"... In PAGE 8: ...epresents the particle speed at the base of the permanent thermocline, i.e., at the fairly sharp interface between the ocean apos;s more active upper layer and less active lower layer. The appropriate scales and physical parameters for the North Atlantic are listed in Table1 , with L chosen as the characteristic length Table 1 of the rst baroclinic deformation radius at mid-latitudes. The nondimensional potential vorticity (PV) equation with this scaling is @q @t + @ @x + J( ; q) = rHr4 ; (1a)... In PAGE 20: ... In the W region the dominant terms are the -term (@ k=@x), lateral di usion rHr4 k and nonlinear advection k11J ( 1; q1), for both k = 0 and k = 1. O the coast and up to a distance of 3=5 from it, the -term is balanced by the horizontal friction in a Munk [2] layer; x = 3=5 is the nondimensional width of the frictional boundary layer obtained for rH as given by the dimen- sional AH in Table1 . Further eastward the role of the nonlinear advection term increases and that of the friction decreases (not shown).... In PAGE 33: ... (5). In prac- tice, for the numerical QG model (7) we use the value 111 = 1:8 for the only triple interaction coe cient that is not equal to 0 or 1 and 1(0) = 4, while 0(z) = 1 and it is customary to set 1(1) = ?1=2 (see Table1 ). These values for 111 and 1(0) correspond to the North Atlantic apos;s strati cation (see Flierl... In PAGE 38: ...t al. [13]. The rectangular domain has an east-west extent of 1000 km and north-south extent of 2000 km. The model apos;s xed parameter values di er in certain details from those given in Table1 here; they are given in Table 1 of JJG. The system of equations (2.... In PAGE 38: ... The system of equations (2.1) of JJG was nondimensionalized using the characteristic scales given in Table1 here, to be consistent with the QG model above. The model equations are solved on a staggered C grid with a mesh size L x = L y = 12:5 km and a time step T t = 600 s, using no-slip boundary conditions.... ..."

"... In PAGE 15: ...oftware platform [23]. The experiments reported below were performed on a 1.2GHz G4 Pow- erPC running on Mac OS-X. The performance results summarized in Table2 correspond to aver- age values computed over several runs of the algorithm. The first experiment shown on Figure 18 compares the level of redundancy obtained depending on the algorithm used: (a), a minimum tree structure obtained with the Visibility-PRM, (b) a first-... In PAGE 16: ... The second scene (b) has a higher geometrical complexity (70 000 facets). The computing time (164 secs) reported in Table2 shows that the algorithm can efficiently handle such geometrically complex scenes. One can also note that the resulting 2D roadmaps contain a very limited number of additional nodes compared to homotopy.... In PAGE 17: ... In both cases, the number of roadmap cycles, although limited, makes it possible to find shorter paths during the query phase. Finally, the performance results are summarized in Table2 which also provides a break-up of the total computing time showing the respective contributions of the visibility tree building and the cycle addition stages.... ..."

"... In PAGE 18: ... At the end we give a table with corresponding apos;s for Table 1. The last two column of Table2 are the number in [BHH] and [M2]. Looking at tables 1 and 2 we see Theorem 3.... ..."

"... In PAGE 7: ... We calculated the ratio between all of the pos- sible NE pairs in the source language and those translated into the target language with the same order of occurrence. Table7 lists the average preservation ratios of the NE order for all NEs ( All ) and for NEs having corresponding NEs in the counterpart ( Corr. only ).... ..."

"... In PAGE 15: ...is simply not much to improve. 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 70 80 90 100 log2(k+1) preserved energy adapk eachk bestk firstk Figure 3: Energy preservation with Haar DWT for sp500 The results for all time series data sets and the Haar DWT are listed in Table3 . The percentage di erences listed correspond to the bold column of Table 2, that is the additional energy preserved by bestk over rstk .... ..."

"... In PAGE 43: ... Figure 10: Deformable roll-nip metering flow. Undeformed mesh (top); de- formed mesh (middle); pattern of streamlines (bottom) Convergence results are shown in Table3 . The first row corresponds to an unordered matrix system.... ..."

"... In PAGE 4: ... If the error a103 a11a0 is greater than predefined tolerance a103 a13a12 , we declare that the estima- tion fails; otherwise, it succeeds. In the result shown in Table1 , a103 a13a12 a1 a58 a18 a58 a16 , a25 a13 a17 a1 a11 a59a58a18a17 , a27 a1 a58 a18 a124 , and a25 a89 a17 is the percentage of the correct deformation parameter esti- mation among 500 realizations for each a25 a26 . To measure the rate of correct correspondence estimation, we let a25 a88 denote the fraction of trials where the estimated corre- spondence contains no mismatch between any of the fish model features and the synthetically generated features.... In PAGE 4: ...correspondence estimation results from two parts: 1) in- herited from deformation parameter estimation step; 2) the correspondence estimation itself. Therefore, the per- centages of correct estimated correspondence as shown in Table1 are slightly less than the corresponding per- centages of correct estimated deformation parameters. 5.... ..."