Sentence examples for bounds on how much from inspiring English sources
If A is perturbed slightly, we give explicit bounds on how much the semigroup and fundamental solution are perturbed.
We are able to give either a theoretical bound on how much one formulation is better than another, or examples that show such a bound does not exist.
Such posterior probabilities provide informative upper bounds of how much confidence one may reasonably place in causal relationships between genes on the basis of observed data when honestly accounting for network uncertainty.
It also provides a striking reminder that substrate affinity and specificity is not simply a matter of the interactions made by the bound ligand, but they depend on how much better those interactions are compared with the interactions made with solvent in the unliganded enzyme.
Or even on how much he earns.
Obviously, that depends on how much is too much.
How much China gives, diplomats believe, will depend on how much of a say it gets.
Depending on how much they could negotiate.
But nobody can agree on how much.
