Sentence examples for repeated differentiation from inspiring English sources

However, the introduction of rational fractions also brought in some other drawbacks such as complex calculation, inconvenience for integrals, higher-order expressions resulting from repeated differentiation, etc. [4].

The dynamic surface controller is designed based on the NNDOB and EML model, which efficiently solves the mismatches and overcomes the problem of "explosion of complexity" resulting from repeated differentiation of virtual control variables.

In the original ENO scheme of Harten et al. and in the ADER schemes of Titarev and Toro, this time evolution is achieved via a Taylor series expansion where the time derivatives are computed by repeated differentiation of the governing PDE with respect to space and time, i.e. by applying the so-called Cauchy Kovalewski procedure.

A new FTT control scheme using the integrated error surfaces is designed without applying any function approximators to estimate unknown nonlinearities including faults and requiring the repeated differentiation of virtual controllers where auxiliary variables are derived to ensure the predefined performance of underactuated systems.

Let F and G be two smooth enough functions such that repeated differentiation and repeated integration by parts are allowed for them.

However, the repeated differentiations in the auxiliary robust controller remain as the price of preserving the global stability.

However, the so-called explosion of complexity problem, arising from the repeated differentiations of the virtual controllers in the backstepping procedure, has not been solved yet.

Wherein, to avoid the tedious analysis and repeated differentiations of virtual control laws in the backstepping technique, a simple and robust finite-time-convergent differentiator is devised to only extract its first-order derivative at each step in the presence of external disturbance.

To further confirm a cell-intrinsic defect in MSCs, we repeated the differentiation assay using the third passage MSCs.

Across replicate populations of Midas cichlids, including populations from completely isolated crater lakes derived from independent colonizations [ 14, 18], we identified considerable and in most cases repeated ecological differentiation between sympatric gold and dark color morphs.

Stable transfected BMSCs were used to repeat osteoblast differentiation and transdifferentiation assay.