Sentence examples for exists equivalent from inspiring English sources

Under weak coupling assumptions, that is, close to and close to in (3) (no proof for strong coupling exists), equivalent phase deviation variables are derived for each node (each variable represents the mean local interactions over one period) and are shown to asymptotically converge to the same value [11].

An implicit assumption in this and other similar studies is that there exists equivalent ability to undertake all these procedures both from a time and skill base, but this is unlikely to be true.

Assume that there exists an equivalent metric on such that for every and every, (2.17).

Moreover, there exists an equivalent metric ρ on X that preserve some inequalities.

A Banach space is said to be -smoothable if there exists an equivalent norm under which is -uniformly smooth.

By Theorem 2.8, there exists an equivalent norm on, such that the dual norm satisfies the UKK* property.

We also show a quadratic upper bound: given a cyclic Boolean circuit with m gates, there exists an equivalent acyclic Boolean circuit with m2 gates.

We also consider ANSPs with restricted features, proving the following normal forms: for any ANSP there exists an equivalent ANSP without input filters, and one without output filters.

We show that for any mechanism there exists an equivalent dominant strategy incentive compatible mechanism for social choice environments with correlated types when agent's matrix of conditional probabilities satisfies the full rank condition.

In addition, this paper mainly focuses on the case that the fractional order is (0<alpha<2), since there exists an equivalent relation of fractional-order systems with order (0 <andhaleq1) and with order (1leqbeta< 2); see [15].

By Proposition ?1.7.59, page 117 in [11], if is an ordered Banach space with positive cone, then is a normal cone if and only if there exists an equivalent norm on which is monotone.