### Table 2 Comparison of iterations to convergence for rst- and second-order Robin transmission conditions with and without under-relaxation.

1997

"... In PAGE 6: ... It is also somewhat simpler to analyze. Is there a better choice for the initial solution? Table2 appears to indicate that the number of iterations is roughly linear in the number of vertical strips. While this general trend is observed in larger tests, the correlation seems to not be as strong as the results presented in Table 2 might suggest.... In PAGE 6: ... Is there a better choice for the initial solution? Table 2 appears to indicate that the number of iterations is roughly linear in the number of vertical strips. While this general trend is observed in larger tests, the correlation seems to not be as strong as the results presented in Table2 might suggest. This implies that the current implementation, with one element per subdomain, is not likely to be optimal for large problems.... ..."

Cited by 4

### Table 1: First- and second-order Taylor approximation in (4.5), p = 1 + p

"... In PAGE 16: ... Table1 presents some numerical results re ecting the error of the rst- and second-order Taylor order expansion in (4.5) where p = 1 + p, k = 1; 2: ek( p) := max 0 t 1 jx(t; p) ? k X i=0 1 i! @ix @pi (t; p0)( pi)j : 5 Conclusion The second-order sensitivity result derived in this paper states that the op- timal solution of a nonlinear control problem is di erentiable with respect to parameters provided that the second-order su cient conditions (SSCs) hold for the unperturbed (nominal) problem.... ..."

### Table 1. Lie apos;s classi cation of invariant second-order ordinary di erential equations No. Equation Symmetry algebra

"... In PAGE 13: ... Surprisingly, it is possible to implement this approach to classifying second-order PDEs (1) by their second-order conditional symmetries in full generality. In Table1 we present the complete list of invariant real second-order ordinary di erential equations together with their maximal invariance algebras, obtained by Lie ([21, 22]). Note that a; k are arbitrary real parameters and f is an arbitrary function.... In PAGE 13: ... Note that a; k are arbitrary real parameters and f is an arbitrary function. As classi cation has been done to within an arbitrary reversible transformation of the variables x; y, the equations given in Table1 are representatives of the conjugacy classes of invariant ordinary di erential equations. Table 1.... In PAGE 14: ...Table1 , since the corresponding ordinary di erential equation is not integrable by quadratures. Next, since our nal aim is to exploit conditional symmetries for the description and reduction of initial value problems, it make no sense to consider case 4.... In PAGE 14: ... Next, since our nal aim is to exploit conditional symmetries for the description and reduction of initial value problems, it make no sense to consider case 4. This is because the symmetry group admitted by the corresponding ordinary di erential equation within the class (18) is the same as that of the more general equation given in case 3 of Table1 . The same argument applies to case 8.... In PAGE 14: ...quation given in case 3 of Table 1. The same argument applies to case 8. Consequently, we will deal only with the remaining cases 2, 3, 5{7, 9. We take as the function in operator (3) the expressions y00 ? f(x; y; y0), where f is one of the right-hand sides of equations listed in the second column of Table1 and make the replacements y ! u, y0 ! ux and y00 ! uxx. We classify PDEs of the form ut = uxx + F (t; x; u; ux) (27) admitting the corresponding Lie-Backlund vector elds.... ..."

### Table 5 Financial intermediation and growth: dynamic panel regressions, system estimator

2000

"... In PAGE 23: ... In Table 4, only the results on the quot;nancial indicators are given. Table5 gives the full results from system dynamic-panel estimation. The analysis was conducted with two conditioning information sets.... In PAGE 23: ... The second uses the policy conditioning information set, and includes initial income, educational attain- ment, government size, openness to trade, in#ation, and the black market exchange rate premium.25 Table5 also presents (1) the Sargan test, where the null hypothesis is that the instrumental variables are uncorrelated with the residuals and (2) the serial correlation test, where the null hypothesis is that the errors in the di!erenced equation exhibit no second-order serial correlation. The three quot;nancial intermediary development indicators (LIQUID LIABILI- TIES, COMMERCIAL-CENTRAL BANK, and PRIVATE CREDIT) are sig- ni quot;cant at the 0.... ..."

Cited by 60

### Table 1 Computational results for Test Problem 1 h Fourth-order scheme Second-order scheme

2003

"... In PAGE 9: ... The test results are tabulated in Table 1. It is clear from Table1 that the fourth-order compact difference scheme computes more accurate solution than the second-order central difference scheme does. Multigrid method with both schemes exhibits grid independent convergence rate.... ..."

### Table 5 . Stability conditions for one-dimensional second-order schemes

### Table 1: Correct responses to the second-order false belief question and the justification question for each story.

"... In PAGE 14: ... All participants with an incorrect answer to any of these three types of questions (the reality control question, the first-order ignorance question, and the linguistic control question) were excluded from further analysis for that story in the second-order false belief task. The results of the remaining children and adults on both second-order false belief stories are given in Table1 below: ... ..."

### Table 2 Standard goodness-of-fit indices: Oblique and second-order factor model

"... In PAGE 17: ...16 The final measurement model of self-control: Testing for structural invariance Table 3 summarizes the main characteristics of the final five-dimensional second-order factor model of self-control. Compared with the solution with six factors ( Table2 ), there are some improvements in the indices of goodness of fit: GFI is now .... ..."

### Table 4: Stochastic Process for Occupational Component of Individual Log Earnings, Second-Order Moving Average Fit to First Differences, 1968-1994

"... In PAGE 29: ... The magnitude of this shock declines with age, because fewer years remain until retirement.20 Table 3 and Table4 display the results of fitting (7) for wages measured in natural units and natural logs, respectively. The tables also report the implied present value multipliers on the occupation-level earnings shocks at ages 30 and 50, assuming a real discount rate of 2.... In PAGE 29: ... Occupations differ quite a bit in terms of magnitude and persistence of occupation- level earnings innovations. The standard deviation of the occupation-level innovations in Table4 ranges from 2.... In PAGE 30: ...age 30 range from 13 to 27 using the natural units wage measure and from 11 to 26 using the log measure. The last two columns in Table 3 and Table4 show how the present value multiplier declines between ages 30 and 50, given our assumptions about discounting and retirement. The age-50 multipliers are fairly sensitive to alternative assumptions about retirement age, but the basic point is not.... ..."

### Table 15. Fourth example. Second order controller design.

2001

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