Many important systems, such as wind turbines, helicopters and turbomachinery, must be modeled with linear time-periodic equations of motion to correctly predict resonance phenomena.
Because of the recent progress in near-infrared Fourier transform (n.i.r.-FT) Raman spectroscopy, it has become possible to circumvent the fluorescence problem which precludes recording Raman spectra of many important systems, such as some polymers widely used in industry.
Targeted genetic engineering in many important model systems and in human tissue culture cells has historically been challenging.
Yet many important practical systems are in the turbulent regime and cannot be approximated by a simplified analysis.
We explain why the main tool used for this problem in finite dimension, namely the iterated Lie brackets, is difficult to use for many important control systems modeled by partial differential equations.
Nonlinear partial differential equations (NLPDEs) are widely used as models to describe many important dynamical systems in various fields of science, particularly in fluid mechanics, solid state physics, plasma physics and nonlinear optics.
However, experimental knockouts cannot be performed systematically, or at all, in many important biological systems.
The Smoluchowski approach seems to be the most appropriate method currently available to study many important biological systems, however a potential weakness of the Smoluchowski approach is the presence of a sharply defined reaction zone (cf. Figure 1).
There are many other important systems that can be deployed to improve customer service; for example, hiring and recruiting benefit greatly from being made systematic.
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