### Table 1: Possible combinations of nite subgroups of O(2): , ~ , and ^ satisfying the mutual relations (3.23). Also listed are pairs of reversing symmetry groups 0 and 1 2q arising in the return maps of surfaces of section S0 and S 1 2q (choosing the time-coordinate such that whenever 6 = ^ , 0 contains a reversing symmetry). Here, Zn and D n denote the standard representation of the cyclic and dihedral groups in R2 (i.e. the cyclic group generated by a rotation and the dihedral group generated by re ections), and p 2 Z+:

1998

"... In PAGE 15: ...xample 4.3 (Spatiotemporal symmetry groups in R2.) As an example, we examine the occurrence of nite subgroups of O(2) arising as spatiotemporal symmetry groups. In Table1 we list the possible combinations of groups , ~ , and ^ and corresponding pairs of reversing symmetry groups 0 and 1 2q (assuming whenever 6 = ^ that 0 con- tains at least one reversing symmetry). Note that pairs of nonisomorphic dual reversing k-symmetry groups only arise in the last entry of this table, when p gt; 1.... In PAGE 17: ...ime-shift symmetry). Recall in this respect from the proof of Theorem 4.1 that whenever q is odd, 0 is conjugate to 1 2q so that whenever q is odd these groups always have equivalent representations. From Table1 one obtains that in the case of O(2) in R2 there is only one situation in which one nds nonequivalent representations: when = D 2, ^ = D 1 and ~ = Id, we nd dual nonequivalent representations of the cyclic group of order two: Z2 and D 1. Example 4.... ..."

Cited by 5

### Table 2: The group D 4 of dihedral symmetry of a square.

"... In PAGE 2: ... DIHEDRAL SYMMETRY OPERATIONS ON JPEG IMAGES The operationsdefined by compositionsof flips aboutthe di- agonal and about the Y-axis form the group of dihedral sym- metry of the square, referred to as D 4 . These operations are listed and described in Table2 . The second column defines the result of of an operation o on pixel block f;; along with the equivalent DCT-domain relationshipbetween oF and F.... In PAGE 3: ... Let F k denote the 8 8 block numbered k in raster or- der of blocks of quantized DCT coefficients for I. Let I o de- note the result of applyingoperation o on the image (where o is one of the D 4 operations from Table2 ). From the preced- ing section, it is apparent that the quantized DCT coefficient blocks of I o will essentially be the same as those in I, with possible block reordering, transposition, and sign changes, and the quantization table will also be the same, with possi- ble transposition.... ..."

### Table 2: The group D 4 of dihedral symmetry of a square.

"... In PAGE 2: ... DIHEDRAL SYMMETRY OPERATIONS ON JPEG IMAGES The operationsdefined by compositionsof flips aboutthe di- agonal and about the Y-axis form the group of dihedral sym- metry of the square, referred to as D 4 . These operations are listed and described in Table2 . The second column defines the result of of an operation o on pixel block f;; along with the equivalent DCT-domain relationshipbetween oF and F.... In PAGE 3: ... Let F k denote the 8 8 block numbered k in raster or- der of blocks of quantized DCT coefficients for I. Let I o de- note the result of applyingoperation o on the image (where o is one of the D 4 operations from Table2 ). From the preced- ing section, it is apparent that the quantized DCT coefficient blocks of I o will essentially be the same as those in I, with possible block reordering, transposition, and sign changes, and the quantization table will also be the same, with possi- ble transposition.... ..."

### Table 2. Timing statistics for preprocessing step-2: artistic mip-map generation (AMG).

"... In PAGE 23: ... 945 Furthermore, examining the AMG results shown in Table2 , when we adopt two levels of down-sampled resolutions for the rendered images, the time required for down-sampling color and vector information is almost negligible, being less than 0.1 second.... ..."

### TABLE I Number of generations in CPm models orbifoldized by cyclic permutation symmetries

### Table 3: Details of artistic enhancements.

in Psychophysically based artistic techniques for increased perceived realism of virtual environments

2003

"... In PAGE 5: ...these twelve images, two were photographs of the scene, one with and one without flash. Of the remaining ten images, one each was rendered at low, medium and high quality respectively and seven were artistically enhanced as described in Table3 . Each observer had a maximum of two minutes to look at the images.... In PAGE 5: ...mage the test statistics was (x2=30.64, df=3, p lt; 0.001). A surprising result was that those enhanced images which included noise, images 3, 6 and 7 (shown in Figure 10) as described in Table3 , appeared to the viewer to be more quot;realistic quot; than the same images without the noise, images 2, 4 (shown in Figure 11) and 5 from Table 3. The real scene does not, of course, contain any noise, however, it emerged from the participants apos; comments that noisier images were perceived as being more similar to a photograph and therefore, the observer considered them more realistic.... In PAGE 5: ...mage the test statistics was (x2=30.64, df=3, p lt; 0.001). A surprising result was that those enhanced images which included noise, images 3, 6 and 7 (shown in Figure 10) as described in Table 3, appeared to the viewer to be more quot;realistic quot; than the same images without the noise, images 2, 4 (shown in Figure 11) and 5 from Table3 . The real scene does not, of course, contain any noise, however, it emerged from the participants apos; comments that noisier images were perceived as being more similar to a photograph and therefore, the observer considered them more realistic.... ..."

Cited by 3

### Table 1. Generating set of the grid symmetries Argument Images

2000

Cited by 7

### Table 5: Summary of Cyclical and Non-cyclical Approaches

2004

"... In PAGE 35: ...ection 2.4). However, once the requirements are set, cyclical schedules are much easier to generate than others because the search space is considerably smaller. Table5 divides approaches into cyclical, semi-cyclical, and non-cyclical methods. The left column enumerates some of the pure cyclical methods.... ..."

Cited by 24

### Table 1 Operating conditions for carbonyl generation, trapping and atomization

"... In PAGE 3: ...ump speed is, the smaller are the signals for nickel. From Fig. 5 it can be seen that the length of the reaction coil is also a factor, which emphasizes the importance of the time of formation of nickel tetracarbonyl. The operating conditions for the carbonyl generation, trapping and atomization are summarized in Table1 . The I I.... In PAGE 5: ... I I I 0 1 10 20 30 40 Concentration/pg I- apos; Fig. 6 Calibration curve in the range 040 yg 1-1 for a 500 p1 sample loop (operating conditions given in Table1 ). A, Peak area; B, peak height.... In PAGE 5: ... To eliminate the matrix effects only the standard additions method was used to obtain accurate results. The samples for the carbonyl-generation system are prepared as mentioned above and measured with the described method by using the parameter in Table1 . The results obtained by this method were compared with those obtained by ETAAS.... In PAGE 5: ...040 Time/s Fig. 7 (a) Signal of 50 ng 1-1 nickel after preconcentration of 10 ml of synthetic rain water acidified with sulfuric acid and using the parameter in Table1 . (b) Signal of blank solution (10 ml sample volume containing only the synthetic rain water acidified with sulfuric acid) in direct comparison with the signal of 50 ng 1-1 nickel.... ..."

### Table5.Summary of cyclical and non-cyclical approaches

"... In PAGE 41: ...see also Section 2.4). However, once the requirements are set, cyclical schedules are much easier to generate than others because the search space is considerably smaller. Table5 divides approaches into cyclical, semi-cyclical, and non-cyclical methods. The left hand column enumerates some of the pure cyclical methods.... ..."