"... In PAGE 2: ... (2003). In the simulation, the mass of the parent star is 1:03M , and those of three orbiting planets are adopted as 0:83Mjup,0:20Mjup and 3:69Mjup respectively (see Table1 ), by assuming sin i = 1. In preparation of the orbital elements for integration, we assume that all of the planets are initially in the same plane, then x their semi-major axes and eccentricities and the remainder angles (nodal longitude, argument of periastron, mean anomaly) are randomly generated for each orbit.... In PAGE 2: ... More than 90 percents of the systems that are not linked to the 3:1 MMR become unstable in thousands of years. In Table1 , we list one set of the values out of 8 orbital solutions in association with the 3:1 MMR and apsidal resonance. To examine our orbital solution based on Fischer et al.... In PAGE 4: ... Hence, we can discuss the secular dynamics of Companions B and C by ignoring Companion D, without changing the quantitative results. The linear L-L secular solutions for the eccentricities(Murray amp; Dermott 1999)can be written: ej sin ~ !j = ej1 sin(g1t + 1)+ej2sin(g2t + 2); ej cos ~ !j = ej1 cos(g1t + 1)+ej2cos(g2t + 2); (1) where eji, gi and i (j; i =1;2, j = 1 for Companion B, j = 2 for Companion C) can be evaluated by the initial conditions in Table1 , and t denotes time. For this case, we obtain two eigenfrequencies g1 =0:727 /yr and g2 =0:128 /yr.... In PAGE 4: ...ncrement of 0.1 from 0.1 to 0.9. In the complementary experiments, we integrate the system for 1 Myr with rescaled masses and the orbital parameters in Table1... ..."

"... In PAGE 1: ... Each technology has unique strengths and weaknesses. Existing systems can be grouped into two categories: active target and passive target ( Table1 ). Active-target systems incorpo- rate powered signal emitters, sensors, and/or landmarks (fiducials) placed in a prepared and calibrated envi- ronment.... In PAGE 2: ... Passive-target vision and iner- tial sensors create a hybrid tracker for mobile robotic navigation and range estimation.10,11 Table1 presents these and other examples. A more complete overview of tracking technologies can be found elsewhere.... ..."

"... In PAGE 5: ... (We note that Mukai 1998 proposes an alter- native model for V1432 Aql in which it is an intermediate polar with a spin period of 67 min and an orbital period of 202 min). The rst three such systems ( Table2 ) had orbital periods which clustered closely around 200 mins giving rise to some speculation that such an orbital period was special in some way for these objects. The discovery of RX J2115{ 5840 with an orbital period of 110 mins suggests that it is not.... ..."

"... In PAGE 15: ... O(n) is much smaller than C(n) as several xed points of Pn correspond to the same periodic orbit and there are some xed poins of Pn with period smaller than n. In Table1 we summarize the values of O(n) and C(n) for n smaller than 11. For example for n = 2 there is only one period-2 orbit of P corresponding to the sequence (0; 1) and there are three xed points of P2 with sequences (0; 0), (0; 1) and (1; 0).... In PAGE 16: ...Table 1: O(n) | the number of di erent periodic orbits of period n, C(n) | the number of xed points of Pn of the orbits (a), (b) and (c) is guaranteed by Theorem 4. These are all of the periodic orbits with period less than four, which exist according to Theorem 4 (compare Table1 ). Apart from these orbits we have found many other periodic orbits.... ..."

"... In PAGE 6: ... As these units are not accessed, the clock power is lower as well, leading to a smaller average power. Table5 shows how much variation there actually exists between the invocations of the services across the bench- marks. The variation is measured using the coefficient of deviation and is expressed as a percentage.... ..."

"... In PAGE 6: ... As these units are not accessed, the clock power is lower as well, leading to a smaller average power. Table5 shows how much variation there actually exists between the invocations of the services across the bench- marks. The variation is measured using the coefficient of deviation and is expressed as a percentage.... ..."

"... In PAGE 6: ... The control system expanded to incorporate the new be- havior, Q 9 as shown in Figure 3#28e#29. From the behavior sequence of Table3 and Figure 5, it is seen that behavior Q 9 quickly exploited the existing behaviors Q 5 , Q 6 and to a greater extent Q 7 and Q 8 . The performance of the hierarchical control system and its component behaviors are shown in Figure 8#28b#29.... ..."

"... In PAGE 6: ... The two existing behaviors quickly integrated the new behav- iors into their action sequences. The hierarchical struc- ture of the control system is further shown in the new action sequence when behavior behavior Q 6 was acti- vated is shown in Table2 and Figure 4. This shows that the sub-behaviors, Q 7 and Q 8 are evident in the state- action-behavior trajectories of the higher level behaviors Q 5 and Q 6 #28not shown#29.... ..."