Sentence examples for and on the proof from inspiring English sources

And in fact the strategy used in [67] is completely different from the one we have seen in the last section, since it relies on an optimal mass transportation argument and on the proof of a very general trace inequality.

We focus here on the definition of a new type of systems of quasi-variational inequalities with random fuzzy mappings whose values are fuzzy sets over complete countable metric spaces and on the proof of the existence of their solutions.

This article describes the MizarMode and focuses on the proof assistance functions and tools available in it.

Thompson made further contributions to Galois theory, representation theory, coding theory, and, working on the proof of the nonexistence of a plane of order 10, the theory of finite projective planes.

"You must consider each individual charge separately and evaluate each on the proof or lack of proof that relates to that charge," Judge Rakoff said.

Thus there exists at least one critical point of on, and the proof is complete.

YC and SW gave YD some advice on the proof and writing.

Equation (9) can be obtained via [8], and so we focus on the proof of (10).

Define on such that Under hypothesis (i) of Theorem 2.2, for all the mappings and are of class on The proof can be found in [19].

Beliefs and theories are possibly true depending on how rational they are whereas knowledge and facts are definitely true based on the proof of observation and experience.

Thus, Hence, is u.s.c. on and the proof is complete.