One product is produced in greater amounts at one time scale and the other is produced in great amounts at a different time scale.
Although a biomarker of exposure may be appropriate in assessing exposures over one time scale, health outcomes, and thus risk, may be associated with time scales markedly different from those being assessed.
The relative strength of the components from one time scale can obscure those operating in a different time scale, interfering with the detection of a signal of interest.
Instead, separate MPC schemes can be implemented, each designed for one time-scale, working in parallel on the same or different tasks, acting on separate time-scales and interacting via updates of each others' constraints and cost terms.
For advances in dynamic equations on time scales, one can see the book by Bohner and Peterson [2].
Based on this definition of the time constant, we can state that there are at least two-time scales in the dataset, one-time scale accounts for the high-transmissivity, low-storativity fractures (τ 1) and the second-time scale accounts for the low-transmissivity, high-storativity reservoir matrix (τ 2 and τ 3).
Analogous to the proof in the real numbers situation, one can deduce the following result on time scales.
In [9], Sun and Li studied the following one-dimensional p-Laplacian boundary value problem on time scales: (1.2).
In recent years, the theory of exponential dichotomies on time scales for the linear dynamic equations on time scales extends the idea of hyperbolicity from autonomous dynamic equations on time scales to explicitly nonautonomous ones and has progressed greatly [20 30].
