Sentence examples for mathematical expressions derived from inspiring English sources

Models are mathematical expressions derived from scientific or engineering principles.

The underlying principles are elucidated, relevant mathematical expressions derived and details given about corresponding implementation techniques.

Hydration forces are included by utilising mathematical expressions derived from the latest results obtained with surface-forces apparatus.

Finally, we present the simulation results which concur with the numerical results and which are also a perfect match with the mathematical expressions derived.

In contrast to packages based on the simulations, packages based on the analytical criteria (i.e. on the mathematical expressions derived in advance) do not need a large number of trial realizations for assessment of statistical significance and, therefore, save a lot of computational time.

The mathematical expression derived by this methodology can be employed to develop predictive models upon setting the levels of the various influencing factors to reach the optimum HMF concentration in food.

Mathematical expressions are derived for both methods and compared.

Mathematical expressions were derived for inner race, outer race and rolling element local defects.

Mathematical expressions were derived to predict the beginning and end of story yielding due to the incident wave.

Based on the Cosine's law, mathematical expressions were derived to predict the thickness distribution along the depth of the part and the thinning limit of the sheet-metal.

On the basis of the Langevin theory of classical statistical mechanics, the magnetization, entropy, and iso-field heat capacity of ferromagnetic materials are analyzed and their mathematical expressions are derived.