Sentence examples for holds with equality from inspiring English sources

holds with equality if and only if all the x k 's are equal.

where the relation holds with equality for a uniform PDP.

Proof Similarly, inequality (2.7) holds with equality for n = 1.

Inequality (4.16) holds, with equality, if and only if (4.20).

Note that (7) holds with equality as N→∞.

Proof Obviously, inequality (3.7) holds with equality for n = 1.

First note that if ({bar {dt}} (theta ^{ell }) = 0), then (23e) must hold with equality, so that (24) holds.

First, we see from Eq. (8) that if (m ne 0), then Eq. (4) must hold with equality.

Furthermore, it is easy to show (e.g., by contradiction) that constraints (15c) and (15e) are tight (i.e., they hold with equality at optimality).

It is possible that the result in Theorem 3 may hold with equality, rather than being an approximation for the diversity order.

The values of can be bounded according to the expression on the right-hand side, holding with equality for a uniform PDP.