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We just give here the main idea to prove both.
In addition, for the continuous case, we provide a new idea to prove its permanence.
And the idea to prove (3.13) comes from Theorem 3.2 of [50].
Next, we use this idea to prove that the scheme (7 - 8) converges.
The comparison principle is the main idea to prove Theorem 4.
Finally, we also apply a similar idea to prove some new norm inequalities in Orlicz spaces in which the properties of N-functions and superquadratic functions are involved.
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Dingane further extends this idea to proving one's heterosexuality and that by having sex with and impregnating a young woman, the threat of being labelled as 'gay' is reduced.
Employing these ideas to prove that the Entscheidungsproblem is unsolvable.
Lurie embraces an extraordinary breadth of vision, rewriting large swaths of mathematics from a fresh point of view, while also working to apply his foundational ideas to prove important new theorems in other areas.
Because of the protocols' complexity, their correctness is not obvious; hence, we present the ideas to prove the lock protocol correctness guaranteeing the specified data processing behavior of the given XDP operations.
With Greenhill having come up with the new ideas to prove people wrong, Walker wants to avoid reinventing the wheel.
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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