It was derived that there is not just one enhancing solution that is the best universal one for all the metals in the sediment and that modeling of the decontamination process should incorporate the particularities of the different species.
By Lemma 2.3 it is derived that there is (x_{0}>0) such that the ratio (f_{1}/f_{2}) is increasing on (( 0,x_{0} ) ) and decreasing on (( x_{0},infty ) ).
From the cell volume, it was derived that there are two PG molecules in the asymmetric unit and from thermogravimetric analysis that there are 0.25 mols of water per mol pyrogallol.
According to Lemma 2.4, we derive that there exists a sufficiently large number R > 0 such that deg ( I − A, B R, 0 ) = 0. (3.3).
Furthermore, by constructing a series of Lyapunov functionals, we derive that there exists a unique almost periodic solution of the system which is uniformly asymptotically stable.
Using the theorem present on p.51 in [28] or Theorem II in Section 1.1 in [62] one derives that there are constants T > 0 and c > 0 independent of ϵ such that ∥ u x ∥ L ∞ ≤ W ( t ) for arbitrary t ∈ [ 0, T ], which leads to the conclusion of Theorem 3.2.
Using (4.4) and (4.5), we derive that there exist (gamma_{k}>0) and a positive diagonal matrix (D_{k}in {mathbb {R}}^{n times n}) such that big|mathcal {A}_{k}[alpha]big|=gamma_{k} big|mathcal {A}_{1}[alpha]big| D_{k}^{- m-1)}cdot underbrace{D_{k}cdots D_{k}}_{m-1}.
2.6.5, to derive that there exits (cinmathopenx,bar{x}[) such that g(x -g(bar{x -ginpartial_{c} g(c) (x-bar{x})subset partinpartial_{cr{x}) (x-bar{x})+ varepsilonmathbb{B}_{mathcal {L}(mathbb {R}^{p},mathbb{R}^{q})}(x- bar{x}).
Then, by choosing (p>n), from the Sobolev embedding theorem we can derive that there exists a constant (C_{2}>0) such that sup_{0< t< T_{max}}bigl| nabla w(cdot,t bigr| _{L^{infty}(Omega)} leq C_{2} quadmbox{for all } tin 0,T_{max}).
On thebasis of Theorem 1, the solution ũ 0 ( z ) = 0. Open image in new window However, from Ĉ ũ ( m ) ( z ), D ¯ = 1 Open image in new window, we can derive that there exists a point z ∗ ∈ D ¯ Open image in new window, such that ũ 0 ( z ) σ + 1 + ũ 0 z z = z ∗ ≠ 0 Open image in new window, which is impossible.
Such a conclusion would also derive that there is no effect of the mutual information measures on the agents' fitness.
