Sentence examples for a certain weaker from inspiring English sources

A similar result holds for the algebra AC+of functions analytic inΔand absolutely continuous on the unit circle T. The result does not, however, hold in the disc algebra A, although we are able to represent homomorphisms into A by means of semigroups in a certain weaker sense.

Vanishing of crossing cumulants can be verified by checking a certain weak freeness condition and the weak singleton condition is satisfied e.g. when the state is tracial.

We show that this is indeed so for all frames and Riesz sequences {eiλnx} studied so far, and we prove that we can always solve both problems in a certain "weak sense".

The self-confidence of strong geopolitical power is always on display (as is the bravado of certain weaker powers).

Above a certain threshold, weak randomness therefore prevents a secure quantum key distribution.

In this paper, we shall prove that this operator is bounded under a certain highly weak integrability assumption.

"It is disappointing because you get a feeling that there are certain weak Australians out there who want to see us get beaten," he snapped feistily.

We establish that such mappings have a unique common end point under certain weak conditions.

Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system.

We present conditions on a network's Species-Reaction Graph that ensure a high degree of stable behavior, so long as the kinetic rate functions satisfy certain weak and natural constraints.

According to a monk of Eynsham Abbey, after Reginald's death "he performed miraculous cures for certain weak and sick people".