### Table 1. Invariant manifolds in the symmetric representation.

in c ○ World Scientific Publishing Company DYNAMICS OF THREE COUPLED EXCITABLE CELLS WITH D3 SYMMETRY

1998

"... In PAGE 5: ...n the following way [Ashwin et al., 1990]. A real variable which corresponds to the aver- age phase, that is: = ( 1 + 2 + 3)=3, and a complex variable = 1 + ei2 3 2 + ei4 3 3.The invariant manifolds in this coordinate system are shown in Table1 . The action of the symmetry group corresponds to (Fig.... ..."

### Table 2 shows the generators of the symmetric group that were obtained through the algorithm.

1990

"... In PAGE 9: ...14 :: 71823564 .... gt;(17653842) ++++++++++++++++++++++++++++++ ============================================== ============================================== Table2 : Generators of Sn. References [1] E.... ..."

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### Table 2 shows the generators of the symmetric group that were obtained through the algorithm.

"... In PAGE 9: ...14 :: 71823564 .... gt;(17653842) ++++++++++++++++++++++++++++++ ============================================== ============================================== Table2 : Generators of Sn. References [1] E.... ..."

### Table 3. Matrix Representation for Component Interdependency

2004

"... In PAGE 15: ... With regard to the software area, the input data represent interdependencies among components. For example, in Table3 , the 1 entries show that the corresponding components are interdependent. For components at the file or function level, the table represents the calling relationships among files or functions.... In PAGE 15: ... For components at the file or function level, the table represents the calling relationships among files or functions. For example, if the components in Table3 represent functions, then function E1 calls E3, E6, and E9. Note that the matrix is symmetrical and 1 entries are used in the main diagonal.... In PAGE 16: ...eyliger (1994) presents an example of coupling analysis. Fig. 5 and Fig. 6 show the component interconnections and an arbitrary grouping, respectively. To apply the clustering technique, the graph is converted to a matrix representation, as shown in Table3 . Given the input, we can calculate resemblance coefficients and apply the clustering method.... ..."

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### Table 4: Normalizers of transitive groups in the symmetric groups

"... In PAGE 8: ... In Table 3 minimum, maximum and overall average times are also shown. Table 3 shows the computation for degree 18, Table 5 for degree 20, 21 and 22, and Table4 shows the total times for computing all the normalizers of the transitive groups of degree from 5 to 19 except 18. When the degree of the transitive group is greater than 19, we interrupted to compute in 20 minutes.... In PAGE 8: ... In these cases our method is usually more than 100 times as fast as the direct computation. If the degrees are small, Table4 shows that almost all groups are computed quickly by the direct computation. Table 4: Normalizers of transitive groups in the symmetric groups... ..."

### Table 7: 2n 2n skew-symmetric skew-Hamiltonian matrices

### Table 1: 4 4 Symmetrics(S) and Skew-symmetrics(K)

"... In PAGE 8: ... For example, k j is its own conjugate, so (k j) must be symmetric; furthermore, (k j)(k j) = kk jj = 1 1, hence (k j) must also be orthogonal. Table1 shows which basis elements are symmetric and which are skew-symmetric.... In PAGE 9: ...le calculation using Eqn. (3) shows that (1 j) = J4. This is indeed fortuitous, as up to sign, B is closed under multiplication. It is easy to check that premultiplication by 1 j permutes the elements of B (again up to sign) in a simple way | the rst and third columns in Table1 are interchanged as are the second and fourth columns. Thus the Hamiltonian and skew-Hamiltonian structure of B can be quickly deduced directly from the properties of the quaternion tensor algebra: 1 i j k 1 W W H W i H H W H j H H W H k H H W H Table 2: 4 4 Hamiltonians(H) and Skew-Hamiltonians(W) Alternatively, one can use Appendix A to verify that each of the matrices in B has the structure speci ed in Table 2.... ..."

### Table 2: Skewness of Optional Parts Skewness

"... In PAGE 6: ...optional parts can be considered with or without the skew- ness of the models. Table2 shows the skewness given to the optional parts. For the eight-merchandizing model case, skewness 1 (FS1) assigns the penetration 0.... In PAGE 9: ...When the skewness is given both on the models and parts, the resulting usage patterns resemble the skewness given in Table2 and no clear skewness effect is found. From these analysis results, appropriate plan with regard to the number of models and optional parts can be developed to reduce customer wait time and condition mismatch.... ..."

### Table 2: Comparison of best solutions found genetically very di erent. The breeders call this e ect inbreeding.The above representation did not give good results, therefore we changed it slightly. The modi cation was motivated by an observation of Golay [10] . He showed that good skew-symmetric solutions of order n can be found by an interleaving of good symmetric and an- tisymmetric solutions of order n=2. We show for the case n = 13; m = 7 how this is done :

1991

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### Table 6. Functions Skewed in Domain Representation between PG and GOS

2007

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