Sentence examples for studied sufficient from inspiring English sources

In the same paper, the authors have studied sufficient conditions of the existence and uniqueness of solution to the ICP (1.1).

Pukach et al. [9] studied sufficient conditions of nonexistence of global in time solution for a nonlinear evolution equation with memory generalizing the Voigt Kelvin model.

The survey article by Bharucha-Reid [6] in 1976, where he studied sufficient conditions for a stochastic analogue of Schauder's fixed point theorem for random operators, gave wings to random fixed point theory.

The survey article by Bharucha-Reid [9] in 1976, where he studied sufficient conditions for a stochastic analog of Schauder's fixed point theorem for random operators, gave wings to random fixed point theory.

For example, for END random variables with heavy tails Liu [7] obtained the precise large deviations and Liu [13] studied sufficient and necessary conditions for moderate deviations, and Qiu et al. [3] and Wu and Guan [14] studied complete convergence for weighted sums and arrays of rowwise END, and so on.

The result was extended to the case of a boundary value problem by Chen et al. [26] who studied sufficient conditions for existence results for the following two point boundary value problem: left { textstylebegin{array}{l} D_{0+}^{alpha} phi_{p} (D_{0+}^{beta}u(t))=f t,u(t),D_{0+}^{beta }u(t)), D_{0+}^{beta}u(0)=D_{0+}^{beta}u(1)=0, end{array}displaystyle right.

Studying sufficient patient numbers to explore this entire continuum while accounting for heterogeneity in type of infection and comorbidity is difficult because of the number of patients required.

They also studied the sufficient conditions of an optimal equation.

Stability of the event-triggered NMPC systems is studied and sufficient stability conditions are obtained.

Recommended Not stated in one study, sufficient in all other studies.

For both trials the target numbers of patients in each treatment group are achieved, giving this study sufficient power to lead to promising results.