Sentence examples for mild condition on from inspiring English sources

Second, we show that under a mild condition on the multiplicity of critical eigenvalues, codimension-one synchrony-breaking steady-state bifurcations in generic coupled cell systems associated with an n-cell coupled cell network with Dn symmetry, a regular network, is reducible for n>2.

Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output.

Thus, ρ y ( y ) ≤ K y − β if g ′ ( y ) ≤ K M y − β, which is a mild condition on g.

(3) Under a mild condition on the spectrum of a cyclic operator T the set of all separating vectors for the commutant {T}′ of T is dense.

Motivated by the above contributions, in this paper we aim to establish some precise large deviations results, which are some equivalent relations, for the random sums of the differences between two sequences of nonnegative r.v.s under a mild condition on the process N ( t ) : N ( t ) λ ( t ) → P 1, t → ∞, (1.2). and λ ( t ) ∼ λ t, t → ∞, (1.3).

Section 4 establishes the existence of the descent functor under a very mild condition on Γ, the main technical difficulty involved being that of finding a Γ-algebra that plays the role of Cb(T,B cont in the group case.

The strong convergence theorems are proved under some mild conditions on scalars.

We show that the schemes converge under mild conditions on the initial control curves, and derive properties of the limit.

Our results apply as well to heteroscedastic polynomial regression models, under mild conditions on the efficiency function.

In the present paper we show that actually most of those results still hold for general uniformly convex metric spaces under mild conditions on the modulus of convexity.

Furthermore, for finding approximate common fixed points of an infinite countable family of nonexpansive mappings under very mild conditions on the parameters.