Sentence examples for with respect to a constant from inspiring English sources

Variations of Z factor at different temperatures with respect to a constant pressure.

Variations of Z factor at different temperatures with respect to a constant pressure when the gas mixture compositions are known.

Let be a stabilizable pair of constant matrices, with respect to a constant matrix satisfying the condition (3.34).

Variations of Z factor at different temperatures with respect to a constant pressure when the gas mixture compositions are unknown.

These have been converted into equivalent rock heights (in spherical approximation, e.g., Rummel et al., 1988) with respect to a constant topographic mass-density of ϱtop = 2670 kg/m3 (Kuhn and Seitz, 2005).

The intermediate performance z LC=1−y LC,h converges roughly with respect to a constant number of decoding iterations h (according to the following simulations, h=40 is adequate for convergence).

T is D -Lipschitz continuous with constant λ T ; H ( A, B ) is cocoercive with respect to A with constant μ > 0 and relaxed cocoercive with respect to B with constant γ > 0 ; A is α-expansive; B is β-Lipschitz continuous; H ( A, B ) is r 1 -Lipschitz continuous with respect to A and r 2 -Lipschitz continuous with respect to B; ( r 1 + r 2 ) < [ ( μ α 2 − γ β 2 ) − λ ] ; μ > γ, α > β.

Since H is η-cocoercive with respect to A with constant μ and η-relaxed cocoercive with respect to B with constant γ, A is α-expansive and B is β-Lipschitz continuous, thus (3.3) becomes 0 ≤ − μ α 2 ∥ x − y ∥ 2 + γ β 2 ∥ x − y ∥ 2 = − ( μ α 2 − γ β 2 ) ∥ x − y ∥ 2 ≤ 0, (3.4).

Theorem 3.2 Let H ( A, B ) be η-cocoercive with respect to A with constant μ > 0 and η-relaxed cocoercive with respect to B with constant γ > 0, A is α-expansive, B is β-Lipschitz continuous and η is τ-Lipschitz continuous and μ > γ, α > β.

Theorem 3.1 Let H ( A, B ) be η-cocoercive with respect to A with constant μ > 0 and η-relaxed cocoercive with respect to B with constant γ > 0, A is α-expansive and B is β-Lipschitz continuous, μ > γ and α > β.

Definition 3.2 Let H ( A, B ) be η-cocoercive with respect to A with constant μ > 0 and η-relaxed cocoercive with respect to B with constant γ > 0, A is α-expansive and B is β-Lipschitz continuous, μ > γ and α > β.