Sentence examples for time scale such that from inspiring English sources

Let be a time scale such that.

Let be any time scale such that be subset of.

Let (mathbb{T}) be a time scale such that (t_{0}inmathbb{T}).

In this paper, let be a time scale such that, 0,.

The adaptation variable then acts as a slow time scale, such that a single spike has a long-lasting effect on the adaptation variable (Fig. 2B).

Definition 2.1 Let a ∈ T L, where T L is a time scale such that sup T L = ∞ and sup { ν ( t ) ; t ∈ T L } < ∞.

In the RTHS tests, a velocity loading method was adopted and the bearings were physically tested in a real-time scale and larger time scales such that the bearings were exerted under different loading rates.

We present necessary and sufficient conditions which guarantee the existence of a coordinate change and/or output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics.

We present necessary and sufficient conditions which guarantee the existence of a coordinate change and output-dependent time scaling, such that in the new coordinates and with respect to the new time the system has linear error dynamics.

In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change.

Note that for special isolated time scales such that ν ( t ) ≠ ν ( s ) for all s, t ∈ T κ, Lemma 4.1 yields a more simple formula h ˆ r ( t, s ) = ν ( t ) h ˆ r ( t, σ ( s ) ) − ν ( σ ( s ) ) h ˆ r ( ρ ( t ), s ) ν ( t ) − ν ( σ ( s ) ). Remark 4.5 Definition 3.1 prescribes nonnegative values of h ˆ β ( t, s ).