### Table 6.2. Accuracy of approximation of the h- and p-version to functions of r - and r log r-type based on Sobolev, Besov and weighted Besov spaces h version p version

Cited by 5

### Table 3. Convergence rates for the ux in example two. References 1. D. Adams, Sobolev Spaces, Academic Press, New York, 1975.

1994

Cited by 5

### Table 1: 7 and 9-tap Sobolev-optimal QMF lowpass lters.

"... In PAGE 8: ... We obtained this minimax solution by a search of the two-parameter space; deeper mathematical analysis of the saddle point behavior is in order. This approach yields a new family of QMFs; the 7- and 9-tap examples are given in Table1 below. The 9- tap Sobolev-optimal QMF is quite distinct from the 9-tap QMF of Adelson-Simoncelli1; its frequency response is plotted in Figure 1, while pictures comparing the corresponding scaling and wavelet functions are shown in Figure... ..."

### Table 2. Atom Types and Contact Weights of the Binary-Surface Complementarity Function.a

"... In PAGE 3: ...19 A pairwise interaction between atoms of different classes is considered as either favorable (weight of H110021) or unfa- vorable (weight of H110011). A description of the classes and the weights is given in Table2 . Interaction with the solvent was optimized using a genetic algorithm and a weight of 2 was ob- tained, as will be described.... In PAGE 6: ... (2)]. The binary pair-wise weight parameters were applied ( Table2 ) and the ASPs at this stage were fixed at H110011. A genetic algorithm program was used then to calibrate the coeffi- cients Kvol, Kprob, and Ksol.... In PAGE 6: ...23 1.309 aThe eight atom types of Table2 were clustered into four groups as shown. The 10 most-fit ASP sets that were generated are presented.... In PAGE 8: ... (3)]. The number of ASPs was reduced from 8 to 4 by separately grouping the three hydrophilic and three neutral classes in Table2 . Optimi- zation of the resulting ASPs produced a small reduction (1.... ..."

### Table 3: Approximation schemes and corresponding functions spaces with the same rate of convergence O(n12 ). The function in the standard sigmoidal function, the function jxj+ in the third entry is the ramp function, and the function Gm in the fth entry is a Bessel potential, that is the Fourier Transform of (1+ksk2)?m2 (Stein, 1970). H2m;1(Rd) is the Sobolev space of functions whose derivatives up to order 2m are integrable (Ziemer, 1989).

1995

Cited by 243

### Table 4: Weighted Time and Space Averages Based on File Type Frequencies

1993

"... In PAGE 9: ... For example, a small, quickly generated index would not be a reasonable tradeoff if one could not use this index to locate desired data. Second, aggregate measure- ments (as given in Table4 ) are affected by the dis- tribution of different file types in the sample file sys- tems. Ideally, we would have measured each index- ing system against the same file system data.... In PAGE 10: ... This machine is approximately one-third as fast as the Sun 4/280. Table4 shows that Essence can index data fas- ter than WAIS. Taking into account the slower machine on which SFS was measured, SFS appears to index data somewhat faster than Essence does.... ..."

Cited by 36

### Table 4: Weighted Time and Space Averages Based on File Type Frequencies

1993

"... In PAGE 9: ... For example, a small, quickly generated index would not be a reasonable tradeoff if one could not use this index to locate desired data. Second, aggregate measure- ments (as given in Table4 ) are affected by the dis- tribution of different file types in the sample file sys- tems. Ideally, we would have measured each index- ing system against the same file system data.... In PAGE 10: ... This machine is approximately one-third as fast as the Sun 4/280. Table4 shows that Essence can index data fas- ter than WAIS. Taking into account the slower machine on which SFS was measured, SFS appears to index data somewhat faster than Essence does.... ..."

Cited by 36

### Table 4: Weighted Time and Space Averages Based on File Type Frequencies

1993

"... In PAGE 9: ... For example, a small, quickly generated index would not be a reasonable tradeoff if one could not use this index to locate desired data. Second, aggregate measure- ments (as given in Table4 ) are affected by the dis- tribution of different file types in the sample file sys- tems. Ideally, we would have measured each index- ing system against the same file system data.... In PAGE 10: ... This machine is approximately one-third as fast as the Sun 4/280. Table4 shows that Essence can index data fas- ter than WAIS. Taking into account the slower machine on which SFS was measured, SFS appears to index data somewhat faster than Essence does.... ..."

Cited by 36

### Table 8: Vector space model. Search Term Weight

2002

Cited by 5