### Table 1. Values taken by the bilinear operator IE( ) A (B) on the basis of spin matrices.

"... In PAGE 40: ...be calculated using (3.4) and Table1 . which fully describes the operator IE( ).... ..."

### Table 1: Source and sink operators used for our propagators. The rst column lists the name used for the operator in the text, and the second column lists the angular momen- tum, parity and charge conjugation. The third column is a shorthand indicating how the operator is constructed. In particular, the hybrid operators are constructed from one of the quark bilinear operators from the top block, combined with either the color electric or color magnetic eld. The last column lists the actual operator. In this column, a and b are color indices, i, j and k Cartesian indices, and , and are avor indices included to indicate how the propagators are connected.

"... In PAGE 6: ...orse. Therefore we have smeared twice in this work. We do expect that as the physical lattice spacing is decreased more iterations of smearing would be advantageous. Table1 shows the various source and sink operators we have used. To construct a meson propagator, we rst xed the gauge to the lattice Coulomb gauge.... In PAGE 6: ... The result was summed over each time slice to get the zero momentum mesons. The rst three operators in Table1 are standard operators for the 0?+, 1?? and 1++ qq mesons. We will call these the \ quot;, \ quot; and \a1 quot; respectively.... In PAGE 8: ... For example, the rst hybrid operator, which has pion quantum numbers, can be considered as a quark and antiquark in a 1??, or state (but a color octet) combined with a color magnetic eld, which has JPC = 1+?, to make a J = 0 color singlet object. The remaining sections of Table1 contain the operators with exotic quantum numbers. We have experimented with three 0+? operators.... In PAGE 9: ... At 6=g2 = 6:15 we evaluated propagators at ve values of the Wilson hopping parameter, with the largest one chosen at approximately the charm quark mass. We used , , a1, and all of the exotic operators in Table1 as source operators. For each source, we used all of the sink operators with the same quantum numbers, except for the Q4 operator.... ..."

### Table II. Average Operation Times (in msec) for 100 Runs of the Third Attempt Bilinear Elgamal Proxy Re-encryption Scheme on our Client and Servera Parameter Decrypt Decrypt

2005

Cited by 31

### Table 1 The absolute differences between the bilinear and the cubic spline interpolation algorithms, along with and accumulations. The image (2563256) was enlarged

"... In PAGE 7: ... It is noted that the histogram is computed after applying a round-up operation ages produced by the bilinear interpolation spline interpolation algorithms. Table1 shows ences between the bilinear interpolation Fig. 15 Pixel maps where the cubic spline interpolation is used (prediction test 2 with T521): (a) horizontally reduced by 1/ amp;, (b) vertically reduced by 1/ amp;, (c) horizontally enlarged by amp;, and (d) vertically enlarged by amp;.... ..."

### Table 2 Numbers of operations for the three interpolations per pix- els in the final image (bilinear interpolation, cubic spline interpola- tion, hybrid interpolation). 6(116)/3651.17 additions are required for computing the cubic spline coefficients.

"... In PAGE 8: ... Furthermore, many digital cameras and camcorders provide digital zooming up to 10 or higher. For instance, when the image is to be enlarged by a factor of 6, the numbers of operations for the three interpolations are shown in Table2 , where 1.17 additions are required for computing the cubic spline coefficients @see Eq.... ..."

### Table 2. Iteration numbers for the pcg-iteration. In the nal test we report analogous numerical results (condition numbers and pcg-iteration count) for the additive preconditioner CK associated with the splitting (4.11) (subscript a), and the preconditioner C K (subscript s) which uses the switch from the system arising from (3.4) to the spectrally equivalent system generated by the conforming bilinear elements via the operators in (5.1) and (5.2). We have implemented the standard BPX-preconditioner [5], with diagonal scaling, as CK.

1998

"... In PAGE 3: ... In this test the problem (6.1) is assumed to have the exact solution u(x; y) = x(1 ? x)y(1 ? y)exy: Table2 shows the number of iterations required to achieve the error reduction 10?6, where the starting vector for the iteration is zero. The iteration numbers (iterv; iterm) correspond to Algorithm 3.... ..."

Cited by 7

### Table 1. Comparison of ID-based Ring Signature from Bilinear Pairings

2005

"... In PAGE 9: ... Before our proposal, the scheme that requires the least number of pairing operations is [4]. Table1 shows a summary of the efficiency of our proposed scheme. Taken into account the total cost of the signature generation and verification, we can see that our proposed scheme is the only scheme using a constant number of pairing operations, and with the least total amount of other operations.... ..."

Cited by 8