### Table 1: Loop classi cation.

"... In PAGE 14: ... 4. SUMMARY AND DISCUSSION Our results are summarized in Table1 . Based on the visibilities in di erent lines, and morphology, more than ten well-resolved loops have been classi ed into four groups.... ..."

### Table 4. Zeroth (wk;0) and rst (wk;1) order semiclassical ap- proximations to the eigenvalues of the circle billiard, obtained simultaneously by harmonic inversion of a 3 3 cross-correlated signal of length smax = 150. The nearly degenerate eigenvalues at w 11:0andw 13:3 are well resolved.

2000

"... In PAGE 17: ... By harmonic inversion of the cross-correlated signal, we obtained simultaneously the semiclassical eigenvalues, their rst order order cor- rections, and the semiclassical matrix elements of the op- erator r. The results for the zeroth order approximations wk;0 to the eigenvalues and the rst order approximations wk;1 = wk;0 + wk;1 are presented in Table4 . For com- parison the exact and the EBK eigenvalues are also given.... ..."

### Table 1 Relative volumes of the polytopes described in the text. The absolute volume is that computed in Fourier transform (i.e. q-) space

2007

"... In PAGE 2: ... Now, computing dimensions shows that a ran- dom site-pattern frequency vector has a non-zero probability of being non-identifiable, which raises the question of the relative volumes of a given tree polytope and the non- identifiable polytopes. This question is answered by computer calculations for the quartet case in Table1 . We also show that surprisingly well-resolved trees sit inside the phylo- genetic mixture polytope for the star tree (Proposition 22).... ..."

### Table 3 Error of the deformation in the L2-norm (column 2 in Table 1) D 45 D 22:5 D 0 DC22:5 DC45

"... In PAGE 7: ...uch less than O.h/. Tables 3(a), 4(a), and 5(a) show the numerical results for the quantities listed in columns 2, 3, and 4 of Table 1. For the L2-error of the deformation in Table3 (a), we observe nearly linear convergence for all angles , which is significantly better than the theoretically predicted rate of O.h1=8/, see Table 1.... In PAGE 13: ... Tables 3(e) and 4(e) exhibit slightly better convergence rates than predicted in Table 1. On the one hand, the absolute values for the error in the deformation in Table3 (e) are slightly higher than for the previous elements due to the wider laminates. On the other hand, the values for the error in the deformation gradient in laminate direction in Table 4(e) are significantly smaller than before, which are well-resolved.... ..."

### Table 1: Speedup and FPGA size for critical loops.

"... In PAGE 3: ... FPGA Size and Speedup 3.1 Experiments Table1 summarizes the benchmarks and our hardware/software partitioning results. The Cycles column displays the total number of software cycles the benchmarks required without any partitioning.... In PAGE 5: ...1x with 25,000 gates. A second observation we might make from the data in Table1 and Figure 2 is that most speedup is obtained by moving the first few critical loops to FPGA - moving additional loops yields little additional speedup improvement. To see this trend more clearly, we continued the plot of Figure 2 for the top ten loops of each benchmark, assuming the remaining loops could be ideally sped up, meaning they could be implemented to execute in hardware in zero time.... ..."

### Table 5 Error in the volume fraction 1 for ! D (column 4 in Table 1 with i D 1) D 45 D 22:5 D 0 DC22:5 DC45

"... In PAGE 7: ...h1=8/, see Table 1. However, the L2-error of the deformation gradient in laminate direction in Table 4(a) as well as the approximation to the volume fraction in Table5 (a) depend crucially on the alignment of the numerical... In PAGE 13: ... On the other hand, the values for the error in the deformation gradient in laminate direction in Table 4(e) are significantly smaller than before, which are well-resolved. Finally, Table5 (e) shows that the volume fraction .!i .... ..."

### Table 2: Formulas found by PSLQ for the ten cases of Figure 1

"... In PAGE 6: ...iagrams with fewer loops. These ten cases as shown in Figure 1. In these diagrams, dots indicate particles with nonzero rest mass. The formulas that have been found, using PSLQ, for the corresponding constants are given in Table2 . The constant C = P k gt;0 sin( k=3)=k 2 .... ..."

### Table 3. Results of Example 7.1 ( =h = 0:32, M = 32).

1999

"... In PAGE 21: ... con rms the O( =h) estimates given in x6.1 and (5.26). In this case, the linear and oscillatory boundary conditions of i lead to the similar accuracy. Moreover, we note that in Table3 , the ratio =h is of order 1, well beyond the validity regime for the asymptotic expansion. Still, the error is rather small.... In PAGE 22: ... In contrast, the LFEM resolves the smallest scale with hs. The comparison in Table3 indicates that the MFEM can produce fairly good results when the well resolved solutions are not obtainable due to practical limitation of computer memory. This makes the MFEM very useful in practice.... ..."

Cited by 23

### Table 9. Results of Example 7.5: l2 norm error (umax 1:73).

1999

"... In PAGE 26: ... It can be seen that a(x; y) oscillates more rapidly as x or y becomes close to 0:5. In the calculations presented in Table9 , we have used P = 1, and = 0:025, so the smallest scale of the problem is about 0:005. Again, we use LFEM to obtain a well resolved solution.... In PAGE 26: ... In this regard, it is most relevant to test the performance of the method when h is su ciently large compared to . In the computations shown in Table9... ..."

Cited by 23

### Table 4 Error of the deformation gradient in laminate direction in the L2-norm (column 3 in Table 1) D 45 D 22:5 D 0 DC22:5 DC45

"... In PAGE 7: ...h1=8/, see Table 1. However, the L2-error of the deformation gradient in laminate direction in Table4 (a) as well as the approximation to the volume fraction in Table 5(a) depend crucially on the alignment of the numerical... In PAGE 13: ... On the one hand, the absolute values for the error in the deformation in Table 3(e) are slightly higher than for the previous elements due to the wider laminates. On the other hand, the values for the error in the deformation gradient in laminate direction in Table4 (e) are significantly smaller than before, which are well-resolved. Finally, Table 5(e) shows that the volume fraction .... ..."