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The relationship between fault and symptom is difficult to describe using an accurate mathematical model due to the complexity of engineering practice.
The modal mass of a real structure differs from that of the mathematical model due to the error introduced by the assumptions made for analysis and by the change in dynamic characteristics occurring during the construction process.
Such an approach may fail to enhance the confidence in simulation-based predictions when the dynamical systems exhibit significant variability in the parameterization and description of the mathematical model due to parametric (data) uncertainty and model uncertainty.
The effect of the axial force induced by mid-plane stretching is accounted for in the derivation of the mathematical model, due to its known importance and significant effect on the nonlinear dynamic behavior of the beam, as it was proved and presented in earlier investigations.
First and foremost is the fact that the systems and networks one infers often have so many units/nodes that the problem is not well-posed, for any mathematical model, due to lack of data [6], [7] (unless one introduces further constraints, such as sparseness).
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According to a different study based on a mathematical model, no limitations due to intracellular resources should occur if one cell produces about 8000 virus particles [ 7].
However, not all metabolites in a focused pathway can be simultaneously measured, and the measured metabolite concentrations are not yet sufficiently accurate for the construction of a precise mathematical model, which is due to the following several factors.
Note that the difference arises not only due to the mathematical model used, but also due to the stability properties of the optimization method chosen.
Moreover, the researchers can apply the efficient proposed approach to solve the fully fuzzy mathematical programming models due to its computational advantages.
The coupled mathematical model predicts permeability damage due to mechanical trapping and adsorption accurately, as evidenced when compared with experimental results.
In representing the mathematical model, the inherent errors due to parameter variations define the parametric (structured) uncertainties; therefore there are differences between the mathematical model used in the design process and the real plant.
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