Sentence examples for determines sufficient from inspiring English sources

For instance, when one determines sufficient conditions for the existence of exponential dichotomy on the half-line, an important hypothesis is that the initial stable subspace is closed and complemented (see, e.g., [5, Theorem 4.3] or [9, Theorem 3.3]).

In N.H.T.S.A.'s denial (PDF) of the petition entered on July 9 by the Center for Auto Safety, the agency said it had determined sufficient cause to open its inquiry independently of the center's efforts.

A simulation-based re-sampling approach was used to determine sufficient sample size.

These questions pose significant motivation for possible study so as to conclusively understand and determine sufficient and satisfactory answers.

The results obtained make it possible to determine sufficient coefficient conditions of regular solvability for the boundary-value problem (1.1), (1.2).

This allows the web server's resource management by determining sufficient server resource for each traffic class in order to meet its delay requirements.

To determine sufficient conditions in order to ensure the existence of the following kind of points is the main aim of the present manuscript.

Our main object in this sequel is to determine sufficient conditions for the solvability of an infinite system of second-order differential equations.

Our purpose in this part is to determine sufficient conditions for the bifurcation of solutions of the linear singular Fredholm differential system with the impulsive action with a small parameter.

Finally, note that Proposition 2 reflects a worst-case scenario by using the minimum and maximum values of the weights and not their exact values so as to determine sufficient conditions that ensure queue stability.

We will determine sufficient conditions on our function f such that the assumptions of the fixed point theorem are satisfied, which in return gives us the existence of solutions.