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Exact(19)
The equation itself is farcical.
The equation itself wasn't the real problem.
The equation itself is accurate for T=0.
And the book might be all the more intriguing (and difficult to do) because Fitzgerald had never been able to give us the equation itself, a tidy little e=mc2.
Not everyone liked the axiom of equality … but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it.
The original work by Rodriguez and van Kampen outlined a method of extracting information from the Fokker-Planck equation without having to solve the equation itself.
Similar(41)
By the compactness theorem, we get the existence of the viscosity solution of the diffusion equation itself.
(The wave equation itself and the fully implicit difference equations satisfy this criterion, but neither of Lees' methods do).
This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the differential equation itself has the oscillatory terms.
For standard collision processes, the Boltzmann equation itself fails to meet the second requirement for d = 2, 3 spatial dimensions, on account of its setting in 2d, while for d = 1 the first requirement is violated because the Boltzmann equation then lacks the convergence-to-equilibrium property that forms the substructure of simplified models.
The condition (i) is trivial based on the disk equation itself.
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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