Sentence examples for weaker assumption from inspiring English sources

So most economists are content with a slightly weaker assumption: that people respond in approximately rational ways to the information available to them.

In 1816 Gauss attempted another proof, this time relying on a weaker assumption known as the intermediate value theorem: if f(x) is a continuous function of a real variable x and if f(a) < 0 and f(b) > 0, then there is a c between a and b such that f(c) = 0 (see figure).

Consequently, all results of the present section stay valid with this weaker assumption.

We replace the completeness of X with the weaker assumption (cc).

However, despite the weaker assumption in the second formulation of the Church Rosser theorem, the two theorems are equivalent.

The proof under this weaker assumption on Ω does not require any modifications of the method in [1].

Remark 3.6 The condition (1.5) of Theorem 3.5 is weaker assumption than assumption (iii) of Theorem 1.1.

Some weaker assumptions are established.

Some weaker assumptions have been established.

Moreover, many results are established under weaker assumptions.

Under some weaker assumptions, the multiplicity and boundedness of solutions for these equations are obtained.