### Table 4. Central weights and confidence factor (pc).

"... In PAGE 13: ... Thus any of the alternatives could be chosen with rather varying weights. Very small confidence factors for alternatives S4, S13, S16, S22 and S40 ( Table4 ) indicate that the values of the first rank acceptability indices for these alternatives are mainly created by the uncertainty in the criteria values. Without more accurate information, these alternatives are not potential candidates for the most preferred solution.... ..."

### Table 3: Design Results for Rectangular Panel without Central Hole

2003

"... In PAGE 26: ... The density of the mesh was determined by parameter studies intended to estimate the minimum number of elements needed to accurately model the stiffness and stress variation without requiring excessive computation time. Results for the panel without a central hole are shown in Table3 for both the original design technique that used the Rayleigh-Ritz solver along with the Laminate Definition Tool as well as the present STAGS solution. Relative increases with respect to the earlier design results are also tabulated.... ..."

### Table 1. Summary of the astrometric solutions.

689

"... In PAGE 2: ... Solution (A) in which the proper motions of all members were con- sidered the same (except for a projection e ect de- scribed by van Leeuwen amp; Evans 1997), and solu- tion (B) where for the central eld the proper mo- tions from the Hipparcos solution were replaced by the proper motions from the ground-based solution. Contrary to the expectations, the second solution is of slightly lower quality than the rst, as indicated by the unit weight standard deviation (uwsd), but overall the results are very similar, as can be seen in Table1 . In both cases the distance of the cluster is found to be 116 pc and the accuracy of the par- allax about 2.... ..."

### Table 3.1: Central extensions of A Proof It follows from the previous lemma that to classify all the central extensions up to equivalence, we may (and we will) restrict ourselves to clas- sifying the simple solutions to (3.2). In what follows m denotes a primitive mth root of 1. Type A Q = I and the de ning equations for A are f1 = cx2 1 + ax2x3 + bx3x2

1996

Cited by 1

### Table 7: Central-di erence results using exact equidistribution of ~ u.

"... In PAGE 17: ... The improved rate of convergence on the equidistributed grids leads to an improved solution accuracy for large N. Finally, Table7 and Figure 3 show the results obtained using the standard second- order central-di erence method on the non-uniform grid (2.10).... ..."

### Table B.1: Comparing the two potential functions on the Satis ability problem To get an idea what a nal unrounded solution may look like, see Figure B.1; this solution is obtained after one iteration. We observe that a lot of variables already approach ?1 or +1, when we compare it to the interior solution of an instance of the RLFAP after one iteration (Figure B.2). This seems to be due to the di erence in starting points: for the satis ability problem we can use a starting point that lies central in the feasible region, while for the RLFAP the starting point is far away from any feasible solution.

### Table 4 Values of a ten year convertible bond which is continuously callable and pays a 5% coupon semi- annually. The solutions were calculated on successively ner meshes using central weighting with = 1 2. The normalized execution times were obtained by using the coarse grid (425 nodes and t = 0:125) execution time as the base time.

"... In PAGE 19: ....2. Convertible Bonds. Results for a ten year convertible bond which is con- tinuously callable with parameters outlined in Table 3 are contained in Table4 . The bond pays a 5% coupon semi-annually.... In PAGE 19: ... Consequently, central weighting with = 1 2 was used to obtain the solutions. Table4 demonstrates that a solution that is no more than $0:10 away from the converged solution can be obtained with a relatively coarse grid. Figure 6 contains a plot of the convertible bond values.... In PAGE 21: ... The solutions were calculated on successively ner meshes using the van Leer ux limiter. The normalized execution times were obtained by using the coarse grid (425 nodes and t = 0:125) execution time, when central weighting was used (see Table4 ), as the base time. 9 0 9 5 1 0 0 1 0 5 B o n d v a l u e 10 20 30 40 50 60 S 0 0.... In PAGE 22: ....3. Two Asset Options. Results for American put options on the worst of two assets are contained in Table 6. As was the case with the Asian option results (Table 2) and convertible bond results ( Table4 ), the results in Table 6 were obtained by succes- sively re ning a regular triangular mesh (see Figure 7). That is, the number of nodes along both axes were doubled for each successive run.... ..."

### Table 2: American put options on the worst of two assets when r = 0:05, S1 = S2 = 0:30, = 0:5, T ? t = 0:5, and S1 = S2 = 40. The solutions were computed using the modi ed van Leer ux limiter on successively re ned meshes (both regular and irregular). In addition, solutions were also computed using central weighting on successively re ned irregular meshes. The normalized execution times were obtained using the coarse grid (2664 nodes and t = 0:02) execution time (when the ux limiter was used) as the base time.

1999

"... In PAGE 19: ... 0:006% of the exercise price away from the analytic solution for the cases considered) can be obtained using a mesh with a relatively small number of nodes. Table2 contains the values of American put options on the worst of two assets with six months until maturity computed using three alternative schemes: i) the ux limiter (72) on a regular mesh; ii) the ux limiter on an irregular mesh; and iii) central weighting on an irregular mesh. This case di ers from the European case above because the early-exercise constraint (14) is being imposed.... In PAGE 19: ... In this context, the initial irregular mesh (similar to the mesh in Figure 4, but with 2664 nodes) was re ned by inserting nodes only near the exercise price. Table2 indicates that an irregular mesh can be used to price options to within $0:01 with an order of magnitude less computation time, relative to when a regular mesh is used. The table also shows that... ..."

### Table 6: Values of a ten year convertible bond (at T ? t = 10:0) which is continuously callable and pays a 5% coupon semi-annually. The solutions were calculated on successively ner irregular meshes using centroid control volumes and the modi ed van Leer ux limiter. The normalized execution times were obtained by using the coarse grid (2698 nodes and t = 0:125) execution time (when central weighting was used (see Table 5)) as the base time.

1999

"... In PAGE 24: ... The values in Table 5 were computed using central weighting and irregular meshes (similar that in Figure 4) with centroid control volumes. Table6 contains values obtained using ux limiting scheme (72) with centroid control volumes on the same irregular meshes used when the solutions were computed using central weighting. Unlike the solutions above for American put options, there is a noticeable di erence here between central weighting and the ux limiting scheme (72), with the ux limiter appearing to be more slowly convergent.... ..."

### Table 2: Results Comparing Coordination Keys to Exhaustive and Optimal Centralized Schedule Generation

"... In PAGE 6: ...Table 2: Results Comparing Coordination Keys to Exhaustive and Optimal Centralized Schedule Generation algorithm to the centralized scheduler and is less of an issue when comparing different distributed algorithms. Table2 presents the results of comparing the coordination key al- gorithm to the optimal and exhaustive centralized scheduler. Each row is the statistical aggregation of one set of trials where each set of trials is drawn from one difficulty class.... In PAGE 6: ... In all cases the median percentile is 100% and the standard de- viation is low. Because there are generally multiple solutions that perform as well as the solutions actually generated by the coordina- tion keys, its percentile is broken down in the last three columns of Table2 . The column marked %-tile Same indicates the mean % of possible solutions that miss exactly as many deadlines as the keys algorithm did.... ..."