### Table 2 Four estimates of the diffusion constant DT = 6.4776 when the number of steps N and the number of walks M increase. 4.1 The Central Limit Theorem

### TABLE II COMPARISONS OF DIFFERENT HARDWARE GAUSSIAN NOISE GENERATORS IMPLEMENTED ON A XILINX VIRTEX-II XC2V4000-6 FPGA. CLT REFERS TO THE CENTRAL LIMIT THEOREM.

### Table V shows the values of K00(O) lim for different coding schemes. Comparing the 3 rightmost columns, we see that Theorem 2 results in the narrower range of information word lengths, while Theorem 3 provides the wider range and Theorem 4 results in an intermediate range. Moreover, we note that the stronger limitation of Theorem 2 corresponds to a generally tighter bound, while the weaker limitation of Theorem 3 corresponds to a looser bound. Finally, Theorem 4 features intermediate values. Since the computation of (23), (27) and (31) might be impractical due to the large number of values to be considered for w, we provide a simplification in the following corollary. Corollary 3: The minimum distance of a serially concatenated convolutional code satisfies the following inequal- ity:

2006

Cited by 1

### Table 1. Results for bsolo and scherzo Let be a clause that must be added in order to explain the assignment , which is implied by applying the limit lower bound theorem. Notice that this theorem is ap- plied because of the values of and . Thus, the assignments that explain these two values are also the explanation sought for the assignment . Therefore,

### Table 5: The optimal moves for n 15 when 0- and 1-moves are allowed everywhere. The terms inside the square bracket have decreasing absolute values and alternating signs. By Leibnitz apos;s Theorem the limit of the sum of this series exists as r ! 1, and can be shown to be p2=2.

1993

"... In PAGE 21: ... These new values will of course in uence the values of almost all other positions, but it turns out that the changes are exponentially diminishing in n for every k = n with lt; c lt; 1. The new optimal moves from positions (n; k) with k n 15 are given in Table5 . There are again some exceptions when n 5 but, apart from that, the only di erence between Table 5 and Table 2, giving the optimal moves in the original version of the game, is that a 0-move is now used from positions (n; 0) with n even.... In PAGE 21: ... The new optimal moves from positions (n; k) with k n 15 are given in Table 5. There are again some exceptions when n 5 but, apart from that, the only di erence between Table5 and Table 2, giving the optimal moves in the original version of the game, is that a 0-move is now used from positions (n; 0) with n even. This was to be expected as the values of these positions were hitherto negative.... ..."

Cited by 1

### Table 1 A comparison of the limiting ccdf Hc(x) in theorem 10 for = 1:5and = 1 with the one-term asymptote and the alternative exact values for = 1:49 and = 1:40.

2000

Cited by 2

### Table 1. Results for bsolo and scherzo Let AX D0D0CQ be a clause that must be added in order to explain the assignment DC CY BP BC, which is implied by applying the limit lower bound theorem. Notice that this theorem is ap- plied because of the values of BVBMD4CPD8CW and BVBMD0D3DBCTD6. Thus, the assignments that explain these two values are also the explanation sought for the assignment DC CY BPBC. Therefore,

### Table 1 shows that the nth power of a linear function has an of n. The second column is the Walsh sum for f(x) = x. The third column is f(x) = x5. For both functions x 2 [0; 2L ? 1]. Notice how (f) is limited by the Polynomial Complexity Theorem to the maximum power of the polynomial.

1999

"... In PAGE 18: ... Table1 : Walsh Sums for f(x) = x and x5... ..."

Cited by 2

### Table 1 shows that the nth power of a linear function has an of n. The second column is the Walsh sum for f(x) = x. The third column is f(x) = x5. For both functions x 2 [0; 2L ? 1]. Notice how (f) is limited by the Polynomial Complexity Theorem to the maximum power of the polynomial.

1999

"... In PAGE 19: ... Table1 : Walsh Sums for f(x) = x and x5 In table 2 we compare the function x5 over the noncentered domain [0; 2L ? 1] to the centered domain [?(2(L?1) ? :5); (2(L?1) ? :5)]. We see in column 2 that without centering x5 has nonzero Walsh sums for all orders less than 6, but with centering the... ..."

Cited by 2