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Applying Taylor approximations to both sides and solving for, one obtains the Arrow-Pratt formula in terms of health rather than wealth (see [28], ch. 3) (7).
Solving for one of the equations in (7) and substituting the result into the other equations, we obtain an -dimensional system in the unknown vector, which can be denoted as.
The first-principle based modeling of the corona device behavior has often involved either back-and-forth iterations of solving for one of the variables with others fixed or using time integrations even when steady states are sought.
For the solution of the linear systems A xV x = Q and A mV m = G(c) V x for the forward problem, respectively, A mW m = D and A xW x = G(c) W m for the adjoint problem, we employ a preconditioned blocked conjugate gradient method (PBCG): instead of solving for one right hand side (i.e. a column in Q) after another, we solve simultaneously for all right hand sides (blocked).
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"You can solve for two variables, but maybe you're only supposed to solve for one variable at a time.
An X-ray crystal structure was solved for one of the designs, revealing a close resemblance to the target structure.
As long as one of these is non-zero (which will happen if the vectors are not all collinear), we can solve for one of the (v_{k}) and reduce the dimension by 1.
Since v j and have the same interpretation in the two model structures, we can set them equal and solve for one of the parameters, e.g., (6) Now, note that Eq. (6) gives a translation between parameters of the original and the reduced model structure.
A full numerical simulation in which the compressible reacting flow equations are solved for one-step, finite-rate chemistry is utilized to examine the effects of stoichiometry, reactant velocities, and preheating on laminar flame location and structure.
What the and mentality provides is the need to create room for both "constraints" (revenue and profit, as an example) versus solving for only one.
Finally, by setting all ∆'s to zero and solving for M, one can derive the long-run steady state relationship for net migration rates.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com