necessary and sufficient condition in a sentence

Examples

1. The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have an incircle.
2. The converse does hold if ? is a Pisot number, although necessary and sufficient conditions are not known.
3. No necessary and sufficient conditions exist.
4. The von Neumann Morgenstern utility theorem provides necessary and sufficient conditions under which the expected utility hypothesis holds.
5. To me, that seems a necessary and sufficient condition for an article entitled " Kingdom of Mysore ".
6. Snow's being white is a necessary and sufficient condition for the truth of the proposition that snow is white.
7. Hiroshi Okamura obtained a necessary and sufficient condition for the solution of an initial value problem to be unique.
8. An indirect method works by analytically constructing the necessary and sufficient conditions for optimality, which are then solved numerically.
9. These background assumptions go up and beyond those necessary and sufficient conditions that correspond to a semantic feature account.
10. Another necessary and sufficient condition for a tetrahedron to be orthocentric is that its three bimedians have equal length.