Let us just deduce the case (J_{s, t, s_{0}}^) on (S a)), since the other case can be done similarly.
Let us dig into these themes and deduce their impact for the end of the trilogy.
Let us describe briefly the substorm scenario deduced from the global MHD simulation (Tanaka et al., 2010).
In order to deduce such a parameter, let us consider a simple model of a wire subjected to a constant current as shown in Figure 2a.
Now, to discuss the uniqueness of the fixed point deduced in Theorem 11, let us consider the following condition: (P): For all u, v ∈ B ( x 0, r ) ¯, there exists w ∈ B ( x 0, r ) ¯ such that α ( u, w ) ≥ 1 and α ( v, w ) ≥ 1.
Let us analyze, first, the pruned decomposed transform and deduce whether the direct or recursive method would be preferable.
Let us observe that by the inequality (6) we deduce ∥ x ∥ + ∥ y ∥ > ∥ x + y ∥, which contradicts the hypothesis ∥ x ∥ + ∥ y ∥ = ∥ x + y ∥, hence ( X, ∥ ⋅ ∥ ) is strictly convex.
Let us present two more results which can be easily deduced from the recursive representation of solutions.
As example, let us consider the symmetric logarithmic mean L. Its weighted mean is not simple to deduce from its explicit form in a and b previously mentioned.
We deduce that the neutral ridges satisfy the relationship r A n A = r B n B. In order to understand these results, let us consider the following process.
