Sentence examples for of their proof from inspiring English sources

"I haven't seen any of their proof," Richardson said.

We adapt here the ideas of their proof to our setting.

By a slight modification of their proof in the case, Lemma 4 is proved.

This is part of their "proof": Chevron argued that Mother Nature had "weathered" the oil so much it was harmless and, as a result, no cleanup was needed.

In fact, an inspection of their proof reveals that their algorithm is O(n d3 τ Bell, where d is the maximum degree of the tree. Bell(k) denotes the kth Bell number, which is the number of unordered partitions of k items; these numbers are known to satisfy the bounds k e In k k < Bell k < k In k k [ 7].

In Section 3, we give the main results as well as some of their proofs.

This leads to both a strengthening of the previously known results and to simplification of their proofs.

While conceptually the results are similar in two notions of the capacity, they differ in the details of their proofs.

Besides a related character of the relevant results, we discuss also a possible related character of their proofs.

Since the proofs are similar to the proofs of Lemma 2.2 and Lemma 2.3, so we omit the details of their proofs.

Some of their proofs used the translation-invariant property of the classical spaces, which is, however, no longer valid on L p.