Sentence examples for norms corresponding from inspiring English sources

Secondly, the theorem deals with the norms for the range of α > d in the Hilbert scale, what can be said about convergence in the stronger norms corresponding to the range of α ∈ [ 0, d ] ?

However, in this paper, take Algorithm 3.2 for example, the projections are with respect to the norms corresponding to G n and D ˜ n, we should use the following methods to calculate them.

In order to solve GSFP (1.2), two preconditioning algorithms are developed in this paper following the iterative scheme g ( x n + 1 ) = P C [ g ( x n ) − γ D A ∗ ( I − P Q ) A g ( x n ) ], n ≥ 0, where the two general constraints C and Q deal with projections with respect to the norms corresponding to some symmetric positive definite matrices.

We were careful to use each laboratory's SCr norms corresponding to the respective period of study (for example, SCr norms of 2000 and 2001 at CHUSJ).

As a consequence of Theorem 3.2 in [10], we introduce an interesting notion of ascending family of α-n-norms corresponding to the fuzzy n-norms in the following theorem.

Let now ([D]_{t}) be the Banach space D endowed with the graph norm corresponding to the operator (A t)).

We denote by ∥ ⋅ ∥ K the norm corresponding to the body K: K = { z ∈ C n : ∥ ⋅ ∥ K ≤ 1 }.

Let ([D]) be the space D endowed with the graph norm corresponding to the operator (A(0)).

Thus it follows from (4) that there exists a positive constant c4 such that, for all y ∈ E ∥ N y ∥ 1, ∞ ≤ 1 2 ∥ M - 1 ∥ 1, ∞ - 1 ∥ y ∥ 1, ∞ + c 4. where || · ||1,∞ denotes by the norm corresponding to 1,∞.

Any norm that satisfies this equality is ipso facto a norm corresponding to an inner product.

□ Let ‖ · ‖ be a matrix norm corresponding to a vector norm.