Sentence examples for modified comparison from inspiring English sources

Here, the key is to establish a modified comparison principle.

The following modified comparison principle plays a crucial role in our proofs, which can be obtained by establishing a suitable test function and Gronwall's inequality.

In this paper, new functions named "modified comparison functions" are introduced and used for vibration analysis of a simply supported rectangular cracked plate.

By using the modified comparison principle and the method of upper-lower solution, we find the influence of weighted function on determining blow-up or not of nonnegative solutions.

The following modified comparison principle plays a crucial role in our proofs, which can be obtained by establishing a suitable test function and using Lemma 1 and Gronwall's inequality.

In Section 2, with the definitions of weak upper and lower solutions, we give the modified comparison principle for problem (1.1 - 1.3), which is an important tool for our research.

The hypobranchial muscles of tetrapods are both reduced and modified in comparison with those of jawed fishes.

Although amphibian gastrulation is considerably modified in comparison with that in animals with oligolecithal eggs (e.g., amphioxus and starfishes), an archenteron forms by a process of invagination.

Acoustic radiation of shock free supersonic jets is modified in comparison with subsonic jet noise because of Mach wave emission.

It is shown that the formed SiNWs are characterized by the optical reflection and transmission, which are strongly modified in comparison with those for c-Si substrate.

The growth rate of transformants was not significantly modified in comparison to the wild type strain indicating that the differences in calculated transformation frequencies were not affected by differences in cell growth or survival (results not shown).