necessary and sufficient condition in a sentence

Examples

1. Serre s criterion gives a necessary and sufficient condition for a quasi-compact scheme to be affine.
2. What's a necessary and sufficient condition to guarantee that the truck can always run over the person?
3. You need an EXPLOSION, and one at SEA, the two necessary and sufficient conditions for a disaster.
4. But one might worry that these so-called necessary and sufficient conditions do not apply in every case.
5. Analogous necessary and sufficient conditions for a " null electrovacuum " have been found by Charles Torre.
6. Necessary and sufficient conditions for this are that their degrees of belief satisfy the axioms of probability.
7. Can we list the necessary and sufficient conditions such that any action which satisfies these conditions is wrong?
8. For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability.
9. This formula is a necessary and sufficient condition for all irreducible representations of a group up to isomorphism.
10. In a paper from 1936 he proved a necessary and sufficient condition for a function to be measurable.