Sentence examples for weak augmented from inspiring English sources

Hypothesis 4.1 (Weak augmented Atkinson condition - finite).

Inequality (4.10) is satisfied with N 0 = N for every column z of the natural conjoined basis Z ˜ of ( S λ ) on [ 0, N + 1 ] Z and every λ ∈ C. Hypothesis 4.2 (Weak augmented Atkinson condition - infinite).

This transformation works under the strong Atkinson condition on the original system, which turns out to be the weak Atkinson condition on the augmented system (Corollaries 4.4 and 4.5).

Furthermore, numerous kinetic differences exist between the ATPase cycles of HscA and DnaK (Table S1 of the Supporting Information, with references therein): compared to DnaK, HscA displays a 10-fold weaker binding affinity for ATP, an augmented rate of ATP association, and a >10-fold higher rate of ADP dissociation.

Corollary 4.4 System ( S λ ) satisfies the strong Atkinson condition on [ 0, N + 1 ] Z (Hypothesis  2.1) if and only if the augmented system ( S λ ) satisfies the corresponding weak Atkinson condition on [ 0, N + 1 ] Z (Hypothesis  4.1).

Corollary 4.5 System ( S λ ) satisfies the strong Atkinson condition on [ 0, ∞ ) Z (Hypothesis  2.2) if and only if the augmented system ( S λ ) satisfies the corresponding weak Atkinson condition on [ 0, ∞ ) Z (Hypothesis  4.2).

The augmented Roe approximate Riemann solver provides a family of weak solutions for the shallow water equations, that are the basis of the upwind treatment of the source term.

Weak solutions of the RPs defined for the DRP are computed using an augmented version of the Roe solver that includes an extra wave that accounts for the contribution of the source term.

Weak solutions of problems with m equations with source terms are proposed using an augmented Riemann solver defined by m + 1 states instead of increasing the number of involved equations.

Using augmented Dickey Fuller and Phillips Perron unit root tests Mejía Reyes and González Núñez find weak evidence of stationarity of the real rate, thus support for the PPP hypothesis, in the three series.

Augmented reality?