### Table2 Description of three-dimensional meshes.

"... In PAGE 6: ... In short, we made these meshes havevery small #28and hence many#29 elements along lines that would result in a split into pieces of roughly equal size. Most meshes in Table2 were obtained from tetrahedralization of objects such as an aircraft #0Dap, or of a domain enclosed between two spherical sections. Twoof the meshes in Table 2, #5Csphere 5 quot; and #5Csphere 6 quot;, are surface triangulations of three dimensional objects.... In PAGE 6: ... Most meshes in Table 2 were obtained from tetrahedralization of objects such as an aircraft #0Dap, or of a domain enclosed between two spherical sections. Twoof the meshes in Table2 , #5Csphere 5 quot; and #5Csphere 6 quot;, are surface triangulations of three dimensional objects. Observe that meshes in the test suite are highly graded and irregular, with element sizes that vary by factors larger than 1000 in the L 1 norm.... ..."

### Table 1: The number of iterations of the parallel domain decomposition algorithm required to solve a typical three-dimensional convection-diffusion problem in [12].

"... In PAGE 5: ... Furthermore, it is applied to a class of convection- diffusion equations in three dimensions that is not covered by the underlying theory in [3]. Nevertheless, it proves to be surprisingly robust, as illustrated by the iteration counts shown in Table1 that are typical of the results in [12]. Furthermore, very creditable parallel performances are recorded, including parallel speed-ups in excess of 12 when using locally refined ... In PAGE 5: ...Table 1: The number of iterations of the parallel domain decomposition algorithm required to solve a typical three-dimensional convection-diffusion problem in [12]. The iteration counts shown in Table1 illustrate that the number of iterations of the parallel solver that are required to obtain a converged solution is essentially independent of the level of the finest mesh and the number of subdomains used. Hence, provided the sequential solver used on each processor (at step 4 of the algorithm in Figure 4) has a computational cost of O(N), the total cost of the parallel algorithm will also be approximately proportional to N.... ..."

### Table 3. Guidelines for positioning atmosphere content in the three-dimensional model space of warmth, activity, and attention Factor Lights Audio Video

"... In PAGE 9: ... A video artist was involved in creating video material for the atmosphere model. The guidelines listed in Table3 were used to select and design the media content for the model, but they should only be considered as rules of thumb, since they are based on the results of the rating sessions for the mood boards. The resulting model space was validated by users.... ..."

### Table 3. Three-dimensional K-optimal lattice rules

"... In PAGE 7: ... One sets NL = NU = Nopt. The list of rules in Table3 was obtained as follows. For each value of ,thesearch module was used with NU large and NL =max(NME(3; );NCL(3; )) as given in (1.... In PAGE 7: ... Finally, the list of matrices was processed to remove all symmetric equivalents. Note that, without the second run, one of the entries for each of = 5 and 11 in Table3 would have been missed. The 4-octahedron has eight facet-pairs.... In PAGE 12: ....2. Three-dimensional lattice rules. For every abscissa count we have listed, we have speci ed at least one cubature rule. Table3 contains speci cations of thirty- one K-optimal rules. This list is complete in the sense that every K-optimal rule of enhanced degree thirty or less is included here or is symmetrically equivalent to one listed here.... ..."

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### Table 1: An example of a three-dimensional table.

1993

"... In PAGE 3: ...Table1 has three categories, D1, D2 and D3; thus, it is a three-dimensional table. The logical relationship among the data items of a table is the association between labels and entries.... In PAGE 3: ... Each entry is associated with one or more sets of labels of di erent categories simultaneously. For example, in Table1 , entry e1 is associated with a set of labels fd11; d21; d311g simultaneously; entry e7 is associated with both fd12; d21; d312g and fd12; d22; d312g simultaneously. The data items and the logical relationship among them provide the logical structure of the table, which is the primary information that a table conveys and which is independent of its format.... In PAGE 6: ... This function guarantees that every entry in E is mapped from at least one ff1; ; fng 2 D1 n. Using this model, Table1 can be abstracted by (3; fD1; D2; D3g; E; ), where D1 = fd11; d12g D2 = fd21; d22; d23g D3 = fd31; d32g d31 = fd311; d312g d11 = d12 = d21 = d22 = d23 = d32 = d311 = d312 = fg E = fe1; e2; e3; e4; e5; e6; e7; e8; e9g (fD1:d11; D2:d21; D3:d31:d311g) = e1; (fD1:d11; D2:d21; D3:d31:d312g) = e2; (fD1:d11; D2:d22; D3:d31:d311g) = e3; (fD1:d11; D2:d22; D3:d31:d312g) = e3; (fD1:d11; D2:d23; D3:d31:d311g) = e4; (fD1:d11; D2:d21; D3:d32g) = e5; (fD1:d11; D2:d22; D3:d32g) = e5; (fD1:d11; D2:d23; D3:d32g) = e5; (fD1:d12; D2:d21; D3:d31:d311g) = e6; (fD1:d12; D2:d21; D3:d31:d312g) = e7; (fD1:d12; D2:d22; D3:d31:d312g) = e7; (fD1:d12; D2:d23; D3:d31:d312g) = e8; (fD1:d12; D2:d21; D3:d32g) = e9; (fD1:d12; D2:d22; D3:d32g) = e9; (fD1:d12; D2:d23; D3:d32g) = e9; 4.2 Basic operators in the tabular model We rst describe the syntax of all basic operators in function form by giving the operator identi ers and the types of their operands and results.... ..."

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### Table 2 Three-dimensional structures of ribosomal proteins

1998

"... In PAGE 14: ... Someday, useful information may be gained by building these structures into low-resolution ribosome mod- els. Table2 lists the structures available, and Figures 6 and 7 display their topologies. Several conclusions have already emerged.... ..."

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### Table 14. Parameters used in MOC3D simulation of three-dimensional transport from a point source with flow in the x-direction and flow at 45 degrees to x and y

"... In PAGE 63: ... Because advective transport occurs only in the x-y plane, the number of layers was held constant at 24. The input parameters for the simulations are presented in Table14 , which includes the several different values used for grid dimensions and spacing. The results for both the analytical and numerical solutions for the case in which flow occurs only in the x-direction are shown in figure 30.... ..."

### Table 3. An algorithm for realizing ternary Shannon expansion of ternary functions in three- dimensional lattice circuits.

"... In PAGE 8: ... 3.3 An algorithm for the expansion of ternary functions into three- dimensional lattice circuits This Section introduces, as an example, an algorithm in Table3 for realizing ternary Shannon expansion of ternary functions in three-dimensional lattice circuits using the joining method that was proposed in Theorem 1. This algorithm is developed for the following convention: in the octant (sub- space) that corresponds to the positive x-axis, positive y-axis, and positive z-axis: (1) expand the nodes in-to-out and (2) join the cofactors counter clock wise (CCW).... ..."

### Table 4. Sales Summary (a) two dimensional cross-tab, (b) three dimensional cross-tab

1997

"... In PAGE 14: ...Table 4. Sales Summary (a) two dimensional cross-tab, (b) three dimensional cross-tab The structure of the result in Table4... In PAGE 15: ... To let a user easily express a roll-up or a cross-tab query, the following extension to the SQL GROUP BY was proposed in [20]. GROUP BY f ( lt;column name gt; j lt;expression gt; ) [ AS lt;correlation name gt; ] [ lt;collate clause gt; ], : : : g [ WITH ( CUBE j ROLLUP ) ] Using this SQL-extension to generate Table4 (a) results in SELECT Product type, Year, Color, SUM(Sales) FROM Sales WHERE Product type = \BIKE quot; AND Year BETWEEN 1994 AND 1995 GROUP BY Product type, Year, Color WITH CUBE; This leads to further questions. First, how to transform the relational results by CUBE or ROLLUP operators to the multidimensional forms? In the architecture we proposed, this task should be performed by the Application Interface Layer.... ..."

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### Table 6. Peak heap use (in K bytes) for Haskell versions with three-dimensional intermediate forms

1997

"... In PAGE 15: ... All the programs were compiled with -O optimization. Table6 shows the peak heap consumption of the Haskell codes that use three- dimensional intermediate arrays, and table 7 shows the same information for the matrix-of-vectors codes. These tables also compare the Glasgow and Chalmers com- pilers.... ..."

Cited by 6