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The deal allows Syrian government warplanes to continue to fly missions in some areas that are to be defined later.
where will be defined later.
for positive constants and will be defined later.
where,,, and are real constants, (here, and will be defined later), and are positive real numbers.
where (w_{1}), α, and (C_{7}) are positive constants which will be defined later.
P is a phase space that will be defined later (see Definition 2.1).
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The Beams object (note the plural) is the object that handles groups of Beam objects; it is defined later on.
(G x,y)=G(M x,y)) is the Green function which is defined later in Theorem 3.1.
For the quintic nonlinearities term (mathcal{G}), which is defined later in (25), we assume the following.
For this purpose, let us define the functional J : = ∫ − s s | ϕ ( M ) | 2 d x ∫ − s s r ˜ | ϕ | 2 d x ( ϕ ∈ W ( M, 2 ), ϕ ≢ 0 ), where is defined later.
and the boundary condition u ( 0, t ) = u ( π, t ) = 0. To consider a more general case, we will replace D in (2) by a given function a ( t ) which is defined later.
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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