It depends on noting that begin{aligned} psi = lim _{t rightarrow infty } e^{iAt}e^{-itB}varphi iff varphi = lim _{t rightarrow infty } e^{itB}e^{-itA}psi end{aligned} (13.8 since begin{aligned} ||psi -e^{iAt}e^{-itB}varphi || = ||e^{itB}e^{-itA}psi -varphi || end{aligned} (13.9)That said, it is a critical realization because it reduces a completeness result to an existence theorem.
Keys threw back her head and sang like her life depended on every note.
Morris saw how human beings depended on nature, noting the effect of the broad sweep and intimate detail of the landscape in lifting the spirits and contributing to psychological equilibrium.
This is one time when you want to depend on your notes to make sure you don't make any mistakes.
I like to be able to depend on my notes, in case my brain just goes to mush.
Although the best test may depend on context, we note that Lin et al. used a different model than we did and, in particular, did not use a variance component approach.
In archaeological bronzes, different layers may form on the surface of artefacts and their composition, depth and shape depends on factors noted above.
"Press freedom depends on safety," noted Guy Berger, UNESCO's director of the Division for Freedom of Expression and Media Development at the opening of a parallel research conference on the safety of journalists, adding that 95% of attacks on media staffers are never resolved.
The success of these establishments will depend on their personalities, she noted, and to a degree the personalities of their developers.
Middle-class children are far more likely to arrive at school with significant language skills; disadvantaged children, she noted, depend on school much more heavily to learn basic skills and benefit more from direct instruction.
