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The phrase "asserts the convergence" is correct and usable in written English.
It can be used in contexts where one is stating or affirming that two or more things are coming together or reaching a common point, often in academic or analytical discussions.
Example: "The study asserts the convergence of various theories in understanding climate change."
Alternatives: "claims the convergence" or "affirms the convergence".
Exact(1)
where f h k + 1 is the L 2 2 -projection of f k + 1 = f ( t k + 1 ) on ( E h ) 2. Let us now state the second main result of this paper, which asserts the convergence of the fully-discrete scheme (61 - 62 61 - 62
Similar(59)
One of the well-known results is proven by Reich [16] for a nonexpansive mapping T on C, which asserts the weak convergence of the sequence { x n } generated by (1.10) in a uniformly convex Banach space with a Frechet differentiable norm under the control condition ∑ n = 1 ∞ α n ( 1 − α n ) = ∞.
Consequently, we can apply Lemma 2.5 with K = Fix ( T ) to assert the weak convergence of { x n } to a point in Fix ( T ).
Finally, one asserts the proposition.
The next statement asserts the converse.
"He can assert the Fifth Amendment".
I assert the same.
With a photo on the cover of Artforum, an accompanying essay by Douglas Crimp asserted that Baltrop's photos show the convergence "of artistic and sexual experimentation in the declining industrial spaces of Manhattan during the 1970s".
Sandor is known for asserting that the next financial revolution will be in the convergence of the financial markets and the environment.
"The convergence of the evidence pointed towards" Xq28 and chromosome 8, he asserts.
Still, the convergence is troubling.
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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