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Suppose that i + j, ζ + η, α + β and k + l are odd, for each a αβ > 0, b ζη > 0, c kl > 0 and p ij < 0; Equation 5 is to be a hyperbolic equation under condition that the power ζ = α + k 2 Open image in new window and η = β + l 2 Open image in new window and the power of x and y in polynomials a x,y), c x,y) are either even or odd.
(3) Suppose that i, ζ + η, α + β, and k + l are odd, for each a αβ > 0, b ζη < 0, c kl > 0, and p i > 0; Equation 5 is to be a hyperbolic equation under the condition that the power ζ = α + k 2 Open image in new window and η = β + l 2 Open image in new window and the power of x and y in polynomials a x,y), c x,y) are either even or odd.
(2) Suppose that i is even and ζ + η, α + β, and k + l are odd, for each a αβ < 0, b ζη > 0, c kl < 0, and p i > 0; Equation 5 is to be an elliptic equation under the condition that the power ζ = α + k 2 Open image in new window and η = β + l 2 Open image in new window and the power of x and y in polynomials a x,y), c x,y) are either even or odd.
Open image in new window (30) (b) Suppose that i + j is even and ζ + η, α + β and k + l are odd, for each a αβ < 0, b ζη > 0, c kl < 0 and p ij > 0; Equation 22 is to be an elliptic or hyperbolic equation under the condition that the power ζ = α + k 2 Open image in new window and η = β + l 2 Open image in new window and the power of x and y in polynomials a x,y), c x,y) are either even or odd.
Now, we can consider some particular cases: (a) Suppose that i + j, ζ + η, α + β and k + l are odd, for each a αβ > 0, b ζη > 0, c kl > 0 and p ij < 0; Equation 5 is to be a hyperbolic equation under condition that the power ζ = α + k 2 Open image in new window and η = β + l 2 Open image in new window and the power of x and y in polynomials a x,y), c x,y) are either even or odd.
Now, we have the following several cases: (1) Suppose that i, ζ + η, α + β and k + l are odd, for each a αβ > 0, b ζη > 0, c kl > 0 and p i < 0; Equation 5 is to be a hyperbolic equation under the condition that the power ζ = α + k 2 Open image in new window and η = β + l 2 Open image in new window and the power of x and y in polynomials a x,y), c x,y) are either even or odd.
Similar(54)
He was odd, for certain.
This confusion is odd for two reasons.
This is odd for a few reasons.
"Ah, that was odd for us, man.
That's odd for a man living in a mission".
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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