Sentence examples for under additional condition from inspiring English sources

In the proof of Lemma 1.1, it is shown that (1.8) is also a sufficient condition of attractivity of solutions of (1.6) to the origin under additional condition − ln C ≤ ∫ T ∞ ( ℜ [ χ 1 ( s ) − χ 2 ( s ) ] ) d s ≤ ln C, C = const > 0. (1.9).

Under additional conditions on Φ, we further show that:.

In the first class, the derived continuous-time observer also leads to the construction of a robust global sampled-data exponential observer, under additional conditions.

Under additional conditions a distributed two-player zero-sum game using static OPFB is also solved and leads to distributed Nash equilibrium on the communication graph.

The author was both motivated and inspired by a previous work of Aldroubi, Baskarov and Krishtal (2008) [1], where similar results were obtained through different methods for X= Zd, under additional conditions on the decay.

It is not a probability, but it can be interpreted as one, under additional conditions.

Below we show that under additional conditions we can consider the problem of the solution's uniqueness.

Then, under additional conditions (a) and (b) the more exact asymptotic formulas, which depend upon the retardation obtained.

Moreover, as detailed below, under additional conditions, a GPE that is almost surely upper bounded can be defined.

In this section, we generalize and improve the results of Section 3 (hence results given in [13]) for three maps (under additional conditions).

Moreover, in [16] a two-term equation with forcing term e has been considered and the oscillation is studied under additional conditions on the function r.