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The study verifies the assumption concerning the uniformity of normal stress distribution and describes the failure mechanism.
The following lemma allows us to prove that functional J verifies the assumption of Bolle's abstract theorem.
Applying the model to predict the concentration profiles, nucleation rates, and crystal-size distribution during the sonocrystallization process shows that the key parameter for understanding induced nucleation seems to be the reduction of the nucleation work, which verifies the assumption of a heterogeneous-nucleation mechanism.
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That is F verifies the assumptions of Theorem 9.
Therefore, ( Y, K ) verifies the assumptions of Lemma 3.9 and the proof is complete.
Then the pair ( Y, K ) verifies the assumptions of Lemma 3.9.
The following lemma verifies the assumptions in Theorem 1, whose proof is given in Appendix Appendix F: Proof of Lemma 3. Assumptions 1 and 2 hold for the controlled Markov process of spectrum sensing.
There are different choices of the function f that verifies the assumptions above such as the choice taken in the algorithm above, we also choose the so-called hypersurface minimal function defined as f(x)= sqrt{1+x^{2}}.
After all, confirming Einstein's theory of relativity only took three years, yet verifying the assumption that the scientist would not have minded a memorial built in his honor here -- being pondered by a gaggle of experts -- is taking a lot longer.
To verify the assumption of random effects, we conduct Cochran's Q-test.
To prove the uniqueness of solutions of (5.1), we just need to verify the assumption.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com