Sentence examples for the equality characterizes from inspiring English sources

We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product.

Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.

We characterize the equality cases in all these inequalities.

Shares in the company were allocated according to members' initial contributions (as well as time spent in the community), in a stroke undoing the equality that had originally characterized communal life.

In what follows, we characterize the equality condition of Inequality (1.3) in Theorem 1.2.

The equality case of these inequalities characterizes the Euclidean spheres.

Second, the equality across the two samples of the parameters characterizing the relationship between the items of the CES-D and the underlying latent constructs are tested.

The equality cases in the Pólya Szegö inequality have been fully characterized first by Brothers and Ziemer in [28], see also [41, 61].

Now we characterize strong (mathcal {H} -tensors sucH} -tensorsequality of (3.6) holdsuch thatcase thet (sum ^{k}_{i=1}r_{i}=1).

Next we characterize strong (mathcal {H} -tensors sucH} -tensorsequality of (3.6) holdsuch thatcase thet (sum ^{k}_{i=1}r_{i}>1).

In this section, we characterize the strong (mathcal {H} -tensors sucH} -tensorsequality of (3.6) holdsuch