We focus on links between the equation-free approach and tools from systems and control theory (design of experiments, data analysis, estimation, identification and feedback).
Achievement of this understanding involves the development of experimental flow measurement techniques, and experimentally verified multiphase flow equations and numerical simulation tools.
These data could also guide the development of equivalent risk factor equations, assessment tools and treatment algorithms for CMD prevention that are often used in other areas of medicine for guiding investment and resource allocation.
The paper describes the equations and methodology behind these tools, and also presents their advantages and drawbacks.
The study unifies existing result in differential and finite difference equations and provides powerful new tools for exploring connections between the traditionally separated fields.
The theory of dynamic equations on time scales unifies existing results in differential and finite difference equations and provides powerful new tools for exploring connections between the traditionally separated fields.
It reveals inconsistencies within the data, avoids compensation among and within equations, and permits quantitative diagnostic tools of whether the assumed mathematical formulations are appropriate or in need of improvement.
Similar to the deterministic setting (Kalman 1960; Wonham 1985; Yong and Lou 2006), Riccati equations (and their variants) are fundamental tools to study SLQs.
To assess how our data for FEV1, FVC, FEV1/FVC% and FEF25 75 conformed with the GLI reference values, the GLI reference values were computed for each subject by means of the GLI-2012 Desktop Soforare for Data Sets vs 1.3.4, available on the web site http://www.lungfunction.org/tools/90-equations-and-tools/196-obtain-software.html.html
This scheme avoids the need for solving the complex set of nonlinear differential equations and gives a computationally efficient tool for rapidly analyzing and designing such systems.
Mathematical tools, such as differential equations and vector analysis, and computer systems are used to evaluate the physical and chemical relations that describe the workings of the atmosphere.
