Sentence examples for equality conditions from inspiring English sources

First, the previously derived MCC-KF equations are revised and the related Kalman-like equality conditions are proved.

The lower bounds in both of our inequalities are the best possible, and we discuss the equality conditions.

Then, the algorithm is derived by combining a Newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility.

The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions.

Similarly, following the equality conditions in Lemma 2.2, we have the equality conditions for (2.21).

From the equality conditions of Theorem 1, we obtain K ( f ) = K ( g ).

The equality conditions of (5.19) follow easily from Lemma 5.1 and 5.2.

In view of the equality conditions of Theorem 1, we obtain that K = L.

Our analysis enables us to discuss the equality conditions in (1.1) for certain unitarily invariant norms.

To obtain the equality conditions, first assume that K is i th p-selfminimal.

The equality conditions for the inequality of Proposition 4.7 are given in Theorem 1.6.