work for #0F =0 and h 0 #3E 0 if the mesh is not aligned with the characteristic; however, due to the small factor 2/625, the number of smoothing steps required to sufficiently damp one V-cycle might be very large. After one V-cycle, Experiment B in Table1 shows large amplifications of 5:4 and 4:7 for five and ten smoothing steps, respectively. However, after several cycles the asymptotic damping is strictly less than 1:0 using five and ten smoothing steps.... In PAGE 27: ... Hence in the two grid method the residual will be damped after four V-cycles provided B=h 0 #3C 10 18 and #17 0 is chosen such that kR 2 k L 1 #14 1=2. Experiments D,E,F in Table1 show that a residual, which has an initial L 1 -norm of size 1.0, may increase after one iteration, but after some additional V-cycles the residual is damped below its initial value.... In PAGE 29: ...1 is bounded by ~ C 1 + ~ C 2 =#0F. Experiment G in Table1 shows that this is a good estimate for #0F=h 0 #15 1=32. For the case #0F #1C h 0 ,theL 1 -norm of the residual after one V-cycle is uniformly bounded; but the experiments also show that the asymptotic residual quotient, in two consecutive V-cycles, becomes arbitrary close to 1, and hence the multigrid... In PAGE 30: ...n a post smoothing step, cf. (3.13). Therefore, we expect the damping for two V-cycles without post smoothing to be close to the damping of one V-cycle with post smoothing. This is confirmed in Table1 , experiments A,C. 7.... ..."

### Table: Damped Newton method

2006

### Table 1. Tu-144LL and Concorde aircraft characteristics.

"... In PAGE 7: ... 3). Table1 shows some Tu-144LL and Concorde characteristics. The Tu-144LL airplane incorporates a conventional wheel and column and conventional rudder pedals for pilot interface; rate feedbacks are added for damping.... ..."

### Table 4: Properties of the Motor

2000

"... In PAGE 5: ... Table 3 shows the moments of inertia of the other components attached between the beam and the motor. The motor characteristics are shown in Table4 . The damping ratio of the first-mode has been determined experimentally as 0.... ..."

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### Table 2: E ect of coupling on accuracy of SISO pole placement The characteristic equations for the remaining degrees of freedom can be obtained in a manner similar to the pitch and x loops. Since these loops are uncoupled, the design equations are exact. The compensator parameters as a function of damping ratios and natural frequencies are given by, P z = !2 zIc ? KBx

"... In PAGE 7: ... On the LAMSTF system this requirement was easily achieved. Table2 shows design versus actual closed loop eigenvalues when the pitch and x loops are closed indepen- dently then analyzed as a coupled system. In each case the desired pole locations for the pitch and x modes were equal.... In PAGE 7: ... In each case the desired pole locations for the pitch and x modes were equal. Table2 shows that the pole placement is inaccurate for low frequencies, but is reasonably accurate for frequencies above 75 rad/s, as expected. The table also shows very little variation between design and actual pole location for changes in... ..."

### Table 1: Damped MUSIC algorithm

"... In PAGE 7: ... In this case, we can search for signal vectors that are most closely orthogonal to the noise subspace. Hence, sk can be obtained by nding the peak of the following DMUSIC spectrum P (s) = 1 rH r (s)(PJ k=K+1 v kvT k ) rr(s) (19) where rr = rr k rr k: (20) The algorithm is summarized in Table1 . The algorithm discussed above is called the damped MUSIC (DMUSIC) algorithm.... ..."