### Table 2. The Lattice MCFQRD POS B Equations.

"... In PAGE 8: ...in Table 1 can now be carried out in a forward manner. The rotation angles Q(i) (k + 1) are obtained through Q(i) (k + 1) i 1(k + 1) 0 = i(k + 1) f(N i+2)(k + 1) (35) and the joint estimation is performed according to e(i) q1 (k + 1) d(N i+1) q2 (k + 1) = Q(N i+1) (k + 1) e(i) q1 (k + 1) 1=2d(N i+1) q2 (k) (36) In order to adequate the equations of steps 1 to 3 of the algorithm as in Table 1 to this formulation, it su ces to observe that they can be easily split up into M M blocks that will be executed recursively as shown in Table2 . It is worth mentioning that, for the sake of simpli cation due to space constraints, we have used matrix notation in the single loop operations as shown in Table 2.... In PAGE 8: ... The rotation angles Q(i) (k + 1) are obtained through Q(i) (k + 1) i 1(k + 1) 0 = i(k + 1) f(N i+2)(k + 1) (35) and the joint estimation is performed according to e(i) q1 (k + 1) d(N i+1) q2 (k + 1) = Q(N i+1) (k + 1) e(i) q1 (k + 1) 1=2d(N i+1) q2 (k) (36) In order to adequate the equations of steps 1 to 3 of the algorithm as in Table 1 to this formulation, it su ces to observe that they can be easily split up into M M blocks that will be executed recursively as shown in Table 2. It is worth mentioning that, for the sake of simpli cation due to space constraints, we have used matrix notation in the single loop operations as shown in Table2 . However, when implementing these equations, it is straightforward to reduce the simple Givens rotations matrices into scalar operations.... ..."

### Table 1. Equational complexity of three classes of lattices

### Table 1. Equational complexity of three classes of lattices

### Table 11: Implementation techniques for some common communication patterns in application kernels. sequentially) indexed. This boson Monte Carlo code uses a Cartesian lattice with periodic boundary conditions and uniform site connectivity resulting in stencil communication. The implementation can bene t strongly from local optimizations. 3{D Di usion Equation: Explicit Finite Di erence This di usion equation simulation is the integration of the three{dimensional heat equation using an explicit nite di erence algorithm, which is stable subject to the Courant condition dt lt; dx2=D, where D is the di usivity. The di erencing scheme of diff-3D is F(x; y; z; t + 1) ? F(x; y; z; t) dt

"... In PAGE 10: ... Both codes perform AABC communication with respect to the index space. On the other hand, Table11 states that if the implementation of AABC in the form of SPREADs is of interest, then md is the code of choice. Alternatively, n-body apos;s AABC includes CSHIFTs and a Broadcast from one processor or the Control Processor.... ..."

### Table 1. Integration statistics for the test equation (15)

"... In PAGE 16: ...Table 1. Integration statistics for the test equation (15) Table1 indicates clearly that the EPOCH scheme is able to integrate... ..."

### Table 2: Weakly singular integral equation, p-version

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### Table 1: Numerical results for integral equation for the domain (5.8)

"... In PAGE 20: ...8) and (5.9) The Table1 gives the values of the approximate solution apos;n at the parameter points t = j=8; j = 0; : : : ; 4; for the coupling parameter in (2.14) chosen to be = 1 and for various n.... ..."

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### Table 1: Numerical results for integral equation for the domain (5.8)

"... In PAGE 20: ...8) and (5.9) The Table1 gives the values of the approximate solution apos;n at the parameter points t = j=8; j = 0; : : : ; 4; for the coupling parameter in (2.14) chosen to be = 1 and for various n.... ..."

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### Table 1: Integration Tests

"... In PAGE 6: ... Definitions and sources of all variables are detailed in an appendix. The time-series properties of the variables in the price equation are described in the upper panel of Table1 . Since world prices are denominated in dollars, the dollar exchange rate (NER) is added to the variables introduced in the previous section as the appropriate means of conversion.... In PAGE 6: ... With the exception of spare capacity all variables are clearly I(1), and therefore candidates for inclusion in tests of cointegration. Table1... ..."

### Table 1. Identi cations for Multicomponent Lattice Boltzmann Gas Lattice Boltzmann Helium II

"... In PAGE 9: ... However, gradients in the passive scalar eld a ect the ow be- cause the equation of state for the uid depends on this passive scalar. Table1 lists the lattice Boltzmann quantities in correspondence to like quantities in Helium II. For small Mach number and in the incompressible regime, the continuity equation,... ..."