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Computers, however, can be used to obtain useful approximate solutions, particularly when a problem is split into simpler spatial or temporal parts.
An analytical model valid for gravity-dominated dynamics is given, and yields useful approximate design formulae.
In so doing I derive useful approximate closed form solutions for both planar and axisymmetric stagnation flow.
The composition of useful approximate fitness functions from physiological and allocational responses is a major challenge, with some leads originating from the model.
Several useful approximate expressions for designing LMS-based channel estimators are herein derived and validated by comparisons with simulation and with a previous work on this kind of analysis.
The adjustment procedure provided a useful approximate method for characterising these variations, which resulted from crack-extension effects and the spatial variation of both intrinsic and extrinsic crack-growth resistance.
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Therefore, to derive a useful mathematical model for each alternative network one needs to use approximate kinetic functions with parameters whose values can be bound to some extent.
The function that a learning classifier with one output approximates to, when has been trained to minimize the Cross-Entropy error, is calculated in Section 3. The condition stated in[1] is applied to demonstrate that the approximated function is useful to approximate the NP detector.
The following theorem presents the convergence result on the approximation of derivatives particularly useful for approximate solving some differential equations.
Nonetheless, given that there is very little information available on water use by pregnant women in the UK, we believe that these results are useful as approximate estimates of water use in pregnancy and indicate issues that should be considered in epidemiological studies of DBPs, e.g. potential differences in water use in relation to ethnicity.
As regards the volume constraint, from the results of the two surveys we can conclude that useful, albeit approximate, information can be obtained from drivers.
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