necessary and sufficient condition in a sentence

Examples

1. A necessary and sufficient condition that a polynomial is Hurwitz is that it passes the Routh Hurwitz stability criterion.
2. Applying this adjustment to the above Slater determinant, one determines the following necessary and sufficient condition for Slater permanency:
3. When solved over the whole of state space, the HJB equation is a necessary and sufficient condition for an optimum.
4. Necessary and sufficient conditions for a mixture of normal distributions to be bimodal have been identified by Ray and Lindsay.
5. More generally, one can describe the necessary and sufficient condition under which a smooth measure is invariant under a flow.
6. All triangles have a characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have a circumcircle.
7. The first set of necessary and sufficient conditions for the embeddability of a semigroup in a group were given in.
8. For we have See below for necessary and sufficient conditions in order for ( " reg to coincide with ( ".
9. He discovered the necessary and sufficient conditions on initial value problems of ordinary differential equations for the solution to be unique.
10. In analytic philosophy, these properties are assumed to establish the conditions which are both necessary and sufficient conditions to capture meaning.