Sentence examples for criterion which improves from inspiring English sources

Next, we establish another criterion which improves Theorem 2.2.

Then a novel parameter estimation approach is designed based on the stochastic gradient method, the fractional order parameter update law and the ALAE criterion, which improves estimation accuracy and enhances robustness at the same time.

and presented oscillation criteria which improved the existing results for the equation.

and obtained some oscillation criteria, which improved and extended the results that were established in [19 21].

The authors obtained some new oscillation criteria which improved the results established by Zhang and Zhu [10] and Şahiner [11].

Erbe et al. [16] considered the general nonlinear delay dynamic equation (1.7), setting out to obtain some new oscillation criteria which improve the results given in [13].

In [18], Sun and Saker considered equation (1.5) and obtained some new oscillation criteria, which improve and complement that given in [16].

where and are positive, real-valued rd-continuous functions defined on, is rd-continuous, and as, and satisfies for some positive constant, for all nonzero, and extended the generalized Riccati transformation techniques in the time scales setting to obtain some new oscillation criteria which improve the results given by Şahiner [23] and Zhang and Shanliang [29].

where and are positive, real-valued rd-continuous functions defined on, is rd-continuous, and as, and such that satisfies for some positive constant,, for all nonzero, and they extended the generalized Riccati transformation techniques in the time scales setting to obtain some new oscillation criteria which improve the results given by Zhang and Shanliang [15] and Sahiner [13].

We obtain a blow-up criterion of smooth solutions to (1.2), which improves our previous result (see [2]).

Taking A = 1 − 2 ρ p, B = − 1, μ = 1 − p, λ = 0, n = − 1 and γ = 1 − β in Theorem 10, we get the following interesting criterion for starlikeness for multivalent functions, which improves the corresponding work in [22] for p = 1.