Sentence examples for prove the concentration from inspiring English sources

We further prove the concentration of (mathcal{S}_{h}^{W}(f)) in small sets.

Combining these results, we get the following theorem that will be needed to prove the concentration theorem.

We further prove the concentration of (mathcal{S}_{h}^{W}(f)) in arbitrary sets of finite measures.

In this section, we will find the variance of the number of the edges and prove the concentration theorem.

Next, we will prove the concentration result of Theorem 2.1 by using a similar method related to Proposition 2.2 in [1].

The following is the main step in proving the concentration result.

We prove the existence and concentration of nodal solutions which concentrate around a k-dimensional sphere of (mathbb{R}^{N}), where (1 leq k leq N-1), as (epsilonto0).

Many mathematicians proved the existence, concentration and multiplicity of solutions for (1.5), we refer to [1, 16 18].

A cell viability test proved that the concentration of NPs used imposed very low toxicity to the cells.

In the celebrated paper [4], del Pino and Felmer used the so called penalization technique to prove the same kind of concentration behavior of solutions of (1.1), considering the potential V under a local version of the Rabinowitz condition.

Variogram analysis proved the HM concentrations in moss and soil to be spatially auto-correlated with nugget-to-sill ratios between 11% (for Hg in 1990) to 55% (for Hg in 2005) in moss and between 37% (for Cd in 1995) and 72% (for Pb in 2005) in natural surface soil.