### Table 2: The Relation N for the Amalgamation

1996

"... In PAGE 11: ... A special subset of the terms is taken as the set of names of amalgamated language strings. These terms consist of the elementary names plus the struc- tural terms identified by Table2 . Table 2 defines the structural portion of the naming relation of the amalgamation for definite metalogic programs.... In PAGE 11: ... In the table we have used the shorthand sn(0) for n applications of the function symbol s to 0. In Table2 the entries for clauses are marked with a star. This is to indicate that these names are subject to the following restriction: No clause can be a defining clause for demo or for names.... In PAGE 13: ... Clearly, (N E) is acyclic. If it is also functional then from Table2 is is easy to see that N also satisfies these properties. Our elementary name assumption identifies a subset of the constant symbols to be used as primitive names.... ..."

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### Table 2: Results of amalgamation obtained for the problem NET3 using di erent thresholds on a SPARC-10 workstation.

"... In PAGE 4: ... We now consider the test problem NET3 to study the behaviour of EBE preconditioning in terms of number of iterations and its performance using di erent amalgamation thresholds. The results are presented in Table2 . In this table, the average density is de ned to be the ratio d = Pp i=1 nzi Pp i=1 s2 i ; (7) where p is the number of elements, nzi is the number of non-zero entries in the element i, and si is the size of the ith element.... In PAGE 4: ... Here, the time spent in the solves (Time for solves) only refers to the solution steps on the preconditioner and excludes the time of matrix-vector products and other cg-related operations (such as dot products). This is simply so that we can compare the results of Table2 for the dense storage scheme with those in the next section where we consider sparse storage. As matrix-vector products and dot-products are performed in the same way in both cases | using the dense initial elements, the construction time and the time spent are the more meaningful parameters to be compared.... In PAGE 7: ... The density of the elements decreases with the threshold. If we compare the times obtained here with the ones in Table2 , we observe that sparse storage becomes more e cient than dense storage for threshold values smaller than -0.00012, which corresponds to a density smaller than 0.... ..."

### Table 1: Summary of the characteristics of each test problem Some important characteristics are: the condition number , which gives an idea of the di culty of the problem, the sizes of the elements; larger elements often encourage faster execution rates, the degree of overlap which characterizes the structure of a problem in terms of overlap between elements. It is de ned as the average number of elements sharing each variable and is an indicator as to how well element-by-element preconditioners will behave on the problem. We now describe the two amalgamation strategies that will be compared.

"... In PAGE 2: ... It o ers considerable scope for parallelism, both in the construction of the preconditioner and during the matrix- vector product and solves that occur during the conjugate gradient calculations. We describe in Table1 a set of test matrices that will be used in our experiments.... ..."

### Table 1. Exceptional Amalgams

"... In PAGE 1: ...In [3] used the most di cult and interesting case of Tro mov apos;s theorem [4] to extend the classi cation to the case n 3. It turned out that besides two in nite series of locally projective amalgams (embedded into the a ne linear groups AGL n (2) and into the orthogonal linear groups O + 2n (2)) there are exactly twelve exceptional ones as in Table1 . Some of the exceptional amalgams are embedded into sporadic simple groups M 22 , M 23 , Co 2 , J 4 and BM.... ..."

### Table 8: Products Information Structure

1994

"... In PAGE 35: ... The products information structure is included in this description of the information base, as it is integral to disseminating information about the results of research projects. Table8 identifies the key contents and linkages of the products information structure. Although represented in Figure 2a, no HTML template for the products information structure is contained in Appendix A because of the variability of types of information that could be presented in this structure.... ..."

### Table 1. Exceptional Amalgams

2004

### Table 2. Structure of the Reverse Engineering Projects Product Process Product operation and

"... In PAGE 3: ... Finally, they implement and monitor the process and propose improvements to their designs. Table2 summarizes the structures of the reverse product and process engineering projects. Table 2.... ..."