Theorem 4.5 proves that for lowest-order elements p = 1, even optimal rates for the discretization error are achieved, while for higher-order elements p ≥ 2 additional regularity of f has to be imposed, e.g., f ∈ H 1 for p = 2. □ The adaptive algorithm leads to convergence with quasi-optimal rate for the estimator η in the sense of Theorem 4.1.
Theorem 4.5 proves that for lowest-order elements p = 1, even optimal rates for the discretization error are achieved, while for higher-order elements p ≥ 2 additional regularity of f has to be imposed, e.g., f ∈ H 1 for p = 2. □ Numerical examples for the 2D Laplacian with mixed Dirichlet Neumann boundary conditions are found in [82] together with a detailed discussion of the implementation.
The expectation of direct (mode 1) orientation in the sense of "deriving" reasonable or even optimal strategies for action from futures studies (see Section 2) is often destroyed by its irreducible diversity.
Given a motif discovered by any method, it is important to be able to assess its statistical significance, as even optimal solutions for their respective objective functions may result in very poor motifs.
As these facets are coupled, and the system complex, mathematical approaches potentially are of significant value since they may reveal improved or even optimal schemes for maximizing hydrogen production.
It is easy to see that for even optimal partitioning ∑ e S w(e S )·(#(S −1)≤∑ e S w(e S )·(| S|−1).
But even for optimal pore size it is not enough to create electrical double-layer (EDL), because notmore than 50% of surface area are taken part in charge/discharge processes [3].
For example, if simulations suggest that a target output of 2 preclinical candidates per year for a particular working group might not be realistic even under optimal conditions for a specific set of assumptions, then the team may wish to consider ways to enhance production that may involve increasing working group size or changing resource deployment strategies.
In plot-level considerations, a very small plot or even a point would be optimal for many of these variables.
However, resistant females are found in soybean fields even when corn tissues are optimal for adult feeding (Rondon and Gray 2003; Pierce and Gray 2007; LMK personal observation).
