### Table 1. Estimated log2 running time based on asymptotic formula.

### Table 1. Estimated log2 running time based on asymptotic formula.

### Table 2: E ective atomic numbers for open charm production in pP b collisions with asymptotic formulae.

in July 1997

"... In PAGE 22: ... A completely di erent result follows for open charm production, for which the prob- abilistic approach gives no absorption altogether. Our asymptotic formulas, on the con- trary, lead to considerable absorption, as presented in Table2 . However these results can only be trusted at very high energies, as we shall presently see.... ..."

### Table 2: E ective atomic numbers for open charm production in pP b collisions with asymptotic formulae.

1997

"... In PAGE 22: ... A completely di erent result follows for open charm production, for which the prob- abilistic approach gives no absorption altogether. Our asymptotic formulas, on the con- trary, lead to considerable absorption, as presented in Table2 . However these results can only be trusted at very high energies, as we shall presently see.... ..."

### Table 1: E ective atomic numbers for J= production in pP b collisions with asymptotic formulae.

in July 1997

"... In PAGE 22: ... However for J= production this di erence is quite small numerically. One can see this from Table1 , where we present Aeff and its three components compared to the probabilistic value Aprob at xF = 0 and 0.5 and various energies.... ..."

### Table1:E ectiveatomicnumbersforJ= production in pP b collisions with asymptotic formulae.

1997

"... In PAGE 22: ... However for J= production this di erence is quite small numerically. One can see this from Table1 , where we present Aeff and its three components compared to the probabilistic value Aprob at xF = 0 and 0.5 and various energies.... ..."

### Table 3. Comparison of Eiy, amp;n calculated by Rayleigh-Schrtidinger perturbation theory and by the asymptotic formula

in i

### Table 2. Simulated Means and Standard Deviations of 98 and 12 for the Model Defined by (7.1) and (7.2). The results are based on 100 simulations. The standard deviations are estimated by 1/2 the sample standard deviation s and the MAD, the asymptotic formula 27 61(V /n)is asymp

1999

"... In PAGE 20: ...espectively. Figures 9(b) and (c) show 10340116 ; 58266741 and 10340116 ; 58733341, respectively. Figure 105 105 9(d) displays 69401214161210340116;58266741 0 58510340116595873334158 Typical sample paths are plotted in 105 105 Figures 9(e), (f), and (g), for 100 61 058359 0, and 583, respectively. The grid 71 in algorithm 1 consisted of 30 equidistant points in the interval 40059 19358 Table2 gives the simulated means and standard deviations of 18 40106 61 1595858585944159 as 106 well as the asymptotic standard deviation obtained from theorem 1. The results are based on 100 simulations.... ..."

Cited by 3

### Table 3.1 A comparison of exact m with the approximation in (3.5). integer m greater than or equal to m , it is clear that the approximation (3.5) serves that purpose extremely well. The dependence of m on = 1= n is shown in Figure 1. Both the exact and approximate values of m are shown, but there is no noticeable di erence. The error of the approximation formula (3.5) is shown in Figure 2. Based on the above asymptotic formula for t and the expansion t = etln 1 + t ln + :::, we have

"... In PAGE 11: ... However, this is consistent with the single precision result obtained from the standard spectral decomposition method. In Table3 , we list the relative errors for = 10?6 and 10?7, together with those errors for the single precision spectral decomposition method. We Method ef e1 e2 Pad e: = 10?6, m = 8 1.... ..."