### Table 1: Expected number of real eigenvalues Exact Formulas for En. (Some notation is de ned below the box.) If n is even,

"... In PAGE 3: ... We provide a Mathematica expression for En below and list enough values of En to suggest a conjecture which turns out to be true. Table1 tabulates En for n from 1 to 10 and suggests a di erence in the algebraic form of En for n even or odd. We see that a 10 by 10 random matrix can be expected to have fewer than 3 real eigenvalues.... ..."

### Table 2. Exact operation sequence of our hardware implementation of formula (8)

2005

Cited by 5

### Table 4.2: Quadrature formulas for triangles. Formula Number of exact for number points

### Table 4.4: Quardature formulas for pentahedra. Formula Number of exact for number points

### Table 2.3: Quadrature formulas for triangles. Formula Number of exact for number points

### Table 2.5: Quadrature formulas for pentahedra. Formula Number of exact for number points

### TABLE III (A): EXACT PROPAGATION CONSTANTS OF THE TE LEAKY MODES AND RELATIVE ERRORS OF THE APPROXIMATE FORMULAS (31) AND (32). (B): EXACT PROPAGATION CONSTANTS OF THE TM LEAKY MODES AND RELATIVE ERRORS OF THE APPROXIMATE FORMULAS (34) AND (35).

### TABLE I EXACT PROPAGATION CONSTANTS OF THE TE LEAKY MODES AND RELATIVE ERRORS OF THE APPROXIMATE FORMULAS (15) AND (16).

### Table 1: Comparison of the exact formulae (12) with nite chain size data for N = 12 and less sites and with the 3rd-order perturbation formula for = 0:50 and = apos; = 2 (superintegrable case). In the last column we indicate how high up in its (Q = 2; P )- sector the quoted energy level appears. For Q = 1 the nite-N-values are always the Q = 1-ground state (1st) levels.

"... In PAGE 8: ...ore than one N can be used, e.g. P = 2 =3 which is reached for N = 12; 9; 6; 3 with k = 4; 3; 2; 1. Table1 gives such data for the case = 0:5 of of Fig. 4.... In PAGE 8: ... About the Q = 1-levels we are on quite safe grounds to assume that these approximate the well-isolated Q = 1-quasiparticle exponentially fast for N ! 1. Table1 shows clearly that the convergence in N to the high-lying Q = 2-levels is practically as good as that of the Q = 1-levels and consequently also 2Also the E1(P)-third order perturbation curve (7) (not shown in the Figure) agrees still within lt; 2% with the exact expression.... In PAGE 10: ...g. for = 0:5 and P = 2 3 the next neighbouring levels to those quoted in Table1 are: for N = 12: 5:8192=6:0000=6:1965, for N = 9: 5:6962=5:9998=6:2942 and for N = 6: 5:3865=5:9964=7:8306. For = 0:5 and P = at N = 12 we have the neighbours 5:2154=5:4755=5:9303 which are also well separated.... In PAGE 11: ... In the last column we indicate how high up in its (Q = 2; P )-sector the particular quoted energy level appears. In contrast to Table1 , here for Q = 1 the levels approximating the curve E1(P ) are not always the Q = 1-ground state levels. Recall Fig.... In PAGE 12: ... 5 one clearly distinguishes three curves, one for each N = 6; 9; 12, which follow each other very closely for 90 and separate in the region lt; 90 . At = 90 this is the Q = 2?particle of (12), and the three values for N = 6; 9; 12 are those of Table1 (5:9999978 etc:). Notice that indeed there are no other levels close to 6.... ..."