Sentence examples for extended proposition from inspiring English sources

Meanwhile, the extended proposition in [1, Section ] does not stand.

Hence Theorem 2.1 extends Proposition 3.1 in [6].

Lemma 2.5 extends Proposition 4.1 of Chen et al. in [4] and Lemma 2.6 of Zhong-Huang in [6].

Remark 2.8 In special cases as those in Section 1 (d), (e) and (f), (i) Lemma 2.5 extends Proposition 4.1 of Chen et al. in [4] and Lemma 2.6 of Zhong-Huang in [6].

Step 4 extends Proposition 6 by establishing a lower bound on the gap between optimal outputs under the two kinds of contract that holds uniformly for all technologies in G with sufficiently small elasticities of substitution.

About $7 billion a year in school funding will be at stake this fall when voters decide whether to extend Proposition 30, a tax on high-income Californians. .

About $7 billion a year in school funding will be at stake this fall when voters decide whether to extend Proposition 30, a tax on high-income Californians.

But even if activists manage to extend Proposition 30, which fully expires in 2018, and if projections of a long stretch of black ink are correct, it will take years to restore many school districts to pre-recession levels, nevermind to raise base funding from a level that's widely seen as inadequate.

We now extend Propositions 4 7 in [1], which were proved under the i.i.d.i.d

From this it follows that ( f n ) n is not ℱ-exhaustive at 0. Moreover, it is not difficult to check that ( f n ) n is ℱ-backward exhaustive at 0, but not ℱ-forward exhaustive at 0. The following two propositions extend [[49], Proposition 3.5] and will be useful in the sequel.

Mastrangelo et al. [ 2] extended this proposition to dairy farmers as an explanation of their low mortality from lung cancer.