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Second, the model provides a natural framework for combining knowledge from experts and stakeholders with quantitative data.
This approach provides a natural framework for modelling pore opening, enlargement and coalescence in the evolution of porosity and internal accessible surface area with solid conversion.
We show that our approach provides a natural framework for incorporating prior biological information, and it has the best overall performance in terms of correctly identifying significant pathways compared to several alternative methods.
Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure.
In particular, the sensitivity boundary value problem must be formulated in a very weak sense, and the resulting variational problem provides a natural framework for developing and analyzing numerical schemes.
The implicit network representation introduced provides a natural framework for expressing the different types of re-engineering transformations which can be used for the study of the natural frequencies assignment.
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Further, the underlying exact equations provide a natural framework for extensions to finite wave amplitudes and any realistic situation.
Relationships for the conservation across arbitrary patches of their strength (the crack opening displacement and opening angle) provide a natural framework for crack dynamics in terms of transport laws for the line defect densities.
The theory of impulsive dynamic equations is generally thought to provide a natural framework for mathematical modeling of many real world phenomena such as chemotherapy, population dynamics, optimal control, ecology, industrial robotics, physics phenomena, etc.
In recent years, the theory of impulsive differential equations has provided a natural framework for mathematical modeling of many real world phenomena, namely in control, biological and medical domains.
Differential equations with fractional derivative provided a natural framework for the discussion of various kinds of real problems modeled by the aid of fractional derivative, such as viscoelastic system, signal processing, diffusion processes, control processing, fractional stochastic system, allometry in biology and ecology (see [1, 4 7] and the references therein).
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