There are three options: (i) a fixed rational basis, (ii) a fixed orthonormal basis, or (iii) an optimal orthonormal basis.
After all rational attempts to fix a broken bike engine have failed, he notes, recalling a passage from the book, there often comes a moment when you let "go of this desire to solve it in a very rational way and just stare at the engine...
Because you (not all of you, but most of you) are the people who consistently, for decades, dismissed, pooh-poohed, and sabotaged every decent, rational attempt to fix America's disastrous trade policy.
For any fixed rational parameter t⩾1, a (tree) t-spanner of a graph G is a spanning subgraph (tree) T in G such that the distance between every pair of vertices in T is at most t times their distance in G. General t-spanners and their variants have multiple applications in the field of communication networks, distributed systems, and network design.
Therefore, it suffices to prove that if a mapping f satisfies equation (1) for any fixed rational k with k ≠ 0, 1, then f is quadratic.
Lemma 2.1 A mapping f : X → Y between linear spaces satisfies the functional equation f ( k x + y ) + f ( k x − y ) = k f ( x + y ) + k f ( x − y ) + 2 ( k − 1 ) [ k f ( x ) − f ( y ) ]. for any fixed rational number k with k ≠ 0, 1 if and only if f is quadratic.
One decoupling approach, a Straight Fixed Variable (SFV) rate design, is a rational way to recover fixed and variable costs because it aligns pricing with variable and fixed cost causation, thereby removing the utility's profit sensitivity to reduced sales.
Since A is additive, A ( r x ) = r A ( x ) for any rational number r. Fix x 0 ∈ X and ρ ∈ Y ∗ (the dual space of Y).
You can't have a rational national debate without fixing that problem.
In Amina, George is relieved to have found a rational, beautiful woman who fixes his cereal and banana in the morning.
