Sentence examples for bound of the first from inspiring English sources

While the progress has been made on the upper bound, not too much is known about the lower bound of the first eigenvalue.

Next, we give a lower bound of the first eigenvalue (lambda_{1}).

Since 1979, Li and Yau have been trying to obtain the lower bound of the first eigenvalue [21, 22].

We give the refinement of the lower bound of the first inequality above for the Frobenius norm.

By Cheng's eigenvalue comparison theorem ([17], Theorem 1.1), we obtain a stronger upper bound of the first eigenvalue (lambda_{1}) (Theorem 4.1).

In this paper, we obtain the following lower bound of the first eigenvalue that is stronger than Osserman's result (1.7): Let S be a simply connected complete surface with Gauss curvature (Kleq0) everywhere.

A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity.

and its corresponding lower bound of the second moment is widetilde{s}_{n,c}^{, 2)} = {(,widetilde{s}_{n,c})}^{2}.

and the lower bound of the second moment of transmission interval is {{s'}_{n,c}}^{(2)} = left(frac{bar{s}_{n,c}}{p_{c}}right)^{2}.

Moreover, we obtain a lower bound on the second largest eigenvalue of the resistance-distance matrix of complete multipartite graphs.

In Section 5, we obtain a lower bound on the second largest eigenvalue of the resistance-distance matrix of complete multipartite graphs.