Sentence examples for proved a sufficient condition from inspiring English sources

Also Ragusa [30] proved a sufficient condition for commutators of fractional integral operators to belong to vanishing Morrey spaces V M p, λ ( R n ).

In this paper, we have formally proved a sufficient condition that determines the minimum number of VCs actually needed for each link of a communication flow such that, request–request type message-dependent deadlocks can be completely avoided.

This paper presents research that proves a sufficient condition for the existence of such a relationship.

We prove a sufficient condition that enables pruning and describe two pruning algorithms, αβ∗ and αβ1p∗.

In Section 3, we prove a sufficient condition and we obtain the explicit solution in terms of and.

We analyze the uniqueness of the NE by proving a sufficient condition for the strong monotonicity of V k.

Finally, we prove a sufficient condition to guarantee unique contracts in the optimal solution for a general number of retailer types.

In what follows, we prove a sufficient condition for the uniqueness of the fixed point in Theorem 2.3 and Theorem 2.4.

We prove a sufficient condition for convergence of a fixed-point iterative algorithm to the numerical solution of the coupled problem.

We prove a sufficient condition for the closability of classical Dirichlet forms on L2(E; μ) which is also necessary if all components of the Dirichlet form are closable.

This paper presents and proves a sufficient condition for data independence, expressed in terms of the behaviour of inputs and outputs of a system, that can be checked in practice by a model checker; and it demonstrates how this condition is used in two design applications.