### Table 6. Resonances of H0, n = 0; 1

"... In PAGE 21: ...ig. 3) while their zeros remain the same. Given a certain number n we watch n changing as increases and compare this eigenvalue with its rst order approximation (see (8)). It is seen from Table 8 that only for a narrow range of do the per- turbation theory formulae (8) approximate actual eigenvalues (com- pare to Table6... ..."

### Table 8. Eigenvalues of H , n = 10; 30

"... In PAGE 21: ...ig. 3) while their zeros remain the same. Given a certain number n we watch n changing as increases and compare this eigenvalue with its rst order approximation (see (8)). It is seen from Table8 that only for a narrow range of do the per- turbation theory formulae (8) approximate actual eigenvalues (com-... ..."

### Table 1. January, July, and Annual mean photochemical per- turbation [%] by dust of NH, SH, and Global O3 and OH.

2003

"... In PAGE 5: ..., 2003]. Table1 lists the mean January, July and annual changes in O3 [%] and OH [%] due to light scattering and absorption by dust. The amplitude of the O3 perturbation in July in the Northern Hemisphere (NH) is much larger than the South- ern Hemisphere (SH) perturbation.... ..."

Cited by 3

### Table 4. Global average indirect aerosol forcing from different per- turbation cases.

2005

"... In PAGE 8: ... 5. Table4 gives the forcing from each of the cases and Fig. 6 shows the change in global average forcing from the reference case.... ..."

### Table 1: Comparison of Infeasible Point Algorithm (IPM) with Local Minimiza- tion (LM) with a starting point equal to global solution with % 75 percent per- turbation to each coordinate

1997

"... In PAGE 11: ... The minimizations using limited memory BFGS were halted when the relative norm of the gradient was reduced to 10?8. In Table1 , the results of the numerical experiments are summarized. We record the number of times each algorithm nds the putative global minimum versus the number of attempts, and the mean energy at the so- lution for each algorithm.... ..."

Cited by 4

### Table 3: Gradients of CL, CD,andCMo due to per- turbations in cruise angle-of-attack (X = ). The nite di erence values are computed from aeroelas- tic analyses at =3:5 (nominal condition) and =4:0 . The gradients are in units of 1=deg.

1999

### Table 7: Gradients of CL, CD,andCMo due to per- turbations in the leading edge sweep angle (X = LE). The nite di erence values are computed from aeroelastic analyses at LE =74:0 (nominal condi- tion) and LE =76:0 . The gradients are in units of 1=deg.

1999

"... In PAGE 14: ... After solving the GSE for the total sensitivity terms dF=d LE and d =d LE, gradients of the aero- dynamic coe cients were estimated using Equation 45. These gradients are listed in Table7 . Taylor Se- ries approximations for CL, CD,andCMo forasweep angle of 76:0 are listed in Table 8.... ..."

### Table 3: Avg. denotes the average perturbation size, max. denotes the maximum per- turbation size, var. denotes the perturbation variance, p time denotes the time of the perturbation (in seconds) and t time denotes the total (perturbation and DCEL construc- tion) time (in seconds). All the given results are from averaging the results of 5 tests for each input.

2003

"... In PAGE 27: ...n R M grid 320 10 140 flower 40 100 100 rand sparse 40 20 100 rand 100 100 49 100 rand 1000 1000 100 1000 rand 2000 2000 100 1000 rand 10000 10000 35 1000 Table 2: n denotes the number of circles, R denotes the maximum radius and M is the maximum input size minus . of the perturbation and running times for those inputs are give in Table3 (all the given results are from averaging the results of 5 tests for each input), with the IEEE double number type and the bound quot; computed using M = 1000 and = 0:03. The tests have been performed on an Intel Pentium III 1 GHz machine with 2 GB RAM, operating under Linux Redhat 7.... ..."

Cited by 13

### Table IV summarizes some of the numerical results for the sign of k0(m): A minus sign in the position (k; m) indicates stability with respect to per- turbations with wave number k for the given value of m, while a plus sign indicates instability. The bifurcation points mk occur between adjacent m- values where the k0(m) have opposite signs. Thus, for example, m4 2 (1:320; 1:321).

### Table 2 shows the results of this experiment. The total half-perimeter bounding box wirelength is shown in the Net Len column, the average perturbation over all nets in the Avg Pert column, the root-mean-square perturbation in the RMS column, and the maximum net perturbation in the Max column. Perturbation is measured with respect to the placement of the original design. Both RMS and maximum perturbation measures characterize the distribution of per- turbation across the design.

"... In PAGE 7: ... Table2 : Placement results table. From the table, we can see that not only does our place- ment tool yield slightly better results in terms of total wire- length, but also we obtain much better results on all three perturbation metrics.... ..."