Sentence examples for any additional condition from inspiring English sources

We detail this proof in Appendix Appendix 4: proof of proposition 4. We remark that the inequality (0<delta _{text {asym}}^{text {min}} alpha _{1}^,alpha _{2}^)<1) holds for any ((alpha _{1}^,alpha _{2}^)) satisfying (12) as explained in Appendix Appendix 4: proof of proposition 4; therefore, (13) does not imply <span class="lh">any additional condition on the system parameters.

These cell lines were chosen for the mouse model as they easily grow without any additional condition media and form homogeneous tumours.

"The administration does not support the attachment of any additional conditions to the payment of these arrears," Philip Reeker, a State Department spokesman, said today.

Accordingly, the C0− continuity at layer interfaces can be naturally satisfied without any additional conditions.

We prove the superstability of (1.6) without any additional conditions on the mapping.

Under the proposed protocol, the leader follower consensus can be also achieved without satisfying any additional conditions.

Ekström [8] showed that MSP estimators are L1-consistent for any unimodal pdf without any additional conditions.

We found that the network structure strongly affects continuation of a cooperation-dominant situation without any additional conditions.

The coupling gains can be chosen randomly in the protocol and the consensus of second-order multi-agent systems can be reached without satisfying any additional conditions.

Then, in the space of L2(F X (dλ)), we get the spectral characteristics of P H η ( t ) ξ with no any additional conditions.

We think that Theorem 1.4 is a natural generalization, because we use only one spectrum to reconstruct the potential q without any additional conditions, as it is in the classical result.