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In the case p = 1/2, application of equation (21) to the martingale fn = Sn, together with the observation that fN = either 0 or m, yields the equalities x = f0 = E fN|f0 = x) = m[1 − Q x)], which can be immediately solved to give the answer in equation (6).
which is easily solved to give a solution in terms of Bessel's functions.
Optimization models are NP-hard and cannot be solved to give generic solution.
The resulting set of ordinary differential equations is solved to give numerical simulations.
By using the direct integration method, the equations of motions were solved to give the dynamic responses of the railway and the carriage.
The model is solved to give unique Nash equilibria for the transaction costs of lobbying, and for the probability of the policy's political success.
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I still use the starting square clue — I'm not sure if I'll ever be good enough at diagramless solving to give that up — and got MAGI right away, but had a hard time with MOPE AROUND.
If x denotes the increased incidence excluding prevalence screens, we have: This solves to give x=1.68, a very minor change.
Finally, the eigenvalue equation is solved numerically to give the desired natural frequencies and mode shapes of the "constrained" plate.
substituted the above equations into Equations 7, 8, and 9 and the three equations solved simultaneously to give the Tg(glass cover), Tf(Air), Tw absorber).
54, 4767 4777] is solved analytically to give exact values of coalescence time in terms of bubble size and relative rise velocity.
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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