Sentence examples for bound on the density from inspiring English sources
The next lemma derives the bound on the density (rho (x,t)) from above.
A lower bound on the density can be computed using the smallest circular cylinder that contains the column.
Based on this, a lower bound on the dislocation density in the kink shear sector is established experimentally.
Condition (2.4) controls the tail behavior of the conditional expectation (E |Y_{1}|^{s}|X_{1}=x)), condition (2.5) places a similar bound on the joint density and conditional expectation.
We demonstrate this by obtaining a non-trivial lower bound on the path density of an arbitrary set of trajectories that contain a sampling set with explicitly specified stability bounds.
Our result improves on the upper bound on the energy density of the stochastic background of gravitational wave in the 0.02 0.05 Hz band obtained by the Apollo missions, with the improvement reaching almost one order of magnitude at around 0.05 Hz.
The study indicates that the upper bound on the energy density may be further improved by another order of magnitude from the Chang'e 3 mission, which will fill the gap in the frequency band from 0.02 Hz to 0.1 Hz in the foreseeable future.
In Section 2, we derive some uniform estimates for the proof of the main Theorem 1.1, which do not depend on the lower bound of the density.
The peak beam density sets a lower bound on the local plasma density required near the focal plane for optimal beam compression, since the simulations show stagnation of the compression when nbeam>nplasma.
The methodology is applied to an example isolation problem to find a lower bound on the root-mean-square acceleration given the disturbance power spectral density.
