### Table 3: Maximal partial ocks of a hyperbolic quadric in PG(3; q) Set Plane Name Group size

1998

"... In PAGE 6: ... The basic orderly algorithm is used to construct maximal cliques in the graphs G1(E) and G2(H) for elliptic and hyperbolic quadrics in the spaces PG(3; q) for all q 13. Table 2 shows the results for the elliptic quadrics and Table3 for the hyperbolic quadrics. For the elliptic quadrics, these results con rm the existence of the maximal partial ocks of de ciency one found by Orr and prove their uniqueness.... ..."

Cited by 6

### Table 7: Estimates for data sets with sample size n (sampling distribution: maximum likelihood estimate of the generalized hyperbolic distribution for Bayer returns). 14

1997

"... In PAGE 7: ... Note that the choice of the sampling distributions restricts the validity of the following results to nancial return data sets. In Table7 we provide the results of the simulation for Bayer. Similar results were also obtained for other sampling distributions.... In PAGE 7: ... Similar results were also obtained for other sampling distributions.In Table7 we see that for large n the parameter is close to the sampling distribution. This reveals that the estimation of sub-classes characterized by is quite good although the di erence between the sub-classes in terms of the likelihood is small.... In PAGE 8: ...Kolmogorov Distance Anderson amp; Darling Statistic 50 0:046873 2748:095 100 0:028267 10:383349 125 0:042437 0:088472 150 0:013544 0:032380 175 0:005031 0:025219 200 0:021564 0:050546 350 0:021612 0:049411 500 0:020363 0:051141 1000 0:018077 0:050193 2000 0:010560 0:025539 5000 0:006787 0:016018 10000 0:001574 0:013654 Table 2: Kolmogorov distance and Anderson amp; Darling statistic for the estimates given in Table7 (sampling distribution: maximum likelihood estimate for Bayer share). sampling and the estimated distribution.... ..."

Cited by 2

### Table 5: Accuracy on UCI data sets when applying other correction methods: (discontinuous) sign (Eq. 11), sigmoid with = 10; 100 (Eq. 14), arctangent (Eq. 13), and hyperbolic tangent (Eq. 12).

2002

"... In PAGE 9: ...ccuracy, and some improvements are very signi cant (e.g., glass and liver-disorder ). We next report performance on these data sets using the sign-based corrections and their smooth approximations as shown in Table5 . The second column gives again the neural network baseline results.... ..."

### Table 2. Estimated parameters for the hyperbolic distribution

1995

"... In PAGE 12: ...0 1 2 3 4 567 8 9 10 Laplace exponential exponential normal H(+) H(-) Figure 6. The hyperbolic shape triangle The location of the estimates for the invariant parameters (^ ; ^ ) is indicated by the numbers 1 to 10, where the numbers correspond to the order of the shares in Table2 . The locations of the limits of hyperbolic distributions are indicated, where H(?) (resp.... ..."

Cited by 39

### Table 4. The rotation angles in hyperbolic co- ordinates

"... In PAGE 5: ... In [2], it was recommended that every 4th, 13th, (3k+1)th iteration should be repeated to complete the angle representation. Table4 shows the incomplete relationship of the angles i. Just as in the case for circular coordinate systems, a correlation between representation of d and the input angle can be obtained (see Fig.... ..."

### Table 3.1: Euclidean and hyperbolic formulas.

2000

### Table 5. The 38 minimal hyperbolic Coxeter diagrams. (Continued on next page.)

2002

"... In PAGE 28: ...61803 (1 + x)3(1 ? 3x + x2) X6 2.61803 (1 + x)4(1 ? 3x + x2) Table5 . (Continued.... In PAGE 29: ... Removing the non-minimal elements from this list of 75, we are left with the 38 diagrams shown in Table 5. Guide to Table5 . The rst column in Table 5 gives the notation for the Coxeter system (W; S); the second, its diagram.... In PAGE 30: ...roof of Theorem 6.1. Suppose (W; S) gt; 1. By the preceding results and the bicolored bound (Theorem 5.1), there is a hyperbolic or higher-rank subsystem (WI; I), I S, and a minimal hyperbolic diagram (W 0; S0) (WI; I) such that (W; S) = Cox(WI; I) (WI; I) (W 0; S0): Inspection of Table5 shows (W 0; S0) Lehmer for all minimal hyperbolic Coxeter systems, completing the proof. 7 Small Salem numbers In this section we conclude by detailing some connections between the sim- plest Coxeter systems and small Salem and Pisot numbers.... In PAGE 31: ... Since Coxeter elements minimize (w), they provide a geometric source of small Salem numbers. For example, from Table5 one can verify: Proposition 7.3 The smallest Salem numbers of degrees 6, 8 and 10 coin- cide with the eigenvalues of Coxeter elements for Eh8, Eh9 and Eh10.... In PAGE 33: ... Indeed, there exists a minimal hyperbolic Coxeter system with (W 0; S0) (W; S) and hence (W 0; S0) lt; Pisot. Referring to Table5 , we nd (W; S) Eh9 = Y2;4;5 or (W; S) Eh10 = Y2;3;7: In particular, D contains a copy of the Y2;3;5 diagram, possibly with higher weights. Next we claim all the edges of D have weight 3.... ..."

### Table Lens Other Focus + Context tools: cone tree, hyperbolic browser

2006