Sentence examples for reduction lemma from inspiring English sources
So, let us start with the reduction lemma proved in [94, Th. 4.4].
In Section 2, we introduce the Hilbert normed space E, show that the corresponding functional I ( z ) of (1.1) is in C 1 ( E, R ), Fréchet differentiable and prove the reduction lemma for the perturbed operator A ϵ.
Customarily, the justification of the instrumental problem is based on the existence of a so-called "Constraint Simplification Lemma", or of a "Constraint Reduction Theorem".
Moreover, (A1) and (A2) prove estimator reduction (4.18) from Lemma 4.7.
By Lemma 2.2 (reduction method), we shall show the existence of the third weak solution of (1.1).
Lemma 1 Reduction Rule 1 is sound.
Lemma 5 Reduction Rule 4 can be computed in polynomial time.
Moreover, the same reduction argument used to prove Lemma 4.2 shows that also in this case we may assume without loss of generality that (Esubset B_{R_0}), where the radius (R_0) depends only on the dimension n, see [74, Lemma 3.2].
To overcome this difficulty, we prove that in a neighborhood of critical points at infinity, a Morse lemmas at infinity reduction holds, then develop a whole Morse theory of this noncompact variational problem.
Lemma 3.5 Stability (A1), reduction (A2), and discrete reliability (A4) imply quasi-monotonicity (3.8) of the estimator.
