Sentence examples for weakening assumption from inspiring English sources

In the particular case of p-Laplacian operators, one can use the positive homogeneity for weakening assumption (2.17) of Theorem 2.4 and widening the class of the admissible Nagumo functions, as we show in the following result.

□. (1) In the above theorem, we can weaken Assumption 2.2.

Pečarić and Raşa [4] extended the inequality by using the method of index set functions; in the process they weakened assumption (1) and obtained a monotonic refinement of the inequality.

One can use the same method in Theorem 3.3 to weaken assumption (7) in Theorem 3.1 if one replaces the standard (L^{p} -norm with an exponentiaL^{p} -normd term (e^{-lambda t}) for some sufficiently large λ.

Under a weaken assumption that the powers of nonlinear functions are relaxed to an interval, the new control strategy implanting sign functions into homogeneous domination idea and observer construction allows time-varying delays to coexist in system state and control input.

This circumstance is not actually of primary importance since the very aim of the interval halving technique discussed here is to weaken assumption (35) by half and, in any case, the difference between the two conditions is quite insignificant because γ 0 − γ ∗ ≈ 0.00727.

Due to the parabolic smoothing property we can weaken assumption (16).

In particular, this nonparametric setting allows us to weaken assumptions considerably.

We prove existence results without compactness on T ( t ) or f and the Lipschitz condition on f, and we weaken assumptions on impulsive functions  I k.

The aim is to weaken assumptions on coefficients (A_{i}^{alpha}) with Hölder continuity in the variables ((xi,u)) to the assumptions of Dini continuity, and to show a partial regularity result with optimal estimates for the modulus of continuity for the horizontal derivative Xu; see [1, 2] for the case of sub-elliptic systems with Hölder continuous coefficients.

Those respondents who reported weakened assumptions about "the world as predictable" had less posttraumatic stress symptoms when controlling for other variables (Model A in Table 5).