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Exact(2)
This solution can be rewritten in the form (4.24).
Consequently, this solution can be rewritten as psi= sqrt{-lambda_{1} / gamma_{2}},qquad u=0.
Similar(58)
In order to clearly address the general solution method, Model (2) can be rewritten as follows: Min f = ∑ i = 1 N e i ± x i ± + ∑ i = 1 N g i ± x i ± y i (21).
We know from the definition of normal cone in convex analysis that the solution mapping S (3) can be rewritten as S x)=bigl{ yinRe^{m}: 0in F x,y)+N_{Omega(x)} y bigr}, where (N_{Omega(x)} y)) denotes the normal cone of (Omega(x)) at y.
end{cases}displaystyle end{aligned} (34) Then (A_{tau^) is the infinitesimal generator induced by the solution of (25) and (21) can be rewritten as the following operator differential equation: begin{aligned} dot{U_{t}}=A_{tau^U_{t}+X_{0}F(U_{t}, mu).
For example, the solutions (12) and (14) in [16] actually can be rewritten as our solutions (3.16) and (3.27), respectively.
Over time, the Pi-paper reaches equilibrium with the solution, and the kinetic Langmuir equation can be rewritten to a Langmuir equation.
Then equation (1) has at least one asymptotically stable solution x : N 0 → R. Proof From Theorem 2, equation (1) has at least one bounded solution x : N 0 → R which can be rewritten in the form x n = ( T x ) n, (18).
The solution representation of the parabolic problem (17) can be rewritten in the following form: u ( x, t ) = ψ 0 k ( 0 ) x + ψ 1 − ψ 0 k ( 0 ) + S ( t ) ζ ( x ) + ∫ 0 t S ( t − s ) χ ( x, s ) d s.
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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