Sentence examples for establishing the lower from inspiring English sources

In this paper, we prove the ratio log-concavity of (U_{n}) by establishing the lower and upper bounds for (frac{U_{n}}{U_{n-1}}).

The entropy establishes the lower bound of the average bit rate achieved by source coding.

In 2004, Lange [2005] established the lower bound of exponential space of (IPDL-SAT).

First, we establish the lower semicontinuity of the solution mapping (S_{AGQEP}).

Now, we establish the lower semicontinuity of the solution mapping (S_{f}).

This information is important because it establishes the lower bound of the CLA.

In Section 3, we establish the lower and upper solutions method for the general boundary value problem (1.1 - 1.2 1.1 - 1.2

Several deliberately chosen regular particle configurations are used to establish the lower and upper bounds for conductivity enhancement.

Santi et al. [34] considered range assignment problems under a homogeneous probabilistic model and established the lower and upper bounds of the network connectivity probability.

Then, Theorem 7 establish the lower bound for the number of R-operations needed to implement a prime constant (Ω = 1).

In order to prove Theorem 1.1, we first establish the lower and upper bounds for (frac{U_{n}}{U_{n-1}}).