### Table 3: Computational times associated with parallel implementation of the finite element model.

2007

"... In PAGE 64: ... This ensured that the perturbed displacement data sets were still contained within the atlases. Results Parallel implementation of the Finite Element Model Table3 illustrates the computational time necessary to solve the biphasic model on a finite element mesh containing 19468 nodes and 104596 elements, using 16 processors (2.8GHz,... ..."

### Table 1. for the three tasks which dominate finite element analysis on SHPC.

"... In PAGE 2: ... Table1 : Interprocessor Communication Eliminated Although both approaches require no interprocessor communication for element generation, the element-based approach requires additional memory to store element information associated with each neighboring element. Furthermore it requires significant communication and synchronization between the processors.... In PAGE 3: ... Since the generated system of equations is distributed on each processor, there is no need to redistribute the matrix.The variable band storage scheme was selected over the skyline storage scheme to eliminate the matrix distribution time (see Table1 ). The slight increase in storage required by the variable band scheme over the skyline storage scheme does not significantly increase the computation time.... ..."

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### Table 1. for the three tasks which dominate finite element analysis on SHPC.

"... In PAGE 2: ... Table1 : Interprocessor Communication Eliminated Although both approaches require no interprocessor communication for element generation, the element-based approach requires additional memory to store element information associated with each neighboring element. Furthermore it requires significant communication and synchronization between the processors.... In PAGE 3: ... Since the generated system of equations is distributed on each processor, there is no need to redistribute the matrix.The variable band storage scheme was selected over the skyline storage scheme to eliminate the matrix distribution time (see Table1 ). The slight increase in storage required by the variable band scheme over the skyline storage scheme does not significantly increase the computation time.... ..."

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### Table 1 Matrix of finite element analyses for oC128-center cracks (five runs per model)

"... In PAGE 7: ...ipe in Fig. 2 with Rm 50:8 mm (2 in.) and t = 5.08 mm (0.2 in.). A matrix of such analyses is defined in Table1 for various combinations of the crack size, crack orientation, and material strain hardening exponent: y=p, c, and n. It involves 21 diC128erent finite element meshes with y=p 1=16, 1/8, and 1/4 and c 0, 15, 30, 45, 60, 75, and 908.... In PAGE 7: ... In this paper, a crack will be denoted as small, intermediate, and large, when y=p 1=16, 1/8, and 1/4, respectively. For each mesh, five analyses were performed using five diC128erent hardening exponents (see Table1 ). For the material properties, the following values were used: E = 207 GPa, n 0:3, s0 344:8 MPa, and a 0 for n = 1 and a 1 for n gt; 1: These values, in addition to the ones given in Table 1, provide complete characterization of the pipe material properties according to Eqs.... In PAGE 7: ... For each mesh, five analyses were performed using five diC128erent hardening exponents (see Table 1). For the material properties, the following values were used: E = 207 GPa, n 0:3, s0 344:8 MPa, and a 0 for n = 1 and a 1 for n gt; 1: These values, in addition to the ones given in Table1 , provide complete characterization of the pipe material properties according to Eqs. (1) and (3).... In PAGE 9: ...4. Results and discussions According to Table1 , 21 finite element meshes similar to the ones in Fig. 4 or Fig.... ..."

### Table 1. Memory Requirement for Solving PB Equation on a Regular (PMG) and Adaptive Grid (MC) Finite Element.29

"... In PAGE 4: ... In this approach, four variables (H9272n, H9272nH110011/3, H9272nH110012/3, and H9272nH110011) are needed in the calculations. However, we were able to implement this approach by using two variables accomplishing a storage requirement iden- tical to the explicit FTCS scheme ( Table1 ). After solving for the x-direction in (15), the results for H9272nH110011/3 are stored in a dummy array.... ..."

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### TABLE V. RESULTS FOR FINITE ELEMENT STRESS ANALYSIS.

1998

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### Table 3: Distribution of n and elements

"... In PAGE 24: ... In this respect, Hypothesis A and the Hybrid Hypothesis fare much better than Hypothesis B, since the former accept the reality of negative concord and put forward proposals to account for it while the latter subsumes it under polarity licensing. Table3 compares the distribution of n-words, negative quanti ers, and existentials in the four langauges listed in rows 1-4 and the ve syntactic environments in columns 1-5: 1 = negative contexts without a licenser; 2 = negative contexts with an explicit licenser (negation or without; 3 = nonnegative yes/no interrogatives (negative yes/no interrogatives count as negative contexts); 4 = if clauses, and 5 = assertive existential statements. The symbol n stands for both n-words and negative quanti ers like Standard English nothing and the symbol stands for nonnegative elements (polarity items like any and existentials):... In PAGE 25: ...tems and existentials). If the arguments presented in Section 6.3 are on the right track, the presence of n elements (exclusively n-words; never +ni minimizers) in columns 3 and 4 is only a historical relic preserved from a time when n-words were not n elements but rather elements. The distribution observable in Table3 , once more, points towards a separate characterization of negative concord and polarity licensing and toward an analysis of the semantics of n-words where negation, directly or indirectly, plays a role. References Bolinger, Dwight L.... ..."

### Table 3: Input data and results of the preliminary Finite Element Analysis of a 40 m diameter ball telescope.

### Table 4. Finite element problem

"... In PAGE 14: ... The matrices were generated by the nite element code VECFEM, see [3]. Table4 shows the reduction of the calculation time by at least a factor of 5. The heavy oscillations of the timings are e ected by the random sample of the values for k.... ..."