### Table 5: Break-even points for page exception and software checks. y is the cost of handling a protection fault.

"... In PAGE 14: ....e., x is 5 and f is 25. Given these assumptions, Table5 shows the break-even point between software checks and exceptions for the two applications. As a reference, an exception and re-enable of protection takes 18 s using the eager amplification optimization in our system.... ..."

### Table 15: Break-even Analysis Worksheet (ECUs)

1998

"... In PAGE 94: ... The benefit is equal to the difference in O amp;S costs of Status Quo and Strategy N accruing from this point in time onward. Table15 : Break-even Analysis Worksheet (ECUs) and Table 16: Economic Assessment Summary Worksheet provide an example of how... ..."

### Table 1. Break-even point for computing M is in terms of q. The break-even point for using M is expressed in terms of PCGLS iterations; Interior point iteration = 2.

"... In PAGE 6: ... The break-even point for using M is de ned as the smallest number of PCGLS iterations required for the cost of an iterative step to exceed the cost of a direct step. For most problems we do not get close to the break-even numbers for using M in Table1 since we terminate after fewer iterations (except for czprob and scsd8 problems). For problems with small break-even values for using M, Table 1 suggests that we may choose a large q and do few PCGLS iterations per step.... In PAGE 6: ... For most problems we do not get close to the break-even numbers for using M in Table 1 since we terminate after fewer iterations (except for czprob and scsd8 problems). For problems with small break-even values for using M, Table1 suggests that we may choose a large q and do few PCGLS iterations per step. Further, the break-even numbers for computing M in Table 1 show that computing the Cholesky factor is much more expensive than carrying out a small number of sparse solves.... In PAGE 6: ... For problems with small break-even values for using M, Table 1 suggests that we may choose a large q and do few PCGLS iterations per step. Further, the break-even numbers for computing M in Table1 show that computing the Cholesky factor is much more expensive than carrying out a small number of sparse solves. Thus we may also choose a large q and do few PCGLS iterations.... ..."

### Table 5. Key economic figures for the handset scenario. If recurring spectrum costs are considered, break even operation can be achieved with handset subsidies as high as $38. This figure rises to $45 if recurring spectrum costs are discarded

"... In PAGE 16: ...osts for the 450MHz band. The subscribers were charged $0.02 per minute and received a subsidy of $30 on each handset. In this scenario, recurring spectrum licensing cost represents 26% of the OpEx and 11% of the revenue (See Table5 ). The IRR in this case is 28.... ..."

### Table 3: The break-even point for using M (BEPUM) in terms of PCGLS iterations, obtained at interior-point iteration number 2.

"... In PAGE 20: ... For a constant q, we de ne the break-even point for using M (BEPUM) as the largest number of PCGLS iterations for which the cost of a PCGLS step is less than or equal to the cost of a direct step, where the cost is measured by oating point operations unless unless otherwise indicated. Table3 indicates that we need to do a few PCGLS iterations per PCGLS step for test problems czprob and scsd8. Recall that Table 1 showed that it... In PAGE 21: ... Hence Tables 1 and 3 together suggest that we should use a large q and do 1 or 2 PCGLS iterations per PCGLS step for czprob and scsd8. For a given q, the break-even points in Table3 if they were available during the computation, could be used as upper bounds for the number of iterations per PCGLS step. However, for most problems we do not get close to these numbers since we terminate after fewer iterations (except for czprob and scsd8 problems).... In PAGE 21: ... However, for most problems we do not get close to these numbers since we terminate after fewer iterations (except for czprob and scsd8 problems). The break-even points in Table3 are non-increasing with respect to q. The higher the value of q is, the smaller the break-even point is.... ..."

### Table 4 Break-even point for using M in one PCGLS iteration compared to a direct step. It is expressed in terms of q. Interior-point step = 2.

"... In PAGE 7: ...of computation associated with the two formulas are different. In Table4 the columns for M1 and M2 indicate the maximum q so that the number of flops for one PCGLS iteration per iterative step do not exceed the number of flops for a direct step. The quantity s% indicates the density of nonzero elements in percentage.... In PAGE 7: ...onzero elements in percentage. Sparsity density of an m-by-n matrix A is nnz(A)=mn. For a constant q, we define the break-even point for using M as the largest number of PCGLS iterations for which the cost of a PCGLS step is less than or equal to the cost of a direct step, where the cost is measured by floating point operations. From Table4 it is seen that column Aj from A is likely to be sparse. For Aj sparse, L?1 Aj is a solve with a sparse right hand side.... ..."

### Table 3. Break Even Contribution Rates for Reformed PAYG Defined Benefit System (percentage of wage bill)

"... In PAGE 18: ... These ratios are retained throughout this analysis. Cost of the PAYG System Under Alternative Reforms Table3 compares the annual break-even contribution rates of the current system and several reform scenarios, all retaining the PAYG defined benefit format. The break-even contribution rate is the payroll tax rate that will just balance revenues and expenditures on a year-to-year basis, given the covered wage base and existing defined benefit formula.... In PAGE 18: ... The current system. Table3 , row 1, shows the break-even contribution rates that would be needed for the current system, given China apos;s demographics and high labor force participation rate. In this baseline scenario, break-even contribution rates rise from 20% in 1995 to 37% in 2030, 49% in 2050 and 60% in 2100.... In PAGE 30: ... The latter requires a payroll tax of 20% initially, but this declines to 3% by 2030 and 1% by 2050 because most of the middlemen have died and the remaining few get compensation for only a small number of years under the old system. Comparing the total cost of this reformed multi-pillar system with a continued but reformed PAYG system ( Table3 , row 9), we see that initially required contribution rates are 8.5 percentage points higher under the multi-pillar system than under PAYG--but by 2100 the former is 7.... In PAGE 46: ... Columns 2 and 3 give the uniform contribution rates for 1995-2050 and 2051-2100 if the system is balanced separately for these two period. See Table3 for other definitions.... ..."

### Table 3. Performance assessment: break-even

1993

"... In PAGE 10: ...Table3 gives a first impression that advisors can actually be useful. bool-n has a single propagator propagating that the sum of 4n + 1 Boolean variables is at least 2n where 2n variables are successively assigned to 0 and then propa- gated.... ..."

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