### Table 1 Comparison between the Fourier and wavelet series Characteristic Fourier Series Wavelet series

"... In PAGE 2: ... Therefore, both transforms are completely alike and share the same basic principles. Table1 shows how this relationship goes even farther. The series expansion is basically the same but the wavelet transform is a double summation instead of a single summation as in the case of the Fourier transform.... In PAGE 2: ... The basis functions are, for Fourier, complex exponentials while for wavelets they can be any function that meet the wavelet conditions [8]. In spite of this, all basis functions are related to a single function called the mother wavelet, which generates the rest of them by simultaneous scaling and translation operations (see Table1 ). A group of conceptually-related mother functions is called a family; some examples of families are Daubechies, Coiflets, Symmlets and B-Splines [8].... In PAGE 13: ... A series of I/O tests using a standard Intel PC computer were performed to test the difference between a text format and a binary format; their results are shown in Table 1. Table1 Times (in seconds) obtained for input and output of a vector from memory to the hard drive using the XDR format and a simple text format Binary (XDR) Text Floating point Integer Floating point Integer Vector size Write Read Write Read Write Read Write Read 500 kb 0.... ..."

### Table 4: Series Expansion Coe cients for the 2 2 Lattice

### Table 5: Series Expansion Coe cients for the 3 3 Lattice

### Table 14: The Laplace expansion for the solution function The coe cient The Laplace expansion

1994

"... In PAGE 59: ... If the given boundary function f has the Laplace series expansion f = 1 X n=0 anSn Then the solution of the equation (3.2), @u @n, will have the expansion @u @n = 1 X n=0 bnSn where bn = ?nan The following Table 13 gives the Laplace expansion for the given boundary function f = x, and Table14 is the Laplace expansion for the solution.... ..."

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### TABLE I Comparison between the polynomial phase coefficients and the Taylor series expansion coefficients

2001

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### Table 2. Comparison of modular exponentiation times

"... In PAGE 5: ... n-bit modular exponentiation requires at most 2n + 2 modular multiplications including the conversion to and from M-residues. Table2 compares the time for 256-bit and 1024-bit exponentiation using various recent hardware and software implementations. For reference, a CLB in a Xilinx 4000XV-series chip contains 32 bits of RAM or two flip-flops and two LUTs.... ..."

### Table 4. Reductions and Expansions for WDC i

"... In PAGE 9: ... With these two-sided circuits (nets), cut-elimination is replaced by normalization, as given by reductions and expansions, as well as by some rewrites that may best be thought of as \permuting reductions quot;, as they are not \directed quot; in any natural way. The reduc- tions and expansions for the multiplicative fragment of our logic are given in (Blute et al 1992) and are shown in Table4 . The reductions and expansions for the exponentials ! and ? are given in Tables 5, 6, and 7.... ..."

### Table 4. Series E performance of the pattern recognition system with varying segment size k compared with the Exponential Smoothing method _________________________________________________________ No. of

"... In PAGE 11: ...Finally, Table4 shows the results for series E. This is the most difficult of all benchmark series to predict.... In PAGE 11: ... This may be directly observed as the success in predicting the direction of series change is much lower than Table 2 and Table 3. Table4 here Here, the best results are obtained for small k, e.... ..."

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### Table 2. Window functions and their de nitions. In the de nition of the Kaiser window, 2 R+ is a free parameter, for which we used values of 5:0, 6:0, 7:0, and 8:0. I0 is the zeroth-order modi ed Bessel function of the rst kind, which can be approximated accurately by using its series expansion [15, 61]. For the free parameter 2 R+ in the de nition of the Gaussian window we used values of 2:5, 3:0, 3:5, and 4:0.

2001

"... In PAGE 8: ... In the quantita- tive evaluation described in this paper we used the following windows: Bartlett, Black- man, Blackman-Harris (both three- and four-term), Bohman, Cosine, Gaussian, Hamming, Hann, Kaiser, Lanczos, Rectangular, and Welch. The window functions and their de ni- tions are given in Table2 . For more elaborate discussions on the spectral properties of these window functions, we refer to Harris [15] or Wolberg [61].... In PAGE 9: ... Of the types described in Section 3, we used all kernels with a spatial support equal to or less than 10 grid intervals (m 6 5), which amounts to a total of 126 kernels (viz.,the nearest-neighbor and linear interpolation kernel, the quadratic convolution kernel, the cubic, quintic, septic, and nonic convolution kernel (using three di erent values for the free parameter ), the quadratic, cubic, quartic, quintic, sextic, septic, octic, and nonic Lagrange and spline interpolation kernels, and nally 13 di erent windowed sinc kernels (using ve settings for m), two of which have a free parameter, for which we used four di erent values (see Table2 for details)). We note that in order to avoid border problems, all test-images were mirrored around the borders in each dimension.... ..."

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### Table 5. Series S amp;P performance of the pattern recognition system with varying segment size k compared with the Exponential smoothing method. _________________________________________________________ No. of

"... In PAGE 13: ... A more general discussion on the nature of international markets may be found in (Levich, 1987). Table5 here Table 5 shows the performance of the pattern recognition system on the difference of difference S amp;P series. Pattern size of k = 3 yields the best performance.... In PAGE 13: ... A more general discussion on the nature of international markets may be found in (Levich, 1987). Table 5 here Table5 shows the performance of the pattern recognition system on the difference of difference S amp;P series. Pattern size of k = 3 yields the best performance.... In PAGE 13: ... Hence, a good forecast system should correctly predict the market position in relation to its current index with better than chance (50%) accuracy. Table5 shows that the proposed system performs well roughly three out of four times. This is a very encouraging performance.... ..."

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