Sentence examples for by using a critical from inspiring English sources

4, by using a critical value of the active damping coefficient, a stability evaluation method is developed.

Our idea here is to investigate the existence of infinitely many solutions to problem (1) by using a critical point theorem obtained in [13]; see Theorem 2.

By using a critical point theorem of Ding, we establish a new criterion to guarantee that the above system has infinitely many nontrivial homoclinic orbits under the assumption that (W t,u)) is asymptotically quadratic or subquadratic as (|u|rightarrowinfty). Recent results in the literature are generalized and significantly improved.

Clusters of individual-channel, diliganded C↔O activity were usually selected by eye or by using a critical time of 50 ms. Typically, ∼50 clusters were selected in each record.

For further analysis, a severity score for anxiety (scores range from 10too 40) was established and syndromal anxiety was estimated by using a critical cut-off value for clinical relevance at a mean score of 1.75 [ 18, 19].

For comparison of day of surgery, the LOS of Tuesday patients was compared to the LOS of Thursday patients using a Student's t-test, measuring significance by using a critical value of 0.05.

Later, three major studies of economic doubt emerged (i) by Rose (ii) by Davidson using a critical discount rate of 7% (iii) by McColl.

By using a single critical value, the method is simpler than the approach of Langsrud and Naes (1998) and Venter and Steel (1998) and is sometimes more powerful.

Candito and D'Agui proved the existence of three solutions for (1.12) by using a three critical points theorem by Jiang and Zhou [[10], Theorem 2.6].

By using a recent critical point theorem, we prove that the nonperiodic system (VS) has at least one homoclinic orbit when W satisfies weak superquadratic at the infinity, which improve and extend the results of [27, 28].

(1.6) Very recently, in [16], by using a three critical points theorem, Ferrara and Hadjian studied the existence of three solutions for the following problem: left { textstylebegin{array}{l} frac{d}{dt} ( {frac{1}{2}_{0}D_{t}^{-beta} ({u}'(t))+frac{1}{2}_{t}D_{T}^{-beta} ({u}'(t))} )+lambda f(t,u(t))+mu g(t,u(t))=0,quad mbox{u.e.