### Table 1 Known APN power functions on F2n. Exponents d Conditions Proven in

"... In PAGE 5: ... AB). Table1 (resp. Table 2) gives all known values of exponents d (up to affine equivalence and up to taking the inverse when a function is a permutation) such that the power function xd is APN (resp.... ..."

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### Table 1 Known APN power functions xd on F2m. Exponents d Conditions w2(d) Proven in

2006

"... In PAGE 4: ... AB). Table1 (resp. Table 2) gives all known values of exponents d (up to EA-equivalence and up to taking the inverse when a function is a permutation) such that the power function xd is APN (resp.... ..."

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### Table 3. Predictions for the combination of critical exponents ? dH from scaling of the rst three Lee{Yang zeros of exactly known partition functions ZN.

"... In PAGE 12: ... Fig. 5 and Table3 show our results for the rst three Lee{Yang zeros. The extracted exponent combination is in reasonable agreement with the KPZ exponents, especially for the rst zero.... In PAGE 12: ...or all j. Fig. 5 and Table 3 show our results for the rst three Lee{Yang zeros. The extracted exponent combination is in reasonable agreement with the KPZ exponents, especially for the rst zero. The errors reported in Table3 are not true statistical errors (which are meaningless in this case). They are computed from the standard formula giving least squares linear t errors and in this case they are simply a measure of the systematic deviation of the points from a straight line.... ..."

### Table 5 Known differentially 2s-uniform power functions xd on F2m.

in Dedication

"... In PAGE 42: ... Table 4 (resp. Table5 ) gives all known values of exponents d (up to cyclotomic equivalence) that xd is s-nonlinear (resp. differentially 2s- uniform).... ..."

### Table 1: The critical exponents , and ! for (1) the LPA of Polchinski equa- tion; (2) derivative expansion at second order of Polchinski equation; (3) deriva- tive expansion at second order of the e ective action RG equation [1]; (4) com- bination of best known estimates taken from Ref. [1].

"... In PAGE 23: ... 6.6 Discussion Table1 contains a summary of our results, together with a comparison with results from the LPA and also from other methods (exact RG for the e ective action and a combination of best known estimates [1]). It is remarkable that with exact RG computations one may obtain numbers quite close to the best known estimates, and with considerably less e ort.... ..."

### Table 2: Known APN functions x

"... In PAGE 11: ... In Table 1 we give the values of exponents k for odd values of n, n =2m + 1, with the indication to which of the three classes the function belongs. In Table2 we give those values of k for even n, n =2m, which give APN functions. Note that the inverse of an APN #28AB#29 function is also APN #28AB#29, but this need not be so for CR functions.... ..."

### Table 1: Critical exponents and mass-to-scale ratio in 2D directed models with defects Model

"... In PAGE 3: ...earlier [3]). For c = 0 the critical exponents are listed in Table1 . An annealed version of defects of the above type was studied numerically in Ref.... In PAGE 6: ... We also calculated lt;n(l) gt;, to obtain the exponent de ned in Eq. (3), as well as the average number of topplings in a cluster of a speci ed length l, lt;n gt;l lDn (9) The scaling exponents are given in Table1 , and as we show in Section 5, they satisfy various scaling relations to within numerical error. It appears that the exponents are independent of the concentration of defect bonds c, suggesting universal criticality.... In PAGE 9: ...Nonequilibrium phase transitions In the preceding sections we have shown that sandpile automata are able to self-organize into a critical state in the presence of frozen-in random defects, provided that the dy- namics conserves the number of grains at each time step. The sets of critical exponents for all three models are summarized in Table1 . For model A without defects the expo- nents are known exactly [2].... ..."

### Table 1: ESSA Algorithm (Ratschek and Rokne) BX denotes the exponent of CP BD , BY the exponent of CQ BD . The terms are stored in two lists of length D1 and D2, one for each sum, and are ordered by decreasing magnitude.

2001

"... In PAGE 10: ... At that point the sign of D7 is known. The algorithm is shown in Table1 ; see [4, 5]. 3.... ..."

### Table 1: Calculated values for the galaxy-galaxy correlation function critical exponent

"... In PAGE 4: ... The operator A in the continuum limit is given by A(r; r0) (3)(r ? r0) ?r2 2 Gm2 0 ; (7) since r2 1 jxj ? 4 (3)(x): As is well known 8, the connected two-point function for the spin system and the eld theory are the same. Moreover, the unavoidable uctuations in the eld result in an anomalous dimension shifting the canonical dimen- sion of the eld such that when jr ? r0j ! 1, the two-point function for the hamiltonian in (6) scales as lim jr?r0j!1 lt; sisj gt; lim jr?r0j!1 Gal(jr ? r0j) jr ? r0j?(d?2+ ): (8) Here d is the dimension of space (d3) and is the critical exponent for the pair correlation function whose value (0:0198?0:064) (see Table1 ) di ers from zero due to the uctuations in . Thus, our calculation shows that for large separations, the galaxy-galaxy correlation function must scale as Gal(jri ? rjj) r?(d?2+ ); (9) with 9 1:0198 1 + 1:064 for d3, and without taking the background expansion into account.... In PAGE 5: ...for a conserved order parameter) and between 1.75 to 1.862 for 1=2 (non- conserved order parameter). Table1 displays these exponents for both the static and expanding cases (C, NC, denote conserved and nonconserved order parameter, respectively). The static values are taken from Ref[9].... ..."

### TABLE 2: THE EXPONENTS RANGES

2002

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