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Increasing h with small Ds resulted in two steady-state solutions; interestingly, the second solution was a reversed solution in which the polarization was at the rear of the cell relative to the gradient (Fig. 7B).
u∗ z,−t) is often referred as the time-reversed solution.
On the other hand, the time-reversed solution of the wave equation is u 2 ( z ) = A ∗ e − i k 1 z + B ∗ e i k 1 z z < − a Ψ ∗ ( z, k 2 ) − a < z < a C ∗ e − i k 3 z + D ∗ e i k 3 z z > a. (13).
Such "three-tier" root curves allowed for reversed polarization solutions in which the intracellular component was concentrated at the wrong end of the cell where the ligand concentration was lower (magenta line; Fig. 3, h = 8); such a situation may arise from flipping the gradient.
The first series (classical P-2) is prepared by reduction of a Ni II) ethanolic solution with sodium borohydride and the second one is derived from reversed micellar solutions of nickel carboxylates.
In this figure, we also indicated the transition to the appearance of "three-tier" root curves described previously that can give rise to reversed polarization solutions.
By using the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, we obtain the extremal solutions of the boundary value problem.
Boundary value problems for first order impulsive functional differential equations with lower and upper solutions in reversed order have been widely discussed in recent years (see [15 20]).
By applying the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, some new sufficient conditions for the existence of solutions are established.
Another mode of Donnan emf measurement, specified by the reversed flow of KCl solution in sce salt bridges, shows zero voltage values.
Therefore,, are lower and upper solutions in the reversed order of (3.5).
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