Quantitative rate data were obtained for all the functional groups in the resins by mathematical differentiation of the time dependence of the concentrations.
However, it is envisaged that the effectiveness of the PE approach can be restricted in practical implementation, due to the involvement of high-order derivatives of structural dynamic deflections, in which measurement noise and uncertainties can overwhelm the damage-associated signal features upon mathematical differentiation.
While fixed costs are, under a constrained budget, decisive to the resources left for allocating measurements, they cancel out in the course of the mathematical differentiation associated with the optimization procedure, and thus will not affect the eventual optimal allocation strategy [ 43].
Locke's contemporary G.W. Leibniz, drawing possible inspiration from his mathematical work on differentiation and integration, offered a theory of mind in the Discourse on Metaphysics (1686) that allowed for infinitely many degrees of consciousness and perhaps even for some thoughts that were unconscious, the so called "petites perceptions".
In contrast, these terms, that appear when acceleration is expressed in polar coordinates, are a mathematical consequence of differentiation; these terms appear wherever polar coordinates are used.
Analyses of mathematical models of differentiation dynamics have shown that the considerations of such flexibility may be important to understand and control cell-fate choices (see, for example [ 5, 9]).
Foster et al. developed a mathematical model for cell differentiation that predicts presence of multiple stable states for differentiated cells, bifurcations and switch-like transitions [ 27, 28].
MathCML contains prototypes for normalisation, validation and differentiation of mathematical expressions.
In this study, we built an experiment-integrated mathematical model for glioma differentiation signaling pathways.
Moreover, by a purely mathematical process involving only differentiation, the first-order conformal structure determines a second-order conformal structure, namely, an equivalence class \(K\) of conformally related symmetric linear connections.
The result shows that some parameters, such as lithology and reservoir fluids, affected on petrophysical logs, but fracture zones can be determined using conventional logs with logs corrections by mathematical methods, such as differentiation, which has great correlation with image logs.
