Sentence examples for us to solve for from inspiring English sources

This formalism allows us to solve for discretized atomic shape function(s) (mathbf {s}_j) using the set of linear equations given by begin{aligned} mathbf {A} begin{bmatrix} A_0 s_1 vdots s_J end{bmatrix} = psi (x,y), end{aligned} (2 which can be solved using typical regression methods.

The first term is then linear in, allowing us to solve for a scaling factor s to minimize the misfit with the satellite-derived current.

Numerical considerations lead us to solve for F, instead of f, since delta functions are difficult to represent in floating point, while the initial conditions for F, the Heaviside step function, H ( x ), faces no such difficulties [24].

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In general, it is not feasible to solve for (g^{H}) symbolically: this requires us to solve for the roots of a cubic polynomial involving exponential functions (e.g. (tanh(g x_{E}))) of implicitly defined parameters (x_{E}), (x_{I_{1}}), and (x_{I_{2}}).

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This allows us to solve directly for equilibrium land temperature, making ENTS very computationally efficient and avoiding problems of numerical instability that beset many land surface schemes.

This transformation allows us to solve problems for which corresponding routines in the LAPACK library as well as widely used projection methods converged either very slowly or not at all.

Finally, the FMM is shown to reduce CPU time and memory requirement thus enabling us apply BEM to solve for large-scale problems.

This allows us to solve the problem for the motion of the two fluids analytically.

Therefore, these results provide the possibility for us to solve the Cauchy type problem for interval-valued fractional equations by the corresponding integral equation.