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The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes.

German government sources suggest that a "constructive solution" mentioned in Merkel's blunt statement could take the form of the UK agreeing to a formula by which Britain's future contributions in specific areas, such as pensions, EU budget, growth funds, would be calculated thus avoiding coming up with concrete sums.

Coupling the flame model with a Galerkin series expansion of the acoustic waves present enables the time evolution of flow disturbances to be calculated, thus providing a platform on which to gain insights on the Rijke tube stability behaviors.

Coupling the unsteady heat release model with a Galerkin series expansion of the acoustic waves present enables the time evolution of flow disturbances and acoustical energy to be calculated, thus providing a platform on which to gain insight on the system's transient stability behaviors and the non-normal response of the system to the dynamic actuators.

In the same method H2 can be calculated, thus the height of COG H is: H = H_{1} - H_{2}.

Otherwise, an inaccurate MVP would be calculated, thus affecting coding efficiency, since an inaccurate MVP means that the optimal (or nearly optimal) matching block cannot be found.

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The distance from the example to all the other samples in the database was calculated, thus the total number of distance calculations in test was, where is the number of samples in the database.

The UK steel industry warned that Washington was planning to get round the WTO ruling by changing the way anti-dumping duties are calculated, thus extending the tariffs for up to three more years.

Second, the electric field along the axis of the round hole is calculated, thus allowing us to evaluate an alternative mechanism for charge redistribution from the plane parallel case to the case of a field with axial symmetry.

Second, the correlation between these two filtered images is calculated, thus obtaining the spatial correlation coefficient (SCC).

The root mean square error (RMSE) between the predicted and actual intrusion volumes; Vpredicted and Vactual, respectively, over n pressure data points for each of the core samples is calculated thus: RMSE = ∑ i = 1 n ( V predicted − V actual ) 2 n, (7)and the pore fractal dimension which quantifies the fractal geometry of the core sample is estimated (see Webb 2001).

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