The phrase "assumed on this" is not correct in standard written English.
It may be intended to convey a meaning related to making an assumption regarding a specific topic, but the preposition "on" is not appropriate in this context.
Example: "It is assumed that the results will improve with further testing."
Alternatives: "assumed regarding this" or "assumed about this."
The danger, as As Nearly Legal pointed out above, it that it is optimistic to assume councils will happily take on this potential new funding burden.
We cannot assume on this record that the action of the senate was without a legitimate object, and so encroach upon the province of that body.
'We cannot assume on this record that the action of the Senate was without a legitimate object;' and also that 'it was certainly not necessary that the resolutions should declare in advance what the Senate meditated doing when the investigation was concluded.' 166 U. S. 669, 670, 17 S. Ct. 681.
We cannot assume, on the basis of this one exemplar, that quadrupeds are inevitably exactly like this one, and thus of the kind deer.
"China cannot assume, on the basis of this election, that he's a one-term president," said William C. Kirby, the director of the Asia Center at Harvard University.
The problems dealt with in this book assume, on the contrary, that the "target" is an independent player of equal status to the Searcher, who cares about when he is found.
Assume, on the contrary, (5.15).
The designers don't really make clothes so much as sample them, turning out reworked pieces they dig up from garage sales, thrift shops and waste bins -- a way of commenting, one can only assume, on how perversely acquisitive this particular affluent society has become.
Following relapse, patients across both arms switch to treatment with quetiapine (QTP) + VPA or QTP + Li (a 50/50 split is assumed), remaining on this treatment until the end of the modeled time horizon.
