Sentence examples for unique derivation from inspiring English sources

Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature.

Then there exists a unique derivation such that (3.3).

Their efficacy is based on science and now their challenge is to educate consumers about their products unique derivation and effectiveness.

If there exists an such that for all, then there exists a unique derivation such that (3.11).

for all μ ∈ T 1 and all x, y ∈ A. Then the limit H ( x ) = lim n → ∞ 2 n f x 2 n exists for all x ∈ A and δ: A → A is a unique derivation such that f ( x ) - δ ( x ) ≤ 2 θ x A r 2 - 2 r (3.20).

for all a, b, c, d ∈ A and all λ ∈ T. Also, if for each fixed a ∈ A the mapping t → f ta) is continuous, then there exists a unique derivation δ on A satisfying ∥ f ( a ) - δ ( a ) ∥ ≤ 2 ε 4 - 2 p ∥ a ∥ p. for all a ∈ A. Proof.

Applying Theorem 3.1 for the case, there exist a unique -Jordan derivation and a unique generalized -Jordan derivation satisfying (3.12).

for all, then there exist a unique -Jordan derivation and a unique generalized -Jordan derivation satisfying (3.7).

Then there exists a unique Lie derivation satisfying (3.3).

Then there exists a unique quadratic derivation D : A → A such that.

for all x, y ∈ A. Then there exists a unique Lie derivation δ: A → A satisfying (3.20).