Sentence examples for is concave only when from inspiring English sources

The objective is concave only when.

This shape is concave when 0 < p < 0.5 and convex when p > 0.5.

Since is twice continuously differentiable, is concave if and only if.

When is concave, then the above inequality is reversed.

Lemma 1. if and only if is concave on.

When only the lower border of C2 is concave and the bodies of C3 and C4 are trapezoid.

The average risk Y in the group is larger than the risk at the average exposure r(X) when the risk function is concave up.

If ψ ∈ C s m - ( I ), then ∇ φ ≤ ∇ ψ (resp. ∇ φ < ∇ ψ ) holds if and only if ψ ∘ φ -1 is concave (resp. strictly concave) on φ(I).

Thus, symmetry can only be favored if s(d) is concave down (negative second derivative).

Moreover, as it has been proved in [24], Lemma 6, a user net utility is maximized only when their power allocation value is in the concave part of their utility function (i.e.e ).e

If none of the sides, when extended, intersects the polygon, it is a convex polygon; otherwise it is concave.