### Table 7: A comparison between two di erent rankings of problem solving modules for elliptic PDEs. The third and fth columns give the subjective rankings made in an earlier study. The fourth and sixth columns give those inferred by our knowledge methodology. The very high correlation between these rankings is readily seen. [MF90] S. Muggleton and C. Feng. E cient induction of logic programs. In S. Arikawa, S. Goto, S. Ohsuga, and T. Yokomori, editors, Proceedings of the First Inter- national Conference on Algorithmic Learning Theory, pages 368{381. Japanese Society for Arti cial Intelligence, Tokyo, 1990. [OWA+98] C. Olston, A. Woodru , A. Aiken, M. Chu, V. Ercegovac, M. Lin, M. Spalding, and M. Stonebraker. Datasplash. In Proceedings of the ACM-SIGMOD Confer- ence on Management of Data, pages 550{552, ACM, New York, NY, 1998. [RHD81] J. R. Rice, E.N. Houstis, and W.R. Dyksen. A population of linear, second order, elliptic partial di erential equations on rectangular domains. Mathematics of Computation, 36:475{484, 1981.

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"... In PAGE 15: ... This shows that these simple rules capture much of the complexity of algorithm selection in this domain. Table7 compares these results. There were several other interesting inferences drawn.... ..."

Cited by 1

### Table 4.4: Rendering times on Intel cluster. These runs were computed with parameters identical to table 4.3 and are directly comparable. In every respect the performance was slightly better than on the SP2. These results have been reported in publications [24, 26].

### Table 2. Access statistics for the learn Greek online course, July 19, 1998, to December 31, 2000

"... In PAGE 4: ...http://www.wusage.com) . Table2 represents the overall access statistics for the 30 - month period. Table 2.... ..."

### Table 1: Main IT learning theories

"... In PAGE 2: ... These theories provide important insights into the problems and opportunities asso- ciated with teaching IT and using IT to teach other subjects. A brief summary of these theories is pro- vided in Table1 , which leaves out the last two theories, namely minimalist theory (Carroll, 1990; 1998) and andragogy theory (Knowles, 1975; 1984, 1984b), from which key principles are implemented in our course. These two theories are reviewed separately and in more detail below with an emphasis on key ... ..."

### Table 1. Number, percent distribution, and annual rate of outpatient department visits with corresponding standard errors by selected patient and hospital characteristics: United States, 1998

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### Table 1: Key elements in learning environments (Summer, amp; Taylor, 1998; Scott, amp; Phillips, 1998)

"... In PAGE 2: ... Key Elements in a Learning Environment A modern learning environment needs to be more than a study guide in computer format. Here we dis- cuss the key elements in a modern learning environment that takes advantage of information technology ( Table1... ..."

### Table 4.3: Results of an initial study on the SP2. In all of these runs the naive strategy was used for the initial mapping followed by algorithm 1. This study revealed the existence of errors in the original distributed algorithm for termination detection. These errors showed up the runs on 128 and 256 computers, where they caused a slowdown rather than a speedup. These results have been reported in publications [24, 26].

### Table 2: Bounds (10), (12), (14), (24), and (26) for Examples 4, 5, 6, and 14.

"... In PAGE 20: ... A Comparison In this appendix we tabulate a brief comparison of some of the upper and lower bounds derived in the body of this paper. Table2 reports bounds (10), (12), (14), (15), (24), and (26) for Examples 4, 5, 6, and the following engineering application. Example 14 The simpli ed, linearized model of a two-dimensional, three-link mobile manipulator derived in [25] is a linear, time invariant descriptor control system E _ x = Ax + Bu y = Cx: The explicit data listed in [25] are E = 2 4 I3 0 0 0 M0 0 0 0 0 3 5 ; A = 2 4 0 I3 0 ?K0 ?D0 FT 0 F0 0 0 3 5 ; B = 2 4 0 S0 0 3 5 ; and C = 2 4 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 3 5 ; where M0 = 2 4 18:7532 ?7:94493 7:94494 ?7:94493 31:8182 ?26:8182 7:94494 ?26:8182 26:8182 3 5 ; D0 = 2 4 ?1:52143 ?1:55168 1:55168 3:22064 3:28467 ?3:28467 ?3:22064 ?3:28467 3:28467 3 5 ; K0 = 2 4 67:4894 69:2393 ?69:2393 69:8124 1:68624 ?1:68617 ?69:8123 ?1:68617 ?68:2707 3 5 ; S0 = 2 4 ?0:216598 ?:033806 0:554659 0:458506 ?0:845154 0:386648 ?:458506 0:845153 0:613353 3 5 ; F0 = 1 0 0 0 0 1 : For Table 2 we applied the bounds to (A; E) for the open-loop pencil A ? E.... In PAGE 20: ... Table 2 reports bounds (10), (12), (14), (15), (24), and (26) for Examples 4, 5, 6, and the following engineering application. Example 14 The simpli ed, linearized model of a two-dimensional, three-link mobile manipulator derived in [25] is a linear, time invariant descriptor control system E _ x = Ax + Bu y = Cx: The explicit data listed in [25] are E = 2 4 I3 0 0 0 M0 0 0 0 0 3 5 ; A = 2 4 0 I3 0 ?K0 ?D0 FT 0 F0 0 0 3 5 ; B = 2 4 0 S0 0 3 5 ; and C = 2 4 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 3 5 ; where M0 = 2 4 18:7532 ?7:94493 7:94494 ?7:94493 31:8182 ?26:8182 7:94494 ?26:8182 26:8182 3 5 ; D0 = 2 4 ?1:52143 ?1:55168 1:55168 3:22064 3:28467 ?3:28467 ?3:22064 ?3:28467 3:28467 3 5 ; K0 = 2 4 67:4894 69:2393 ?69:2393 69:8124 1:68624 ?1:68617 ?69:8123 ?1:68617 ?68:2707 3 5 ; S0 = 2 4 ?0:216598 ?:033806 0:554659 0:458506 ?0:845154 0:386648 ?:458506 0:845153 0:613353 3 5 ; F0 = 1 0 0 0 0 1 : For Table2 we applied the bounds to (A; E) for the open-loop pencil A ? E.... In PAGE 21: ...Table 2: Bounds (10), (12), (14), (24), and (26) for Examples 4, 5, 6, and 14. In Table2 , the bound (14) requires a choice of Q and Z in the generalized Schur decomposition. For Examples 4, 5, and 6 we used Q = Z = I, because in these three examples E and A are already upper triangular.... ..."