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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.... ..."
Cited by 15
Table 5 Estimated computational requirements in 1,000 operations per second for different front ends (italic) and sub-band SNR or noise level estimation algorithms. The val- ues are given in four categories. ADD contains additions, subtractions and compar- isons, MULT multiplications, DIV divisions and FUNC any non-standard operation (logarithm, square-root or sigmoid), that takes longer time to compute ,e.g., by us- ing a table look-up or a Taylor series expansion. The estimates are given in order of magnitudes only, because the exact numbers vary depending on implementation parameters.
2002
Cited by 2
Table 3. The exact eigenvalues of a few rst NIM for the = 0 vacuum state in the Lee-Yang CFT (as given by (A.2), (A.7), (A.8), (A.10) with a = 2=5 and p = 3=10) and numerical values of the same NIM obtained with a polynomial t of Y1( ) determined from the numerical solution of the integral equation (4.37). The quantity Gvac 0 (p) denotes the constant term in power series expansion (2:26a)
Table 8: E ect of number of expansion terms In a rst series of experiments, we considered single word only. We used Q2/D1 (lsp document indexing) as training sample and Q2/D2 (ltc indexing) as test
1994
Cited by 7
Table 8: E ect of number of expansion terms In a rst series of experiments, we considered single word only. We used Q2/D1 (lsp document indexing) as training sample and Q2/D2 (ltc indexing) as test
1994
Cited by 7
Table 2 indicate that both solutions, E1 and SW 1, have negative eigenvalues along tangent directions to the corresponding xed-point subspaces Fix(Z2( ) S1) and Fix(Z2( ) Zc 2). Inside P1, symmetry forces the remaining eigenvectors to be perpendicular to those xed- point subspaces. A Taylor series expansion of the corresponding eigenvalues leads to coe - cients 1 and 3, which appear in the column for Fix(Z2( )) in Table 4. When 1 and 3 are nonzero, the sign of the relevant eigenvalues are determined near bifurcation by the sign of j. Similar calculations for the remaining transitions complete the entries in Table 4. When (10) and (11) hold, (a) is veri ed when gt; 0.
2000
"... In PAGE 11: ... Next we determine the stability of the branching solutions. We do this by considering the isotypic decomposition of C3 into a direct sum of -irreducible subspaces C3 = V0 V1 Vq: In Table2 , we show the isotypic decomposition by each of the isotropy subgroups of solutions. Other isotropy subgroups are shown as well for later use in this section.... In PAGE 11: ... Furthermore, observe that when is a subgroup of a periodic solution, (D6 S1)= forces one eigenvalue of dg to be zero. The corresponding null vector is also listed in Table2 . In each case, the stability of solutions with maximal isotropy is determined by tr(dgjVj).... In PAGE 11: ... We compute the Jacobian dg in complex coordinates (dg)( ) = gz0 0 + g z0 0 + gz1 1 + g z1 1 + gz2 2 + g z2 2; where = ( 0; 1; 2), g = (g0; g1; g2) and gzj = (g0 zj; g1 zj; g2 zj). The eigenvalues of dg are also listed in Table2... In PAGE 12: ...Isotropy Isotypic decomposition Null vectors Eigenvalues D6 S1 V0 = C3 p1 [4 times] c1 [twice] Z2( ) S1 V0 = (x; 0; 0) V1 = (ix; 0; 0) V2 = (0; z; z) V3 = (0; z; ?z) V0 : 2(c1 + 2c5x2)x2 V1 : ?6c5x4 V2 : p1 + (p1 + p3)x2 + p7x4 [ ] V3 : p1 + (p1 ? p3)x2 ? p7x4 [ ] Z2( ) S1 V0 = (ei =2x; 0; 0) V1 = (ei =2ix; 0; 0) V2 = (0; z; e? iz) V3 = (0; z; ?e? iz) V0 : 2(c1 ? 2c5x2)x2 V1 : 6c5x4 V2 : p1 + (p1 + p3)x2 ? p7x4 [ ] V3 : p1 + (p1 ? p3)x2 + p7x4 [ ] Z2( ) Zc 2 V0 = (0; z; z) V1 = (x; 0; 0) V2 = (ix; 0; 0) V3 = (0; z; ?z) (0; i; i) V0 : 0; 4(p1 N + p9r2)r2 V1 : c1 + (2c1 N + c3)r2 + c7r4 V2 : c1 + (2c1 N + c3)r2 ? c7r4 V3 : ?2(p2 + 2p9r2)r2 [ ] Z2( ) Zc 2 V0 = (0; z; e? iz) V1 = (ei =2x; 0; 0) V2 = (ei =2ix; 0; 0) V3 = (0; z; ?e? iz) (0; i; e? ii) V0 : 0; 4(p1 N ? p9r2)r2 V1 : c1 + (2c1 N + c3)r2 ? c7r4 V2 : c1 + (2c1 N + c3)r2 + c7r4 V3 : ?2(p2 ? 2p9r2)r2 [ ] Z6 V0 = (0; z; 0) V1 = (z; 0; 0) V2 = (0; 0; z) (0; i; 0) V0 : 0; 2(p1 N ? p2 + (2p1 ? p2 N)r2)r2 V1 : c1 [ ] V2 : 2p2r2 [ ] Table2 : Isotypic decomposition by isotropy subgroups of D6 S1, where x 2 R, z 2 C, and [ ] indicates real part of a complex conjugate pair. In Table 3, we list maximal and submaximal isotropy subgroups and their xed-point subspaces.... ..."
Cited by 4
TABLES TABLE I. Comparison for -He scattering lengths a( He) (in fm) from various stages of the series expansion in Eq. (7) with the results from direct calculation with the corresponding optical potential [12]. The numbers are for 3He and those in the brackets refer to 4He. The results are illustrated with four sets of the N input: a( N) = 0:476 + i 0:279 fm (I), 0:579 + i 0:399 fm (II), 0:430 + i 0:394fm (III) and 0:291 + i 0:360fm (IV). In all cases RRMS = 1:788 [1:618] fm.
Table 1 Parameters for single refinement and recalculation steps. Included are the resolution C14 of the grid of specimen directions of S2, the cumulative total number C22 N of measured diffraction intensities with respect to the locally refined grids, the total number C22 Nreg of diffraction intensities to be measured in a conventional experiment with a regular grid, the cumulative measurement time, the total number M of ansatz functions involved in the PDF-to-ODF inversion problem, the maximum order of harmonic series expansion (bandwidth) L of the ansatz functions, and the computational time to solve the PDF-to-ODF inversion problem with Core 2 Duo c.p.u. with 186 GHz c.p.u. frequency and 2 Gbyte RAM.
2007
"... In PAGE 9: ... (1988). In Table1 the parameters of the individual steps are summarized. The first column displays the angular resolution C14 research papers J.... ..."
Table 2: Hyperkernels by Power Series Construction.
"... In PAGE 12: ... It is straightforward to find other hyperkernels of this sort, simply by consulting tables on power series of functions. Table2 contains a short list of suitable expansions.... ..."
Table 2: Hyperkernels by Power Series Construction.
"... In PAGE 13: ... It is straightforward to find other hyperkernels of this sort, simply by consulting tables on power series of functions. Table2 contains a short list of suitable expansions.... ..."
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