The phrase "asserts that in some" is correct and usable in written English.
You can use it when discussing claims or statements made in a text or argument, particularly when referring to specific contexts or situations.
Example: "The author asserts that in some cases, the evidence may not be sufficient to support the conclusion."
Alternatives: "claims that in certain" or "states that in some instances".
The hypothesis asserts that r* xy in any window is approximately equal to a constant.
The friends of (H) aren't rejecting abduction outright: they are merely asserting that in some situations abduction is trumped by the more fundamental principle (H).
The indictment asserted that in some instances the defendants knew that the bus company owners were making payments in the belief that they would receive improper benefits in exchange, even though the defendants could not actually deliver those benefits.
Bear's executives have asserted that in some instances they refused to accept new capital because it would only exacerbate Bear's crisis by making the company look weak.
Recall that inwardness conditions are the ones which assert that, in some sense, points from the domain are mapped toward the domain.
Indeed, classical liberals and libertarians have often asserted that in some way liberty and property are really the same thing; it has been argued, for example, that all rights, including liberty rights, are forms of property; others have maintained that property is itself a form of freedom (Gaus, 1994; Steiner, 1994).
Undeterred, Mommsen, in his Beamtentum im Dritten Reich (The Civil Service in the Third Reich, 1966), provocatively asserted that Hitler was in some respects a "weak dictator" – essentially a propagandist preoccupied with upholding his own standing, an indecisive leader who stood under the influence of his entourage.
The trustee asserts that in the case against Wilpon his legal burden is modest.
To the collective chortle of the telecommunications industry, DoJ asserts that in any event telecommunications equipment does not include telephones.
