Sentence examples for sufficiency conditions from inspiring English sources
Remark 1 We can similarly obtain second-order sufficiency conditions of the problem by applying the following KKT sufficient conditions (page 320, Proposition 3.3.2 in [20]): If (27) to (37) hold for some x and μ i > 0, i = 1, … m, then x is a strict local minimum.
Second, the traditional FCT limiting based on sufficiency conditions is augmented by an iterative procedure which approaches the necessity requirements.
By using a stochastic Lyapunov approach, sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique.
By reviewing the existing impulse control models in the literature, we point out that meaningful problems do not satisfy the sufficiency conditions.
We then give sufficiency conditions for particular knowledge representation formalisms that guarantee that abductive reasoning can indeed be done through filtering and present examples from the knowledge representation literature where abductive reasoning is done through filtering.
Even though we provide only sufficiency conditions for the design of stabilizing distributed controllers, simulations show that the synthesized controllers we obtain provide good performance in spite of being suboptimal compared to the centralized controller.
The sufficiency condition for such resonances to occur is derived.
This condition is a quantified version of McNeal's condition (˜P) for compactness of the ¯∂-Neumann operator, and it extends Catlin's sufficiency condition for subellipticity as it is less stringent.
The Schur sufficiency condition for boundedness of any integral operator with non-negative kernel betweenL2-spaces is deduced from an observation, Proposition 1.2, about the central role played byL2-spaces in the general theory of these operators.
The relative magnitude of this deviation, however, provides a theoretical basis for readily determining a sufficiency condition for the number of Fourier components to be used in any specific application.
Is there a simple and general sufficiency condition?
